We released a new algorithm called orbital optimized unitary coupled cluster (OO-UCC) for improving the efficiency of chemistry calculations on a quantum computer with our advisor Assoc. Prof. Wataru Mizukami (Quantum information and biology division, Osaka Univ.) as the first author of the paper (preprint). Mitarai, Nakagawa, Yamamoto, and Yan at QunaSys Inc. and Dr. Ohnishi at JSR Corporation contributed to the work as co-authors.

The on-going joint research between Qunasys Inc. and JSR Corp. has led to the work.

The preprint is available on arXiv:
”Orbital optimized unitary coupled cluster theory for quantum computer”, arxiv:1910.11526.
-> Published as Phys. Rev. Research 2, 033421 (2020), https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.2.033421

BACKGROUND

Recent attraction in the field of quantum computation is the hardware called noisy intermediate-scale quantum (NISQ) device, which has a non-negligible amount of noise during the operation, but whose behavior is difficult to track by a classical computer. As a possible application of such NISQ devices, an algorithm called variational quantum eigensolver (VQE), which is an algorithm for finding a stable state of a quantum system such as a molecule, is becoming popular. The VQE algorithm works by first making a quantum state with some suitable quantum circuit, and then iteratively tuning the circuit so that the generated state is closer to the stable state. We expect that, if employed with a quantum circuit that cannot be simulated by a classical computer efficiently, it may be able to reveal various physical properties of materials that were not attainable previously by a classical computer.

ISSUE ON THE VQE

Because NISQ devices are so fragile to environmental noise, we have to use a quantum circuit that is as small as possible. Many circuits for the VQE have been proposed but they are yet to be improved.

CONTRIBUTION OF THIS WORK

A quantum state called unitary coupled cluster (UCC) state can be generated with a rather simple quantum circuit that is difficult to track by classical computers. We made the UCC circuit, or the quantum circuit which generates the UCC state, smaller by separating the circuit into the classically-easy part and the rest. More concretely, we observed that the operation called orbital rotation in the UCC is simulatable on classical computers, and impose that task on classical computers. We named the method as orbital optimized unitary coupled cluster (OO-UCC). Proof-of-principle numerical simulations are also performed and presented in the paper.

RESULT

We performed numerical simulations for the nitrogen, lithium hydride, and water molecules. We found that our method provides results closer to exact solutions than the coupled cluster method, which is standard in conventional quantum chemistry, and comparable to the original UCC method. Moreover, we performed geometry optimization for the water molecule. This work is, even though it is done by numerical simulations, the first example of performing the geometry optimization of a molecule consisting of three atoms in the framework of the VQE.

FUTURE

The circuit which generates the UCC state still requires many quantum gates although our work lowered the count. We do not think that the circuit can be executed on the NISQ devices immediately for large molecules that classical computers cannot handle and we aim to utilize a quantum computer for. With this in mind, the future work will be to combine the orbital optimization technique developed in this work with small (shallow) circuits such as the one used by Google to demonstrate quantum supremacy.