18 research outputs found
Annealing by simulating the coherent Ising machine
The coherent Ising machine (CIM) enables efficient sampling of low-lying
energy states of the Ising Hamiltonian with all-to-all connectivity by encoding
the spins in the amplitudes of pulsed modes in an optical parametric oscillator
(OPO). The interaction between the pulses is realized by means of
measurement-based optoelectronic feedforward which enhances the gain for
lower-energy spin configurations. We present an efficient method of simulating
the CIM on a classical computer that outperforms the CIM itself as well as the
noisy mean-field annealer in terms of both the quality of the samples and the
computational speed. It is furthermore advantageous with respect to the CIM in
that it can handle Ising Hamiltonians with arbitrary real-valued node coupling
strengths. These results illuminate the nature of the faster performance
exhibited by the CIM and may give rise to a new class of quantum-inspired
algorithms of classical annealing that can successfully compete with existing
methods
Advantages of Unfair Quantum Ground-State Sampling
The debate around the potential superiority of quantum annealers over their
classical counterparts has been ongoing since the inception of the field by
Kadowaki and Nishimori close to two decades ago. Recent technological
breakthroughs in the field, which have led to the manufacture of experimental
prototypes of quantum annealing optimizers with sizes approaching the practical
regime, have reignited this discussion. However, the demonstration of quantum
annealing speedups remains to this day an elusive albeit coveted goal. Here, we
examine the power of quantum annealers to provide a different type of quantum
enhancement of practical relevance, namely, their ability to serve as useful
samplers from the ground-state manifolds of combinatorial optimization
problems. We study, both numerically by simulating ideal stoquastic and
non-stoquastic quantum annealing processes, and experimentally, using a
commercially available quantum annealing processor, the ability of quantum
annealers to sample the ground-states of spin glasses differently than
classical thermal samplers. We demonstrate that i) quantum annealers in general
sample the ground-state manifolds of spin glasses very differently than thermal
optimizers, ii) the nature of the quantum fluctuations driving the annealing
process has a decisive effect on the final distribution over ground-states, and
iii) the experimental quantum annealer samples ground-state manifolds
significantly differently than thermal and ideal quantum annealers. We
illustrate how quantum annealers may serve as powerful tools when complementing
standard sampling algorithms.Comment: 13 pages, 11 figure
Exponentially Biased Ground-State Sampling of Quantum Annealing Machines with Transverse-Field Driving Hamiltonians
We study the performance of the D-Wave 2X quantum annealing machine on
systems with well-controlled ground-state degeneracy. While obtaining the
ground state of a spin-glass benchmark instance represents a difficult task,
the gold standard for any optimization algorithm or machine is to sample all
solutions that minimize the Hamiltonian with more or less equal probability.
Our results show that while naive transverse-field quantum annealing on the
D-Wave 2X device can find the ground-state energy of the problems, it is not
well suited in identifying all degenerate ground-state configurations
associated to a particular instance. Even worse, some states are exponentially
suppressed, in agreement with previous studies on toy model problems [New J.
Phys. 11, 073021 (2009)]. These results suggest that more complex driving
Hamiltonians are needed in future quantum annealing machines to ensure a fair
sampling of the ground-state manifold.Comment: 6 pages, 5 figures, 1 tabl