Dr. D. Michael Miller Profile

Dr. D. Michael Miller

at Univ of Victoria

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Proceedings Article | 13 June 2023 Presentation + Paper

Automated quantum oracle synthesis with a minimal number of qubits

Jessie Henderson, Elena Henderson, Aviraj Sinha, Mitchell Thornton, D. Michael Miller

Proceedings Volume 12517, 1251706 (2023) https://doi.org/10.1117/12.2663240

KEYWORDS: Quantum communications, Quantum gates, Quantum circuits, Quantum circuit implementation, Databases, Quantum computing, Quantum algorithms, Quantum search

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Several prominent quantum computing algorithms—including Grover’s search algorithm and Shor’s algorithm for finding the prime factorization of an integer—employ subcircuits termed ‘oracles’ that embed a specific instance of a mathematical function into a corresponding bijective function that is then realized as a quantum circuit representation. Designing oracles, and particularly, designing them to be optimized for a particular use case, can be a non-trivial task. For example, the challenge of implementing quantum circuits in the current era of NISQ-based quantum computers generally dictates that they should be designed with a minimal number of qubits, as larger qubit counts increase the likelihood that computations will fail due to one or more of the qubits decohering. However, some quantum circuits require that function domain values be preserved, which can preclude using the minimal number of qubits in the oracle circuit. Thus, quantum oracles must be designed with a particular application in mind. In this work, we present two methods for automatic quantum oracle synthesis. One of these methods uses a minimal number of qubits, while the other preserves the function domain values while also minimizing the overall required number of qubits. For each method, we describe known quantum circuit use cases, and illustrate implementation using an automated quantum compilation and optimization tool to synthesize oracles for a set of benchmark functions; we can then compare the methods with metrics including required qubit count and quantum circuit complexity.

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