Next-Generation Topology of D-Wave Quantum Processors

Boothby, Kelly; Bunyk, P.; Raymond, Jack; Roy, Aidan

doi:10.48550/arxiv.2003.00133

Cited by 51 publications

(66 citation statements)

References 11 publications

(18 reference statements)

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“…For arbitrary graphs without an obvious relation to such a structure, being too large to simply use the complete graph scheme but small enough that they might fit, we always need to find a suitable embedding before we are able to calculate on the machine. This still holds for the new hardware architecture with the Pegasus graph, although it yields a higher connectivity [3].…”

Section: Introductionmentioning

confidence: 97%

“…Above we use the term ideal as it refers to the graph provided from the built-in hardware structure of overlapping superconducting loops forming the qubits, which is for instance described in [3]. However, some qubits, or in rare cases also couplings, are switched off by the programming interface of the currently operating hardware, because they do not show the expected behaviour [7].…”

Section: Introductionmentioning

confidence: 99%

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Minor Embedding in Broken Chimera and Pegasus Graphs is NP-complete

Lobe¹,

Lutz²

2021

Preprint

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The embedding is an essential step when calculating on the D-Wave machine. In this work we show the hardness of the embedding problem for both types of existing hardware, represented by the Chimera and the Pegasus graphs, containing unavailable qubits. We construct certain broken Chimera graphs, where it is hard to find a Hamiltonian cycle. As the Hamiltonian cycle problem is a special case of the embedding problem, this proves the general complexity result for the Chimera graphs. By exploiting the subgraph relation between the Chimera and the Pegasus graphs, the proof is then further extended to the Pegasus graphs.

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Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Minor Embedding in Broken Chimera and Pegasus Graphs is NP-complete

Lobe¹,

Lutz²

2021

Preprint

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“…Increasing both the graph dimensionality of qubit networks [2,30], and improving connectivity [31], the degree to which the qubits are coupled to one another, would greatly reduce physical hardware overhead by increasing the types and sizes of optimization problems that can be natively embedded. Existing quantum annealing processors based on superconducting qubits possess either nearest neighbor [32] or a combination of inter-and intra-unit cell interactions [33] between qubits. Commercial annealers, possessing this combination of inter-and intra-unit cell interactions, currently rely on minor embedding [34,35], a procedure of extending logical qubits over multiple physical qubits to implement problems that require higher dimensionality or connectivity than the processor's hardware natively allows.…”

Section: Introductionmentioning

confidence: 99%

Demonstration of long-range correlations via susceptibility measurements in a one-dimensional superconducting Josephson spin chain

Tennant,

Dai,

Martinez

et al. 2021

Preprint

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Spin chains have long been considered an effective medium for long-range interactions, entanglement generation, and quantum state transfer. In this work, we explore the properties of a spin chain implemented with superconducting flux circuits, designed to act as a connectivity medium between two superconducting qubits. The susceptibility of the chain is probed and shown to support long-range, cross chain correlations. In addition, interactions between the two end qubits, mediated by the coupler chain, are demonstrated. This work has direct applicability in near term quantum annealing processors as a means of generating long-range, coherent coupling between qubits.

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“…Programmable quantum annealers have developed significantly in the last decade and now host thousands of interacting qubits realizing an effective transverse field Hamiltonian [1][2][3] . While these developments are primarily motivated by the hope that such quantum annealers will efficiently solve classical optimization problems, there is accumulating evidence that they may be used to probe the statistical physics of frustrated magnets [4][5][6][7] .…”

mentioning

confidence: 99%

Quantum orders in the frustrated Ising model on the bathroom tile lattice

Hearth,

Morampudi,

Laumann

2022

Preprint

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We determine the zero and finite temperature phase diagram of the fully frustrated quantum Ising model on the bathroom tile (4-8) lattice. The phase diagram exhibits a wealth of 2+1d physics, including 1. classical Coulomb dimer liquids of both square and triangular lattice types; 2. quantum order-by-disorder induced phases breaking Z4, Z6, and Z8 symmetries; 3. finite temperature Kosterlitz-Thouless (KT) phases floating over the Z6 and Z8 orders; and, 4. staircases of (in)commensurate symmetry breaking phases at intermediate coupling. We establish this elaborate phase diagram using a combination of dimer model mapping, perturbation theory, Landau analysis and Stochastic Series Expansion Quantum Monte Carlo (QMC-SSE). Our results provide a baseline for studying frustrated magnetism with D-Wave architecture annealers, where the 4-8 lattice can be embedded naturally without 'cloning', reducing the number of competing energy scales. Simulations with the D-Wave 2000Q demonstrate qualitative agreement with the high temperature portion of the phase diagram, but are unable to access the low temperature phases.

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Next-Generation Topology of D-Wave Quantum Processors

Cited by 51 publications

References 11 publications

Minor Embedding in Broken Chimera and Pegasus Graphs is NP-complete

Minor Embedding in Broken Chimera and Pegasus Graphs is NP-complete

Demonstration of long-range correlations via susceptibility measurements in a one-dimensional superconducting Josephson spin chain

Quantum orders in the frustrated Ising model on the bathroom tile lattice

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