Fast clique minor generation in Chimera qubit connectivity graphs

Boothby, Tomas; King, Andrew D.; Roy, Aidan

doi:10.1007/s11128-015-1150-6

Cited by 141 publications

(149 citation statements)

References 21 publications

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“…One aspect which could be explored in statics and dynamics is the extension to two or higher dimensional systems which we have excluded due to the limitation of MPS algorithms to one spatial dimension for studies of this kind. Two-dimensional setups allow more options for quantum computation to apply gates [48]. In the case of the antiferromagnetic case triangular lattices can lead to the similar concurrence of the staggered order than for long-range interactions in the onedimensional case.…”

Section: Conclusion and Open Questionsmentioning

confidence: 99%

Critical phenomena and Kibble–Zurek scaling in the long-range quantum Ising chain

et al. 2017

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We investigate an extension of the quantum Ising (QI) model in one spatial dimension including longrange r 1 a interactions in its statics and dynamics with possible applications from heteronuclear polar molecules in optical lattices to trapped ions described by two-state spin systems. We introduce the statics of the system via both numerical techniques with finite size and infinite size matrix product states (MPSs) and a theoretical approaches using a truncated Jordan-Wigner transformation for the ferromagnetic and antiferromagnetic case and show that finite size effects have a crucial role shifting the quantum critical point of the external field by fifteen percent between thirty-two and around fivehundred spins. We numerically study the Kibble-Zurek hypothesis in the long-range QI model with MPSs. A linear quench of the external field through the quantum critical point yields a power-law scaling of the defect density as a function of the total quench time. For example, the increase of the defect density is slower for longer-range models and the critical exponent changes by twenty-five percent. Our study emphasizes the importance of such long-range interactions in statics and dynamics that could point to similar phenomena in a different setup of dynamical systems or for other models.

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Section: Conclusion and Open Questionsmentioning

confidence: 99%

Critical phenomena and Kibble–Zurek scaling in the long-range quantum Ising chain

et al. 2017

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“…In practice, we add an element x n+1 to the Q matrix that is strongly coupled to any node i with the following elements modified based on the value of penalty term M. Figure 4 provides an example of the changes made when adding node 6 that is strongly coupled to node 1. 1 2 3 4 5 1 2 3 4 5 6 1 5 2 2 2 2 1 -45 2 2 100 2 8 2 2 2 8 2 2 3 3 3 Future work will investigate the application of Rules 1-5 in conjunction with strong coupling in order to transform a given graph to one that meets a target graph's node and edge specifications [5].…”

Section: Graph Expansion Via Strongly Coupled Nodesmentioning

confidence: 99%

Quadratic unconstrained binary optimization problem preprocessing: Theory and empirical analysis

Lewis

Glover

2017

Networks

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Abstract. The Quadratic Unconstrained Binary Optimization problem (QUBO) has become a unifying model for representing a wide range of combinatorial optimization problems, and for linking a variety of disciplines that face these problems. A new class of quantum annealing computer that maps QUBO onto a physical qubit network structure with specific size and edge density restrictions is generating a growing interest in ways to transform the underlying QUBO structure into an equivalent graph having fewer nodes and edges. In this paper we present rules for reducing the size of the QUBO matrix by identifying variables whose value at optimality can be predetermined. We verify that the reductions improve both solution quality and time to solution and, in the case of metaheuristic methods where optimal solutions cannot be guaranteed, the quality of solutions obtained within reasonable time limits.We discuss the general QUBO structural characteristics that can take advantage of these reduction techniques and perform careful experimental design and analysis to identify and quantify the specific characteristics most affecting reduction. The rules make it possible to dramatically improve solution times on a new set of problems using both the exact Cplex solver and a tabu search metaheuristic.

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“…Considering this order statistic, and the fact that QuAMax considers only the best solution found by all the anneals in a run, the expected BER of instance I after N a anneals can be expressed as (9) where N is qubit count, L (≤ N a ) is the number of distinct solutions, r (1 ≤ r ≤ L) is the rank index of each solution, p(r ) is the probability of obtaining the r th solution, and F I (k) is the number of bit errors of the k th solution against ground truth. 7 To calculate TTB(p), we replace the left hand side of Eq. 9 with p, solve for N a , and compute TTB(p) = N a T a /P f .…”

Section: Ourmentioning

confidence: 99%

Leveraging quantum annealing for large MIMO processing in centralized radio access networks

Kim

Venturelli

Jamieson

2019

Proceedings of the ACM Special Interest Group on Data Communication

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User demand for increasing amounts of wireless capacity continues to outpace supply, and so to meet this demand, significant progress has been made in new MIMO wireless physical layer techniques. Higher-performance systems now remain impractical largely only because their algorithms are extremely computationally demanding. For optimal performance, an amount of computation that increases at an exponential rate both with the number of users and with the data rate of each user is often required. The base station's computational capacity is thus becoming one of the key limiting factors on wireless capacity. QuAMax is the first large MIMO centralized radio access network design to address this issue by leveraging quantum annealing on the problem. We have implemented QuAMax on the 2,031 qubit D-Wave 2000Q quantum annealer, the state-of-the-art in the field. Our experimental results evaluate that implementation on real and synthetic MIMO channel traces, showing that 10 µs of compute time on the 2000Q can enable 48 user, 48 AP antenna BPSK communication at 20 dB SNR with a bit error rate of 10 −6 and a 1,500 byte frame error rate of 10 −4 .

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Fast clique minor generation in Chimera qubit connectivity graphs

Cited by 141 publications

References 21 publications

Critical phenomena and Kibble–Zurek scaling in the long-range quantum Ising chain

Critical phenomena and Kibble–Zurek scaling in the long-range quantum Ising chain

Quadratic unconstrained binary optimization problem preprocessing: Theory and empirical analysis

Leveraging quantum annealing for large MIMO processing in centralized radio access networks

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