Adiabatic quantum optimization with qudits

Amin, M. H. S.; Dickson, Neil G.; Smith, Peter M.

doi:10.1007/s11128-012-0480-x

Cited by 15 publications

(10 citation statements)

References 18 publications

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“…excitations, and non-adiabaticity due to the finite annealing time [63]. Added to this is the qubit approximation to the rf SQUID [64]. Control errors such as miscalibration and the finite digitalto-analog (DAC) converter resolution contribute as well.…”

Section: Resultsmentioning

confidence: 99%

Max 2-SAT with up to 108 qubits

et al. 2014

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We experimentally study the performance of a programmable quantum annealing processor, the D-Wave One (DW1) with up to 108 qubits, on maximum SAT problem with 2 variables per clause (MAX 2-SAT) problems. We consider ensembles of random problems characterized by a fixed clause density, an external parameter which we tune through its critical value in our experiments. We demonstrate that the DW1 is sensitive to the critical value of the clause density. The DW1 results are verified and compared with akmaxsat, an exact, state-of-the-art algorithm. We study the relative performance of the two solvers and how they correlate in terms of problem hardness. We find that the DW1 performance scales more favorably with problem size and that problem hardness correlation is essentially non-existent. We discuss the relevance and limitations of such a comparison.Keywords: adiabatic quantum computation, quantum annealing, computational complexity IntroductionAdiabatic quantum computation (AQC) is a model of solving computational problems, in particular hard optimization problems, by evolving a closed system in the ground state manifold Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. P f ad, represents the solution to the computational problem. AQC has been proven to be polynomially equivalent to standard, closed-system, circuit model QC [3][4][5][6][7], but so far it is unclear whether this equivalence extends to the open system, non-zero New J. Phys. 16 (2014) 045006 S Santra et al 2 New J. Phys. 16 (2014) 045006 S Santra et al 3 5 In more detail, the McGeoch and Wang (MW) study [35], working with the DW2, used a 439 qubit subgraph of Chimera and considered three problems: (1) Chimera-structured QUBO instances (this is actually an ensemble of uniform samples from the Ising model on Chimera with ∈ − J h , { 1,1} ij j[36]), (2) Weighted Max 2-SAT, (3) the Quadratic Assignment Problem. Their main conclusion is that in their experiments the DW2 (together with a software layer called Blackbox) outperformed the software against which it was tested. In the case of problem (1), the DW2 is reported as outperforming its nearest rival (CPLEX), amongst those tried, by a factor of 3600. The times recorded by MW were for the first point that CPLEX found the optimal solution, and not the time at which it proved it optimality. However, several researchers have reported classical implementations for all three problems which outperform the DW2 and in particular the MW benchmarks [36,37]. Our ensemble of MAX 2-SAT problems differs from the weighted MAX 2-SAT problems considered by MW, since we used uniform weights with the additional constraint of a fixed clause density. In addition, unlike MWʼs case (2), our MAX 2-SAT problem ensemble inherits the native Chimera graph structure along with the connectivity contraints of the processor by design, which eliminates the ...

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Section: Resultsmentioning

confidence: 99%

Max 2-SAT with up to 108 qubits

et al. 2014

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“…These features play an important role in the reduction of the circuit complexity, the simplification of the experimental setup and the enhancement of the algorithm efficiency [100,106,108,109]. The advantage of the qudit not only applies to the circuit model for quantum computers but also applies to adiabatic quantum computing devices [5,166]; topological quantum systems [16,37,38] and more. The qudit-based quantum computing system can be implemented on various physical platforms such as photonic systems [60,106]; continuous spin systems [2,11]; ion trap [91]; nuclear magnetic resonance [48,62] and molecular magnets [99].…”

Section: Introductionmentioning

confidence: 99%

Qudits and High-Dimensional Quantum Computing

et al. 2020

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“…The function of CMULT is the multiplication of the input complex number with a constant complex number which is derived based on the controlled phase-shift gate. As expressed previously in (21), it is used in unitary transformation 3:…”

Section: 1mentioning

confidence: 99%

“…Nevertheless, only small-scale quantum computation implementations have been achieved [19,20]. Instead of focusing on the realization of quantum gates, a different approach known as quantum annealing which solves optimization problems by finding the minimum point is used in the 128-qubit D-Wave One, 512-qubit D-Wave Two, and 1000-qubit D-Wave 2X systems [21,22]. However, based on the research report presented in [23], the expected quantum speed-ups were not found in the D-Wave systems.…”

Section: Introductionmentioning

confidence: 99%

An FPGA-Based Quantum Computing Emulation Framework Based on Serial-Parallel Architecture

Lee

Khalil-Hani

Marsono

2016

International Journal of Reconfigurable Computing

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Hardware emulation of quantum systems can mimic more efficiently the parallel behaviour of quantum computations, thus allowing higher processing speed-up than software simulations. In this paper, an efficient hardware emulation method that employs a serial-parallel hardware architecture targeted for field programmable gate array (FPGA) is proposed. Quantum Fourier transform and Grover’s search are chosen as case studies in this work since they are the core of many useful quantum algorithms. Experimental work shows that, with the proposed emulation architecture, a linear reduction in resource utilization is attained against the pipeline implementations proposed in prior works. The proposed work contributes to the formulation of a proof-of-concept baseline FPGA emulation framework with optimization on datapath designs that can be extended to emulate practical large-scale quantum circuits.

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Adiabatic quantum optimization with qudits

Cited by 15 publications

References 18 publications

Max 2-SAT with up to 108 qubits

Max 2-SAT with up to 108 qubits

Qudits and High-Dimensional Quantum Computing

An FPGA-Based Quantum Computing Emulation Framework Based on Serial-Parallel Architecture

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