Randomized Quantum Phase Estimation With Single-Ancilla Sampling
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Solution Overview
Problem
Existing quantum computing methods for phase and energy level estimation are inefficient and require high gate complexity and qubit costs, especially for complex Hamiltonians, and suffer from biased errors that cannot be statistically suppressed.
Innovation Solution
A randomized quantum algorithm that combines statistical phase estimation with random compilation of quantum circuits, using a single ancilla and random gate sequences to suppress compilation errors through increased data sampling, optimizing gate complexity and qubit usage.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If existing quantum computing methods are used for phase and energy level estimation, then estimation capability is achieved, but gate complexity and qubit costs are high
Solution Approach 1:
The algorithm segments the Hamiltonian into multiple terms and processes them separately through random sampling. Instead of handling the entire complex Hamiltonian at once, the method divides it into manageable components that can be estimated individually and combined, reducing the gate complexity required for each measurement step.
Solution Approach 2:
The algorithm performs partial phase estimation by randomly sampling subsets of Hamiltonian terms rather than completing full estimation for all terms. This partial action approach achieves sufficient estimation accuracy with fewer quantum gates and qubits than traditional complete estimation methods.
2Measurement precision
If existing quantum computing methods are used for phase and energy level estimation, then estimation capability is achieved, but biased errors cannot be suppressed
Solution Approach 1:
The algorithm incorporates feedback through random sampling and statistical analysis. By repeatedly sampling different Hamiltonian term combinations and using statistical methods to aggregate results, the system identifies and suppresses biased errors, improving the reliability of phase and energy level estimates.
Solution Approach 2:
The method changes the parameters of the quantum algorithm by using random sampling distributions and varying the number of samples. This parameter variation allows statistical error suppression techniques to be applied, transforming systematic biased errors into reducible statistical fluctuations.
3Measurement precision
If more qubits and gates are used for complex Hamiltonians, then estimation accuracy may improve, but computational efficiency decreases
Solution Approach 1:
The algorithm performs sufficient but not excessive phase estimation by randomly sampling Hamiltonian terms. It achieves the necessary accuracy threshold without performing complete estimation on all terms, thereby maintaining computational efficiency while ensuring adequate measurement precision for complex Hamiltonians.
Data Source
AI summary
A system and method for estimating values of an operator, such as energy levels of a Hamiltonian, is disclosed. The estimation is performed in a way such that the runtime of performing the estimation is independent of a complexity of the operator, e.g., a number of terms in the Hamiltonian. Also, errors can be statistically suppressed by performing additional sampling, due to a lack of biased error in the estimator. Additionally, samples may be tested using only a single ancilla qubit.