Verified Quantum Phase Estimation With Post-Selection Error Filtering
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Solution Overview
Problem
Existing quantum phase estimation routines accumulate errors that degrade the accuracy of eigenphase estimation, particularly in quantum computing systems.
Innovation Solution
Implement a post-selection mechanism in quantum phase estimation protocols that verify the system register's initial state after measurement, mitigating errors by discarding experiments where the register is not in the initial state, and using control qubits to estimate eigenphases and eigenvalues.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If standard quantum phase estimation is performed without verification, then the protocol is simple and fast, but errors accumulate and degrade estimation accuracy
Solution Approach 1:
The patent applies preliminary action by performing verification measurements before the main phase estimation protocol. Specifically, it measures whether the system register is in the initial state before applying the unitary operator, and only proceeds with phase estimation if verification passes. This pre-check eliminates erroneous measurements from the dataset, improving accuracy without requiring complex real-time correction mechanisms.
Solution Approach 2:
The patent implements feedback by using the verification measurement results to determine whether to include subsequent phase estimation measurements in the final analysis. The verification outcome feeds back into the selection of valid measurement data, creating a feedback loop that filters out erroneous results and improves the accuracy of eigenphase estimation.
2Measurement precision
If verification measurements are added to detect errors, then estimation accuracy improves, but the number of measurements and experimental time increase
Solution Approach 1:
The patent applies the extraction principle by separating the verification function from the main phase estimation protocol. Instead of integrating verification into every measurement step, it extracts verification as a separate preliminary measurement that filters the dataset before analysis. This allows efficient error detection without requiring continuous verification during the entire estimation process.
Solution Approach 2:
The patent changes the parameter approach by using the verification measurement to create a binary filter (pass/fail) for measurement data inclusion. Rather than continuously adjusting measurement parameters during the protocol, it uses a single verification parameter (whether the system register is in the initial state) to determine which measurements are valid, reducing the overhead of repeated verification.
3Reliability
If post-selection on initial state is implemented, then error mitigation is achieved, but hardware complexity increases
Solution Approach 1:
The patent applies universality by using the same quantum register and measurement apparatus for both verification and phase estimation. The verification measurement utilizes the existing system register in its initial state, and the same hardware components (qubits, gates, detectors) are used for both the verification check and the subsequent phase estimation protocol, avoiding the need for separate verification hardware.
Solution Approach 2:
The patent uses copying by creating a copy of the initial state for verification purposes. Instead of modifying the main quantum state during verification, it prepares a copy of the initial state and compares the system register against this copy through measurement. This copying approach allows verification without disturbing the main phase estimation process, maintaining hardware simplicity.
Data Source
AI summary
Methods, systems, and apparatus for verified quantum phase estimation. In one aspect, a method includes repeatedly performing a experiment. Performing one repetition of the experiment includes: applying a second unitary to a system register of N qubits prepared in a target computational basis state; applying, conditioned on a state of a control qubit, a first unitary to the system register; applying an inverse of the second unitary to the system register and measuring each qubit to determine an output state of the system register; measuring the control qubit to obtain a corresponding measurement result m; and post-selecting on the target computational basis state by, in response to determining that the output state indicates that each qubit was in the target computational basis state prior to measurement, incrementing a first or second classical variable by (−1)m. Phases or expectation values of the first unitary are estimated based on the classical variables.