Unconstrained Binary Models of the Travelling Salesman Problem Variants for Quantum Optimization

Salehi, Özlem; Glos, Adam; Miszczak, Jarosław Adam

doi:10.48550/arxiv.2106.09056

Cited by 8 publications

(11 citation statements)

References 30 publications

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“…Although we have only considered the TSP problem in our numerical experiments, it is worth noting that the proposed schemes can be used with different objective Hamiltonians. Our ancilla-free post-selection through compression scheme can be applied to any problem where the feasible states are one-hot, including the problems defined over permutations such as Vehicle Routing Problem [53], variations of TSP [54,55], Railway Dispatching Problem [56,57], Graph Isomorphism Problem [58], Flight Gate Assignment Problem [59].…”

Section: Discussionmentioning

confidence: 99%

Error mitigation for variational quantum algorithms through mid-circuit measurements

Botelho,

Glos,

Kundu

et al. 2021

Preprint

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Noisy Intermediate-Scale Quantum (NISQ) algorithms require novel paradigms of error mitigation. To obtain noise-robust quantum computers, each logical qubit is equipped with hundreds or thousands of physical qubits. However, it is not possible to use memoryconsuming techniques for current quantum devices having at most hundreds or at best thousands of physical qubits on their own. For specific problems, valid quantum states have a unique structure as in the case of Fock states and W-states where the Hamming weight is fixed, and the evolution takes place in a smaller subspace of the full Hilbert space. With this pre-knowledge, some errors can be detected in the course of the evolution of the circuit, by filtering the states not obeying the pattern through post-selection. In this paper, we present mid-circuit post-selection schemes for frequently used encodings such as one-hot, binary, gray, and domain-wall encoding. For the particular subspace of one-hot states, we propose a method that works by compressing the full Hilbert space to a smaller subspace, allowing projecting to the desired subspace without using any ancilla qubits. We demonstrate the effectiveness of the approach for the Quantum Alternating Operator Ansatz algorithm. Our method is particularly suitable for the currently available hardware, where measuring and resetting is possible, but classical control conditional operators are not.

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Section: Discussionmentioning

confidence: 99%

Error mitigation for variational quantum algorithms through mid-circuit measurements

Botelho,

Glos,

Kundu

et al. 2021

Preprint

Self Cite

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“…To make a stronger statement, the limitations of our model have to be studied further, both analytically (by elaborating e.g., on the more precise determination of α) and empirically by applying the method to many samples. We plan to use it for additional problems of the field of logistics and operations research, similarly to those e.g., in [31,32].…”

Section: Discussionmentioning

confidence: 99%

Statistical quality assessment of Ising-based annealer outputs

Domino,

Koniorczyk,

Puchała

2021

Preprint

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The ability to evaluate the outcomes of quantum annealers is essential for such devices to be used in complex computational tasks. We introduce a statistical test of the quality of Ising-based annealers' output based on the data only, assessing the ground state's probability of being sampled. A higher probability value implies that at least the lower part of the spectrum is a part of the sample. Assuming a plausible model of the univariate energy distribution of the sample, we express the ground-state energy and temperature as a function of cumulants up to the third order. Using the annealer samples, we evaluate this multiple times using Bootstrap resampling, resulting in an estimated histogram of ground-state energies, and deduce the desired parameter on this basis. The approach provides an easily implementable method for the primary validation of Ising-based annealers' output. We demonstrate its behavior through experiments made with actual samples originating from quantum annealer devices.

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“…The upper bound should be large enough so that the equality is satisfied when k i=1 a i y i has the lowest possible. Further details can be found in [13].…”

Section: Converting Ilp To Qubomentioning

confidence: 99%

Music Composition Using Quantum Annealing

Arya¹,

Botelho²,

Cañete³

et al. 2022

Preprint

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With the emergence of quantum computers, a new field of algorithmic music composition has been initiated. The vast majority of previous work focuses on music generation using gate-based quantum computers. An alternative model of computation is adiabatic quantum computing (AQC), and a heuristic algorithm known as quantum annealing running in the framework of AQC is a promising method for solving optimization problems. In this chapter, we lay the groundwork of music composition using quantum annealing. We approach the process of music composition as an optimization problem. We describe the fundamental methodologies needed for generating different aspects of music including melody, rhythm, and harmony. The discussed techniques are illustrated through examples to ease the understanding. The music pieces generated using D-Wave quantum annealers are among the first examples of their kind and presented within the scope of the chapter. The text is an unedited pre-publication version of a chapter which will appear in the book "Quantum Computer Music", Miranda, E. R. (Editor).

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Unconstrained Binary Models of the Travelling Salesman Problem Variants for Quantum Optimization

Cited by 8 publications

References 30 publications

Error mitigation for variational quantum algorithms through mid-circuit measurements

Error mitigation for variational quantum algorithms through mid-circuit measurements

Statistical quality assessment of Ising-based annealer outputs

Music Composition Using Quantum Annealing

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