Rigorous measurement error correction

Abstract

We review an experimental technique used to correct state preparation and measurement errors on gate-based quantum computers, and discuss its rigorous justification. Within a specific biased quantum measurement model, we prove that nonideal measurement of an arbitrary $n$-qubit state is equivalent to ideal projective measurement followed by a classical Markov process $\Gamma$ acting on the output probability distribution. Measurement errors can be removed, with rigorous justification, if $\Gamma$ can be learned and inverted. We show how to obtain $\Gamma$ from gate set tomography (R. Blume-Kohout et al., arXiv:1310.4492) and apply the error correction technique to single IBM Q superconducting qubits.

References in corpus (9)

• Demonstration of a small programmable quantum computer with atomic qubits
• 10-qubit entanglement and parallel logic operations with a superconducting circuit
• Generation of Three-Qubit Entangled States using Superconducting Phase Qubits
• Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography
• Quantum Process Tomography of a Universal Entangling Gate Implemented with Josephson Phase Qubits
• Genuine 12-qubit entanglement on a superconducting quantum processor
• Detector Tomography on IBM 5-qubit Quantum Computers and Mitigation of Imperfect Measurement
• Machine learning for discriminating quantum measurement trajectories and improving readout
• Characterization of a two-transmon processor with individual single-shot qubit readout

Cited by in corpus (46)

• The Variational Quantum Eigensolver: a review of methods and best practices
• Quantum Error Mitigation
• Mitigating measurement errors in multi-qubit experiments
• Scalable mitigation of measurement errors on quantum computers
• Model-free readout-error mitigation for quantum expectation values
• Near-Term Quantum Computing Techniques: Variational Quantum Algorithms, Error Mitigation, Circuit Compilation, Benchmarking and Classical Simulation
• Generation and verification of 27-qubit Greenberger-Horne-Zeilinger states in a superconducting quantum computer
• Measuring nonstabilizerness via multifractal flatness
• Probing quantum processor performance with pyGSTi
• Measurement Error Mitigation in Quantum Computers Through Classical Bit-Flip Correction
• Efficient correction of multiqubit measurement errors
• Computationally Efficient Zero Noise Extrapolation for Quantum Gate Error Mitigation
• Modeling and mitigation of cross-talk effects in readout noise with applications to the Quantum Approximate Optimization Algorithm
• Readout Rebalancing for Near Term Quantum Computers
• Preserving Symmetries for Variational Quantum Eigensolvers in the Presence of Noise
• Characterizing the Reproducibility of Noisy Quantum Circuits
• Enhancing quantum utility: simulating large-scale quantum spin chains on superconducting quantum computers
• Benchmarking variational quantum eigensolvers for the square-octagon-lattice Kitaev model
• Improving Qubit Readout with Hidden Markov Models
• Optimal protocols for quantum metrology with noisy measurements
• Conditionally rigorous mitigation of multiqubit measurement errors
• Towards the real-time evolution of gauge-invariant ${\mathbb{Z}}_2$ and $U(1)$ quantum link models on NISQ Hardware with error-mitigation
• General error mitigation for quantum circuits
• Readout error mitigated quantum state tomography tested on superconducting qubits
• Operational, gauge-free quantum tomography
• SPAM-Robust Multi-axis Quantum Noise Spectroscopy in Temporally Correlated Environments
• Self-consistent quantum measurement tomography based on semidefinite programming
• A Bayesian Approach for Characterizing and Mitigating Gate and Measurement Errors
• Quantum SWAP gate realized with CZ and iSWAP gates in a superconducting architecture
• Mitigating Quantum Errors via Truncated Neumann Series
• Learning a quantum channel from its steady-state
• Improving the Performance of Digitized Counterdiabatic Quantum Optimization via Algorithm-Oriented Qubit Mapping
• Initial-State Dependent Optimization of Controlled Gate Operations with Quantum Computer
• Perturbative readout error mitigation for near term quantum computers
• Anticipative measurements in hybrid quantum-classical computation
• Readout Error Mitigation for Mid-Circuit Measurements and Feedforward
• Robust projective measurements through measuring code-inspired observables
• Speeding Up Quantum Measurement Using Space-Time Trade-Off
• Detecting and Eliminating Quantum Noise of Quantum Measurements
• Circuit-Noise-Resilient Virtual Distillation
• Qubit Readout Error Mitigation with Bit-flip Averaging
• Testing the necessity of complex numbers in traditional quantum theory with quantum computers
• State preparation and evolution in quantum computing: a perspective from Hamiltonian moments
• Error-mitigated inference of quantum network topology
• Scaling of Computational Order Parameters in Rydberg Atom Graph States
• Molecular resonance identification in complex absorbing potentials via integrated quantum computing and high-throughput computing