Quantum Conditional Logic for Eigenvalue Inversion
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Solution Overview
Problem
Noisy Intermediate Scale Quantum (NISQ) devices face limitations in the number and quality of qubits, making it challenging to efficiently perform eigenvalue inversion using quantum algorithms like the HHL algorithm.
Innovation Solution
The implementation of quantum conditional logic in the Quantum Phase Estimation Algorithm (QPEA) reduces the number of ancilla qubits required for eigenvalue inversion, using a single ancilla qubit that is frequently measured and reset, thereby reducing noise exposure and increasing robustness.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the standard Quantum Phase Estimation Algorithm is used for eigenvalue inversion, then the algorithm can solve quantum linear systems problems, but the number of ancilla qubits required becomes large which exceeds the capabilities of NISQ devices
Solution Approach 1:
The patent extracts and eliminates the need for multiple ancilla qubits by using a single ancilla qubit with quantum conditional logic. The standard QPEA requires n ancilla qubits to estimate n-bit eigenvalues, but this invention reduces it to just one ancilla qubit that is reused across multiple iterations, directly addressing the resource consumption problem.
Solution Approach 2:
The patent introduces dynamic quantum conditional logic where the single ancilla qubit undergoes repeated cycles of unitary operations, measurement, and reset. The qubit transitions between different states and roles dynamically across iterations, allowing it to perform the work of multiple static qubits through temporal reuse rather than spatial multiplication.
2Measurement precision
If more ancilla qubits are used for eigenvalue inversion, then the precision of eigenvalue estimation improves, but the noise exposure and error rates increase on NISQ devices
Solution Approach 1:
The patent removes multiple ancilla qubits from the system, extracting only the essential single qubit needed for the measurement process. By reducing the number of qubits from n to 1, the patent directly reduces the total noise exposure surface area while maintaining precision through the quantum conditional logic that processes eigenvalue information sequentially.
Solution Approach 2:
The patent uses rapid sequential operations including measurements and resets that occur between quantum operations. The single ancilla qubit is measured and reset multiple times within the eigenvalue estimation process, rushing through the information extraction process without requiring multiple qubits to be exposed to noise simultaneously.
3Device complexity
If a single ancilla qubit is reused multiple times, then the number of qubits is reduced, but the coherence time requirements become more stringent
Solution Approach 1:
The patent makes the ancilla qubit dynamic by repeatedly measuring and resetting it between quantum operations. Instead of requiring long continuous coherence, the qubit undergoes short-lived coherent evolution during each iteration followed by measurement and reset, allowing the coherence requirement to be satisfied over much shorter durations while achieving the same computational function.
Solution Approach 2:
The patent implements periodic cycles of unitary operation, measurement, and reset for the single ancilla qubit. This periodic action allows the qubit to be reused across multiple iterations, reducing the total number of qubits needed while the coherence time requirement is satisfied by the short duration of each periodic cycle rather than requiring long continuous coherence.
Data Source
AI summary
Embodiments use quantum conditional logic in the Quantum Phase Estimation Algorithm (QPEA) to compute eigenvalues prior to inversion. Embodiments estimate the eigenvalues of a unitary, U=eiÂt, generated by a N×N Hermitian matrix Â. The binary representations of the n-bit estimations of eigenvalues of  may be encoded in these states: |λi=|b1b2 . . . bn; λi is an estimation of the i-th eigenvalue, excluding degeneracy, and .b1b2 . . . bn is its binary representation. To perform the eigenvalue inversion, an n-qubit controlled Ry rotation with angle λi/2(n−1) conditioned on seeing |b1b2 . . . bn is applied for each possible n-bit binary string b1b2 . . . bn (2n values). The overall unitary is called a “uniformly controlled Ry rotation” in literature.