Dynamical subset sampling of quantum error correcting protocols

Abstract

Quantum error correcting (QEC) stabilizer codes enable protection of quantum information against errors during storage and processing. Simulation of noisy QEC codes is used to identify the noise parameters necessary for advantageous operation of logical qubits in realistic quantum computing architectures. Typical quantum error correction techniques contain intermediate measurements and classical feedback that determine the actual noisy circuit sequence in an instance of performing the protocol. Dynamical subset sampling enables efficient simulation of such non-deterministic quantum error correcting protocols for any type of quantum circuit and incoherent noise of low strength. As an importance sampling technique, dynamical subset sampling allows one to effectively make use of computational resources to only sample the most relevant sequences of quantum circuits in order to estimate a protocol's logical failure rate with well-defined error bars. We demonstrate the capabilities of dynamical subset sampling with examples from fault-tolerant (FT) QEC. We show that, in a typical stabilizer simulation with incoherent Pauli noise of strength $p=10^{-3}$, our method can reach a required sampling accuracy on the logical failure rate with two orders of magnitude fewer samples than direct Monte Carlo simulation. Furthermore, dynamical subset sampling naturally allows for efficient simulation of realistic multi-parameter noise models describing faulty quantum processors. It can be applied not only for QEC in the circuit model but any noisy quantum computing framework with incoherent fault operators including measurement-based quantum computation and quantum networks.

arXiv comment33 pages, 26 figures

References in corpus (44)

• Quantum Computing in the NISQ era and beyond
• Fault-tolerant quantum computation by anyons
• Surface codes: Towards practical large-scale quantum computation
• Quantum Teleportation is a Universal Computational Primitive
• Topological quantum memory
• Improved Simulation of Stabilizer Circuits
• The Quantum Jump Approach to Dissipative Dynamics in Quantum Optics
• Quantum Error Correction for Quantum Memories
• Multiple Particle Interference and Quantum Error Correction
• Measurement-based quantum computation
• Fault-tolerant quantum computation with high threshold in two dimensions
• Quantum Error Correction for Beginners
• Topological Quantum Distillation
• Topological fault-tolerance in cluster state quantum computation
• Stim: a fast stabilizer circuit simulator
• Overhead and noise threshold of fault-tolerant quantum error correction
• Fault-Tolerant Error Correction with Efficient Quantum Codes
• Quantum Low-Density Parity-Check Codes
• Demonstration of fault-tolerant universal quantum gate operations
• Low-distance Surface Codes under Realistic Quantum Noise
• The XZZX Surface Code
• QuEST and High Performance Simulation of Quantum Computers
• Quantum error correction with only two extra qubits
• Ultrahigh Error Threshold for Surface Codes with Biased Noise
• Assessing the progress of trapped-ion processors towards fault-tolerant quantum computation
• Flag fault-tolerant error correction with arbitrary distance codes
• Error Threshold for Color Codes and Random 3-Body Ising Models
• Tailoring surface codes for highly biased noise
• Fault-tolerant thresholds for the surface code in excess of 5% under biased noise
• Fault-tolerant magic state preparation with flag qubits
• Phase Structure of the Random-Plaquette Z_2 Gauge Model: Accuracy Threshold for a Toric Quantum Memory
• Simulating the performance of a distance-3 surface code in a linear ion trap
• Crosstalk Suppression for Fault-tolerant Quantum Error Correction with Trapped Ions
• 2-D color code quantum computation
• Approximation of real error channels by Clifford channels and Pauli measurements
• Simulation of rare events in quantum error correction
• Performance of planar Floquet codes with Majorana-based qubits
• Transversality and lattice surgery: exploring realistic routes towards coupled logical qubits with trapped-ion quantum processors
• Fault Tolerance with Bare Ancillae for a [[7,1,3]] Code
• Tailored XZZX codes for biased noise
• Strategies for practical advantage of fault-tolerant circuit design in noisy trapped-ion quantum computers
• Analytic asymptotic performance of topological codes
• Conditional generation of error syndromes in fault-tolerant error correction
• Efficient algorithm to compute the Berry conductivity

Cited by in corpus (4)

• Efficient fault-tolerant code switching via one-way transversal CNOT gates
• Decoding across transversal Clifford gates in the surface code
• Improved performance of the Bacon-Shor code with Steane's syndrome extraction method
• Comparison of spin-qubit architectures for quantum error-correcting codes