Graph comparison via nonlinear quantum search

Chiew, Mitchell; Lacy, K. de; Yu, Chao‐Hua; Marsh, Samuel; Wang, Jingbo

doi:10.1007/s11128-019-2407-2

Cited by 6 publications

(4 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We label this unitary to prepare the desired state |s〉 starting in the |0〉 state as G, as shown in Figure 3. A similar approach was used by Chiew et al [15] for preparing superpositions over set permutations. Let m Q log 2 MS be the number of qubits, and 2 m the dimension of the corresponding Hilbert space.…”

Section: B Quantum Circuitsmentioning

confidence: 99%

Quantum Walk-Based Vehicle Routing Optimisation

et al. 2021

Self Cite

View full text Add to dashboard Cite

This paper demonstrates the applicability of the Quantum Walk-based Optimisation Algorithm (QWOA) to the Capacitated Vehicle Routing Problem (CVRP). Efficient algorithms are developed for the indexing and unindexing of the solution space and for implementing the required alternating phase-walk unitaries, which are the core components of QWOA. Results of numerical simulation demonstrate that the QWOA is capable of producing convergence to near-optimal solutions for a randomly generated eight location CVRP. Preparation of the amplified quantum state in this example problem is demonstrated to produce higher-quality solutions than expected from classical random sampling of equivalent computational effort.

show abstract

Section: B Quantum Circuitsmentioning

confidence: 99%

Quantum Walk-Based Vehicle Routing Optimisation

et al. 2021

Self Cite

View full text Add to dashboard Cite

show abstract

“…Ebrahimi Kahou and Feder study this problem with coupled discrete nonlinear Schrödinger equations, and discuss the implementability of the model with BECs [74]. Meyer and Gong study quantum search with the Gross-Pitaevskii equation [75,76] concluding that it solves the unstructured search problem more efficiently than does the Schrödinger equation, because it includes a cubic nonlinearity, and Chiew et al [77] demonstrate that the nonlinear quantum search can be more efficient than quantum search for graph comparison. Di Molfetta and Herzog [78] generalize the Meyer-Gross algorithm to two dimensions finding a clear advantage over the linear QW.…”

Section: Nonlinear Dqwmentioning

confidence: 99%

Bright and dark solitons in a photonic nonlinear quantum walk: lessons from the continuum

Anglés-Castillo,

Pérez,

Roldán

2024

New J. Phys.

View full text Add to dashboard Cite

We propose a nonlinear quantum walk model inspired in a photonic implementation in which thepolarization state of the light field plays the role of the coin-qubit. In particular, we take profit of thenonlinear polarization rotation occurring in optical media with Kerr nonlinearity, which allows toimplement a nonlinear coin operator, one that depends on the state of the coin-qubit. We considerthe space-time continuum limit of the evolution equation, which takes the form of a nonlinear Diracequation. The analysis of this continuum limit allows us to gain some insight into the existenceof different solitonic structures, such as bright and dark solitons. We illustrate several propertiesof these solitons with numerical calculations, including the effect on them of an additional phasesimulating an external electric field.

show abstract

“…. , π n that requires O(n 2 log n) elementary gates [AL97;Chi+19]. Then, we can build a circuit with O(poly(n)) gates that takes as an input π ∈ S n , s ∈ {0, 1, .…”

Section: Quantum Algorithmmentioning

confidence: 99%

Quantum speedups for dynamic programming on $n$-dimensional lattice graphs

Glos,

Kokainis,

Mori

et al. 2021

Preprint

View full text Add to dashboard Cite

Motivated by the quantum speedup for dynamic programming on the Boolean hypercube by Ambainis et al. (2019), we investigate which graphs admit a similar quantum advantage. In this paper, we examine a generalization of the Boolean hypercube graph, the n-dimensional lattice graph Q(D, n) with vertices in {0, 1, . . . , D} n . We study the complexity of the following problem: given a subgraph G of Q(D, n) via query access to the edges, determine whether there is a path from 0 n to D n . While the classical query complexity is Θ((D + 1) n ), we show a quantum algorithm with complexity O(T n D ), where T D < D + 1. The first few values of T D are T 1 ≈ 1.817, T 2 ≈ 2.660, T 3 ≈ 3.529, T 4 ≈ 4.421, T 5 ≈ 5.332 (the D = 1 case corresponds to the hypercube and replicates the result of Ambainis et al.).We then show an implementation of this algorithm with time complexity poly(n) log n T n D , and apply it to the Set Multicover problem. In this problem, m subsets of [n] are given, and the task is to find the smallest number of these subsets that cover each element of [n] at least D times. While the time complexity of the best known classical algorithm is O(m(D + 1) n ), the time complexity of our quantum algorithm is poly(m, n) log n T n D .1 f (n) = O(g(n)) if f (n) = O(log c (g(n))g(n)) for some constant c.

show abstract

Graph comparison via nonlinear quantum search

Cited by 6 publications

References 29 publications

Quantum Walk-Based Vehicle Routing Optimisation

Quantum Walk-Based Vehicle Routing Optimisation

Bright and dark solitons in a photonic nonlinear quantum walk: lessons from the continuum

Quantum speedups for dynamic programming on $n$-dimensional lattice graphs

Contact Info

Product

Resources

About