Toward Quantum Gate-Model Heuristics for Real-World Planning Problems

Stollenwerk, Tobias; Hadfield, Stuart; Wang, Zhihui

doi:10.1109/tqe.2020.3030609

Cited by 25 publications

(19 citation statements)

References 34 publications

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“…Future research could incorporate our approach with further variants of ZX-calculus, like the ZH-calculus [3] or the ZX-framework for qudits [41,50]. In particular the latter could facilitate novel insights into performance analysis of quantum alternating operator ansätze [26] for problems like graph-coloring [53] and beyond [44]. Similarly, our approach could be likewise applied to applications beyond combinatorial optimization, like variational quantum eigensolvers for quantum chemistry applications [15].…”

Section: Discussionmentioning

confidence: 99%

Diagrammatic Analysis for Parameterized Quantum Circuits

Stollenwerk¹,

Hadfield²

2022

Preprint

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March 2022Diagrammatic representations of quantum algorithms and circuits offer novel approaches to their design and analysis. In this work, we describe extensions of the ZX-calculus especially suitable for parameterized quantum circuits, in particular for computing observable expectation values as functions of or for fixed parameters, which are important algorithmic quantities in a variety of applications ranging from combinatorial optimization to quantum chemistry. We provide several new ZX-diagram rewrite rules and generalizations for this setting. In particular, we give formal rules for dealing with linear combinations of ZX-diagrams, where the relative complex-valued scale factors of each diagram must be kept track of, in contrast to most previously studied single-diagram realizations where these coefficients can be effectively ignored. This allows us to directly import a number useful relations from the operator analysis to ZX-calculus setting, including causal cone and quantum gate commutation rules. We demonstrate that the diagrammatic approach offers useful insights into algorithm structure and performance by considering several ansätze from the literature including realizations of hardware-efficient ansätze and QAOA. We find that by employing a diagrammatic representation, calculations across different ansätze can become more intuitive and potentially easier approach systematically than by alternative means. Finally, we outline how diagrammatic approaches may aid in the design and study of new and more effective quantum circuit ansätze.

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Section: Discussionmentioning

confidence: 99%

Diagrammatic Analysis for Parameterized Quantum Circuits

Stollenwerk¹,

Hadfield²

2022

Preprint

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“…Note that both constraints are equivalent to the proper coloring of a graph with edged E. This relation to graph coloring is extensively discussed e.g. in [41].…”

Section: Table I: Flight-gate Assignment Problem Parametermentioning

confidence: 99%

“…Again, the penalty weight μ must be sufficiently large to ensure the constraint satisfaction in the ground state (see [13] for details). Note that both constraints are equivalent to the proper coloring of a graph with edged E. This relation to graph coloring is extensively discussed, e.g., in [44].…”

Section: Flight Gate Assignmentmentioning

confidence: 99%

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Performance of Domain-Wall Encoding for Quantum Annealing

Chen

Stollenwerk

Chancellor

2021

IEEE Trans. Quantum Eng.

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In this article, we experimentally test the performance of the recently proposed domain-wall encoding of discrete variables Chancellor, 2019, on Ising model flux qubit quantum annealers. We compare this encoding with the traditional one-hot methods and find that they outperform the one-hot encoding for three different problems at different sizes of both the problem and the variables. From these results, we conclude that the domain-wall encoding yields superior performance against a variety of metrics furthermore; we do not find a single metric by which one hot performs better. We even find that a 2000Q quantum annealer with a drastically less connected hardware graph but using the domain-wall encoding can outperform the next-generation Advantage processor if that processor uses one-hot encoding.

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“…Various problems of practical significance are naturally linked to the graph colouring problem. This includes planning and scheduling problems as they occur in industrial settings like manufacturing [7] and cost optimization [8].In the present paper we introduce an algorithm that finds a graph colouring on a quantum com-…”

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confidence: 99%

Withdrawn: A Measurement-based Algorithm for Graph Colouring

Epping¹,

Stollenwerk²

2021

Preprint

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We present a novel algorithmic approach to find a proper vertex colouring of a graph with d colours, if it exists. We associate a d-dimensional quantum system with each vertex and the initial state is a mixture of all possible colourings, from which we obtain a random proper colouring of the graph by measurements. The nondeterministic nature of the quantum measurement is tackled by a reset operation, which can revert the effect of unwanted projections. As in the classical case, we find that the runtime scales exponentially with the number of vertices. However, we provide numerical evidence that the average runtime for random graphs scales polynomially in the number of edges.A proper vertex colouring, often simply called a colouring of a graph, is an assignment of colours to vertices of a graph g, such that no adjacent vertices have the same colour [1]. A colouring that uses d different colours is called a d-colouring and a graph for which a d-colouring exists is called dcolourable. The chromatic number χ(g) is the smallest number d such that g is d-colourable. See Figure 1 for a graph with chromatic number 3.It is hard to compute χ(g). In fact finding χ(g) is one of Karp's 21 famous 3,4,5], which means that every problem in NP can be solved by calling an oracle version of the graph colouring a polynomial number of times. And even when considering only planar graphs with vertex degree at most four and d = 3 different colours the problem remains NPcomplete [6]. Various problems of practical significance are naturally linked to the graph colouring problem. This includes planning and scheduling problems as they occur in industrial settings like manufacturing [7] and cost optimization [8].In the present paper we introduce an algorithm that finds a graph colouring on a quantum com-

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Toward Quantum Gate-Model Heuristics for Real-World Planning Problems

Cited by 25 publications

References 34 publications

Diagrammatic Analysis for Parameterized Quantum Circuits

Diagrammatic Analysis for Parameterized Quantum Circuits

Performance of Domain-Wall Encoding for Quantum Annealing

Withdrawn: A Measurement-based Algorithm for Graph Colouring

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