arXiv subjects

J. B. Wang

Publications and source records attributed to J. B. Wang.

At least 55 records · Page 3Linked to original sources

arXiv2016

Efficient quantum circuits for Szegedy quantum walks

A major advantage in using Szegedy's formalism over discrete-time and continuous-time quantum walks lies in its ability to define a unitary quantum walk on directed and weighted graphs. In this paper, we present a general scheme to construct efficient quantum circuits for Szegedy quantum walks that correspond to classical Markov chains possessing transformational symmetry in the columns of the transition matrix. In particular, the transformational symmetry criteria do not necessarily depend on the sparsity of the transition matrix, so this scheme can be applied to non-sparse Markov chains. Two classes of Markov chains that are amenable to this construction are cyclic permutations and complete bipartite graphs, for which we provide explicit efficient quantum circuit implementations. We also prove that our scheme can be applied to Markov chains formed by a tensor product. We also briefly discuss the implementation of Markov chains based on weighted interdependent networks. In addition, we apply this scheme to construct efficient quantum circuits simulating the Szegedy walks used in the quantum Pagerank algorithm for some classes of non-trivial graphs, providing a necessary tool for experimental demonstration of the quantum Pagerank algorithm.

quant-ph↗

arXiv2016

Proper motions of 15 pulsars: a comparison between Bayesian and frequentist algorithms

We present proper motions for 15 pulsars which are observed regularly by the Nanshan 25-m radio telescope. Two methods, the frequentist method (Coles et al.2011) and the Bayesian (Lentati et al. 2014) method, are used and the results are compared. We demonstrate that the two methods can be applied to young pulsar data sets that exhibit large amounts of timing noise with steep spectral exponents and give consistent results. The measured positions also agree with very-long-baseline interferometric positions. Proper motions for four pulsars are obtained for the first time, and improved values are obtained for five pulsars.

astro-ph.IM↗

arXiv2016

Efficient quantum circuits for Toeplitz and Hankel matrices

Toeplitz and Hankel matrices have been a subject of intense interest in a wide range of science and engineering related applications. In this paper, we show that quantum circuits can efficiently implement sparse or Fourier-sparse Toeplitz and Hankel matrices. This provides an essential ingredient for solving many physical problems with Toeplitz or Hankel symmetry in the quantum setting with deterministic queries.

quant-ph↗

arXiv2016

Quantum Fourier Transform in Computational Basis

The conventional Quantum Fourier Transform, with exponential speedup compared to the classical Fast Fourier Transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, the Shor's factoring algorithm). However, situations arise where it is not sufficient to encode the Fourier coefficients within the quantum amplitudes, for example in the implementation of control operations that depend on Fourier coefficients. In this paper, we detail a new quantum algorithm to encode the Fourier coefficients in the computational basis, with success probability $1-δ$ and desired precision $ε$. Its time complexity %$\mathcal{O}\big((\log N)^2\log(N/δ)/ε)\big)$ depends polynomially on $\log(N)$, where $N$ is the problem size, and linearly on $\log(1/δ)$ and $1/ε$. We also discuss an application of potential practical importance, namely the simulation of circulant Hamiltonians.

quant-ph↗

arXiv2015

Structures of the Vela pulsar and the glitch crisis from the Brueckner theory

Detailed structures of the Vela pulsar (PSR B0833-45, with a period of $89.33$ milliseconds) are predicted by adopting a recently-constructed unified treatment of all parts of neutron stars: the outer crust, the inner crust and the core based on modern microscopic Brueckner-Hartree-Fock calculations. To take the pulsar mass ranging from $1.0M_{\odot}$ to $2.0M_{\odot}$, we calculate the central density, the core/crust radii, the core/crust mass, the core/crustal thickness, the moment of inertia, and the crustal moment of inertia. Among them, the crustal moment of inertia could be effectively constrained from the accumulated glitch observations, which has been a great debate recently, known as "glitch crisis". Namely, superfluid neutrons contained in the inner crust, which are regarded as the origin of the glitch in the standard two-component model, could be largely entrained in the nuclei lattices, then there may not be enough superfluid neutrons ($\sim 4/5$ less than the previous value) to trigger the large glitches ($Δν/ν_0 \sim 10^{-6}$) in the Vela pulsar. We then provide the first analysis of the crisis based on the microscopic basis, by confronting the glitch observations with the theoretical calculations for the crustal moment of inertia. We find that despite some recent opposition to the crisis argument, the glitch crisis is still present, which means that besides the crust superfluid neutrons, core neutrons might be necessary for explaining the large glitches of the Vela pulsar.

astro-ph.SR↗

arXiv2015

Comparing classical and quantum PageRanks

Following recent developments in quantum PageRanking, we present a comparative analysis of discrete-time and continuous-time quantum-walk-based PageRank algorithms. For the discrete-time case, we introduce an alternative PageRank measure based on the maximum probabilities achieved by the walker on the nodes. We demonstrate that the required time of evolution does not scale significantly with increasing network size. We affirm that all three quantum PageRank measures considered here distinguish clearly between outerplanar hierarchical, scale-free, and Erdös-Rényi network types. Relative to classical PageRank and to different extents, the quantum measures better highlight secondary hubs and resolve ranking degeneracy among peripheral nodes for the networks we studied in this paper.

physics.soc-ph↗

arXiv2015

Entanglement dynamics of two-particle quantum walks

This paper explores the entanglement dynamics generated by interacting two-particle quantum walks on degree-regular and -irregular graphs. We performed spectral analysis of the time-evolution of both the particle probability distribution and the entanglement between the two particles for various interaction strength. While the particle probability distributions are stable and not sensitive to perturbations in the interaction strength, the entanglement dynamics are found to be much more sensitive to system variations. This property may be utilised to probe small differences in the system parameters.

quant-ph↗

arXiv2015

Single-point position and transition defects in continuous time quantum walks

We present a detailed analysis of continuous time quantum walks (CTQW) with both position and transition defects defined at a single point in the line. Analytical solutions of both traveling waves or bound states are obtained, which provide valuable insight into the dynamics of CTQW. The number of bound states is found to be critically dependent on the defect parameters, and the localized probability peaks can be readily obtained by projecting the CTQW wavefunction on to these bound states. The interference between two bound states are also observed in the case of a transition defect. The spreading of CTQW probability over the line can be finely tuned by varying the position and transition defect parameters, offering the possibility of precision quantum control of the system.

quant-ph↗

arXiv2015

Pulsar Observations of Extreme Scattering Events

Extreme scattering events (ESEs) in the interstellar medium (ISM) were first observed in regular flux measurements of compact extragalactic sources. They are characterized by a flux variation over a period of weeks, suggesting the passage of a "diverging plasma lens" across the line of sight. Modeling the refraction of such a lens indicates that the structure size must be of order AU and the electron density of order 10s of cm^{-3}. Similar structures have been observed in measurements of pulsar intensity scintillation and group delay. Here we report observations of two ESEs showing increases in both intensity scintillation and dispersion made with the Parkes Pulsar Timing Array (PPTA). These allow us to make more complete models of the ESE, including an estimate of the "outer-scale" of the turbulence in the plasma lens. These observations show clearly that the ESE structure is fully turbulent on an AU scale. They provide some support for the idea that the structures are extended along the line of sight, such as would be the case for a scattering shell. The dispersion measurements also show a variety of AU scale structures which would not be called ESEs, yet involve electron density variations typical of ESEs and likely have the same origin.

astro-ph.SR↗

arXiv2014

Searching for gravitational wave memory bursts with the Parkes Pulsar Timing Array

Anisotropic bursts of gravitational radiation produced by events such as super-massive black hole mergers leave permanent imprints on space. Such gravitational wave "memory" (GWM) signals are, in principle, detectable through pulsar timing as sudden changes in the apparent pulse frequency of a pulsar. If an array of pulsars is monitored as a GWM signal passes over the Earth, the pulsars would simultaneously appear to change pulse frequency by an amount that varies with their sky position in a quadrupolar fashion. Here we describe a search algorithm for such events and apply the algorithm to approximately six years of data from the Parkes Pulsar Timing Array. We find no GWM events and set an upper bound on the rate for events which could have been detected. We show, using simple models of black hole coalescence rates, that this non-detection is not unexpected.

astro-ph.GA↗

arXiv2014

OptQC: An optimised parallel quantum compiler

The software package \emph{Qcompiler} (CPC, 184 (2013) 853) provides a general quantum compilation framework, which maps any given unitary operation into a quantum circuit consisting of a sequential set of elementary quantum gates. In this paper, we present an extended software \emph{OptQC}, which finds permutation matrices $P$ and $Q$ for a given unitary matrix $U$ such that the number of gates in the quantum circuit of $U = Q^TP^TU'PQ$ is significantly reduced, where $U'$ is equivalent to $U$ up to a permutation and the quantum circuit implementation of each matrix component is considered separately. We extend further this software package to make use of high-performance computers with a multiprocessor architecture using MPI. We demonstrate its effectiveness in reducing the total number of quantum gates required for various unitary operators.

quant-ph↗

arXiv2014

Complexity analysis of quantum walk based search algorithms

We present several families of graphs that allow both efficient quantum walk implementations and efficient quantum walk based search algorithms. For these graphs, we construct quantum circuits that explicitly implement the full quantum walk search algorithm, without reference to a `black box' oracle. These circuits provide a practically implementable method to explore quantum walk based search algorithms with the aim of eventual real-world applications. We also provide a numerical analysis of a quantum walk based search along a twisted toroid family of graphs, which requires O($\sqrt{n}$ log($n$)) elementary 2-qubit quantum gate operations to find a marked node.

quant-ph↗

arXiv2014

Fault-Tolerant Quantum Walks

Quantum walks are expected to serve important modelling and algorithmic applications in many areas of science and mathematics. Although quantum walks have been successfully implemented physically in recent times, no major efforts have been made to combat the error associated with these physical implementations in a fault-tolerant manner. In this paper, we propose a systematic method to implement fault-tolerant quantum walks in discrete time on arbitrarily complex graphs, using quantum states encoded with the Steane code and a set of universal fault tolerant matrix operations.

quant-ph↗

arXiv2012

Qcompiler: quantum compilation with CSD method

In this paper, we present a general quantum computation compiler, which maps any given quantum algorithm to a quantum circuit consisting a sequential set of elementary quantum logic gates based on recursive cosine-sine decomposition. The resulting quantum circuit diagram is provided by directly linking the package output written in LaTex to Qcircuit.tex $<$http://www.cquic.org/Qcircuit$>$. We illustrate the use of the Qcompiler package through various examples with full details of the derived quantum circuits. Besides its generality and simplicity, Qcompiler produces quantum circuits which reflect the symmetry of the systems under study.

quant-ph↗

arXiv2012

Invariant graphical method for electron-atom scattering coupled-channel equations

We present application examples of a graphical method for the efficient construction of potential matrix elements in quantum physics or quantum chemistry. The simplicity and power of this method are illustrated through several examples. In particular, a complete set of potential matrix elements for electron-Lithium scattering are derived for the first time using this method, which removes the frozen core approximation adopted by previous studies. This method can be readily adapted to study other many-body quantum systems.

quant-ph↗

arXiv2012

An efficient quantum circuit analyser on qubits and qudits

This paper presents a highly efficient decomposition scheme and its associated Mathematica notebook for the analysis of complicated quantum circuits comprised of single/multiple qubit and qudit quantum gates. In particular, this scheme reduces the evaluation of multiple unitary gate operations with many conditionals to just two matrix additions, regardless of the number of conditionals or gate dimensions. This improves significantly the capability of a quantum circuit analyser implemented in a classical computer. This is also the first efficient quantum circuit analyser to include qudit quantum logic gates.

quant-ph↗

arXiv2009

Quantum random walks without walking

Quantum random walks have received much interest due to their non-intuitive dynamics, which may hold the key to a new generation of quantum algorithms. What remains a major challenge is a physical realization that is experimentally viable and not limited to special connectivity criteria. We present a scheme for walking on arbitrarily complex graphs, which can be realized using a variety of quantum systems such as a BEC trapped inside an optical lattice. This scheme is particularly elegant since the walker is not required to physically step between the nodes; only flipping coins is sufficient.

quant-ph↗

arXiv2009

Efficient quantum circuit implementation of quantum walks

Quantum walks, being the quantum analogue of classical random walks, are expected to provide a fruitful source of quantum algorithms. A few such algorithms have already been developed, including the `glued trees' algorithm, which provides an exponential speedup over classical methods, relative to a particular quantum oracle. Here, we discuss the possibility of a quantum walk algorithm yielding such an exponential speedup over possible classical algorithms, without the use of an oracle. We provide examples of some highly symmetric graphs on which efficient quantum circuits implementing quantum walks can be constructed, and discuss potential applications to quantum search for marked vertices along these graphs.

quant-ph↗