Quantum Error Mitigation via Symmetry Verification and Extrapolation
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Solution Overview
Problem
Current error mitigation techniques in quantum computing, such as symmetry verification, quasi-probability, and error extrapolation, face limitations in effectively reducing errors in noisy intermediate-scale quantum (NISQ) devices, including high costs, requirement for increased noise levels, and inability to detect undetectable errors.
Innovation Solution
A method that combines quasi-probability, symmetry verification, and error extrapolation by performing operations with different basis operations and symmetry measurements to fit state measurements to exponential decay curves, allowing for improved error estimation at reduced costs by modifying the effective error rate through random selection of basis operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If quasi-probability error mitigation is used, then error elimination is achieved, but the cost increases significantly requiring a high number of repetitions
Solution Approach 1:
The patent combines symmetry verification and error extrapolation techniques with quasi-probability methods to create a hybrid error mitigation approach. By integrating multiple techniques, the system achieves error elimination while reducing the number of repetitions needed compared to using quasi-probability alone.
Solution Approach 2:
The patent modifies the error mitigation approach by changing parameters such as using symmetry operations and adjusting probability distributions. This allows the system to achieve error elimination with reduced computational cost by optimizing the parameters of the error mitigation process.
2Ease of operation
If symmetry verification is used, then the method is straightforward to perform, but errors can combine in such a way that the overall error is undetectable
Solution Approach 1:
The patent creates a composite error mitigation method that combines symmetry verification with other techniques. This composite approach maintains the ease of operation of symmetry verification while adding layers of error detection that prevent undetectable error combinations.
Solution Approach 2:
The patent introduces intermediary error mitigation steps between the quantum circuit execution and measurement. These intermediary operations act as mediators that enhance error detectability while preserving the straightforward nature of symmetry verification.
3Measurement precision
If error extrapolation is used, then noise-free expectation value can be predicted, but the noise level must be increased by physically altering the hardware
Solution Approach 1:
The patent creates virtual copies of the quantum circuit with different noise characteristics through classical processing and simulation. Instead of physically altering hardware to increase noise levels, the system uses computational copies to achieve the same error extrapolation effect, thereby avoiding hardware modification complexity.
Solution Approach 2:
The patent replaces the mechanical/hardware-based noise injection required by traditional error extrapolation with a software-based approach. By using classical computation to simulate different noise levels, the system eliminates the need for physical hardware alterations while maintaining the ability to predict noise-free expectation values.
4Measurement precision
If the number of basis operations is increased, then error mitigation accuracy is improved, but the cost given by the number of times the operation is performed increases
Solution Approach 1:
The patent applies partial action by selecting a subset of basis operations that provide sufficient error mitigation accuracy without requiring all possible operations. This selective approach achieves adequate error correction while keeping the operation cost manageable.
Solution Approach 2:
The patent performs preliminary analysis to identify which basis operations provide the most significant error mitigation benefit. By pre-selecting the most effective operations before execution, the system achieves high accuracy without performing unnecessary operations, thereby reducing overall cost.
Data Source
AI summary
A method of mitigating errors in quantum computing, wherein the method comprises: performing (S101) an operation on the state of a qubit in a group of qubits a plurality of times, wherein the operation has a first error rate, and wherein each performance of the operation comprises: performing a first operation comprising: a gate operation, a symmetry operation, and a first basis operation; or performing a second operation comprising: the gate operation, the symmetry operation, and a second basis operation; wherein the first and second basis operations are different basis operations selected from a set of basis operations; and measuring the state of the qubit; wherein the probability of performing the first operation is a first probability, and the probability of performing the second operation is a second probability; obtaining (S102) a symmetry measurement for the group of qubits after each performance of the operation using the symmetry operation, wherein the group of qubits comprises a plurality of qubits; wherein the symmetry measurement is a first symmetry outcome if the number of errors is even or a second symmetry outcome if the number of errors is odd; obtaining (S103) a first state measurement by determining the average state of the qubit for the first symmetry outcome; obtaining (S104) a second state measurement by determining the average state of the qubit for the second symmetry outcome; fitting (S105) the first state measurement to a first curve having the form (I); fitting the second state measurement to a second curve having the form (II); wherein n is an error rate and A and γ are fitting parameters; and extrapolating (S106) the average state of the qubit at a second error rate using the first and second fitted curves; wherein the second error rate is lower than the first error rate.A cosh((1-γ)n)cosh(n)(I)A sinh((1-γ)n)sinh(n)(II)