Quantum Phase Estimation Using Arbitrary States
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Solution Overview
Problem
Determining the eigenphases of multiple eigenvalues of a unitary operator is computationally difficult and inefficient, especially when requiring large numbers of applications of the unitary operator and coherent quantum evolution, and existing methods are limited by the need for eigenstate preparation.
Innovation Solution
A quantum phase estimation system using a quantum circuit with ancilla qubits, Hadamard gates, phase gates, and a unitary operator, performing phase estimation experiments and interpreting results with a classical mixture model to learn phases of eigenvalues without requiring the quantum state to be an eigenstate, allowing for noise modeling and mitigation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If quantum phase estimation is performed using traditional methods requiring eigenstate preparation, then measurement precision of eigenphases is improved, but device complexity and ease of operation deteriorate due to the need for precise eigenstate preparation and large numbers of coherent quantum operations
Solution Approach 1:
The patent extracts the eigenphase estimation task from the constraint of requiring eigenstate preparation. By using arbitrary quantum states instead of eigenstates, the method removes the complexity of eigenstate preparation while still enabling accurate eigenphase estimation through the quantum phase estimation algorithm modified to work with arbitrary states.
Solution Approach 2:
The patent changes the parameter of quantum state preparation from requiring specific eigenstates to allowing arbitrary states. This parameter change simplifies the operational requirements while maintaining the ability to extract eigenphase information through multiple measurements and statistical analysis of measurement outcomes.
2Measurement precision
If large numbers of applications of the unitary operator are used in phase estimation, then measurement precision is improved, but productivity deteriorates due to increased computational time and resource requirements
Solution Approach 1:
The patent applies partial action by using a limited number of unitary operator applications combined with statistical sampling of multiple arbitrary quantum states. Instead of requiring many applications on a single eigenstate, the method uses fewer applications on multiple states, achieving similar precision with better productivity through parallelizable measurements.
3Measurement precision
If coherent quantum evolution is maintained for extended periods, then measurement precision is improved, but reliability deteriorates due to increased susceptibility to decoherence and noise
Solution Approach 1:
The patent applies preliminary action by preparing multiple arbitrary quantum states before executing the phase estimation protocol. This allows the actual quantum evolution to be kept short and repeated across different prepared states, reducing the time each quantum state must maintain coherence while still gathering sufficient statistical information for accurate eigenphase estimation.
Data Source
AI summary
Methods, systems, and apparatus for quantum phase estimation. In one aspect, an apparatus includes a quantum circuit comprising a first quantum register comprising at least one ancilla qubit, quantum gates, comprising at least (i) two Hadamard gates, (ii) a phase gate, (iii) a unitary operator, and (iv) a measurement operator, a second quantum register comprising one or more qubits, wherein the second quantum register is prepared in an arbitrary quantum state that is not an eigenstate of the unitary operator; and a phase learning system, configured to perform phase estimation experiments on the quantum circuit, comprising repeatedly measuring the state of an ancilla qubit for each phase estimation experiment to determine an expectation value of the state of the ancilla qubit and learn phases of the eigenvalues of the unitary operator.