Reliable Characterization for Improving and Validating Accurate Quantum Operations
arXiv:1806.02696 · doi:10.1103/PhysRevA.103.062615
Abstract
A reliable method for characterizing quantum operations that is suitable for improving and validating their accuracies is indispensable for realizing a practical quantum computer. Known methods are still not sufficient because they lack reliability or are not suitable for use in the improvement and validation steps. Here we propose a reliable characterization method that is suitable for the accuracy validation step. First, we introduce a new self-consistent estimator with regularization and physicality constraints that are designed for improvement and validation. Second, we mathematically prove that the method provides estimation results that are stringently physical and converge to the gauge-equivalence class of the quantum operations of interest at the limit of data size going to infinity. The asymptotic convergence guarantees the reliability of the method, and the physical and regularized results ensure the suitability to the validation task. We also derive the asymptotic convergence rate, which would be optimal. Finally, we show numerical results on 1-qubit system, which confirm the theoretical results and prove that the method proposed is practical.
33 pages, 9 figures, 5 tables. Numerical results have been added to v2, and large amount of revisions have been done over the manuscript
References in corpus (37)
- A survey of cross-validation procedures for model selection
- A Quantum Engineer's Guide to Superconducting Qubits
- Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
- Quantum state tomography via compressed sensing
- Randomized Benchmarking of Quantum Gates
- Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
- Prescription for experimental determination of the dynamics of a quantum black box
- Unknown Quantum States and Operations, a Bayesian View
- Robust randomized benchmarking of quantum processes
- Complete Characterization of a Quantum Process: the Two-Bit Quantum Gate
- Quantum state estimation
- Scalable Noise Estimation with Random Unitary Operators
- Procedure for systematically tuning up crosstalk in the cross resonance gate
- Characterizing Quantum Gates via Randomized Benchmarking
- The Bloch Vector for N-Level Systems
- Efficient measurement of quantum gate error by interleaved randomized benchmarking
- Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography
- Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators
- Maximum-likelihood estimation of the density matrix
- Characterization of addressability by simultaneous randomized benchmarking
- Self-Consistent Quantum Process Tomography
- Symmetrised Characterisation of Noisy Quantum Processes
- Characterization of the Positivity of the Density Matrix in Terms of the Coherence Vector Representation
- Estimating the Coherence of Noise
- Characterizing errors on qubit operations via iterative randomized benchmarking
- Investigating the limits of randomized benchmarking protocols
- What randomized benchmarking actually measures
- Robust Extraction of Tomographic Information via Randomized Benchmarking
- Hedged maximum likelihood estimation
- Scalable randomized benchmarking of non-Clifford gates
- Calibration of the cross-resonance two-qubit gate between directly-coupled transmons
- Characterization of Leakage Errors via Randomized Benchmarking
- Self-consistent tomography of the state-measurement Gram matrix
- Robust Characterization of Loss Rates
- A complete Randomized Benchmarking Protocol accounting for Leakage Errors
- Effect of nonnegativity on estimation errors in one-qubit state tomography with finite data
- Comparing randomized benchmarking figure with average infidelity of quantum gate-set