Duality quantum computer and the efficient quantum simulations

TL;DR

This paper reviews the duality quantum computer, highlighting its ability to implement all linear bounded operators, and demonstrates its superior efficiency in quantum simulation algorithms compared to traditional quantum computers.

Contribution

It introduces the concept of duality quantum computing, showing how it can simulate quantum systems more efficiently than standard quantum computers.

Findings

Duality quantum computer can realize all linear bounded operators.

It provides a more flexible framework for quantum algorithm design.

Enhanced efficiency in simulating quantum systems with sparse Hamiltonians.

Abstract

In this paper, we firstly briefly review the duality quantum computer. Distinctly, the generalized quantum gates, the basic evolution operators in a duality quantum computer are no longer unitary, and they can be expressed in terms of linear combinations of unitary operators. All linear bounded operators can be realized in a duality quantum computer, and unitary operators are just the extreme points of the set of generalized quantum gates. A d-slits duality quantum computer can be realized in an ordinary quantum computer with an additional qudit using the duality quantum computing mode. Duality quantum computer provides flexibility and clear physical picture in designing quantum algorithms, serving as a useful bridge between quantum and classical algorithms. In this review, we will show that duality quantum computer can simulate quantum systems more efficiently than ordinary quantum computers by providing descriptions of the recent efficient quantum simulation algorithms of Childs et al [Quantum Information & Computation, 12(11-12): 901-924 (2012)] for the fast simulation of quantum systems with a sparse Hamiltonian, and the quantum simulation algorithm by Berry et al [Phys. Rev. Lett. 114, 090502 (2015)], which provides exponential improvement in precision for simulating systems with a sparse Hamiltonian.