107 research outputs found
Synchronously-pumped OPO coherent Ising machine: benchmarking and prospects
The coherent Ising machine (CIM) is a network of optical parametric oscillators (OPOs) that solves for the ground state of Ising problems through OPO bifurcation dynamics. Here, we present experimental results comparing the performance of the CIM to quantum annealers (QAs) on two classes of NP-hard optimization problems: ground state calculation of the Sherrington-Kirkpatrick (SK) model and MAX-CUT. While the two machines perform comparably on sparsely-connected problems such as cubic MAX-CUT, on problems with dense connectivity, the QA shows an exponential performance penalty relative to CIMs. We attribute this to the embedding overhead required to map dense problems onto the sparse hardware architecture of the QA, a problem that can be overcome in photonic architectures such as the CIM
Solving Set Cover with Pairs Problem using Quantum Annealing
Here we consider using quantum annealing to solve Set Cover with Pairs (SCP), an NP-hard combinatorial optimization problem that plays an important role in networking, computational biology, and biochemistry. We show an explicit construction of Ising Hamiltonians whose ground states encode the solution of SCP instances. We numerically simulate the time-dependent Schrödinger equation in order to test the performance of quantum annealing for random instances and compare with that of simulated annealing. We also discuss explicit embedding strategies for realizing our Hamiltonian construction on the D-wave type restricted Ising Hamiltonian based on Chimera graphs. Our embedding on the Chimera graph preserves the structure of the original SCP instance and in particular, the embedding for general complete bipartite graphs and logical disjunctions may be of broader use than that the specific problem we deal with
Synchronously-pumped OPO coherent Ising machine: benchmarking and prospects
The coherent Ising machine (CIM) is a network of optical parametric oscillators (OPOs) that solves for the ground state of Ising problems through OPO bifurcation dynamics. Here, we present experimental results comparing the performance of the CIM to quantum annealers (QAs) on two classes of NP-hard optimization problems: ground state calculation of the Sherrington-Kirkpatrick (SK) model and MAX-CUT. While the two machines perform comparably on sparsely-connected problems such as cubic MAX-CUT, on problems with dense connectivity, the QA shows an exponential performance penalty relative to CIMs. We attribute this to the embedding overhead required to map dense problems onto the sparse hardware architecture of the QA, a problem that can be overcome in photonic architectures such as the CIM
Experimental investigation of performance differences between Coherent Ising Machines and a quantum annealer
Physical annealing systems provide heuristic approaches to solving NP-hard
Ising optimization problems. Here, we study the performance of two types of
annealing machines--a commercially available quantum annealer built by D-Wave
Systems, and measurement-feedback coherent Ising machines (CIMs) based on
optical parametric oscillator networks--on two classes of problems, the
Sherrington-Kirkpatrick (SK) model and MAX-CUT. The D-Wave quantum annealer
outperforms the CIMs on MAX-CUT on regular graphs of degree 3. On denser
problems, however, we observe an exponential penalty for the quantum annealer
() relative to CIMs () for fixed anneal times, on both the SK model and on 50%-edge-density
MAX-CUT, where the coefficients and
are problem-class-dependent. On instances with over vertices, a
several-orders-of-magnitude time-to-solution difference exists between CIMs and
the D-Wave annealer. An optimal-annealing-time analysis is also consistent with
a significant projected performance difference. The difference in performance
between the sparsely connected D-Wave machine and the measurement-feedback
facilitated all-to-all connectivity of the CIMs provides strong experimental
support for efforts to increase the connectivity of quantum annealers.Comment: 12 pages, 5 figures, 1 table (main text); 14 pages, 12 figures, 2
tables (supplementary
Glassy Chimeras could be blind to quantum speedup: Designing better benchmarks for quantum annealing machines
Recently, a programmable quantum annealing machine has been built that
minimizes the cost function of hard optimization problems by adiabatically
quenching quantum fluctuations. Tests performed by different research teams
have shown that, indeed, the machine seems to exploit quantum effects. However
experiments on a class of random-bond instances have not yet demonstrated an
advantage over classical optimization algorithms on traditional computer
hardware. Here we present evidence as to why this might be the case. These
engineered quantum annealing machines effectively operate coupled to a
decohering thermal bath. Therefore, we study the finite-temperature critical
behavior of the standard benchmark problem used to assess the computational
capabilities of these complex machines. We simulate both random-bond Ising
models and spin glasses with bimodal and Gaussian disorder on the D-Wave
Chimera topology. Our results show that while the worst-case complexity of
finding a ground state of an Ising spin glass on the Chimera graph is not
polynomial, the finite-temperature phase space is likely rather simple: Spin
glasses on Chimera have only a zero-temperature transition. This means that
benchmarking optimization methods using spin glasses on the Chimera graph might
not be the best benchmark problems to test quantum speedup. We propose
alternative benchmarks by embedding potentially harder problems on the Chimera
topology. Finally, we also study the (reentrant) disorder-temperature phase
diagram of the random-bond Ising model on the Chimera graph and show that a
finite-temperature ferromagnetic phase is stable up to 19.85(15)%
antiferromagnetic bonds. Beyond this threshold the system only displays a
zero-temperature spin-glass phase. Our results therefore show that a careful
design of the hardware architecture and benchmark problems is key when building
quantum annealing machines.Comment: 8 pages, 5 figures, 1 tabl
Performance Models for Split-execution Computing Systems
Split-execution computing leverages the capabilities of multiple
computational models to solve problems, but splitting program execution across
different computational models incurs costs associated with the translation
between domains. We analyze the performance of a split-execution computing
system developed from conventional and quantum processing units (QPUs) by using
behavioral models that track resource usage. We focus on asymmetric processing
models built using conventional CPUs and a family of special-purpose QPUs that
employ quantum computing principles. Our performance models account for the
translation of a classical optimization problem into the physical
representation required by the quantum processor while also accounting for
hardware limitations and conventional processor speed and memory. We conclude
that the bottleneck in this split-execution computing system lies at the
quantum-classical interface and that the primary time cost is independent of
quantum processor behavior.Comment: Presented at 18th Workshop on Advances in Parallel and Distributed
Computational Models [APDCM2016] on 23 May 2016; 10 page
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