Quantum Gate Fidelity Benchmarking via Basis Function Sampling
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Solution Overview
Problem
Conventional benchmarking techniques for quantum computing devices are impractical for large sets of gates, especially those on high-dimensional manifolds, making it difficult to identify gate sets with superior fidelity.
Innovation Solution
The method involves generating an approximate fidelity function for a set of quantum gates by sampling from the set according to a distribution created using basis functions, such as trigonometric, polynomial, or wavelet functions, through randomized benchmarking protocols like interleaved Fully Randomized Benchmarking (iFRB) and Interleaved Randomized Benchmarking of a Distribution (iRBD).
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional benchmarking techniques are used to characterize a large set of quantum gates, then measurement precision can be improved, but the complexity and resource requirements become impractical
Solution Approach 1:
The patent segments the benchmarking process into two distinct phases: (1) sampling phase where a distribution over the gate set is generated using basis functions, and (2) measurement phase where randomized benchmarking is performed according to this distribution. This segmentation allows the complex problem of characterizing large gate sets to be divided into manageable components, reducing overall benchmarking complexity while maintaining measurement precision.
Solution Approach 2:
The patent transforms the benchmarking approach by changing parameters from uniform sampling to distribution-based sampling using basis functions. By representing the fidelity function as a combination of basis functions with specific parameters (coefficients), the system can efficiently characterize gate sets by determining these parameters through targeted measurements rather than exhaustive benchmarking of all gates.
2Measurement precision
If individual gates in a finite gate set are characterized by benchmarking, then measurement precision is improved, but the quantity of gates becomes too large for practical characterization
Solution Approach 1:
The patent creates a mathematical model (distribution represented by basis functions) that copies or represents the collective behavior of all gates in the set. Instead of measuring each gate individually, the system measures samples according to the distribution and uses the basis function model to represent all gates, significantly reducing the number of actual measurements needed while maintaining comprehensive characterization.
Solution Approach 2:
The basis function distribution serves as a universal representation that can characterize any gate set through a single unified framework. The same basis function approach works for different gate sets and dimensions, providing a multi-functional solution that replaces the need for separate benchmarking procedures for each individual gate or gate set.
3Adaptability or versatility
If gates are sampled from a continuous gate set on a high-dimensional manifold, then adaptability is improved, but the complexity of characterization becomes unfeasible
Solution Approach 1:
The patent addresses the high-dimensional challenge by introducing a functional dimension - representing gates not as points in high-dimensional space but as evaluations of a fidelity function. The basis function expansion adds a mathematical dimension that allows efficient representation and sampling, transforming the intractable high-dimensional sampling problem into a manageable function approximation problem.
Data Source
AI summary
Systems and methods are disclosed for benchmarking a set of quantum gates. The set of quantum gates can have an input domain and a fidelity function defined over this input domain. Benchmarking the set of quantum gates can include determining an approximate value of the fidelity function over the input domain. Such benchmarking can include determining multiple fidelity measures. Each fidelity measure can be associated with one of a set of basis functions. This basis function can be used to generate a probability distribution. The probability distribution can be used to determine the fidelity measure. The approximate fidelity function can be generated using the fidelity measures and corresponding basis functions.