Universal quantum simulation with pre-threshold superconducting qubits: Single-excitation subspace method

TL;DR

This paper introduces a novel method for quantum simulation using the single-excitation subspace of superconducting qubits, enabling large-scale computations without error correction and potentially achieving quantum speedup with current technology.

Contribution

It presents a non-scalable yet practical approach to universal quantum simulation that bypasses gate decomposition, suitable for pre-threshold superconducting qubits.

Findings

Potential for a 1000-qubit SES processor built today

Capability to simulate arbitrary Hamiltonians efficiently

Possible quantum speedup over classical supercomputers

Abstract

We propose a method for general-purpose quantum computation and simulation that is well suited for today's pre-threshold-fidelity superconducting qubits. This approach makes use of the $n$-dimensional single-excitation subspace (SES) of a system of $n$ tunably coupled qubits. It can be viewed as a nonscalable special case of the standard gate-based quantum computing model, but allows many operations in the unitary group SU($n$) to be implemented by a single application of the Hamiltonian. Our approach bypasses the need to decompose the evolution operator into elementary gates, making large, nontrivial computations possible without error correction. The method is especially well suited for universal quantum simulation, specifically simulation of the Schr\"odinger equation with a real but otherwise arbitrary $n \times n$ Hamiltonian. We argue that a 1000-qubit SES processor, which would require no known improvements in superconducting device technology and which could be built today, should be capable of achieving quantum speedup relative to a petaflop supercomputer. We speculate on the utility and practicality of such a universal quantum simulator.