2 research outputs found
Quantum-circuit design for efficient simulations of many-body quantum dynamics
We construct an efficient autonomous quantum-circuit design algorithm for
creating efficient quantum circuits to simulate Hamiltonian many-body quantum
dynamics for arbitrary input states. The resultant quantum circuits have
optimal space complexity and employ a sequence of gates that is close to
optimal with respect to time complexity. We also devise an algorithm that
exploits commutativity to optimize the circuits for parallel execution. As
examples, we show how our autonomous algorithm constructs circuits for
simulating the dynamics of Kitaev's honeycomb model and the
Bardeen-Cooper-Schrieffer model of superconductivity. Furthermore we provide
numerical evidence that the rigorously proven upper bounds for the simulation
error here and in previous work may sometimes overestimate the error by orders
of magnitude compared to the best achievable performance for some
physics-inspired simulations.Comment: 20 Pages, 6 figure
Can One Trust Quantum Simulators?
Various fundamental phenomena of strongly-correlated quantum systems such as
high- 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 that are designed to capture the relevant quantum
correlations of the many-body system of interest. In his seminal 1982 paper
[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.Comment: 20 pages. Minor changes with respect to version 2 (some additional
explanations, added references...