Approximate Autonomous Quantum Error Correction with Reinforcement Learning

• URL: http://arxiv.org/abs/2212.11651v2
• Date: Tue, 12 Sep 2023 16:57:14 GMT
• Title: Approximate Autonomous Quantum Error Correction with Reinforcement Learning
• Authors: Yexiong Zeng, Zheng-Yang Zhou, Enrico Rinaldi, Clemens Gneiting, Franco Nori
• Abstract summary: Autonomous quantum error correction (AQEC) protects logical qubits by engineered dissipation. Bosonic code spaces, where single-photon loss represents the dominant source of error, are promising candidates for AQEC. We propose a bosonic code for approximate AQEC by relaxing the Knill-Laflamme conditions.
• Score: 4.015029887580199
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Autonomous quantum error correction (AQEC) protects logical qubits by engineered dissipation and thus circumvents the necessity of frequent, error-prone measurement-feedback loops. Bosonic code spaces, where single-photon loss represents the dominant source of error, are promising candidates for AQEC due to their flexibility and controllability. While existing proposals have demonstrated the in-principle feasibility of AQEC with bosonic code spaces, these schemes are typically based on the exact implementation of the Knill-Laflamme conditions and thus require the realization of Hamiltonian distances $d\geq 2$. Implementing such Hamiltonian distances requires multiple nonlinear interactions and control fields, rendering these schemes experimentally challenging. Here, we propose a bosonic code for approximate AQEC by relaxing the Knill-Laflamme conditions. Using reinforcement learning (RL), we identify the optimal bosonic set of codewords (denoted here by RL code), which, surprisingly, is composed of the Fock states $\vert 2\rangle$ and $\vert 4\rangle$. As we show, the RL code, despite its approximate nature, successfully suppresses single-photon loss, reducing it to an effective dephasing process that well surpasses the break-even threshold. It may thus provide a valuable building block toward full error protection. The error-correcting Hamiltonian, which includes ancilla systems that emulate the engineered dissipation, is entirely based on the Hamiltonian distance $d=1$, significantly reducing model complexity. Single-qubit gates are implemented in the RL code with a maximum distance $d_g=2$.

Related papers

• Computational-Statistical Tradeoffs at the Next-Token Prediction Barrier: Autoregressive and Imitation Learning under Misspecification [50.717692060500696]
  Next-token prediction with the logarithmic loss is a cornerstone of autoregressive sequence modeling. Next-token prediction can be made robust so as to achieve $C=tilde O(H)$, representing moderate error amplification. No computationally efficient algorithm can achieve sub-polynomial approximation factor $C=e(log H)1-Omega(1)$.
  arXiv  Detail & Related papers  (2025-02-18T02:52:00Z)
• Demonstrating dynamic surface codes [138.1740645504286]
  We experimentally demonstrate three time-dynamic implementations of the surface code. First, we embed the surface code on a hexagonal lattice, reducing the necessary couplings per qubit from four to three. Second, we walk a surface code, swapping the role of data and measure qubits each round, achieving error correction with built-in removal of accumulated non-computational errors. Third, we realize the surface code using iSWAP gates instead of the traditional CNOT, extending the set of viable gates for error correction without additional overhead.
  arXiv  Detail & Related papers  (2024-12-18T21:56:50Z)
• Robust analog quantum simulators by quantum error-detecting codes [22.034646136056804]
  We provide a recipe for error-resilient Hamiltonian simulations, making use of an excited encoding subspace stabilized by solely $2$-local commuting Hamiltonians. Our method is scalable as it only requires penalty terms that scale to system size.
  arXiv  Detail & Related papers  (2024-12-10T18:58:05Z)
• Families of $d=2$ 2D subsystem stabilizer codes for universal Hamiltonian quantum computation with two-body interactions [0.0]
  In the absence of fault tolerant quantum error correction for analog, Hamiltonian quantum computation, error suppression via energy penalties is an effective alternative. We construct families of distance-$2$ stabilizer subsystem codes we call trapezoid codes'' We identify a family of codes achieving the maximum code rate, and by slightly relaxing this constraint, uncover a broader range of codes with enhanced physical locality.
  arXiv  Detail & Related papers  (2024-12-09T18:36:38Z)
• Settling the Sample Complexity of Online Reinforcement Learning [92.02082223856479]
  We show how to achieve minimax-optimal regret without incurring any burn-in cost. We extend our theory to unveil the influences of problem-dependent quantities like the optimal value/cost and certain variances.
  arXiv  Detail & Related papers  (2023-07-25T15:42:11Z)
• Hardware efficient autonomous error correction with linear couplers in superconducting circuits [0.5428370406156905]
  Large-scale quantum computers will inevitably need quantum error correction (QEC) to protect information against decoherence. AQEC schemes work by transforming error states into excitations that can be efficiently removed through engineered dissipation. The recently proposed AQEC scheme by Li et al., called the Star code, can autonomously correct or suppress all single qubit error channels using two transmons as encoders with a tunable coupler and two lossy resonators as a cooling source.
  arXiv  Detail & Related papers  (2023-03-02T09:44:55Z)
• Simulating excited states of the Lipkin model on a quantum computer [0.0]
  We show that the accuracy strongly depends on the fermion to qubit encoding. We use IBM quantum machines to compute the energy spectrum for a system of $N=2, 3$ and $4$ particles.
  arXiv  Detail & Related papers  (2022-03-03T01:43:12Z)
• Quantum Error Correction with Gauge Symmetries [69.02115180674885]
  Quantum simulations of Lattice Gauge Theories (LGTs) are often formulated on an enlarged Hilbert space containing both physical and unphysical sectors. We provide simple fault-tolerant procedures that exploit such redundancy by combining a phase flip error correction code with the Gauss' law constraint.
  arXiv  Detail & Related papers  (2021-12-09T19:29:34Z)
• Breaking the Sample Complexity Barrier to Regret-Optimal Model-Free Reinforcement Learning [52.76230802067506]
  A novel model-free algorithm is proposed to minimize regret in episodic reinforcement learning. The proposed algorithm employs an em early-settled reference update rule, with the aid of two Q-learning sequences. The design principle of our early-settled variance reduction method might be of independent interest to other RL settings.
  arXiv  Detail & Related papers  (2021-10-09T21:13:48Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)
• Exponential Error Suppression for Near-Term Quantum Devices [0.0]
  In NISQ era, complexity and scale required to adopt even the smallest QEC is prohibitive. We show that for the crucial case of estimating expectation values of observables one can indeed achieve an effective exponential suppression.
  arXiv  Detail & Related papers  (2020-11-11T18:00:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.