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@article{nokey,

title = {QuOp_MPI: A framework for parallel simulation of quantum variational algorithms},

author = {Edric Matwiejew and Jingbo Wang },

year  = {2022},

date = {2022-06-08},

urldate = {2022-06-08},

journal = {Journal of Computational Science (IF 3.817)},

volume = {62},

pages = {101711},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{nokey,

title = {Quantum Walk-Based Vehicle Routing Optimisation},

author = {T. Bennett and E. Matwiejew and S. Marsh and J. B. Wang},

url = {https://www.frontiersin.org/articles/10.3389/fphy.2021.730856/full?utm_source=dlvr.it&utm_medium=twitter},

doi = {10.3389/fphy.2021.730856},

year  = {2021},

date = {2021-12-20},

urldate = {2021-12-20},

journal = {Frontiers in Physics (IF 3.563)},

volume = {9},

pages = {730856},

abstract = {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 un-indexing 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 a classical random sampling of equivalent computational effort.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Marsh_2021,

title = {A framework for optimal quantum spatial search using alternating phase-walks},

author = {Samuel Marsh and Jingbo Wang},

url = {https://iopscience.iop.org/article/10.1088/2058-9565/ac26af},

doi = {10.1088/2058-9565/ac26af},

year  = {2021},

date = {2021-09-28},

urldate = {2021-09-28},

journal = {Quantum Science and Technology (IF 6.568)},

volume = {6},

number = {4},

pages = {045029},

publisher = {IOP Publishing},

abstract = {We present a novel methodological framework for quantum spatial search, generalising the Childs & Goldstone () algorithm via alternating applications of marked-vertex phase shifts and continuous-time quantum walks. We determine closed form expressions for the optimal walk time and phase shift parameters for periodic graphs. These parameters are chosen to rotate the system about subsets of the graph Laplacian eigenstates, amplifying the probability of measuring the marked vertex. The state evolution is asymptotically optimal for any class of periodic graphs having a fixed number of unique eigenvalues. We demonstrate the effectiveness of the algorithm by applying it to obtain search on a variety of graphs. One important class is the n × n 3 rook graph, which has N = n 4 vertices. On this class of graphs the algorithm performs suboptimally, achieving only overlap after time . Using the new alternating phase-walk framework, we show that overlap is obtained in phase-walk iterations.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{PhysRevA.104.022216,

title = {Deterministic spatial search using alternating quantum walks},

author = {S. Marsh and J. B. Wang},

url = {https://link.aps.org/doi/10.1103/PhysRevA.104.022216},

doi = {10.1103/PhysRevA.104.022216},

year  = {2021},

date = {2021-08-24},

urldate = {2021-08-24},

journal = {Physical Review A (IF 3.140)},

volume = {104},

pages = {022216},

publisher = {American Physical Society},

abstract = {This paper examines the performance of spatial search where the Grover diffusion operator is replaced by continuous-time quantum walks on a class of interdependent networks. We prove that, for a set of optimal quantum walk times and marked vertex phase shifts, a deterministic algorithm for structured spatial search is established that finds the marked vertex with 100% probability. This improves on the Childs and Goldstone spatial search algorithm on the same class of graphs, which we show can only amplify to 50% probability. Our method uses ⌈(π/2√2)√N⌉ marked vertex phase shifts for an N-vertex graph, making it comparable to Grover's algorithm for an unstructured search. It is expected that this framework can be readily extended to deterministic spatial search on other families of graph structures.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Khalique_2021,

title = {Controlled information transfer in continuous-time chiral quantum walks},

author = {A Khalique and A Sett and J B Wang and J Twamley},

url = {https://doi.org/10.1088/1367-2630/ac1551},

doi = {10.1088/1367-2630/ac1551},

year  = {2021},

date = {2021-08-01},

urldate = {2021-08-01},

journal = {New Journal of Physics (IF 3.740)},

volume = {23},

number = {8},

pages = {083005},

publisher = {IOP Publishing},

abstract = {In this paper we investigate properties of continuous time chiral quantum walks, which possess complex valued edge weights in the underlying graph structure, together with an initial Gaussian wavefunction spread over a number of vertices. We demonstrate that, for certain graph topology and phase matching conditions, we are able to direct the flow of probability amplitudes in a specific direction inside the graph network. We design a quantum walk graph analogue of an optical circulator which is a combination of a cycle and semi-infinite chain graphs. Excitations input into the circulator from a semi-infinite chain are routed in a directionally biased fashion to output to a different semi-infinite chain. We examine in detail a two port circulator graph which spatially separates excitations flowing back in forth between the two semi-finite chains to directionally occupy the top or bottom half of the cycle portion of the circulator. This setup can be used, for example, to detect non-Markovian processes, which leads to information and energy back-flow from the bath back into the system.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Qiang2021,

title = {Implementing graph-theoretic quantum algorithms on a silicon photonic quantum walk processor},

author = {X. Qiang and Y. Wang and Y. Xue and R. Ge and L. Chen and Y. Liu and A. Huang and X. Fu and P. Xu and T. Yi and F. Xu and M. Deng and J. Wang and J. Meinecke and J. Matthews and X. Cai and X. Yang and J. Wu},

url = {https://advances.sciencemag.org/content/7/9/eabb8375},

doi = {10.1126/sciadv.abb8375},

year  = {2021},

date = {2021-02-26},

urldate = {2021-02-26},

journal = {Science Advances (IF 14.140)},

volume = {7},

pages = {eabb8375},

abstract = {Applications of quantum walks can depend on the number, exchange symmetry and indistinguishability of the particles involved, and the underlying graph structures where they move. Here, we show that silicon photonics, by exploiting an entanglement-driven scheme, can realize quantum walks with full control over all these properties in one device. The device we realize implements entangled two-photon quantum walks on any five-vertex graph, with continuously tunable particle exchange symmetry and indistinguishability. We show how this simulates single-particle walks on larger graphs, with size and geometry controlled by tuning the properties of the composite quantum walkers. We apply the device to quantum walk algorithms for searching vertices in graphs and testing for graph isomorphisms. In doing so, we implement up to 100 sampled time steps of quantum walk evolution on each of 292 different graphs. This opens the way to large-scale, programmable quantum walk processors for classically intractable applications.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{MATWIEJEW2021107724,

title = {QSW_MPI: A framework for parallel simulation of quantum stochastic walks},

author = {Edric Matwiejew and Jingbo Wang},

url = {http://www.sciencedirect.com/science/article/pii/S0010465520303581},

doi = {https://doi.org/10.1016/j.cpc.2020.107724},

issn = {0010-4655},

year  = {2021},

date = {2021-01-01},

urldate = {2021-01-01},

journal = {Computer Physics Communications (IF 4.390)},

volume = {260},

pages = {107724},

abstract = {QSW_MPI is a Python package developed for time-series simulation of continuous-time quantum stochastic walks. This model allows for the study of Markovian open quantum systems in the Lindblad formalism, including a generalisation of the continuous-time random walk and continuous-time quantum walk. Consisting of a Python interface accessing parallelised Fortran libraries utilising sparse data structures, QSW_MPI is scalable to massively parallel computers, which makes possible the simulation of a wide range of walk dynamics on directed and undirected graphs of arbitrary complexity. },

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Slate2021quantumwalkbased,

title = {Quantum walk-based portfolio optimisation},

author = {N Slate and E Matwiejew and S Marsh and J B Wang},

url = {https://doi.org/10.22331/q-2021-07-28-513},

doi = {10.22331/q-2021-07-28-513},

issn = {2521-327X},

year  = {2021},

date = {2021-01-01},

urldate = {2021-01-01},

journal = {Quantum (IF 6.777)},

volume = {5},

pages = {513},

publisher = {Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften},

abstract = {This paper proposes a highly efficient quantum algorithm for portfolio optimisation targeted at near-term noisy intermediate-scale quantum computers. Recent work by Hodson et al. (2019) explored potential application of hybrid quantum-classical algorithms to the problem of financial portfolio rebalancing. In particular, they deal with the portfolio optimisation problem using the Quantum Approximate Optimisation Algorithm and the Quantum Alternating Operator Ansatz. In this paper, we demonstrate substantially better performance using a newly developed Quantum Walk Optimisation Algorithm in finding high-quality solutions to the portfolio optimisation problem.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{PhysRevLett.125.240501,

title = {Experimental Parity-Time Symmetric Quantum Walks for Centrality Ranking on Directed Graphs},

author = {Tong Wu and J A Izaac and Zi-Xi Li and Kai Wang and Zhao-Zhong Chen and Shining Zhu and J B Wang and Xiao-Song Ma},

url = {https://link.aps.org/doi/10.1103/PhysRevLett.125.240501},

doi = {10.1103/PhysRevLett.125.240501},

year  = {2020},

date = {2020-12-01},

urldate = {2020-12-01},

journal = {Physical Review Letters (IF 9.161)},

volume = {125},

pages = {240501},

publisher = {American Physical Society},

abstract = {Quantum walks (QW) are of crucial importance in the development of quantum information processing algorithms. Recently, several quantum algorithms have been proposed to implement network analysis, in particular to rank the centrality of nodes in networks represented by graphs. Employing QW in centrality ranking is advantageous comparing to certain widely used classical algorithms (e.g. PageRank) because QW approach can lift the vertex rank degeneracy in certain graphs. However, it is challenging to implement a directed graph via QW, since it corresponds to a non-Hermitian Hamiltonian and thus cannot be accomplished by conventional QW. Here we report the realizations of centrality rankings of both a three-vertex and four-vertex directed graphs with parity-time (PT) symmetric quantum walks. To achieve this, we use high-dimensional photonic quantum states, optical circuitries consisting of multiple concatenated interferometers and dimension dependent loss. Importantly, we demonstrate the advantage of QW approach experimentally by breaking the vertex rank degeneracy in a four-vertex graph. Our work shows that PT-symmetric quantum walks may be useful for realizing advanced algorithm in a quantum network.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}