Bayesian Quantum Circuit Fidelity Estimation via Series Inversion
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Solution Overview
Problem
Current methods for estimating the fidelity of quantum circuits are inaccurate and not scalable, particularly for larger quantum systems, as they often rely on cross-entropy benchmarking which has high variance and is limited to specific sets of quantum gates.
Innovation Solution
A method using depolarizing channels and series inversion to estimate the polarization parameter of quantum circuits, allowing for maximum-likelihood estimation of fidelity with reduced variance, applicable to moderate-sized quantum circuits and various gate sets.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If cross-entropy benchmarking is used to estimate quantum circuit fidelity, then the method is applicable to specific sets of quantum gates, but the estimation accuracy deteriorates due to high variance and limited scalability
Solution Approach 1:
The patent changes the parameter being measured from cross-entropy to polarization parameter. By maximizing the likelihood of the polarization parameter instead of using cross-entropy benchmarking, the method achieves lower variance and higher estimation accuracy while maintaining applicability to various gate sets including Clifford and non-Clifford gates
Solution Approach 2:
The patent segments the fidelity estimation process into two independent stages: first estimating the polarization parameter through likelihood maximization, then converting to fidelity estimate. This segmentation allows the use of series inversion to solve the likelihood equation efficiently, reducing computational complexity and improving scalability to larger quantum systems
2Device complexity
If traditional fidelity estimation methods are used, then the computational complexity is manageable, but the method becomes intractable for larger quantum systems due to scalability limitations
Solution Approach 1:
The patent performs preliminary action by deriving an infinite series representation of the likelihood derivative before attempting to solve for the polarization parameter. This series expansion allows for efficient computation using series inversion, making the method scalable to larger quantum systems without exponential growth in computational complexity
Solution Approach 2:
The patent transforms the original likelihood maximization problem into a series inversion problem by changing the mathematical parameter representation. This transformation reduces computational complexity from exponential to polynomial scaling, enabling application to moderate-sized quantum circuits with many qubits
3Measurement precision
If maximum-likelihood estimation with series inversion is used, then the fidelity estimation accuracy improves with reduced variance, but the computational steps increase due to derivative calculations and series inversion
Solution Approach 1:
The patent performs preliminary action by pre-computing the infinite series representation of the likelihood derivative and its inverse. This preparation work, including calculating the series coefficients and establishing the inversion formula, is done once and then reused for the actual parameter estimation, reducing the complexity of the main estimation procedure
Solution Approach 2:
The patent uses the series expansion as a mathematical copy or approximation of the original likelihood function. Instead of directly maximizing the complex likelihood function, the method works with its series representation, which is computationally simpler while preserving the essential properties needed for accurate parameter estimation
Data Source
AI summary
Methods, systems and apparatus for estimating the fidelity of a quantum computing system. In one aspect, a method includes defining one or more random quantum circuits, wherein a noisy experimental implementation of each random quantum circuit is approximated by a depolarizing channel with respective polarization parameter; generating, for each defined random quantum circuit and by the quantum computing system, a set of experimental data, wherein data items in the set of experimental data comprise measured bit strings corresponding to experimental implementations of the random quantum circuit; determining, for each of the one or more random quantum circuits, an estimate of the respective polarization parameter, comprising maximizing a log-likelihood of the polarization parameter conditioned on the respective set of experimental data using series inversion; and determining an estimate of the fidelity of the quantum computing system based on the determined estimates of respective polarization parameters.