16,127 research outputs found
First-order transitions and the performance of quantum algorithms in random optimization problems
We present a study of the phase diagram of a random optimization problem in
presence of quantum fluctuations. Our main result is the characterization of
the nature of the phase transition, which we find to be a first-order quantum
phase transition. We provide evidence that the gap vanishes exponentially with
the system size at the transition. This indicates that the Quantum Adiabatic
Algorithm requires a time growing exponentially with system size to find the
ground state of this problem.Comment: 4 pages, 4 figures; final version accepted on Phys.Rev.Let
What is the Computational Value of Finite Range Tunneling?
Quantum annealing (QA) has been proposed as a quantum enhanced optimization
heuristic exploiting tunneling. Here, we demonstrate how finite range tunneling
can provide considerable computational advantage. For a crafted problem
designed to have tall and narrow energy barriers separating local minima, the
D-Wave 2X quantum annealer achieves significant runtime advantages relative to
Simulated Annealing (SA). For instances with 945 variables, this results in a
time-to-99%-success-probability that is times faster than SA
running on a single processor core. We also compared physical QA with Quantum
Monte Carlo (QMC), an algorithm that emulates quantum tunneling on classical
processors. We observe a substantial constant overhead against physical QA:
D-Wave 2X again runs up to times faster than an optimized
implementation of QMC on a single core. We note that there exist heuristic
classical algorithms that can solve most instances of Chimera structured
problems in a timescale comparable to the D-Wave 2X. However, we believe that
such solvers will become ineffective for the next generation of annealers
currently being designed. To investigate whether finite range tunneling will
also confer an advantage for problems of practical interest, we conduct
numerical studies on binary optimization problems that cannot yet be
represented on quantum hardware. For random instances of the number
partitioning problem, we find numerically that QMC, as well as other algorithms
designed to simulate QA, scale better than SA. We discuss the implications of
these findings for the design of next generation quantum annealers.Comment: 17 pages, 13 figures. Edited for clarity, in part in response to
comments. Added link to benchmark instance
Reinforcement Learning in Different Phases of Quantum Control
The ability to prepare a physical system in a desired quantum state is
central to many areas of physics such as nuclear magnetic resonance, cold
atoms, and quantum computing. Yet, preparing states quickly and with high
fidelity remains a formidable challenge. In this work we implement cutting-edge
Reinforcement Learning (RL) techniques and show that their performance is
comparable to optimal control methods in the task of finding short,
high-fidelity driving protocol from an initial to a target state in
non-integrable many-body quantum systems of interacting qubits. RL methods
learn about the underlying physical system solely through a single scalar
reward (the fidelity of the resulting state) calculated from numerical
simulations of the physical system. We further show that quantum state
manipulation, viewed as an optimization problem, exhibits a spin-glass-like
phase transition in the space of protocols as a function of the protocol
duration. Our RL-aided approach helps identify variational protocols with
nearly optimal fidelity, even in the glassy phase, where optimal state
manipulation is exponentially hard. This study highlights the potential
usefulness of RL for applications in out-of-equilibrium quantum physics.Comment: A legend for the videos referred to in the paper is available on
https://mgbukov.github.io/RL_movies
Molecular-orbital-free algorithm for excited states in time-dependent perturbation theory
A non-linear conjugate gradient optimization scheme is used to obtain
excitation energies within the Random Phase Approximation (RPA). The solutions
to the RPA eigenvalue equation are located through a variational
characterization using a modified Thouless functional, which is based upon an
asymmetric Rayleigh quotient, in an orthogonalized atomic orbital
representation. In this way, the computational bottleneck of calculating
molecular orbitals is avoided. The variational space is reduced to the
physically-relevant transitions by projections. The feasibility of an RPA
implementation scaling linearly with system size, N, is investigated by
monitoring convergence behavior with respect to the quality of initial guess
and sensitivity to noise under thresholding, both for well- and ill-conditioned
problems. The molecular- orbital-free algorithm is found to be robust and
computationally efficient providing a first step toward a large-scale, reduced
complexity calculation of time-dependent optical properties and linear
response. The algorithm is extensible to other forms of time-dependent
perturbation theory including, but not limited to, time-dependent Density
Functional theory.Comment: 9 pages, 7 figure
Painless Breakups -- Efficient Demixing of Low Rank Matrices
Assume we are given a sum of linear measurements of different rank-
matrices of the form . When and under
which conditions is it possible to extract (demix) the individual matrices
from the single measurement vector ? And can we do the demixing
numerically efficiently? We present two computationally efficient algorithms
based on hard thresholding to solve this low rank demixing problem. We prove
that under suitable conditions these algorithms are guaranteed to converge to
the correct solution at a linear rate. We discuss applications in connection
with quantum tomography and the Internet-of-Things. Numerical simulations
demonstrate empirically the performance of the proposed algorithms
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