Reese qubits

Intelligently protecting cat qubits against control parameter drift.

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Reese Qubits: Adaptive Optimization for Cat Qubit Stabilization

Inspiration

Realizing the full potential of quantum computing remains contingent on overcoming a critical hardware bottleneck: the scarcity of fault-tolerant architectures. Cat qubits offer a promising solution by leveraging two-photon dissipation to suppress bit-flip errors exponentially.

However, their performance depends heavily on precise calibration. In real systems, control parameters drift over time, degrading stability and logical protection.

Inspired by recent work in adaptive quantum control and reinforcement learning, we developed Reese Qubits, a system that continuously optimizes cat qubit parameters under drift and noise.

What it does

Check out the paper for more specifics!

Reese Qubits is an online optimization framework that:

  • Tunes control parameters:
    • Nonlinear coupling: g₂
    • Drive amplitude: ε_d
  • Tracks system performance using logical proxies:
    • Phase-flip proxy: s_x
    • Bit-flip proxy: s_z
    • Logical bias: η ≈ T_Z / T_X
  • Adapts to drift in real time

Key Results

  • Phase-flip proxy improved:
    • s_x: 0.93 → 0.995
  • Bit-flip proxy improved:
    • s_z: 0.42 → 0.89
  • Logical bias stabilized around target:
    • η: → ~450 (target = 500)
  • Cat size stabilized near target:
    • α ≈ 1.6 → 1.94 (target = 2.0)

How we built it

Loss Function: Simulate cat qubit dynamics given some input parameters using the Lindblad Master Equation in dynamiqs -> Calculate reward based on measurement proxies for T_X and T_P.

Training Loop: For each epoch: call loss function -> update params

System Model

  • Two-mode bosonic system:
    • Storage mode (logical qubit)
    • Lossy buffer mode (dissipation)
  • Hilbert space truncation:
    • N_A = 15, N_B = 5

Hamiltonian

[ H = g_2^* a^2 b^\dagger + g_2 a^{\dagger 2} b - \epsilon_d b^\dagger - \epsilon_d^* b ]

Dissipation

  • Buffer loss: κ_B = 10 MHz
  • Storage loss: κ_A = 1 MHz

Optimization

  • Algorithm: Sep-CMA-ES
  • Parameters:
    • x = [Re(g₂), Im(g₂), Re(ε_d), Im(ε_d)]
  • Search setup:
    • Population size: 8
    • Epochs: 60
    • Initial σ: 0.3

Loss Function

[ L = -λX s_x - λ_Z s_z + λ{bias} L_{bias} + λα Lα ]

Weights:

  • λ_X = 1.0
  • λ_Z = 0.5
  • λ_bias = 0.1
  • λ_α = 0.5

Challenges we ran into

  • Achieving stable convergence in a noisy, non-convex landscape
  • Understanding cat qubit physics deeply
  • Designing a loss function aligned with physical meaning
  • Developing robust and measurement-efficient measurement proxies
  • Handling:
    • drift
    • measurement noise
    • competing objectives

Accomplishments that we're proud of

This is was easily the most technically involved project any of us have ever worked on. In just 24 hours, our team -- half of whom came into YQuantum with no experience in quantum computing -- learned the physics of cat qubits in exhaustive detail and engineered a full adaptive quantum control pipeline end-to-end.

Technical Accomplishments:

  • Demonstrated robust convergence:
    • Loss reduced: -0.8 → -1.37
  • Achieved strong improvement in:
    • bit-flip protection (s_z ↑)
    • coherence (s_x ↑)
  • Showed recovery under drift:
    • g₂ amplitude step (+30%) recovered in ~15 epochs
  • Demonstrated benefit of control knobs:
    • Detuning compensation improved recovery speed

What we learned

A LOT. A sizable chunk of our time was spent whiteboarding out concepts, defining unfamiliar vocab, teaching each other what we understood in order to build this system from the ground up. We owe a huge huge thanks to Shantanu for his help and patience!

A summary of our structured drift analysis:

Drift sensitivity hierarchy:

  • Most disruptive:
    • g₂ amplitude drift (+30%)
  • Moderate:
    • detuning drift (Δ_a = +0.5 MHz)
  • Minimal:
    • Kerr drift (K = 0.15 MHz)

Key insights:

  • Slow drift → easy to track
  • Sudden drift → temporary performance drop

  • Measurement noise:

    • SNR: 50 → 5
    • did not break optimization, but reduced final performance

  • Optimization quality depends heavily on:

    • loss design
    • not just the optimizer

What's next for Reese qubits

  • Improve logical bias performance beyond η ≈ 450
  • Fix mismatch in phase-flip reward design
  • Compare:
    • CMA-ES vs Reinforcement Learning
  • Extend drift models:
    • richer hardware noise
    • non-Markovian effects
  • Test on real quantum hardware

  • Explore improved encodings:

    • squeezed cat qubits
    • enhanced dissipative designs

  • Explore an Augmented Lagrangian encoding for our loss function, which natively supports objective and penalty terms, in addition to featuring tunable parameters.

  • Expand the generalizability of our model by tuning its function on the whole zoo of cat qubits as well as one-qubit gates applied to cat qubits.

Final Takeaway

Reese Qubits shows that:

Adaptive optimization can stabilize quantum systems under realistic drift, but achieving full fault tolerance requires better objective design, richer control knobs, and tighter integration between physics and learning.

Quantum controls are really cool!

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