Time-optimal multi-qubit gates: Complexity, efficient heuristic and gate-time bounds

• URL: http://arxiv.org/abs/2307.11160v2
• Date: Tue, 5 Mar 2024 08:17:33 GMT
• Title: Time-optimal multi-qubit gates: Complexity, efficient heuristic and gate-time bounds
• Abstract summary: A fixed multi-qubit Ising-type interaction together with single-qubit X-gates can be used to synthesize global ZZ-gates. We show that the synthesis of such quantum gates that are time-optimal is NP-hard. We conjecture that any GZZ gate can be executed in a time O(n) for n qubits.
• Score: 0.2302001830524133
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Multi-qubit entangling interactions arise naturally in several quantum computing platforms and promise advantages over traditional two-qubit gates. In particular, a fixed multi-qubit Ising-type interaction together with single-qubit X-gates can be used to synthesize global ZZ-gates (GZZ gates). In this work, we first show that the synthesis of such quantum gates that are time-optimal is NP-hard. Second, we provide explicit constructions of special time-optimal multi-qubit gates. They have constant gate times and can be implemented with linearly many X-gate layers. Third, we develop a heuristic algorithm with polynomial runtime for synthesizing fast multi-qubit gates. Fourth, we derive lower and upper bounds on the optimal GZZ gate-time. Based on explicit constructions of GZZ gates and numerical studies, we conjecture that any GZZ gate can be executed in a time O(n) for n qubits. Our heuristic synthesis algorithm leads to GZZ gate-times with a similar scaling, which is optimal in this sense. We expect that our efficient synthesis of fast multi-qubit gates allows for faster and, hence, also more error-robust execution of quantum algorithms.

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