Can one trust quantum simulators?

Abstract

Various fundamental phenomena of strongly correlated quantum systems such as high-T(c) superconductivity, the fractional quantum-Hall effect and quark confinement are still awaiting a universally accepted explanation. The main obstacle is the computational complexity of solving even the most simplified theoretical models which are designed to capture the relevant quantum correlations of the many-body system of interest. In his seminal 1982 paper (Feynman 1982 Int. J. Theor. Phys. 21 467), Richard Feynman suggested that such models might be solved by 'simulation' with a new type of computer whose constituent parts are effectively governed by a desired quantum many-body dynamics. Measurements on this engineered machine, now known as a 'quantum simulator,' would reveal some unknown or difficult to compute properties of a model of interest. We argue that a useful quantum simulator must satisfy four conditions: relevance, controllability, reliability and efficiency. We review the current state of the art of digital and analog quantum simulators. Whereas so far the majority of the focus, both theoretically and experimentally, has been on controllability of relevant models, we emphasize here the need for a careful analysis of reliability and efficiency in the presence of imperfections. We discuss how disorder and noise can impact these conditions, and illustrate our concerns with novel numerical simulations of a paradigmatic example: a disordered quantum spin chain governed by the Ising model in a transverse magnetic field. We find that disorder can decrease the reliability of an analog quantum simulator of this model, although large errors in local observables are introduced only for strong levels of disorder. We conclude that the answer to the question 'Can we trust quantum simulators?' is … to some extent.

Matter-wave solitons supported by field-induced dipole-dipole repulsion with spatially modulated strength

“…On the other hand, for narrow solitons with large P , one can still use the asymptotic equation (22) for the soliton's tail (at |x| → ∞), while inside the integral one may substitute g(x) ≈ g 0 , as suggested by Eq. (26). This means that, for the narrow solitons, scaling relations are obtained in the form of Eqs.…”

“…The DDIs account for a number of remarkable phenomena in ultracold Bose gases [9]- [11], such as various pattern-formation scenarios [12][13][14][15][16], fractional domain walls [17], d -wave collapse [18,19], specific possibilities for precision measurements [20][21][22], stabilization of the dipolar BEC by optical lattices [23,24], the Einstein -de Haas effect [25], etc. Dipolar BECs can be also used as matter-wave simulators [26], to emulate, in particular, the creation of multi-dimensional solitons via the nonlocal nonlinearity-a subject which has also drawn much attention in optics, where nonlocal interactions of other types (with different interaction kernels) occur too [27][28][29]. In fact, the dipolar condensates not only emulate the situation known in optics, but also make it possible to predict the existence of solitons with novel properties.…”

Gap Solitons in a Spin-Orbit-Coupled Bose-Einstein Condensate

“…The last property allows one using neutral atoms to simulate numerous condensed matter phenomena [4] in a tunable way, what would be impossible in direct condensed matter experiments. In other words, a spinor BEC is a promising candidate for implementation of a quantum simulator, which due to the technologies available nowadays was already implemented using cold atoms [5], ions [6], or photonics [7].…”

Floquet engineering from long-range to short-range interactions

“…To get only nearest-neighbor interactions, we choose f n (t) so as to suppress all β r except for β 1 .…”

“…A quantum simulator with a large number of particles would be able to simulate quantum many-body systems beyond what a classical computer could handle [3]. One goal of quantum simulation is to implement models that describe solid-state systems and thereby gain direct insight into phenomena like high-T c superconductivity.There has been a lot of progress on quantum simulation using cold atoms [1,2]. A common feature of such systems is the presence of long-range interactions that decay with a power law in distance due to dipolar or Coulomb interactions [4][5][6][7][8][9].…”