Using Quantum Computers for Quantum Simulation

Abstract

Numerical simulation of quantum systems is crucial to further our understanding of natural phenomena. Many systems of key interest and importance, in areas such as superconducting materials and quantum chemistry, are thought to be described by models which we cannot solve with sufficient accuracy, neither analytically nor numerically with classical computers. Using a quantum computer to simulate such quantum systems has been viewed as a key application of quantum computation from the very beginning of the field in the 1980s. Moreover, useful results beyond the reach of classical computation are expected to be accessible with fewer than a hundred qubits, making quantum simulation potentially one of the earliest practical applications of quantum computers. In this paper we survey the theoretical and experimental development of quantum simulation using quantum computers, from the first ideas to the intense research efforts currently underway.

Quantum simulation

“…In general, DQS consists of three steps: initial state preparation |ψ(0) , unitary evolution U and the final measurement. These steps will be discussed in detail in the remainder of this subsections (see also (Brown et al, 2010)). …”

Prospects for Spin-Based Quantum Computing in Quantum Dots

“…A recent review on using quantum computers for quantum simulations can be found in Ref. [11]. In addition, the theories of quantum complexity and entanglement are currently being established, a process which is still far from being complete.…”

Simulation of single-qubit open quantum systems

“…However, as per [20] we can utilise basis transformations to further decompose the constituent semigroups {T (k) t }, and hence simplify the task of implementing channels from these semigroups, which is tackled in Section V. Firstly, note that for k = 1, L k simply generates Hamiltonian evolution, which can be simulated using a single unitary operation on a single qubit. We therefore focus on the generators of dissipative evolution, for which k ∈ [2,4]. We begin by defining unitary conjugation of a channel T t as the procedure transforming T t according to U † T t U, where U(ρ) = U ρU † for some unitary operator U .…”

“…However, equally as important is the development of methods for the simulation of open quantum systems [15,16], crucial for enhancing our understanding of nonequilibrium dynamics and thermalisation in a wide range of systems, from damped-driven spin-boson models to complex many fermion-boson models [2,3]. In particular, one would like to begin by simulating quantum channels, representing the most general quantum dynamics possible, and dynamical semigroups of quantum channels, which describe Markovian dynamics -continuous time processes resulting from interactions with a Markovian environment in the Born approximation [17].…”