A taxonomy of small Markovian errors

Abstract

Errors in quantum logic gates are usually modeled by quantum process matrices (CPTP maps). But process matrices can be opaque, and unwieldy. We show how to transform a gate's process matrix into an error generator that represents the same information more usefully. We construct a basis of simple and physically intuitive elementary error generators, classify them, and show how to represent any gate's error generator as a mixture of elementary error generators with various rates. Finally, we show how to build a large variety of reduced models for gate errors by combining elementary error generators and/or entire subsectors of generator space. We conclude with a few examples of reduced models, including one with just $9N^2$ parameters that describes almost all commonly predicted errors on an N-qubit processor.

18 pages, 12 figures, all the customized error models you could ever want

References in corpus (12)

• Robust randomized benchmarking of quantum processes
• Assessing non-Markovian dynamics
• Detecting arbitrary quantum errors via stabilizer measurements on a sublattice of the surface code
• Direct Fidelity Estimation from Few Pauli Measurements
• Low-distance Surface Codes under Realistic Quantum Noise
• Precision tomography of a three-qubit donor quantum processor in silicon
• Experimental demonstration of fault-tolerant state preparation with superconducting qubits
• Microwave-driven coherent operations of a semiconductor quantum dot charge qubit
• Compressed sensing quantum process tomography for superconducting quantum gates
• Approximation of real error channels by Clifford channels and Pauli measurements
• Gate-error analysis in simulations of quantum computers with transmon qubits
• Comparison of a quantum error correction threshold for exact and approximate errors

Cited by in corpus (25)

• High-fidelity operation and algorithmic initialisation of spin qubits above one kelvin
• Operating semiconductor quantum processors with hopping spins
• Benchmarking quantum computers
• Assessment of error variation in high-fidelity two-qubit gates in silicon
• Noise-assisted digital quantum simulation of open systems
• Artificial Intelligence for Quantum Computing
• A Practical Introduction to Benchmarking and Characterization of Quantum Computers
• Demonstrating scalable randomized benchmarking of universal gate sets
• Benchmarking quantum logic operations relative to thresholds for fault tolerance
• Fully scalable randomized benchmarking without motion reversal
• Violating Bell's inequality in gate-defined quantum dots
• Analysis and mitigation of residual exchange coupling in linear spin qubit arrays
• Quantum circuit debugging and sensitivity analysis via local inversions
• Compressed gate characterization for quantum devices with time-correlated noise
• Operational Markovianization in Randomized Benchmarking
• Efficient characterization of qudit logical gates with gate set tomography using an error-free Virtual-Z-gate model
• Machine learning of quantum channels on NISQ devices
• Efficient Lindblad synthesis for noise model construction
• Efficient self-consistent learning of gate set Pauli noise
• Near-Minimal Gate Set Tomography Experiment Designs
• Streaming quantum gate set tomography using the extended Kalman filter
• Unifying non-Markovian characterisation with an efficient and self-consistent framework
• A Theory of Direct Randomized Benchmarking
• Learning a quantum computer's capability
• Comparing the performance of practical two-qubit gates for individual ${}^{171}$Yb ions in yttrium orthovanadate