Simulating chemistry efficiently on fault-tolerant quantum computers

TL;DR

This paper develops fast, fault-tolerant quantum gate construction methods to improve the efficiency of quantum chemical simulations, enabling more practical and scalable quantum computations for chemistry problems.

Contribution

It introduces new techniques for constructing arbitrary quantum gates faster than traditional methods, optimizing quantum algorithms for chemical simulation on fault-tolerant quantum computers.

Findings

Arbitrary single-qubit gates can be implemented in time $O( ext{log} \, ext{epsilon})$ or $O( ext{log} \, ext{log} \, ext{epsilon})$.

Constant average depth is achievable with parallel ancilla preparation.

Efficient fault-tolerant algorithms for simulating molecules like Lithium hydride are analyzed.

Abstract

Quantum computers can in principle simulate quantum physics exponentially faster than their classical counterparts, but some technical hurdles remain. Here we consider methods to make proposed chemical simulation algorithms computationally fast on fault-tolerant quantum computers in the circuit model. Fault tolerance constrains the choice of available gates, so that arbitrary gates required for a simulation algorithm must be constructed from sequences of fundamental operations. We examine techniques for constructing arbitrary gates which perform substantially faster than circuits based on the conventional Solovay-Kitaev algorithm [C.M. Dawson and M.A. Nielsen, \emph{Quantum Inf. Comput.}, \textbf{6}:81, 2006]. For a given approximation error $\epsilon$, arbitrary single-qubit gates can be produced fault-tolerantly and using a limited set of gates in time which is $O(\log \epsilon)$ or $O(\log \log \epsilon)$; with sufficient parallel preparation of ancillas, constant average depth is possible using a method we call programmable ancilla rotations. Moreover, we construct and analyze efficient implementations of first- and second-quantized simulation algorithms using the fault-tolerant arbitrary gates and other techniques, such as implementing various subroutines in constant time. A specific example we analyze is the ground-state energy calculation for Lithium hydride.