We published an algorithm to calculate the non-equilibrium steady states using a quantum computer.

Yoshioka, Nakagawa, and Mitarai from QunaSys Inc., and our advisor, Prof. Fujii, published a paper (preprint) that proposed an algorithm named “dissipative-system Variational Quantum Eigensolver (dVQE)” to simulate the non-equilibrium steady state on a quantum computer.

Variational Quantum Algorithm for Non-equilibrium Steady States
https://arxiv.org/abs/1908.09836

Background 

The recent technological developments in quantum technology have now reached a stage to realize Noisy Intermediate-Scale Quantum (NISQ) devices with tens to hundreds of qubits that are not fault-tolerant. In particular, the quantum algorithm named the variational quantum eigensolver (VQE) is expected to enable larger-scale calculations in various fields including quantum chemistry, condensed matter physics and material science.

Problem

The targets of calculation, such as the molecules and materials, are investigated mainly under two setups: the isolated system which is decoupled from others and the open system which exchanges energy with its external environment. The effect of such energy dissipation, or non-equilibrium phenomena, could be observed quite ubiquitously in, e.g., electric transport. Despite its significance in industrial application including device design, no method has been proposed to compute the non-equilibrium steady state using the NISQ devices.

Our Method and Result

Yoshioka, Nakagawa, and Mitarai from QunaSys Inc., and our advisor, Prof. Fujii, proposed an algorithm named “the dissipative-system Variational Quantum Eigensolver (dVQE)” to simulate the non-equilibrium steady state on a quantum computer. First, we apply an mapping from the open system to an appropriate equivalent system in which the VQE can be applied. The structure of the variational quantum circuit is restricted so that the solution is assured to be a valid physical state. Secondly, the VQE is executed to optimize the parameters of the quantum circuit. A measurement scheme for the physical observables that is far more efficient than a naive approach is also proposed. Finally, our algorithm has been demonstrated by both numerical simulations on a classical computer and also actual quantum simulations that are performed on the NISQ device provided by the Rigetti Quantum Cloud Service.

Future Prospects

The dVQE algorithm opens up a path to simulate microscopic systems under more realistic setups by considering the effect of the dissipation. This enables us to carry out calculations that take the environmental effect from, e.g., the solvent, electric voltage, or heat bath into account. We have established a method to compute the non-equilibrium steady state using the NISQ devices, and thus expect to invoke further research that applies quantum computers for industrial application.