Local Randomized Benchmarking for Quantum Error Estimation
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Solution Overview
Problem
Conventional methods for characterizing quantum noise processes in multi-qubit systems require an exponential amount of experiments and classical computational resources, making it impractical for scalable quantum computing due to the exponential growth of Hilbert space, and existing randomized benchmarking techniques face limitations in estimating error rates of individual gates with high precision.
Innovation Solution
The implementation of scalable characterization techniques using single-qubit randomizing gates, which convert noise in universal quantum circuits into Pauli noise, allowing for efficient estimation of error rates through randomized compiling and cycle benchmarking protocols.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional randomized benchmarking uses uniformly random Clifford gates, then noise characterization can be performed, but the number of primitive gates required scales as O(n^2) leading to large uncertainty in individual gate error rate estimates
Solution Approach 1:
The patent segments the randomizing operation into two distinct parts: (1) a short randomizing circuit using only single-qubit gates that prepares a randomized state, and (2) the target gate whose error rate is being measured. This segmentation allows the randomizing portion to be kept simple and short while still achieving the necessary randomization for accurate error rate estimation, thereby resolving the contradiction between measurement precision and device complexity
Solution Approach 2:
The patent changes the parameter of gate selection from uniformly random Clifford gates (which require O(n^2) gates) to a specific structured set of single-qubit gates applied in a randomized sequence. This parameter change in the gate distribution and circuit structure reduces the number of required primitive gates while maintaining the ability to characterize noise accurately, thus improving the precision of individual gate error rate estimates without increasing device complexity
2Reliability
If completely characterizing quantum noise processes is attempted, then full noise information is obtained, but exponential experimental and computational resources are required
Solution Approach 1:
The patent extracts only the essential noise information needed for practical quantum computing from the full noise characterization problem. By focusing specifically on estimating individual gate error rates through a simplified randomized benchmarking protocol, the method extracts the most relevant noise parameters without requiring complete characterization of all noise processes, thereby achieving useful reliability information with polynomial rather than exponential resources
Solution Approach 2:
The patent applies partial action by performing a simplified version of noise characterization that focuses on single-qubit gate errors using restricted randomizing circuits. Rather than attempting complete noise characterization which would require exponential resources, the method performs sufficient characterization to enable error correction and improve quantum computing reliability, accepting that not all noise parameters are measured but obtaining adequate information for practical purposes
Data Source
AI summary
Systems and methods for estimating a property of an error in a circuit implemented on an n-qubit quantum system are provided, where the circuit comprises a gate set that comprises a first subset () and a second subset () of elementary gates. The first subset comprises a third subset () of elementary gates each of which consists of an n-fold tensor product of a plurality of single qubit gates. A first procedure is executed that comprises preparing the system in a state ψ and then applying D1=T1 to the system. The procedure further comprises, for each respective clock cycle t in clock cycles t∈{2, . . . , m+1}, (a) applying H to the system, where H is an elementary gate in the second subset, and then (b) applying a gate Dt=TtGHTt−1†H† to the system, where Dt is an element of the first subset. The procedure further comprises performing a measurement readout R. The procedure is repeated for one or more values of {right arrow over (T)} or one or more states ψ or one or more measurement readout procedures R, where m is a positive integer greater than 1, G is an element of the first subset of elementary gates, {right arrow over (T)}=(T1, . . . , Tm, Tm+1=I), and T1, . . . , Tm are elements of , with the proviso that n>2.