QVECTOR: an algorithm for device-tailored quantum error correction

Abstract

Current approaches to fault-tolerant quantum computation will not enable useful quantum computation on near-term devices of 50 to 100 qubits. Leading proposals, such as the color code and surface code schemes, must devote a large fraction of their physical quantum bits to quantum error correction. Building from recent quantum machine learning techniques, we propose an alternative approach to quantum error correction aimed at reducing this overhead, which can be implemented in existing quantum hardware and on a myriad of quantum computing architectures. This method aims to optimize the average fidelity of encoding and recovery circuits with respect to the actual noise in the device, as opposed to that of an artificial or approximate noise model. The quantum variational error corrector (QVECTOR) algorithm employs a quantum circuit with parameters that are variationally-optimized according to processed data originating from quantum sampling of the device, so as to learn encoding and error-recovery gate sequences. We develop this approach for the task of preserving quantum memory and analyze its performance with simulations. We find that, subject to phase damping noise, the simulated QVECTOR algorithm learns a three-qubit encoding and recovery which extend the effective T2 of a quantum memory six-fold. Subject to a continuous-time amplitude- plus phase-damping noise model on five qubits, the simulated QVECTOR algorithm learns encoding and decoding circuits which exploit the coherence among Pauli errors in the noise model to outperform the five-qubit stabilizer code and any other scheme that does not leverage such coherence. Both of these schemes can be implemented with existing hardware.

11 + 5 pages, 5 figures, 2 tables

References in corpus (33)

• A variational eigenvalue solver on a quantum processor
• Charge insensitive qubit design derived from the Cooper pair box
• Surface codes: Towards practical large-scale quantum computation
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Good Quantum Error-Correcting Codes Exist
• QuTiP 2: A Python framework for the dynamics of open quantum systems
• The theory of variational hybrid quantum-classical algorithms
• QuTiP: An open-source Python framework for the dynamics of open quantum systems
• A Quantum Approximate Optimization Algorithm
• Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
• Characterizing Quantum Supremacy in Near-Term Devices
• Dynamical decoupling and noise spectroscopy with a superconducting flux qubit
• Coherent Josephson qubit suitable for scalable quantum integrated circuits
• Efficient measurement of quantum gate error by interleaved randomized benchmarking
• Experimental Quantum Computations on a Topologically Encoded Qubit
• Stabilizer Formalism for Operator Quantum Error Correction
• Virtual Quantum Subsystems
• Low-distance Surface Codes under Realistic Quantum Noise
• Solving strongly correlated electron models on a quantum computer
• Experimental Quantum Hamiltonian Learning
• Approximate quantum error correction can lead to better codes
• Coherence and Decay of Higher Energy Levels of a Superconducting Transmon Qubit
• Efficient error models for fault-tolerant architectures and the Pauli twirling approximation
• Iterative Optimization of Quantum Error Correcting Codes
• Fault-tolerant error correction with the gauge color code
• Practical optimization for hybrid quantum-classical algorithms
• Structured Near-Optimal Channel-Adapted Quantum Error Correction
• On Protected Realizations of Quantum Information
• Gate-error analysis in simulations of quantum computers with transmon qubits
• Approximate quantum error correction for generalized amplitude damping errors
• Comparison of a quantum error correction threshold for exact and approximate errors
• Channel-Optimized Quantum Error Correction
• A dynamical interpretation of the Pauli Twirling Approximation and Quantum Error Correction

Cited by in corpus (14)

• Quantum computational chemistry
• Noise-Induced Barren Plateaus in Variational Quantum Algorithms
• Variational Quantum Computation of Excited States
• Quantum-assisted quantum compiling
• PennyLane: Automatic differentiation of hybrid quantum-classical computations
• Variational Quantum State Diagonalization
• Variational Quantum State Eigensolver
• Quantum circuit optimization with deep reinforcement learning
• Variational Consistent Histories as a Hybrid Algorithm for Quantum Foundations
• Practical distributed quantum information processing with LOCCNet
• Operator Sampling for Shot-frugal Optimization in Variational Algorithms
• Efficient diagnostics for quantum error correction
• Toward a quantum computing algorithm to quantify classical and quantum correlation of system states
• Wildcard error: Quantifying unmodeled errors in quantum processors