Talks

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Monday

In the first part of the talk I will present an efficient protocol for estimating the stabilizer fidelity of an unknown quantum state ρ from copies. This protocol is a corollary of a more general result that we show, establishing a protocol even for the harder task of outputting the closest stabilizer state to ρ.

In the second part of the talk, I will discuss the related question of Pauli shadow tomography. I will present bounds that simultaneously and optimally trade off between the number of samples needed, the set of Pauli properties in question, the target precision, and the amount of quantum memory available.

Trotterization is the most standard quantum algorithm for computing the time evolution of quantum many-body systems. Recent studies have pointed out that when the initial state is a low-energy state, its error and computational cost can be reduced. However, the improvement in system-size dependence is very small, and the low-energy region where such improvement is observed is narrow, making it impractical in many cases. In this study, we significantly improve the dependence on the initial state’s energy in a polynomial manner and the dependence on system size in an exponential manner. We show that as long as the initial state’s energy is even slightly smaller than the scale of the entire system, there is always a significant reduction in error and computational cost, regardless of the Trotter order.

Product formulae are a popular class of digital quantum simulation algorithms due to their conceptual simplicity, low overhead, and performance which often exceeds theoretical expectations. Recently, Richardson extrapolation and polynomial interpolation have been proposed to mitigate the Trotter error incurred by the use of these formulae. This work provides a rigorous, general analysis of these techniques for computing time-evolved observables, simplifying the interpolation algorithm in the process, and shows that extrapolation generically improves the performance of product formulae for this task. We demonstrate that, to achieve error $\epsilon$ in a simulation of time $T$ using a $p^\text{th}$-order product formula with extrapolation, circuits depths of $O(T^{1+1/p}\polylog(1/\epsilon))$ are sufficient — an exponential improvement in the precision over product formulae alone. Furthermore, we prove that these algorithms achieve commutator scaling, and improve the $T$-complexity for the interpolation algorithm. By relaxing the requirement of performing exact Chebyshev interpolation, our simplified algorithm eliminates the need for fractional implementations of Trotter steps, reducing computational overhead. Finally, we show these techniques can be combined with the classical shadows method to estimate many time-evolved local observables. Taken together, our findings provide the strongest evidence yet for the utility of Trotter error mitigation techniques in algorithmic applications.

How do we extract meaningful information from a quantum system once quantum chaos is approached? In complex many-body dynamics, scrambling and entanglement growth quickly erase the fine-grained details, rendering most measurements useless for understanding the system’s evolution. Harnessing a 103-qubit digital superconducting processor and its ability to invert time we circumvent this challenge. We measure the 2nd and 4th moments of the correlation operator, a generalization of out-of-time order correlators, OTOC and OTOC2, respectively. These moments reveal macroscopic features of its spectrum and serve as a smoking gun of quantum chaos. Unlike standard correlation function measurements remain remarkably sensitive to the underlying dynamics at long times, allowing us to characterize the circuit close to the ergodic regime. We discovered that this sensitivity arises from a fascinating mechanism: constructive interference between paths in Pauli string space. By controllably manipulating these interference pathways, we show that the resulting OTOC2 signal is incredibly complex to predict. We present large-scale OTOC2 measurements from our processor that exceed the simulation capacity of the best-known classical algorithms. Our results light a viable path toward using near-term quantum processors for Hamiltonian learning.

Learning unknown processes affecting a quantum system reveals underlying physical mechanisms and enables suppression, mitigation, and correction of unwanted effects. Generally, learning quantum processes requires exponentially many measurements. We show how entanglement with an ideal auxiliary quantum memory can provide an exponential advantage in learning certain quantum processes. In practice, though, quantum memory and entangling operations are always noisy and introduce errors, making the advantage of using noisy quantum memory unclear. To address these challenges, we introduce error-mitigated entanglement-enhanced learning and show, both theoretically and experimentally, that even with noise, entanglement with auxiliary quantum memory combined with error mitigation considerably enhances the learning of quantum processes.

There is a deep connection between ordered phases of matter and models for noise-robust computing and memory in information theory. In particular, the presence of a passive quantum memory is generally associated with a low-temperature thermodynamic phase with thermally stable topological order, which is only known to exist in dimensions D >= 4. I will introduce a new phase of matter – a topological quantum spin glass (TQSG) – which furnishes a new paradigm for quantum memory. Like many conventional models of classical spin-glasses, the TQSG exhibits a provably complex “rugged” free-energy landscape at low temperatures, with numerous local and global minima hosting long-lived equilibrium Gibbs states. Also similar to many classical glasses, the phase transition into the glass phase is dynamical and can take place even as the partition function remains analytic, so there is no (ordinary) thermodynamic ordered phase or phase transition. However, unlike conventional glasses, the TQSG preserves quantum information, and the equilibrium (mixed) states display robust long-range entanglement even at finite temperatures. This phase describes the physics of various novel quantum low density parity check (LDPC) codes, including “good LDPC codes”, which live on non-Euclidean expander graphs, and which have been a topic of much recent interest in quantum error correction. Separately, our work also solves a longstanding problem in classical spin-glasses by  furnishing a rigorous proof of a complex landscape and finite temperature spin glass order for a family of finite-connectivity models.Our work opens new avenues in statistical mechanics and quantum computer science, and the study of many-body phases in non-local geometries which are increasingly accessible to modern day quantum simulators.

Spin-boson models are common throughout physics. Trapper ion quantum computers are built off internal degrees of freedom in the ions (qubits) and external degrees of freedom (phonons). For quantum computation, the phonons are used as an information bus for generating entanglement between qubits, but are not used to store quantum information. We have recently used the spin and motional modes to perform quantum simulations of molecular dynamics of conical intersections and vibrational energy transfer with structured baths. After describing these results, I will discuss how these methods can be extended to other chemical dynamics simulations and the simulation of nuclear physics.

The utility of near-term quantum computers for simulating realistic quantum systems hinges on the stability of digital quantum matter—realized when discrete quantum gates approximate continuous time evolution—and whether it can be maintained at system sizes and time scales inaccessible to classical simulations. Here, we use Quantinuum’s H2 quantum computer to simulate digitized dynamics of the quantum Ising model and observe the emergence of Floquet prethermalization on timescales where accurate simulations using current classical methods are extremely challenging (if feasible at all). In addition to confirming the stability of dynamics subject to achievable digitization errors, we show direct evidence of the resultant local equilibration by computing diffusion constants associated with an emergent hydrodynamic description of the dynamics. Our results were enabled by continued advances in two-qubit gate quality (native partial entangler fidelities of $99.94(1)\%$) that allow us to access circuit volumes of over $2000$ two-qubit gates. This work establishes digital quantum computers as powerful tools for studying continuous-time dynamics and demonstrates their potential to benchmark classical heuristics in a regime of scale and complexity where no known classical methods are both efficient and trustworthy.

Fundamental particles and interactions in nature, which are at the core of nuclear- and particle-physics phenomena, are described by the Standard Model, via the relativistic and quantum framework of gauge field theories. Exploring Standard-Model physics and beyond continues to be an active and growing field of research and discovery. Some of the questions are: What does the phase diagram of matter governed by strong interactions, such as the interior of neutron stars, look like? How does matter evolve and equilibrate after energetic processes, such as after the Big Bang or in particle colliders? While many successful formal, analytical, and computational paradigms have been developed over the years to advance this frontier, many such questions have not yet been satisfactorily answered. Can a large reliable quantum simulator/computer eventually enable studies of matter governed by the fundamental interactions? What does a quantum simulator have to offer to simulate (beyond-the-)Standard-Model dynamics, and how far away are we from such a dream? In this talk, I will describe a vision for how we may go on a journey toward quantum simulating Standard Model and beyond, will motivate the need for novel theoretical, algorithmic, and hardware approaches to quantum simulating this unique problem, and will provide examples of the steps taken to date in establishing a quantum-computational nuclear- and particle-physics program.

We probe the thermalization dynamics of nonequilibrium states by extracting their entanglement structure using randomized measurement protocols. For the first time, we experimentally explore the approach to thermal equilibrium by measuring the spectral gap ratio and spectral form factors of the entanglement Hamiltonian (EH). These entanglement-based observables reveal universal early-time signatures of quantum chaos and ergodicity—features that remain hidden in conventional studies based solely on expectation values of local observables. Our work is based on experiments on a digital quantum computer based on fully connected, optically controlled trapped ions.

We explore the potential for quantum speedups in convex optimization using discrete simulations of the Quantum Hamiltonian Descent (QHD) framework, as proposed by Leng et al., and establish the first rigorous query complexity bounds. We develop enhanced analyses for quantum simulation of Schrödinger operators with black-box potential via the pseudo-spectral method, providing explicit resource estimates independent of wavefunction assumptions. These bounds are applied to assess the complexity of optimization through QHD, leading to speedups in certain settings. To our knowledge, these results represent the first rigorous quantum speedups for convex optimization achieved through a dynamical algorithm.

Tuesday

We will discuss recent advances in realizing programmable quantum systems using neutral atom arrays excited into Rydberg states. These systems allow control over several hundred qubits in two dimensions and the exploration of quantum algorithms with encoded logical qubits and quantum error correction techniques. Recent experiments using neutral atom systems have redefined this exciting scientific frontier of quantum computing. They herald the advent of early error-corrected quantum computation and chart a path towards large-scale logical processors. Examples of emerging scientific directions, in areas ranging from architectural mechanisms for universal fault tolerant quantum processing and many-body physics to quantum chemistry and quantum gravity will be discussed.

We bridge quantum thermodynamics and quantum information sciences by uncovering a relation between thermodynamic quantities and the entanglement Hamiltonian of a system coupled strongly to a reservoir. We use this bridge to propose a route to measuring thermodynamic quantities in quantum simulations of instantaneous, non-equilibrium quenches. Along the way, we identify quantum-work and quantum-heat definitions that are consistent with the first and second laws of thermodynamics. We further posit that lattice gauge theories (LGTs) fit the strong-coupling quantum-thermodynamic framework. In a simple LGT model, we find that an experimentally accessible thermodynamic quantity signals a phase transition. We, thus, offer a recipe for measuring potentially useful thermodynamic properties of gauge theories.

Quantum spin liquids are exotic phases of matter whose low-energy physics is described as the deconfined phase of an emergent gauge theory. With recent theory proposals and an experiment showing preliminary signs of Z2 topological order [G. Semeghini et al., Science 374, 1242 (2021)], Rydberg atom arrays have emerged as a promising platform to realize a quantum spin liquid. In this work, we propose a way to realize a U(1) quantum spin liquid in three spatial dimensions, described by the deconfined phase of U(1) gauge theory in a pyrochlore lattice Rydberg atom array. We study the ground state phase diagram of the proposed Rydberg system as a function of experimentally relevant parameters. Within our calculation, we find that by tuning the Rabi frequency, one can access both the confinement-deconfinement transition driven by a proliferation of “”magnetic”” monopoles and the Higgs transition driven by a proliferation of “”electric”” charges of the emergent gauge theory. We suggest experimental probes for distinguishing the deconfined phase from ordered phases. This work serves as a proposal to access a confinement-deconfinement transition in three spatial dimensions on a Rydberg-based quantum simulator.

The quantum-computational cost of determining ground state energies through quantum phase estimation depends on the overlap between an easily preparable initial state and the targeted ground state. The Van Vleck orthogonality catastrophe has frequently been invoked to suggest that quantum computers may not be able to efficiently prepare ground states of large systems because the overlap with the initial state tends to decrease exponentially with the system size, even for non-interacting systems. We show that this intuition is not necessarily true. Specifically, we introduce a divide-and-conquer strategy that repeatedly uses phase estimation to merge ground states of increasingly larger subsystems. We provide rigorous bounds for this approach and show that if the minimum success probability of each merge is lower bounded by a constant, then the query complexity of preparing the ground state of $N$ interacting systems is in $O(N^{\log\log(N)} {\rm poly}(N))$, which is quasi-polynomial in $N$, in contrast to the exponential scaling anticipated by the Van Vleck catastrophe. We also discuss sufficient conditions on the Hamiltonian that ensure a quasi-polynomial running time.

Quantum simulators based on neutral atoms in optical lattices offer access to ultra-low temperatures and long coherence times. Recent advances pave the way towards high-fidelity simulations using arrays of several thousand atoms with single-atom resolution and control in homogeneous lattice potentials, where the atoms are confined in a box. In this talk, I will demonstrate how such systems enable the exploration of interacting topological phases of matter using Floquet engineering and provide insights into fundamental questions regarding the thermalization of isolated quantum systems in the regime of Hilbert-space fragmentation. In addition, I will highlight recent advances facilitated by the programmability of these platforms enabling access to arbitrary orbital operators, such as current and kinetic energy, beyond conventional density or occupation measurements. Moreover, by analyzing subsystem return probabilities we reveal the relevance of genuine higher-order connected correlation functions for the observed dynamical quantum phase transition and conduct a quantitative measurement of the size of the accessible Hilbert space in the thermodynamic limit. Finally, I will conclude by providing an outlook towards new capabilities by combining optical lattices with tweezer arrays.

Quantum thermalization is one of the most universal phenomena in quantum many-body dynamics, forming a fundamental bridge between quantum and statistical mechanics. Recent advances in programmable quantum simulators have not only enabled experimental verification of thermalization but also opened new avenues for discovering universal behaviors in complex quantum systems. In this talk, I will introduce a recently discovered phenomenon known as deep thermalization, which extends the concept of thermalization beyond local observables. I will present its core principles and survey recent developments in this rapidly evolving topic. The deep thermalization reveals a profound connection between quantum many-body physics and information theory, offering fresh insights into the fundamental nature of quantum dynamics.

One of the most challenging problems in the computational study of localization in quantum many-body systems is to capture the effects of rare events, which requires sampling over exponentially many disorder realizations. We implement an efficient procedure on a quantum processor, leveraging quantum parallelism, to efficiently sample over all disorder realizations. We observe localization without disorder in quantum many-body dynamics in one and two dimensions: perturbations do not diffuse even though both the generator of evolution and the initial states are fully disorder-free. The disorder strength as well as its density can be readily tuned using the initial state. Furthermore, we demonstrate the versatility of our platform by measuring Rényi entropies. Our method could also be extended to higher moments of the physical observables and disorder learning.

Wednesday

The potential of quantum algorithms to enable significant computational speed up has generated significant interest in advancing the capabilities of quantum chemistry, which addresses the computation of ground and excited electronic states of molecular systems. While worst case evaluation of molecular ground states is hard even for quantum computers, empirical studies have suggested that generic chemical systems show no exponential quantum advantage over standard classical algorithms. However, for the important class of strongly correlated electronic systems, the situation is different. I shall describe quantum algorithms for systems with both strong and weak correlations that provide both algorithmic and practical advantages over the best-known classical algorithms for these systems, enabling efficient solutions for both ground and excited states of molecular systems undergoing bond breaking and catalysis, and for systems possessing multiple unpaired electrons or multivalent metal atoms. These approaches are based on non-orthogonal methods, employing linear combinations of either exponentially correlated UCC ansatz states (the non-orthogonal quantum eigensolver, NOQE) or matrix product states (the tensor network quantum eigensolver, TNQE), with the latter allowing calculations linear in the system size. I shall also describe recent work proving the classical simulation hardness of the corresponding quantum circuits, showing that exponential quantum speedups are possible in quantum chemistry with linear depth, for important molecular systems in which both strong and weak electronic correlations are important.

We introduce sum-of-squares spectral amplification (SOSSA), a framework for improving quantum simulation algorithms relevant to low-energy problems. SOSSA first represents the Hamiltonian as a sum-of-squares and then applies spectral amplification to amplify the low-energy spectrum. The sum-of-squares representation can be obtained using semidefinite programming. We show that SOSSA can improve the efficiency of traditional methods in several simulation tasks involving low-energy states. Specifically, we provide fast quantum algorithms for energy and phase estimation that improve over the state-of-the-art in both query and gate complexities, complementing recent results on fast time evolution of low-energy states. To further illustrate the power of SOSSA, we apply it to the Sachdev-Ye-Kitaev model, a representative strongly correlated system, where we demonstrate asymptotic speedups by a factor of the square root of the system size. Notably, SOSSA was recently used in [G.H. Low et al., arXiv:2502.15882 (2025)] to achieve state-of-art costs for phase estimation of real-world quantum chemistry systems.

AND

The most advanced techniques using fault-tolerant quantum computers to estimate the ground-state energy of a chemical Hamiltonian involve compression of the Coulomb operator through tensor factorizations, enabling efficient block-encodings of the Hamiltonian. A natural challenge of these methods is the degree to which block-encoding costs can be reduced. We address this challenge through the technique of spectrum amplification, which magnifies the spectrum of the low-energy states of Hamiltonians that can be expressed as sums of squares. Spectrum amplification enables estimating ground-state energies with significantly improved cost scaling in the block encoding normalization factor $\Lambda$ to just $\sqrt{2\Lambda E_{\text{gap}}}$, where $E_{\text{gap}} \ll \Lambda$ is the lowest energy of the sum-of-squares Hamiltonian. To achieve this, we show that sum-of-squares representations of the electronic structure Hamiltonian are efficiently computable by a family of classical simulation techniques that approximate the ground-state energy from below. In order to further optimize, we also develop a novel factorization that provides a trade-off between the two leading Coulomb integral factorization schemes– namely, double factorization and tensor hypercontraction– that when combined with spectrum amplification yields a factor of 4 to 195 speedup over the state of the art in ground-state energy estimation for models of Iron-Sulfur complexes and a CO$_{2}$-fixation catalyst.

Quantum computation of the energy of molecules and materials is one of the most promising applications of fault-tolerant quantum computers. Practical applications require development of quantum algorithms with reduced resource requirements. Previous work has mainly focused on quantum algorithms where the Hamiltonian is represented in second quantization with compact basis sets while existing methods in first quantization are limited to a grid-based basis. In this work, we present a new method to solve the generic ground-state chemistry problem in first quantization using any basis set. We achieve asymptotic speedup in Toffoli count for molecular orbitals, and orders of magnitude improvement using dual plane waves as compared to the second quantization counterparts. In some instances, our approach provides similar or even lower resources compared to previous first quantization plane wave algorithms that, unlike our approach, avoids the loading of the classical data. The developed methodology can be applied to variety of applications, where the matrix elements of a first quantized Hamiltonian lack simple circuit representation.

This talk will present recent experiments where we explore the dynamics of hole in a spin background, implementing a bosonic version of the t-J model usually introduced to describe the properties of doped magnets. To do so, we use the resonant dipole interaction between Rydberg atoms in tweezer arrays and rely on three Rydberg states in each atom to encode the spin and the hole. Varying the ration t/J, we observe in a one dimensional chain the binding of holes and the influence of the dipolar tail of the interaction on the propagation of the holes. Working in a triangular ladder geometry and in a regime where t ≫ J, we observe the binding of a magnon and hole and explore kinetic frustration in this system.

Quantum simulations of many-body systems are among the most promising applications of quantum computers. In particular, models based on strongly-correlated fermions are central to our understanding of quantum chemistry and materials problems, and can lead to exotic, topological phases of matter. However, due to the non-local nature of fermions, such models are challenging to simulate with qubit devices. Here we realize a digital quantum simulation architecture for two-dimensional fermionic systems based on reconfigurable atom arrays. We utilize a fermion-to-qubit mapping based on Kitaev’s model on a honeycomb lattice, in which fermionic statistics are encoded using long-range entangled states. We prepare these states efficiently using measurement and feedforward, realize subsequent fermionic evolution through Floquet engineering with tunable entangling gates interspersed with atom rearrangement, and improve results with built-in error detection. Leveraging this fermion description of the Kitaev spin model, we efficiently prepare topological states across its complex phase diagram and verify the non-Abelian spin liquid phase by evaluating an odd Chern number. We further explore this two-dimensional fermion system by realizing tunable dynamics and directly probing fermion exchange statistics. Finally, we simulate strong interactions and study dynamics of the Fermi-Hubbard model on a square lattice. These results pave the way for digital quantum simulations of complex fermionic systems for materials science, chemistry, and high-energy physics.

Quantum simulation can provide a route to understanding the complex quantum dynamics of correlated models. Rydberg atom arrays, featuring coherent control of hundreds of atoms in programmable geometries and hybrid analogue-digital capabilities constitute a promising platform for both quantum simulation and computation. With the aim of expanding the range of Hamiltonians accessible in atom array systems, we employ a Floquet driving scheme to generate effective stroboscopic Hamiltonians, including a constrained XX Heisenberg model and ring exchange terms on 2D lattices. By tuning the drive parameters, we demonstrate precise control over the strength of individuals terms in the Hamiltonian and use this to study the dynamics of many-body states if systems with different geometries. Furthermore, we characterize the effective Hamiltonian with complementary techniques including many-body spectroscopy and Hamiltonian learning, finding good agreement between the different probes. Models with local kinetic constraints are known to host exotic phases and dynamics, and as examples here we use entanglement dynamics as a probe of the Luttinger liquid phase in 1D chains, as well as leveraging multi-body interactions to study ring exchange dynamics in 2D. These experiments demonstrate the new framework for robust Floquet engineering under Rydberg blockade and advanced technical capabilities enabling highly programmable quantum simulation, paving the way for exploration of a broad set of complex models with neutral atom arrays.

Thursday

Shadow Hamiltonian simulation is a framework for simulating quantum dynamics using a compressed quantum state that we call the “shadow state”. The amplitudes of this shadow state are proportional to the expectations of a set of operators of interest. Under some assumptions, the shadow state evolves according to its own Schrödinger equation, and this evolution can be simulated on a quantum computer efficiently under broad conditions. As a consequence, shadow Hamiltonian simulation enables the efficient solution to numerous problems in quantum simulation that would otherwise require exponential resources using traditional quantum-simulation methods. Examples include simulating dynamics of exponentially large quantum systems of free fermions or bosons, and simulating dynamics of exponentially large systems of classical oscillators. The framework can be extended to other problems, including the simulation of the evolution of operators in the Heisenberg picture and learning unitary oracles. In this talk, I will describe the shadow Hamiltonian simulation framework and also discuss applications to quantum simulation problems.

Analog quantum simulators have provided key insights into quantum many-body dynamics. However, in many platforms, their scalability is limited by shot-to-shot fluctuations in Hamiltonian parameters in addition to incoherent noise, constraining simulations of regimes beyond classical simulability. Here, we introduce an error-mitigation technique that effectively suppresses shot-to-shot fluctuations within existing hardware-level control requirements. We rigorously prove that amplifying shot-to-shot noise and extrapolating to the zero-noise limit can recover noiseless results for experimentally relevant noise distributions. Experimentally implementing this technique on a 27-ion trapped-ion quantum simulator with individual addressing, we significantly extend the two-qubit exchange oscillation lifetime. Additionally, we predict a large enhancement in many-body coherence time for Rydberg atom arrays under realistic conditions using numerical simulations. Our scheme provides a possible route towards addressing a barrier to scaling trapped-ion and Rydberg-atom analog experiments, extending their coherent evolution timescales to enable deeper explorations of quantum many-body dynamics.

Many-body fermionic systems can be simulated in a hardware-efficient manner using a fermionic quantum processor. Neutral atoms trapped in optical potentials can realize such processors, where non-local fermionic statistics are guaranteed at the hardware level. Implementing quantum error correction in this setup is however challenging, due to the atom-number superselection present in atomic systems, that is, the impossibility of creating coherent superpositions of different particle numbers. In this work, we overcome this constraint and present a blueprint for an error-corrected fermionic quantum processor that can be implemented using current experimental capabilities. To achieve this, we first consider an ancillary set of fermionic modes and design a fermionic reference, which we then use to construct superpositions of different numbers of referenced fermions. This allows us to build logical fermionic modes that can be error corrected using standard atomic operations. Here, we focus on phase errors, which we expect to be a dominant source of errors in neutral-atom quantum processors. We then construct logical fermionic gates, and show their implementation for the logical particle-number conserving processes relevant for quantum simulation. Finally, our protocol is illustrated with a minimal fermionic circuit, where it leads to a quadratic suppression of the logical error rate.

Quantum circuits with local unitaries have emerged as a rich playground for the exploration of many-body quantum dynamics of discrete-time systems. While the intrinsic locality makes them particularly suited to run on current quantum processors, the task of verification at non-trivial scales is complicated for non-integrable systems. Here, we study a special class of maximally chaotic circuits known as dual unitary circuits — exhibiting unitarity in both space and time — that are known to have exact analytical solutions for certain correlation functions. With advances in noise learning and the implementation of novel error mitigation methods, we show that a superconducting quantum processor with 91 qubits is able to accurately simulate these correlators. We then probe dynamics beyond exact verification, by perturbing the circuits away from the dual unitary point, and compare our results to classical approximations with tensor networks. These results cement error-mitigated digital quantum simulation on pre-fault-tolerant quantum processors as a trustworthy platform for the exploration and discovery of novel emergent quantum many-body phases. In addition I will discuss some work on embedding non-ergodic subspaces within dual unitary circuits.
References: [1] https://doi.org/10.48550/arXiv.2411.00765
Ref [2]: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.132.010401

Quantum algorithms exploiting real-time evolution under a target Hamiltonian have demonstrated remarkable efficiency in extracting key spectral information. However, the broader potential of these methods, particularly beyond ground state calculations, is underexplored. In this work, we introduce the framework of multi-observable dynamic mode decomposition (MODMD), which combines the observable dynamic mode decomposition, a measurement-driven eigensolver tailored for near-term implementation, with classical shadow tomography. MODMD leverages random scrambling in the classical shadow technique to construct, with exponentially reduced resource requirements, a signal subspace that encodes rich spectral information. Notably, we replace typical Hadamard-test circuits with a protocol designed to predict low-rank observables, thus marking a new application of classical shadow tomography for predicting many low-rank observables. We establish theoretical guarantees on the spectral approximation from MODMD, taking into account distinct sources of error. In the ideal case, we prove that the spectral error scales as exp(−ΔE*tmax), where ΔE is the Hamiltonian spectral gap and tmax is the maximal simulation time. This analysis provides a rigorous justification of the rapid convergence observed across simulations. To demonstrate the utility of our framework, we consider its application to fundamental tasks, such as determining the low-lying, i.e. ground or excited, energies of representative many-body systems. Our work paves the path for efficient designs of measurement-driven algorithms on near-term and early fault-tolerant quantum devices.

We present Quantinuum’s trapped-ion quantum computers, based on the quantum charge-coupled device (QCCD) architecture, and highlight their unique capabilities for quantum simulation. Core features—including arbitrary-angle gates, mid-circuit measurement and reset, all-to-all connectivity, and industry-leading low error rates—make these systems exceptionally well-suited for simulating quantum dynamics, while also enabling high-performance quantum error correction (QEC) and other advanced applications.

We showcase several recent breakthroughs enabled by these capabilities: the observation of Floquet prethermalization of the quantum Ising model on timescales where classical methods break down, an experimental demonstration of break-even for the compact Fermionic encoding, quantum computation of the electronic structure of molecular systems utilizing QEC. These results are complemented by key demonstrations of QEC protocols that lay the groundwork for fault-tolerant quantum simulation. Together, they illustrate the power and versatility of the QCCD platform for advancing both near-term applications and the foundations of scalable quantum computing.

What happens when quantum simulations get cold enough to surprise us? Quantum simulations have served as impressive proof-of-principle demonstrations— creating a wide range of many-body quantum phases. Temperatures so far, however, were too high to truly get into uncharted territory, where we can address open questions on quantum materials such as cuprate superconductors. I will present a recent breakthrough in which we show a several-fold temperature reduction in an atomic Hubbard system, bringing quantum simulations into a regime of emergent low-temperature phenomena where the physics is not well understood theoretically. We achieve this by adiabatically transforming a low-entropy product state of ~300 atoms into a correlated final state. Using a quantum gas microscope, we report the first signs of novel physics appearing in this system upon cooling, including a line of thermodynamic anomalies separating the low-doping from high-doping regimes, the pseudo gap state, and a region of enhanced rotational symmetry breaking that may indicate a state of fluctuating stripes. This work signals the emergence of novel physics at low temperatures in the Hubbard model, and directly demonstrates the utility of quantum simulation in addressing open problems in correlated electron physics.

The simulation of high-temperature superconducting materials by implementing strongly correlated fermionic models in optical lattices is one of the major objectives in the field of analog quantum simulation. In this talk we present that local control and optical bilayer capabilities combined with spatially resolved measurements create a versatile toolbox to study fundamental properties of both nickelate and cuprate high-temperature superconductors. On the one hand, we propose a scheme to implement a mixed-dimensional (mixD) bilayer model that has been proposed to capture the essential pairing physics of pressurized bilayer nickelates. This allows for the long-sought realization of a state with long-range superconducting order in current lattice quantum simulation machines. In particular, we show how coherent pairing correlations can be accessed in a partially particle-hole transformed and rotated basis. On the other hand, we demonstrate that control of local gates enables the observation of d-wave pairing order in the two-dimensional (single-layer) repulsive Fermi-Hubbard model through the simulation of a system with attractive interactions.

Friday

In the last decade, variational algorithms have been the tool of choice for researchers and practitioners of quantum computing to tackle ground state problems on pre-fault-tolerant quantum processors. Currently, several practical and theoretical issues prevent scalability of variational algorithms to large system sizes. In this talk, I will discuss three quantum diagonalization methods, based on subspaces obtained from quantum computers, which overcome the scaling limitations of variational algorithms. First, the Krylov quantum diagonalization, which allowed us to perform quantum ground state calculations for lattice models of up to 50 spins, and the sample-based quantum diagonalization, which enabled realistic chemistry computations of up to 77 qubits on a quantum centric supercomputing architecture, using a Heron quantum processor and the supercomputer Fugaku. Finally, merging these two ideas together leads to a ground state algorithm with convergence similar to phase estimation, combined with robustness against noise, leading to an experimental demonstration obtained with IBM quantum computers and the supercomputer Frontier.

Presenters: Zhiyan Ding AND Yongtao Zhan

Inspired by natural cooling processes, dissipation has become a promising approach for preparing low-energy states of quantum systems. However, the potential of dissipative protocols remains unclear beyond certain commuting Hamiltonians. This work provides significant analytical and numerical insights into the power of dissipation for preparing the ground state of non-commuting Hamiltonians. For quasi-free dissipative dynamics, including certain 1D spin systems with boundary dissipation, our results reveal a new connection between the mixing time in trace distance and the spectral properties of a non-Hermitian Hamiltonian, leading to an explicit and sharp bound on the mixing time that scales polynomially with system size. For more general spin systems, we develop a tensor network-based algorithm for constructing the Lindblad jump operator and for simulating the dynamics. Using this algorithm, we demonstrate numerically that dissipative ground state preparation protocols can achieve rapid mixing for certain 1D local Hamiltonians under bulk dissipation, with a mixing time that scales logarithmically with the system size. We then prove the rapid mixing result for certain weakly interacting spin and fermionic systems in arbitrary dimensions, extending recent results for high-temperature quantum Gibbs samplers to the zero-temperature regime. Our theoretical approaches are applicable to systems with singular stationary states, and are thus expected to have applications beyond the specific systems considered in this study.

Simulating time evolution under quantum Hamiltonians is one of the most natural applications of quantum computers. We introduce TE-PAI, which simulates time evolution exactly by sampling random quantum circuits for the purpose of estimating observable expectation values at the cost of an increased circuit repetition. The approach builds on the Probabilistic Angle Interpolation (PAI) technique and we prove that it simulates time evolution without discretisation or algorithmic error while achieving optimally shallow circuit depths that saturate the Lieb-Robinson bound. Another significant advantage of TE-PAI is that it only requires executing random circuits that consist of Pauli rotation gates of only two kinds of rotation angles $\pm\Delta$ and $\pi$, along with measurements. While TE-PAI is highly beneficial for NISQ devices, we additionally develop an optimised early fault-tolerant implementation using catalyst circuits and repeat-until-success teleportation, concluding that the approach requires orders of magnitude fewer T-states than conventional techniques, such as Trotterization — we estimate $3 \times 10^{5}$ T states are sufficient for the fault-tolerant simulation of a $100$-qubit Heisenberg spin Hamiltonian. Furthermore, TE-PAI allows for a highly configurable trade-off between circuit depth and measurement overhead by adjusting the rotation angle $\Delta$ arbitrarily. We expect that the approach will be a major enabler in the late NISQ and early fault-tolerant periods as it can compensate circuit-depth and qubit-number limitations through an increased circuit repetition.

Holographic quantum matter—i.e., field theories that are dual to bulk gravity—represent paradigms for non-Fermi-liquid behavior and for extreme quantum chaos, cementing a deep interest throughout communities ranging from quantum gravity, over quantum information, to condensed matter. Yet, existing laboratory implementations in quantum simulators have been able to tackle only relatively small systems.

In this talk, I will present our ongoing efforts towards scalably realizing the Sachdev-Ye-Kitaev model, a paradigm for holographic quantum matter, by analog quantum simulation in cavity QED setups. I will discuss first experimental steps done by the group of Jean-Philippe Brantut, EPF Lausanne, the realization of a disordered spin system showing grey polaritons and finite-size disorder transitions. I will also discuss how deformations such as algebraic power-law interactions affect the behavior of such systems as well as how non-stabilizerness and entanglement increase as one reaches the holographic and chaotic regime. With this talk, I aim to illustrate the extreme richness of physics encountered in the quantum simulation of holographic models.

Block encodings are a fundamental primitive in quantum algorithms, but can often have large ancilla overhead. In this work, we introduce novel techniques for reducing this overhead in two distinct ways. In Part I, we prove the existence of a “”space-time tradeoff”” by deriving an algorithm that, for any block encoding, approximately uncomputes all but one of its ancilla (freeing up those ancilla for reuse in later parts of a quantum algorithm). In Part II, we evaluate the minimum number of ancilla required to perform coherent multiplication of block encodings. We prove that logarithmic ancilla is optimal for exact multiplication of block encodings. However, in certain block encoding regimes, we show that approximate multiplication of block encodings can be achieved to high-precision with just one ancilla.

Presenters: Diyi Liu and Shuchen Zhu

The success of many quantum simulation algorithms depends on the construction of efficient quantum circuits that can be implemented on a quantum computer to realize the effect of a many-body Hamiltonian on a properly prepared quantum state. These circuit constructions often rely on oracles that encode the Hamiltonian as a sequence of unitary transformations in some way. Such oracles form what is called the input model, which can generally be separated into two parts: a prepare oracle and a select oracle. One particular strategy for implementing a physical Hamiltonian on a quantum computer is known as block encoding, where the Hamiltonian is embedded into a larger unitary matrix.

We present an efficient block encoding scheme for a second quantized Hamiltonian to address the following two challenges. (a) The number of terms $L$ in Hamiltonian is large; (b) Unnecessary resources used for $\eta$ particle state simulation.

The quantum circuit we construct for the block encoding scheme has two desireable features: (a) T gate count is sublinear in $L$; (b) sublinear subnormalization factor in $L$ for $\eta$ particle state block encoding.

Under the most general setting where the Hamiltonian’s coefficients $\alpha_i=\mathcal{O}(1)$ , the T gate counts can be reduced from $\mathcal{O}(L)$ to $\mathcal{O}(\sqrt{L})$ and the Clifford gate count equals $L\log(\frac{1}{\epsilon})+o(L)$ where $\epsilon$ is the precision for input model. In addition, we also developed $\eta$ particle block encoding with subnormalization reduced from $\mathcal{O}(L)$ to $\mathcal{O}(\sqrt{L})$. Further improvements are discussed if certain decay properties are assumed for the coefficients.

The optimal quantum measurements for estimating different unknown parameters in a parameterized quantum state are usually incompatible with each other. Traditional approaches to addressing the measurement incompatibility issue, such as the Holevo Cram\'{e}r–Rao bound, suffer from multiple difficulties towards practical applicability, as the optimal measurement strategies are usually state-dependent, difficult to implement and also take complex analyses to determine. Here we study randomized measurements as a new approach for multi-parameter quantum metrology. We show quantum measurements on single copies of quantum states given by 3-design perform near-optimally when estimating an arbitrary number of parameters in pure states and more generally, approximately low-rank states, whose metrological information is largely concentrated in a low-dimensional subspace. The near-optimality is also shown in estimating the maximal number of parameters for three types of mixed states that are well-conditioned on its support. Examples of fidelity estimation and Hamiltonian estimation are explicitly provided to demonstrate the power and limitation of randomized measurements in multi-parameter quantum metrology.

The threshold theorem in quantum computing guarantees that it is possible to perform reliable computation with a provable advantage over classical computers.  Experimental progress in quantum devices has advanced this concept from a theoretical curiosity to one of increasing technological relevance.  These developments inspire new questions at the intersection of many-body physics and computer science about how to characterize, describe, and exploit dynamical phases of quantum matter that arise in fault-tolerant quantum computers.  In this talk, I will describe several examples in this direction from my research, illustrated also by experiments on current quantum devices.

Symmetry is fundamental in the description and simulation of quantum systems. Leveraging symmetries in classical simulations of many-body quantum systems can results in significant overhead due to the exponentially growing size of some symmetry groups as the number of particles increases. Quantum computers hold the promise of achieving exponential speedup in simulating quantum many-body systems; however, a general method for utilizing symmetries in quantum simulations has not yet been established. In this work, we present a unified framework for incorporating symmetry group transforms on quantum computers to simulate many-body systems. The core of our approach lies in the development of efficient quantum circuits for symmetry-adapted projection onto irreducible representations of a group or pairs of commuting groups. We provide resource estimations for common groups, including the cyclic and permutation groups. Our algorithms demonstrate the capability to prepare coherent superpositions of symmetry-adapted states and to perform quantum evolution across a wide range of models in condensed matter physics and \textit{ab initio} electronic structure in quantum chemistry. Specifically, we execute a symmetry-adapted quantum subroutine for small molecules in first-quantization on noisy hardware. In addition, we present a discussion of open problems regarding treating symmetries in digital quantum simulations of many-body systems, paving the way for future systematic investigations into leveraging symmetries \emph{quantumly} for practical quantum advantage. The broad applicability and rigorous resource estimation for symmetry transformations make our framework appealing for achieving provable quantum advantage on fault-tolerant quantum computers, especially for symmetry-related properties.

Presenters: Yuanjie Ren and Kevin Smith

The classification of topological phases of matter is a fundamental challenge in quantum many-body physics, with applications to quantum technology. Recently, this classification has been extended to the setting of Adaptive Finite-Depth Local Unitary (AFDLU) circuits which allow global classical communication. In this setting, the trivial phase is the collection of all topological states that can be prepared via AFDLU. Here, we propose a complete classification of the trivial phase by showing how to prepare all solvable anyon theories that admit a gapped boundary via AFDLU, extending recent results on solvable groups. Our construction includes non-Abelian anyons with irrational quantum dimensions, such as Ising anyons, and more general acyclic anyons. Specifically, we introduce a sequential gauging procedure, with an AFDLU implementation, to produce a string-net ground state in any topological phase described by a solvable anyon theory with gapped boundary. In addition, we introduce a sequential ungauging and regauging procedure, with an AFDLU implementation, to apply string operators of arbitrary length for anyons and symmetry twist defects in solvable anyon theories. We apply our procedure to the quantum double of the group S3 and to several examples that are beyond solvable groups, including the doubled Ising theory, the Z3 Tambara-Yamagami string-net, and doubled SU(2)4 anyons.

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Adaptive quantum circuits, which combine local unitary gates, midcircuit measurements, and feedforward operations, have recently emerged as a promising avenue for efficient state preparation, particularly on near-term quantum devices limited to shallow-depth circuits. Matrix product states (MPS) comprise a significant class of many-body entangled states, efficiently describing the ground states of one-dimensional gapped local Hamiltonians and finding applications in a number of recent quantum algorithms. Recently, it was shown that the AKLT state — a paradigmatic example of an MPS — can be exactly prepared with an adaptive quantum circuit of constant-depth, an impossible feat with local unitary gates due to its nonzero correlation length [Smith et al., PRX Quantum 4, 020315 (2023)]. In this work, we broaden the scope of this approach and demonstrate that a diverse class of MPS can be exactly prepared using constant-depth adaptive quantum circuits, outperforming optimal preparation protocols that rely on unitary circuits alone. We show that this class includes short- and long-ranged entangled MPS, symmetry-protected topological (SPT) and symmetry-broken states, MPS with finite Abelian, non-Abelian, and continuous symmetries, resource states for MBQC, and families of states with tunable correlation length. Moreover, we illustrate the utility of our framework for designing constant-depth sampling protocols, such as for random MPS or for generating MPS in a particular SPT phase. We present sufficient conditions for particular MPS to be preparable in constant time, with global on-site symmetry playing a pivotal role. Altogether, this work demonstrates the immense promise of adaptive quantum circuits for efficiently preparing many-body entangled states and provides explicit algorithms that outperform known protocols to prepare an essential class of states.

Presenters: Xin Zhang and Stefano Reale

Gate-defined semiconductor quantum dot arrays are a promising platform for digital and analog quantum simulations due to their scalability and precise control capabilities [1]. Recent advancements have enabled the engineering of interacting spin systems expected to exhibit signatures of complex many-body states [2]. However, characterizing the energy spectrum of such systems is challenging, since interactions give rise to many-body eigenstates that are far more complex than the simple spin-flip excitations that define the computational (Zeeman) basis. Here we demonstrate a time-domain spectroscopic technique that provides a one-to-one mapping from computational basis states prepared in the non-interacting regime to the many-body regime. We initialize quantum superpositions through Landau-Zener transitions at spin-orbit-induced anticrossings in Ge/SiGe quantum dots, then adiabatically evolve these states into the interacting regime and back, realizing a protocol similar to many-body Ramsey interferometry [3]. This approach allows us to selectively probe the energy states in the interacting regime and reconstruct the spectrum of a chain of up to 8 spins in a gate-defined Ge/SiGe quantum dot ladder. To our knowledge, this work presents the first comprehensive spectroscopic characterization of many-body states in a semiconductor quantum dot array of this scale, advancing our ability to study quantum phases of matter in scalable solid-state platforms. [1] Hensgens, T., Fujita, T., Janssen, L. et al., Nature 548, 70–73 (2017). [2] Appel, M.H., Ghorbal, A., Shofer, N. et al., Nature Physics 21, 368–373 (2025). [3] Roberts, G., Vrajitoarea, A., Saxberg, B., et al., Science Advances 10, eado1069 (2024).

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Bose–Einstein condensation (BEC), where a large number of bosons collectively occupy a single quantum state, has been extensively studied across various fields, ranging from condensed matter physics to particle physics and astrophysics. In condensed matter physics, the BEC has been observed in solids hosting quasiparticles, such as triplons in dimerized quantum magnets, which exhibit BEC behavior via magnetic field-induced phase transitions [1]. However, in these solids, the geometry and the interaction strengths are mostly fixed, and site-resolved measurements are not possible, which prevents more advanced studies of BEC formation in magnetic systems. Gate-defined semiconductor quantum dot arrays offer a promising platform for quantum simulation of a wide range of phenomena, with site-resolved electrical readout and control of both charge and spin states. Recent studies have demonstrated simulations of the Fermi-Hubbard model, Nagaoka ferromagnetism, Heisenberg spin chains, and exciton transport in a quantum dot array [2-5]. Building on these advances, we use a 2×4 germanium quantum dot ladder (see Figure 1) [6] to explore quantum phase transitions of triplons under a magnetic field. In our experiment, we first form weakly coupled spin dimers along the rungs of the ladder. As intra-dimer exchange couplings are reduced, which is analogous to increasing the external magnetic field, we observe an increase in spin-triplet (triplon) populations. In Figure 2, a corresponding rise in average magnetization and a peak in magnetization variance indicate the onset of a phase transition. Also, the site-resolved readout of dimer states allows us to track the sequential population of triplons during the phase transition—an observation not possible in bulk materials. In the thermodynamic limit, this would correspond to transitions from a quantum disordered state (gapped singlets) to a polarized state (gapped triplets) via a gapless canted antiferromagnet state, which forms a BEC of triplons at low temperature. Furthermore, as shown in Figure 3, by enhancing the exchange couplings along one leg of the ladder, we observe a splitting of the magnetization variance peak—an effect that remains under investigation.

The native spin and bosonic degrees of freedom and their programmable interactions in trapped ion systems make them a suitable platform for simulating quantum chemistry models of excitation transfer. Trapped-ion simulators can also incorporate the environmental effects on these chemical systems [1–5] thanks to the capability of reservoir engineering with tunable properties [6–8]. Here, we experimentally investigate the excitation transfer dynamics in a multi-mode linear vibronic coupling model, which consists of two environmentally damped vibrational modes independently coupled to two donor and acceptor electronic sites. By controlling the vibronic coupling strengths, we access the real-time transfer dynamics in two distinct phenomenological regimes, charge transfer (CT) and vibrationally assisted excitation transfer (VAET), highlighting their key differences. In both cases, the transfer rates are enhanced at high donor-acceptor energy differences when the two vibrational modes are degenerate. Conversely, when they have different energies, the slower mode enables additional transfer pathways, making the process more energetically accessible. Our results provide insights into the multi-mode excitation transfer in non-perturbative regimes, whose understanding is paramount to the design and development of efficient organic photovoltaics and molecular electronics. [1] A. Lemmer, et al. New J. Phys. 20, 073002 (2018). [2] R. J. MacDonell, et al. Chem. Sci. 12, 9794 (2021). [3] F. Schlawin, et al. PRX Quantum 2, 010314 (2021). [4] M. Kang, et al. Nat. Rev. Chem. 8, 340-358 (2024). [5] V. C. Olaya-Agudelo, et al. arXiv:2407.17819 (2024). [6] V. So, et al. Sci. Adv. 10, eads8011 (2024). [7] K. Sun, et al. arXiv:2405.14624 (2024). [8] T. Navickas, et al. arXiv:2409.04044 (2024).

Presenters: Annika Böhler AND Anka Van de Walle

Probing real-time dynamics is a key goal of quantum simulation, but experiments with cold atoms, Rydberg arrays, or trapped ions often yield limited, or hard-to-interpret data. We introduce time-dependent neural quantum states (t-NQS): a machine learning method that reconstructs the full quantum state evolution from time-evolved snapshots. At the core of t-NQS is a neural network that represents the quantum wave function as a function of time. By using Variational Monte Carlo, the network is trained globally to satisfy the time-dependent Schrödinger equation across all times at once. This continuous representation enables efficient simulation using tools like automatic differentiation, while avoiding explicit time integration. Crucially, t-NQS naturally integrates with experimental data: snapshots of the system at various times can be used to pre-train the model, significantly improving convergence and accuracy in practice. This synergy goes further. By training on various time-evolved measurements at once, t-NQS can reconstruct the underlying wave function and phase structure, enabling access to observables which are experimentally inaccessible. It even allows for reconstruction of complex initial states, including entangled and topological ones, from data collected only during the system’s evolution. We demonstrate these capabilities by simulating quantum state preparation protocols relevant to current experiments, including the evolution of a 2D Heisenberg anti-ferromagnet under a staggered field and the preparation of a quantum spin liquid in a Rydberg atom array. These results highlight t-NQS as a versatile tool for extracting physics from limited data and enhancing the interpretability of quantum simulation experiments.

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Simulating strongly correlated electron systems remains a major challenge in condensed matter physics. Quantum simulation platforms have become powerful tools for exploring these systems beyond the limits of classical computation. In particular, ultracold alkaline-earth atoms and molecules now enable experimental access to Fermi-Hubbard models with SU(N)-symmetric interactions. However, theoretical understanding of these models remains limited, especially at finite dopings. In this talk, I present a neural network-based variational approach to the strongly correlated limit of the Fermi-Hubbard model, using a combination of Gutzwiller projection and a Hidden Fermion Determinant State ansatz (G-HFDS). I will show that this method captures magnetic and polaronic correlations in the SU(2) t-J model across the full doping range, and extend the framework to the SU(3) symmetric case, demonstrating that it can access finite-doping regimes that are challenging for conventional approaches yet highly relevant for state of the art quantum simulators. Our results provide a first step towards studying finite doping regimes of Fermi Hubbard models with higher SU(N) symmetries.

Dynamical Decoupling (DD) is a widely used error suppression technique that plays a crucial role in implementing state-of-the-art quantum processors across various platforms. In this work, inspired by recent advancements in (randomized) Hamiltonian simulation, we present a novel randomized DD protocol that can quadratically improve the performance of any given deterministic DD, by using no more than two additional pulses. Our construction is implemented by probabilistically applying sequences of pulses, which, when combined, effectively eliminate the coherent error terms. As a result, we show that our randomized protocol using a few pulses can outperform deterministic DD protocols that require considerably more pulses. Our method applies universally to all existing DD protocols, including to Uhrig DD, which had been previously regarded to be optimal. We also introduce new analytical methods for rigorous performance analysis of higher-order DD protocols, potentially offering a new tool for rigorous performance analysis of Hamiltonian simulation. Finally, we present numerical simulations confirming the significant advantage of using randomized protocols compared to widely used deterministic protocols.