Adiabatic Quantum Graph Matching with Permutation Matrix Constraints

Seelbach, Benkner, Marcel; Golyanik, Vladislav; Theobalt, Christian; Moeller, Michael

doi:10.1109/3dv50981.2020.00068

Cited by 19 publications

(25 citation statements)

References 43 publications

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“…This young field seeks to identify how challenging problems can be formulated for and benefit from quantum hardware. While it remained predominantly theoretical at early stages [63,21], QCV methods from various domains were evaluated on real quantum hardware during the recent few years, including image classification [62,64,19], object detection [55], graph matching [72], mesh alignment [6], robust fitting [29] and permutation synchronisation [9].…”

Section: Related Workmentioning

confidence: 99%

“…Albeit restricted, experimental realisations of QA, such as DWave [26], can solve non-convex, quadratic unconstrained binary optimization (QUBO) problems, without resorting to continuous relaxations. This premise of AQC and QA has led to the emergence of quantum computer vision (QCV), where researchers started to port existing computer vision problems into forms amenable to quantum computation [42,55,38,72,79,9].…”

Section: Introductionmentioning

confidence: 99%

“…For example, estimating correspondences require solving QBOs for permutations and not for arbitrary binary vectors. To this end, the state of the art QCV methods either use a regularization with cherry picked coefficients [9] or resort to heuristics for auto-controlling the impact of the constraints [72,79]. Unfortunately, none of these approaches are optimal and jeopardize the solution quality guarantees of quantum computers.…”

Section: Introductionmentioning

confidence: 99%

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Q-FW: A Hybrid Classical-Quantum Frank-Wolfe for Quadratic Binary Optimization

Yurtsever¹,

Birdal²,

Golyanik³

2022

Preprint

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We present a hybrid classical-quantum framework based on the Frank-Wolfe algorithm, Q-FW, for solving quadratic, linearly-constrained, binary optimization problems on quantum annealers (QA). The computational premise of quantum computers has cultivated the re-design of various existing vision problems into quantum-friendly forms. Experimental QA realisations can solve a particular non-convex problem known as the quadratic unconstrained binary optimization (QUBO). Yet a naive-QUBO cannot take into account the restrictions on the parameters. To introduce additional structure in the parameter space, researchers have crafted ad-hoc solutions incorporating (linear) constraints in the form of regularizers. However, this comes at the expense of a hyper-parameter, balancing the impact of regularization. To date, a true constrained solver of quadratic binary optimization (QBO) problems has lacked. Q-FW first reformulates constrained-QBO as a copositive program (CP), then employs Frank-Wolfe iterations to solve CP while satisfying linear (in)equality constraints. This procedure unrolls the original constrained-QBO into a set of unconstrained QUBOs all of which are solved, in a sequel, on a QA. We use D-Wave Advantage QA to conduct synthetic and real experiments on two important computer vision problems, graph matching and permutation synchronization, which demonstrate that our approach is effective in alleviating the need for an explicit regularization coefficient.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Q-FW: A Hybrid Classical-Quantum Frank-Wolfe for Quadratic Binary Optimization

Yurtsever¹,

Birdal²,

Golyanik³

2022

Preprint

Self Cite

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“…In the following, we will describe how to encode Problem (18) or equivalently (22) in a quantum circuit. We will proceed by steps.…”

Section: Preliminariesmentioning

confidence: 99%

“…In the approach put forward in [21] (as well as in the more recent paper [22]), if the underlying graph A has N vertices then one needs O(N 2 ) qubits to represent the graph isomorphism problem as a QUBO (quadratic unconstrained binary optimization) in a quantum computer. The authors of [21] conjecture that this is a hard constraint for this type of formulation, which immediately requires ≈ 10 12 qubit machines to hope to match current classical results.…”

Section: Introductionmentioning

confidence: 99%

A Quantum Algorithm for the Sub-Graph Isomorphism Problem

Mariella¹,

Simonetto²

2021

Preprint

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We propose a novel variational method for solving the sub-graph isomorphism problem on a gatebased quantum computer. The method relies (1) on a new representation of the adjacency matrices of the underlying graphs, which requires a number of qubits that scales logarithmically with the number of vertices of the graphs; and (2) on a new Ansatz that can efficiently probe the permutation space. Simulations are then presented to showcase the approach on graphs up to 16 vertices, whereas, given the logarithmic scaling, the approach could be applied to realistic sub-graph isomorphism problem instances in the medium term.

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