Error models in quantum computation: an application of model selection

Abstract

Threshold theorems for fault-tolerant quantum computing assume that errors are of certain types. But how would one detect whether errors of the "wrong" type occur in one's experiment, especially if one does not even know what type of error to look for? The problem is that for many qubits a full state description is impossible to analyze, and a full process description is even more impossible to analyze. As a result, one simply cannot detect all types of errors. Here we show through a quantum state estimation example (on up to 25 qubits) how to attack this problem using model selection. We use, in particular, the Akaike Information Criterion. The example indicates that the number of measurements that one has to perform before noticing errors of the wrong type scales polynomially both with the number of qubits and with the error size.

5 pages, 3 figures

References in corpus (10)

• Entanglement detection
• 14-qubit entanglement: creation and coherence
• Randomized Benchmarking of Quantum Gates
• Robust randomized benchmarking of quantum processes
• Permutationally invariant quantum tomography
• Permutationally invariant state reconstruction
• Proof of finite surface code threshold for matching
• When quantum tomography goes wrong: drift of quantum sources and other errors
• Practical methods for witnessing genuine multi-qubit entanglement in the vicinity of symmetric states
• Rank-based model selection for multiple ions quantum tomography

Cited by in corpus (10)

• On the permutationally invariant part of a density matrix and nonseparability of N-qubit states
• Detecting correlated errors in SPAM tomography
• High posterior density ellipsoids of quantum states
• Quantum Model Averaging
• Behavior of the maximum likelihood in quantum state tomography
• In-situ characterization of quantum devices with error correction
• Estimation of coherent error sources from stabilizer measurements
• Quantum information criteria for model selection in quantum state estimation
• Macroscopic instructions vs microscopic operations in quantum circuits
• Quantum Assemblage Tomography