Simulating the Effect of Decoherence and Inaccuracies on a Quantum Computer

TL;DR

This paper presents simulations of a quantum computer considering decoherence and inaccuracies, demonstrating that maintaining error rates around 10^-6 is crucial for quantum advantage in factoring and database search tasks.

Contribution

The study provides detailed simulation results showing the impact of errors and decoherence on quantum computations, establishing error rate thresholds necessary for quantum advantage.

Findings

Error rate per gate is approximately 10^-6 for effective quantum computation.

Decoherence rate of 10^-6 is manageable with current trapped ion technology.

Simulations indicate quantum advantage is feasible at low error rates.

Abstract

A Quantum Computer is a new type of computer which can solve problems such as factoring and database search very efficiently. The usefulness of a quantum computer is limited by the effect of two different types of errors, decoherence and inaccuracies. In this paper we show the results of simulations of a quantum computer which consider both decoherence and inaccuracies. We simulate circuits which factor the numbers 15, 21, 35, and 57 as well as circuits which use database search to solve the circuit satisfaction problem. Our simulations show that the error rate per gate is on the order of 10^-6 for a trapped ion quantum computer whose noise is kept below pi/4096 per gate and with a decoherence rate of 10^-6. This is an important bound because previous studies have shown that a quantum computer can factor more efficiently than a classical computer if the error rate is of order 10^-6.