Learning the quantum algorithm for state overlap

• Published in: New journal of physics Vol. 20; no. 11; pp. 113022 - 113035
• Main Authors: Cincio, Lukasz, Suba, Yi it, Sornborger, Andrew T, Coles, Patrick J
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 14.11.2018
• Subjects: Algorithms; Computer Science; Error reduction; Information Science; Machine learning; Mathematics; MATHEMATICS AND COMPUTING; Physics; Quantum computers; Quantum computing; quantum computing algorithms; Quantum entanglement; state overlap; Support vector machines
• ISSN: 1367-2630; 1367-2630
• DOI: 10.1088/1367-2630/aae94a

Short-depth algorithms are crucial for reducing computational error on near-term quantum computers, for which decoherence and gate infidelity remain important issues. Here we present a machine-learning approach for discovering such algorithms. We apply our method to a ubiquitous primitive: computing the overlap Tr ( ) between two quantum states and . The standard algorithm for this task, known as the Swap Test, is used in many applications such as quantum support vector machines, and, when specialized to = , quantifies the Renyi entanglement. Here, we find algorithms that have shorter depths than the Swap Test, including one that has a constant depth (independent of problem size). Furthermore, we apply our approach to the hardware-specific connectivity and gate sets used by Rigetti's and IBM's quantum computers and demonstrate that the shorter algorithms that we derive significantly reduce the error-compared to the Swap Test-on these computers.