Multi-Exponential Error Extrapolation for Noisy Qubit Measurements
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Quantum computers in the noisy intermediate-scale quantum (NISQ) era face challenges in accurately estimating error-free observable values due to error mitigation techniques that rely on error extrapolation, which can be improved by using a multi-exponential decay curve to model noise and reduce error rates.
Innovation Solution
The method involves performing multiple operations on a qubit at different error rates, obtaining measurements, and fitting them to a multi-exponential decay curve to extrapolate the average state at a lower error rate, using a form like E=Σk=1KAke−γkn, where K≥2, to enhance accuracy and prevent overfitting.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a single exponential decay curve is used for error extrapolation, then the method is simple, but the estimation accuracy of noiseless observable is insufficient
Solution Approach 1:
The patent segments the error decay process into multiple exponential components, each representing different error sources or mechanisms in the quantum system. By fitting measurements to a sum of K exponential curves rather than a single curve, the method captures complex error trends more accurately, improving noiseless observable estimation while managing complexity through systematic segmentation of the error model.
2Measurement precision
If measurements are performed at multiple error rates, then the extrapolation accuracy improves, but the number of measurements and computational resources increase
Solution Approach 1:
The patent systematically varies the error rate parameter by performing measurements at multiple different error rates (first, second, third, and fourth error rates). This parameter changes approach enables the collection of data points across different noise conditions, which are then fitted to a multi-exponential decay model to improve extrapolation accuracy for the noiseless case, balancing the increased measurement requirements against the significant gain in estimation precision.
Data Source
AI summary
A method of mitigating errors when using a quantum computer comprising: performing S101 a first operation (21) on the state of a qubit a plurality of times; wherein the first operation (21) has a first error rate (32); obtaining S102 a first measurement of the average state of the qubit; modifying S103 the error rate of the quantum computer from the first error rate (32) to a second error rate (34); performing S104 a second operation (23) on the state of the qubit a plurality of times; wherein the second operation (23) has the second error rate (34); obtaining S105 a second measurement of the average state of the qubit; modifying S106 the error rate of the quantum computer from the second error rate to a third error rate; performing S107 a third operation on the state of the qubit a plurality of times; wherein the third operation has the third error rate; obtaining S108 a third measurement of the average state of the qubit; modifying S109 the error rate of the quantum computer from the third error rate to a fourth error rate; performing S110 a fourth operation on the state of the qubit a plurality of times; wherein the fourth operation has the fourth error rate; obtaining S111 a fourth measurement of the average state of the qubit; fitting S112 the first, second, third and fourth measurements to a multi-exponential decay curve (35); and extrapolating S113 the average state of the qubit at a fifth error rate (37) using the fitted curve (35), wherein the fifth error rate (37) is lower than the first, second, third and fourth error rates.