Ancilla-Free Quantum Phase Estimation via Bayesian Inference
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing phase estimation techniques in quantum computing require external control and ancilla qubits, limiting their application due to increased cost and complexity, especially for tasks like characterizing unknown Rabi frequencies, which can be performed with quadratically less experimental time and exponentially fewer measurements if such constraints are lifted.
Innovation Solution
The use of Bayesian inference with randomized experiments to learn spectral gaps of a unitary operation without external qubits or well-calibrated gates, employing rejection filtering and Haar-random unitaries to estimate eigenphases and gaps, allowing for ancilla-free phase estimation and amplitude estimation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional phase estimation techniques are used, then measurement precision is improved, but device complexity increases due to ancilla qubits and controlled operations
Solution Approach 1:
The patent extracts and removes the ancilla qubit from the phase estimation circuit, transforming the traditional controlled-U approach into an ancilla-free randomized measurement protocol. This extraction eliminates the need for external control qubits while preserving the ability to estimate eigenphases through statistical analysis of measurement outcomes from random unitary operations
Solution Approach 2:
The patent replaces the mechanical quantum control mechanism (controlled-unitary operations requiring ancilla qubits) with a statistical measurement approach using random unitaries and classical post-processing. Instead of physically controlling the system evolution with external qubits, the method uses randomized measurements and Bayesian inference to extract spectral information
2Measurement precision
If traditional phase estimation with ancilla qubits is used, then eigenphase estimation is achievable, but loss of time increases due to additional measurement requirements
Solution Approach 1:
The patent applies preliminary randomized unitary operations to the quantum state before measurement, preparing the system in a way that encodes spectral information into measurable probabilities. By pre-applying random unitaries and their adjoints, the method transforms eigenphase information into observable measurement statistics that can be extracted through classical Bayesian inference, avoiding the need for repeated controlled operations
3Measurement precision
If controlled operations are performed for phase estimation, then eigenvalue sampling is possible, but device complexity increases due to operation calibration requirements
Solution Approach 1:
The patent enables the quantum system to self-characterize its spectral properties through randomized measurements without requiring external control or calibration. The method uses the system's own natural evolution under random unitaries to reveal eigenphase information, eliminating the need for precisely calibrated controlled operations and external reference frames
Data Source
Figure 1A~1C
Figure 2
Figure 3
AI summary
Methods and apparatus are provided that permit estimation of eigenphase or eigenvalue gaps in which random or pseudo-random unitaries are applied to a selected initial quantum state to produce a random quantum state. A target unitary is then applied to the random quantum state one or more times, or an evolution time is allowed to elapse after application of the target unitary. An inverse of the pseudo-random unitary used to produce the random quantum state is applied, and the resultant state is measured with respect to the initial quantum state. Measured values are used to produce Bayesian updates, and eigenvalue/eigenvector gaps are estimated. In some examples, the disclosed methods are used in amplitude estimate and control map determinations. Eigenvalue gaps for time-dependent Hamiltonians can be evaluated by adiabatic evolution of the Hamiltonian from an initial Hamiltonian to a final Hamiltonian.