Quantum simulation

Abstract

Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum system to study another less controllable or accessible quantum system, i.e., quantum simulation. Quantum simulation promises to have applications in the study of many problems in, e.g., condensed-matter physics, high-energy physics, atomic physics, quantum chemistry and cosmology. Quantum simulation could be implemented using quantum computers, but also with simpler, analog devices that would require less control, and therefore, would be easier to construct. A number of quantum systems such as neutral atoms, ions, polar molecules, electrons in semiconductors, superconducting circuits, nuclear spins and photons have been proposed as quantum simulators. This review outlines the main theoretical and experimental aspects of quantum simulation and emphasizes some of the challenges and promises of this fast-growing field.

Exploiting Locality in Quantum Computation for Quantum Chemistry

“…Some of these results have already appeared in the quantum computation literature in the context of in depth studies of state preparation [24,25]. A general review of quantum simulation [26,27] and one on quantum computation for chemistry [28] cover these topics in more depth. A collection covering several aspects of quantum information and chemistry recently appeared [29].…”

Boson sampling for molecular vibronic spectra

“…Particularly significant is the exponential speed up achieved for the prime factorization of large numbers [3], a problem for which no efficient classical algorithm is currently known. Another attractive area for quantum computers is quantum simulation [4][5][6][7][8][9] where it has recently been shown that the dynamics of chemical reactions [10] as well as molecular electronic structure [11] are attractive applications for quantum devices. For all these instances, the realization of a quantum computer would challenge the Extended Church-Turing thesis (ECT), which claims that a Turing machine can efficiently simulate any physically realizable system, and even disprove it if prime factorization was finally demonstrated to be not efficiently solvable on classical machines.…”

Simulation of single-qubit open quantum systems

“…One of the primary motivations for the development of quantum computation is the possibility of efficiently simulating quantum systems [1]- [3], as suggested in Feynman's seminal paper on the topic [4]. The natural first step towards this vision is the simulation of closed quantum systems, undergoing Hamiltonian generated unitary evolution, and over the past two decades consistent progress has been made in this field.…”