Quantum control

RL for Quantum Gate Control in Noisy Environments

KAK-based reference pulses, Walsh-basis corrections, and reinforcement learning for calibration of noisy two-qubit gates.

Year: 2026
Status: Ongoing
Topics: Reinforcement learning · Quantum control · Robustness

The project in brief

Can a learned calibration strategy improve pulses for unseen two-qubit gates without retraining?

Given a target $U_\star\in\mathrm{SU}(4)$ , find a control pulse whose noisy evolution approximates that gate. The reusable object is a calibration policy: it proposes corrections for new target–noise pairs without retraining.

Cartan decomposition supplies a reference pulse. A Walsh expansion turns nearby waveforms into a finite-dimensional search space, and reinforcement learning selects corrections from feedback. The chapters below develop this formulation and show the saved simulation results.

A conceptual single-qubit Bloch trajectory and pulse sequence

A conceptual single-qubit Bloch-sphere illustration. The marked point is a target state, not a gate. The separate pulse explorer compares ideal and noisy single-qubit evolution, including an ensemble of detunings. The research concerns two-qubit gates; these illustrations are not benchmark results or learned-policy demonstrations.

Objective

Optimize a calibration procedure across tasks

A task consists of a Haar-random two-qubit target $U_\star$ and hidden noise $\xi$ . Policy $\pi$ uses target information and pulse-evaluation feedback to return a pulse $c_{\mathrm{out}}^\pi$ . The channel $\mathcal{E}$ is obtained from noisy time evolution; policy weights stay fixed during testing.

\max_{\pi}\;\mathbb{E}_{U_\star,\xi}\!\left[F_{\mathrm{avg}}\!\left(\mathcal{E}_{c_{\mathrm{out}}^\pi,\xi},U_\star\right)\right]

Research formulation; the Bloch explorer below is a separate single-qubit illustration of ideal and noisy dynamics, without a learned policy.

Interactive · single-qubit noise explorer

One pulse. Many possible paths.

Paused

Compare an ideal rotation with a qubit under detuning, relaxation, and dephasing. The same pulse drives both. Turn on the ensemble to see what changes across noise realizations.

Ideal · open circleOne realization · dot

Show 24 realizations

Faint curves show the complete pulse; moving markers show the current time. Sample set 2718. Resampling changes all detunings, not the dissipative rates.

Initial state

u_xx-axis amplitude1.0

u_yy-axis amplitude0.4

u_zz-axis amplitude0.5

Try a pulse

u = 1 means Ω_ref = 29.920 × 10⁶ rad/s. Pulse changes restart time, but keep the same detuning.

Pulse duration (ns)physical time

Noise preset

Noise settings

Detuning standard deviationσδ · rad/s

Relaxation rateγ₁ · s⁻¹

Dephasing coefficientγz · s⁻¹

Press Enter or leave a field to apply it. Rates stay fixed within a run and across the ensemble. Changing σδ rescales the same Gaussian samples; each detuning stays constant throughout its pulse.

Selected detuning δ: -7.411e+5 rad/s

Physical time 0.0 / 210 ns

Playback

Selected realization r(t)(0.000, 0.000, 1.000)

P(0) / P(1) · selected1.000 / 0.000

Selected purity Tr(ρ²)1.0000

Ideal reference r(t)(0.000, 0.000, 1.000)

Hδ = ½Ω_refu · σ + δσ_zρ̇ = −i[Hδ, ρ] + γ₁D[σ₋](ρ) + γzD[σ_z](ρ)

ℏ = 1; Ω_ref = 2π/(210 ns), constant controls, δ ∼ N(0, σδ²). Paper convention: σ₋ = |1〉〈0|, so undriven relaxation tends to the south pole; 1/T₂ = γ₁/2 + 2γz. The ideal reference has no detuning or dissipation. At 1× playback, a complete pulse takes four screen seconds; this does not change physical time. Paper presets borrow one qubit’s rates, not the two-qubit experiment or trained policy. Model and conventions ↗

JavaScript is disabled. The static sphere shows the initial state with ideal and noisy full-pulse paths under the qubit 1 preset. Enable JavaScript to adjust controls, inspect the ensemble, or animate the physical evolution.

Question: Can a fixed learned controller improve analytical pulses for previously unseen quantum gates and hidden noise realizations, using feedback during calibration without retraining its policy for every new task?
Method: Combine a KAK-based reference pulse, Walsh-basis residual corrections, and eight sequential reinforcement-learning policies. Evaluate each proposed pulse and retain improvements; richer feedback adds selected directions of the residual gate error.
Progress: Held-out simulations show substantial fidelity gains, with further improvement from projection feedback in a matched comparison. Measurement cost, imperfect feedback, and robustness beyond the training distribution remain open parts of the research.

Explore the project

01 / Problem

↳

My contribution

Developing and evaluating reinforcement-learning methods for quantum gate calibration under simulated noise.

Last updated September 27, 2026

RL for Quantum Gate Control in Noisy Environments

Can a learned calibration strategy improve pulses for unseen two-qubit gates without retraining?

Optimize a calibration procedure across tasks

One pulse. Many possible paths.

Explore the project

From specifying a gate to learning how to calibrate it

Analytical structure first, learned corrections second

What the simulations establish—and what they leave open

My contribution