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@article{PhysRevA.99.032113,

title = {Dirac quantum walks on triangular and honeycomb lattices},

author = {Gareth Jay and Fabrice Debbasch and J B Wang},

url = {https://link.aps.org/doi/10.1103/PhysRevA.99.032113},

doi = {10.1103/PhysRevA.99.032113},

year  = {2019},

date = {2019-03-01},

urldate = {2019-03-01},

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

volume = {99},

pages = {032113},

publisher = {American Physical Society},

abstract = {In this paper, we present a detailed study on discrete-time Dirac quantum walks (DQWs) on triangular and honeycomb lattices. At the continuous limit, these DQWs coincide with the Dirac equation. Their differences in the discrete regime are analyzed through the dispersion relations, with special emphasis on Zitterbewegung. An extension which couples these walks to arbitrary discrete electromagnetic field is also proposed and the resulting Bloch oscillations are discussed.

},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{PhysRevA.99.022301,

title = {Quantum algorithm for visual tracking},

author = {Chao-Hua Yu and Fei Gao and Chenghuan Liu and Du Huynh and Mark Reynolds and Jingbo Wang},

url = {https://link.aps.org/doi/10.1103/PhysRevA.99.022301},

doi = {10.1103/PhysRevA.99.022301},

year  = {2019},

date = {2019-02-01},

urldate = {2019-02-01},

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

volume = {99},

pages = {022301},

publisher = {American Physical Society},

abstract = {Visual tracking (VT) is the process of locating a moving object of interest in a video. It is a fundamental problem in computer vision, with various applications in human-computer interaction, security and surveillance, robot perception, traffic control, etc. In this paper, we address this problem for the first time in the quantum setting, and present a quantum algorithm for VT based on the framework proposed by Henriques et al. [IEEE Trans. Pattern Anal. Mach. Intell., 7, 583 (2015)]. Our algorithm comprises two phases: training and detection. In the training phase, in order to discriminate the object and background, the algorithm trains a ridge regression classifier in the quantum state form where the optimal fitting parameters of ridge regression are encoded in the amplitudes. In the detection phase, the classifier is then employed to generate a quantum state whose amplitudes encode the responses of all the candidate image patches. The algorithm is shown to be polylogarithmic in scaling, when the image data matrices have low condition numbers, and therefore may achieve exponential speedup over the best classical counterpart. However, only quadratic speedup can be achieved when the algorithm is applied to implement the ultimate task of Henriques's framework, i.e., detecting the object position. We also discuss two other important applications related to VT: (1) object disappearance detection and (2) motion behavior matching, where much more significant speedup over the classical methods can be achieved. This work demonstrates the power of quantum computing in solving computer vision problems.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Marsh2019,

title = {A quantum walk-assisted approximate algorithm for bounded NP optimisation problems},

author = {S Marsh and J B Wang},

url = {https://doi.org/10.1007/s11128-019-2171-3},

doi = {10.1007/s11128-019-2171-3},

issn = {1573-1332},

year  = {2019},

date = {2019-01-16},

urldate = {2019-01-16},

journal = {Quantum Information Processing (IF 2.349)},

volume = {18},

number = {3},

pages = {61},

abstract = {This paper describes an application of the quantum approximate optimisation algorithm (QAOA) to efficiently find approximate solutions for computational problems contained in the polynomially bounded NP optimisation complexity class (NPO PB). We consider a generalisation of the QAOA state evolution to alternating quantum walks and solution-quality-dependent phase shifts and use the quantum walks to integrate the problem constraints of NPO problems. We apply the concept of a hybrid quantum-classical variational scheme to attempt finding the highest expectation value, which contains a high-quality solution. We synthesise an efficient quantum circuit for the constrained optimisation algorithm, and we numerically demonstrate the behaviour of the circuit with respect to an illustrative NP optimisation problem with constraints, minimum vertex cover. With examples, this paper demonstrates that the degree of accuracy to which the quantum walks are simulated can be treated as an additional optimisation parameter, leading to improved results.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Qiang2018,

title = {Large-scale silicon quantum photonics implementing arbitrary two-qubit processing},

author = {Xiaogang Qiang and Xiaoqi Zhou and Jianwei Wang and Callum M Wilkes and Thomas Loke and Sean O'Gara and Laurent Kling and Graham D Marshall and Raffaele Santagati and Timothy C Ralph and Jingbo B Wang and Jeremy L O'Brien and Mark G Thompson and Jonathan C F Matthews},

url = {https://doi.org/10.1038/s41566-018-0236-y},

doi = {10.1038/s41566-018-0236-y},

issn = {1749-4893},

year  = {2018},

date = {2018-09-01},

urldate = {2018-09-01},

journal = {Nature Photonics (IF 38.770)},

volume = {12},

number = {9},

pages = {534-539},

abstract = {Photonics is a promising platform for implementing universal quantum information processing. Its main challenges include precise control of massive circuits of linear optical components and effective implementation of entangling operations on photons. By using large-scale silicon photonic circuits to implement an extension of the linear combination of quantum operators scheme, we realize a fully programmable two-qubit quantum processor, enabling universal two-qubit quantum information processing in optics. The quantum processor is fabricated with mature CMOS-compatible processing and comprises more than 200 photonic components. We programmed the device to implement 98 different two-qubit unitary operations (with an average quantum process fidelity of 93.2thinspacetextpmthinspace4.5%), a two-qubit quantum approximate optimization algorithm, and efficient simulation of Szegedy directed quantum walks. This fosters further use of the linear-combination architecture with silicon photonics for future photonic quantum processors.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{deLacy2018,

title = {Controlled quantum search},

author = {K de Lacy and L Noakes and J Twamley and J B Wang},

url = {https://doi.org/10.1007/s11128-018-2031-6},

doi = {10.1007/s11128-018-2031-6},

issn = {1573-1332},

year  = {2018},

date = {2018-08-28},

urldate = {2018-08-28},

journal = {Quantum Information Processing (IF 2.349)},

volume = {17},

number = {10},

pages = {266},

abstract = {Quantum searching for one of N marked items in an unsorted database of n items is solved in $$backslashmathcal O(backslashsqrtn/N)$$O(n/N)steps using Grover's algorithm. Using nonlinear quantum dynamics with a Gross--Pitaevskii-type quadratic nonlinearity, Childs and Young (Phys Rev A 93:022314, 2016, https://doi.org/10.1103/PhysRevA.93.022314) discovered an unstructured quantum search algorithm with a complexity $$backslashmathcal O( backslashmin backslash 1/g backslash, backslashlog (g n), backslashsqrtn backslash) $$O(min1/glog(gn),n), which can be used to find a marked item after $$o(backslashlog (n))$$o(log(n))repetitions, where g is the nonlinearity strength. In this work we develop an quantum search on a complete graph using a time-dependent nonlinearity which obtains one of the N marked items with certainty. The protocol has runtime $$backslashmathcal O(n /(g backslashsqrtN(n-N)))$$O(n/(gN(n-N))), where g is related to the time-dependent nonlinearity. We also extend the analysis to a quantum search on general symmetric graphs and can greatly simplify the resulting equations when the graph diameter is less than 4.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{PhysRevA.96.032305,

title = {Quantum centrality testing on directed graphs via PT-symmetric quantum walks},

author = {J A Izaac and J B Wang and P C Abbott and X S Ma},

url = {https://link.aps.org/doi/10.1103/PhysRevA.96.032305},

doi = {10.1103/PhysRevA.96.032305},

year  = {2017},

date = {2017-09-01},

urldate = {2017-09-01},

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

volume = {96},

pages = {032305},

publisher = {American Physical Society},

abstract = {Various quantum-walk based algorithms have been proposed to analyse and rank the centrality of graph vertices. However, issues arise when working with directed graphs --- the resulting non-Hermitian Hamiltonian leads to non-unitary dynamics, and the total probability of the quantum walker is no longer conserved. In this paper, we discuss a method for simulating directed graphs using PT-symmetric quantum walks, allowing probability conserving non-unitary evolution. This method is equivalent to mapping the directed graph to an undirected, yet weighted, complete graph over the same vertex set, and can be extended to cover interdependent networks of directed graphs. Previous work has shown centrality measures based on the CTQW provide an eigenvector-like quantum centrality; using the PT-symmetric framework, we extend these centrality algorithms to directed graphs with a significantly reduced Hilbert space compared to previous proposals. In certain cases, this centrality measure provides an advantage over classical algorithms used in network analysis, for example by breaking vertex rank degeneracy. Finally, we perform a statistical analysis over ensembles of random graphs, and show strong agreement with the classical PageRank measure on directed acyclic graphs.

},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{PhysRevE.96.032136,

title = {Systematic dimensionality reduction for continuous-time quantum walks of interacting fermions},

author = {J A Izaac and J B Wang},

url = {https://link.aps.org/doi/10.1103/PhysRevE.96.032136},

doi = {10.1103/PhysRevE.96.032136},

year  = {2017},

date = {2017-09-01},

urldate = {2017-09-01},

journal = {Physical Review E (IF 2.529)},

volume = {96},

pages = {032136},

publisher = {American Physical Society},

abstract = {To extend the continuous-time quantum walk (CTQW) to simulate P distinguishable particles on a graph G composed of N vertices, the Hamiltonian of the system is expanded to act on an NP -dimensional Hilbert space, in effect, simulating the multiparticle CTQW on graph G via a single-particle CTQW propagating on the Cartesian graph product GP . The properties of the Cartesian graph product have been well studied, and classical simulation of multiparticle CTQWs are common in the literature. However, the above approach is generally applied as is when simulating indistinguishable particles, with the particle statistics then applied to the propagated NP state vector to determine walker probabilities. We address the following question: How can we modify the underlying graph structure GP in order to simulate multiple interacting fermionic CTQWs with a reduction in the size of the state space? In this paper, we present an algorithm for systematically removing “redundant” and forbidden quantum states from consideration, which provides a significant reduction in the effective dimension of the Hilbert space of the fermionic CTQW. As a result, as the number of interacting fermions in the system increases, the classical computational resources required no longer increases exponentially for fixed N.

},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{PhysRevA.95.032318,

title = {Centrality measure based on continuous-time quantum walks and experimental realization},

author = {Josh A Izaac and Xiang Zhan and Zhihao Bian and Kunkun Wang and Jian Li and Jingbo B Wang and Peng Xue},

url = {https://link.aps.org/doi/10.1103/PhysRevA.95.032318},

doi = {10.1103/PhysRevA.95.032318},

year  = {2017},

date = {2017-03-01},

urldate = {2017-03-01},

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

volume = {95},

pages = {032318},

publisher = {American Physical Society},

abstract = {Network centrality has important implications well beyond its role in physical and information transport analysis; as such, various quantum walk-based algorithms have been proposed for measuring network vertex centrality. In this work, we propose a continuous-time quantum walk algorithm for determining vertex centrality, and show that it generalizes to arbitrary graphs via a statistical analysis of randomly generated scale-free and Erdős-Rényi networks. As a proof of concept, the algorithm is detailed on a 4-vertex star graph and physically implemented via linear optics, using spatial and polarization degrees of freedoms of single photons. This paper reports the first successful physical demonstration of a quantum centrality algorithm.

},

keywords = {},

pubstate = {published},

tppubtype = {article}

}