The current state of quantum computers is limited by the small number of quantum bits (qubits) and the significant impact of noise, making it challenging to handle large-scale problems. To harness quantum computers within these constraints, algorithms that work in conjunction with classical computers (conventional computers widely used today) are being developed. These algorithms, known as quantum-classical hybrid algorithms, are making progress, with Variational Quantum Algorithms (VQAs) being a widely used category among them.

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However, it is predicted that a decade from now, advances in hardware technology will lead to the emergence of quantum computers equipped with error correction and a large number of qubits, ushering in the era of full-fledged quantum computing. In anticipation of such a time, algorithms are being developed to enable quantum computers to demonstrate their true potential. This will allow quantum computers to perform calculations that are currently impossible with classical computers.

Recently, we have proposed a general non-variational algorithm called Probabilistic Imaginary-Time Evolution (PITE®️) that does not rely on the concurrent use of classical computers. [Kosugi et al., Phys. Rev. Research 4, 033121 (2022)] Unlike VQAs, which can only optimize quantum states within the range anticipated by user-defined variational circuits, PITE®️ stands out for its capability to perform genuine quantum optimization. Figure 1 depicts a schematic diagram of the PITE circuit.

One of the promising application areas for PITE®️ (Probabilistic Imaginary-Time Evolution) is quantum chemistry calculations. In particular, we have demonstrated that PITE®️ can efficiently perform structural optimization calculations, where the goal is to find the optimal structure among multiple candidate molecules, surpassing the capabilities of classical computers [Kosugi et al., arXiv:2210.09883, Nishi et al., arXiv:2308.03605]. Figure 2 illustrates how structural optimization based on PITE proceeds, using a simple example involving four molecules with a common chemical formula C2H6O.

The process begins by generating a quantum superposition state of quantum bit (qubit) states that represent each candidate structure, which serves as the initial state. This initial state contains all four candidate structures with equal proportions. Starting from this initial state, PITE calculations are performed. Each application of the circuit shown in Figure 1 is referred to as a PITE step. In the first PITE step, the proportions of the three non-optimal structures decrease. In the second step and subsequent steps, the proportions of these three structures continue to decrease. After multiple steps, the proportions of the non-optimal structures become so small that they can be effectively ignored, while the proportion of the optimal structure becomes relatively large.

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Importantly, at this stage, the user of the quantum computer has no knowledge of which structure has a small or large proportion. Measurement is conducted on the quantum bits after many PITE steps, and the state with the largest proportion (Structure 2 in Figure 2) is observed with high probability. Only then does the user of the quantum computer learn that Structure 2 is the optimal one. This method of optimizing the optimal structure is impossible without a quantum computer, and we have discovered that it is also more efficient than classical computers.

PITE®️ is a versatile technique, making it applicable not only in quantum chemistry but also in other fields. As we approach the era of full-fledged quantum computing in the near future, PITE®️ holds promise as a standard technology for various applications.