Low-cost quantum circuits for classically intractable instances of the Hamiltonian dynamics simulation problem

Yunseong Nam,Dmitri Maslov

doi:10.1038/s41534-019-0152-0

Yunseong Nam, Dmitri Maslov

Open Access

https://doi.org/10.1038/s41534-019-0152-0

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Abstract

We develop circuit implementations for digital-level quantum Hamiltonian dynamics simulation algorithms suitable for implementation on a reconfigurable quantum computer, such as trapped ions. Our focus is on the codesign of a problem, its solution, and quantum hardware capable of executing the solution at the minimal cost expressed in terms of the quantum computing resources used, while demonstrating the solution of an instance of a scientifically interesting problem that is intractable classically. The choice for Hamiltonian dynamics simulation is due to the combination of its usefulness in the study of equilibrium in closed quantum mechanical systems, a low cost in the implementation by quantum algorithms, and the difficulty of classical simulation. By targeting a specific type of quantum computer and tailoring the problem instance and solution to suit physical constraints imposed by the hardware, we are able to reduce the resource counts by a factor of 10 in a physical-level implementation and a factor of 30–60 in a fault-tolerant implementation over state-of-the-art.

Highlights

Quantum supremacy is a computational experiment designed to demonstrate a computational capability of a quantum machine that cannot be matched by a classical computer
The supremacy experiment proposed in ref. 1, in particular, reduces to the execution of a random quantum circuit on a quantum computer that is too large for a classical computer to cope with simulating
Rather than focusing on an artificial problem designed purely for demonstrating quantum supremacy,1 we target the selection of a known computational problem and a specific input instance, such that, to the best of our knowledge, the problem/ instance pair requires a classically intractable computation

Summary

Introduction

Quantum supremacy is a computational experiment designed to demonstrate a computational capability of a quantum machine that cannot be matched by a classical computer. Rather than focusing on an artificial problem designed purely for demonstrating quantum supremacy, we target the selection of a known computational problem and a specific input instance, such that, to the best of our knowledge, the problem/ instance pair requires a classically intractable computation. We develop an optimized quantum circuit computing the answer for the selected problem/instance pair that can be suitable for the execution on near-term quantum computers. A quantum computation described by such circuit constitutes a qualitative step forward, where a quantum computer can be thought of as being a tool in the solution of a problem rather than the focus of the study. A more advanced demonstration past the one we are reporting in this work could target the solution of a problem with a commercial value

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