Variational circuit compiler for quantum error correction

Abstract

Quantum error correction is vital for implementing universal quantum computing. A key component is the encoding circuit that maps a product state of physical qubits into the encoded multipartite entangled logical state. Known methods are typically not 'optimal' either in terms of the circuit depth (and therefore the error burden) or the specifics of the target platform, i.e. the native gates and topology of a system. This work introduces a variational compiler for efficiently finding the encoding circuit of general quantum error correcting codes with given quantum hardware. Focusing on the noisy intermediate scale quantum regime, we show how to systematically compile the circuit following an optimising process seeking to minimise the number of noisy operations that are allowed by the noisy quantum hardware or to obtain the highest fidelity of the encoded state with noisy gates. We demonstrate our method by deriving novel encoders for logic states of the five qubit code and the seven qubit Steane code. We describe ways to augment the discovered circuits with error detection. Our method is applicable quite generally for compiling the encoding circuits of quantum error correcting codes.

arXiv comment12 pages, 8 figures

References in corpus (39)

• Double-slit photoelectron interference in strong-field ionization of the neon dimer
• Mixed State Entanglement and Quantum Error Correction
• Good Quantum Error-Correcting Codes Exist
• Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
• A Theory of Fault-Tolerant Quantum Computation
• State preservation by repetitive error detection in a superconducting quantum circuit
• Efficient variational quantum simulator incorporating active error minimisation
• Quantum error correction in a solid-state hybrid spin register
• Realization of Three-Qubit Quantum Error Correction with Superconducting Circuits
• Preparation and Measurement of Three-Qubit Entanglement in a Superconducting Circuit
• Unconditional quantum teleportation between distant solid-state qubits
• Theory of variational quantum simulation
• Universal control and error correction in multi-qubit spin registers in diamond
• Experimental Quantum Computations on a Topologically Encoded Qubit
• Quantum-assisted quantum compiling
• Polynomial-time T-depth Optimization of Clifford+T circuits via Matroid Partitioning
• Detecting bit-flip errors in a logical qubit using stabilizer measurements
• Soundness and completeness of quantum root-mean-square errors
• Quantum Circuit Simplification and Level Compaction
• QuEST and High Performance Simulation of Quantum Computers
• Repeated quantum error correction on a continuously encoded qubit by real-time feedback
• Low-cost error mitigation by symmetry verification
• Error-mitigated digital quantum simulation
• Automated optimization of large quantum circuits with continuous parameters
• Experimental demonstration of topological error correction
• Noise Resilience of Variational Quantum Compiling
• Fault-tolerant quantum error detection
• Multi-Element Logic Gates for Trapped-Ion Qubits
• Optimizing Quantum Error Correction Codes with Reinforcement Learning
• Methodology for replacing indirect measurements with direct measurements
• Experimental demonstration of a graph state quantum error-correction code
• Decoding quantum errors with subspace expansions
• Realization of Universal Ion Trap Quantum Computation with Decoherence Free Qubits
• Fault-tolerant magic state preparation with flag qubits
• Demonstration of Quantum Error Correction using Linear Optics
• Experimental quantum coding against photon loss error
• Network architecture for a topological quantum computer in silicon
• A Silicon Surface Code Architecture Resilient Against Leakage Errors
• An integrity measure to benchmark quantum error correcting memories

Cited by in corpus (20)

• Variational Quantum Algorithms
• Experimental benchmarking of an automated deterministic error suppression workflow for quantum algorithms
• Quantum Architecture Search with Meta-learning
• Trainability Enhancement of Parameterized Quantum Circuits via Reduced-Domain Parameter Initialization
• Simulating Noisy Variational Quantum Algorithms: A Polynomial Approach
• Variational quantum algorithm for experimental photonic multiparameter estimation
• A High Performance Compiler for Very Large Scale Surface Code Computations
• Quantum variational learning for quantum error-correcting codes
• Automated Quantum Circuit Design with Nested Monte Carlo Tree Search
• Optimal local unitary encoding circuits for the surface code
• Beyond unital noise in variational quantum algorithms: noise-induced barren plateaus and limit sets
• Adaptive projected variational quantum dynamics
• Efficient Quantum Circuit Compilation for Near-Term Quantum Advantage
• Near-Term Spin-Qubit Architecture Design via Multipartite Maximally-Entangled States
• Training Computer Scientists for the Challenges of Hybrid Quantum-Classical Computing
• Assisted quantum simulation of open quantum systems
• Quantum Circuit Discovery for Fault-Tolerant Logical State Preparation with Reinforcement Learning
• Quantum Circuit Design using a Progressive Widening Enhanced Monte Carlo Tree Search
• Ancillary entangling Floquet kicks for accelerating quantum algorithms
• Optical Quantum Computing