Implementing time-evolution operators in shallow quantum circuits is important for quantum simulations. The standard method of Trotterization requires a large number of gates to achieve practical accuracy. Variational quantum simulation (VQS) is an algorithm that calculates the time evolution of a quantum state and can be executed with shallower circuits than Trotterization. However, the operator obtained by VQS evolves only a fixed initial state and is not the time-evolution operator itself. In this paper, we propose variational quantum operator simulation (VQOS), a method to realize time-evolution operators in shallow quantum circuits. This method is based on the variational principle for operators and does not require the implementation of the desired Trotter decomposition of the time-evolution operator. We performed numerical simulations of the VQOS algorithm and successfully implemented the time-evolution operator for closed systems in a quantum circuit that is up to five times shallower than the Trotterization. By providing a more practical way to implement time-evolution operators, VQOS increases the applicability of near-term quantum computers.

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• Quantum circuits
• Quantum computation
• Quantum simulation