93 citations · 870 across the 38 of their papers we have counts for
38 papers
Implementing Quantum Gates Using Length-3 Dynamic Quantum Walks
Ibukunoluwa A. Adisa, Thomas G. Wong
It is well-known that any quantum gate can be decomposed into the universal gate set {T, H, CNOT}, and recent results have shown that each of these gates can be implemented using a…
Search by Lackadaisical Quantum Walk with Symmetry Breaking
Jacob Rapoza, Thomas G. Wong
The lackadaisical quantum walk is a lazy version of a discrete-time, coined quantum walk, where each vertex has a weighted self-loop that permits the walker to stay put. They have…
Equivalent Laplacian and Adjacency Quantum Walks on Irregular Graphs
Thomas G. Wong, Joshua Lockhart
The continuous-time quantum walk is a particle evolving by Schrödinger's equation in discrete space. Encoding the space as a graph of vertices and edges, the Hamiltonian is proport…
Simplifying Continuous-Time Quantum Walks on Dynamic Graphs
Rebekah Herrman, Thomas G. Wong
A continuous-time quantum walk on a dynamic graph evolves by Schrödinger's equation with a sequence of Hamiltonians encoding the edges of the graph. This process is universal for q…
Unstructured Search by Random and Quantum Walk
Thomas G. Wong
The task of finding an entry in an unsorted list of elements famously takes queries to an oracle for a classical computer and queries for a quantum compute…
Search on Vertex-Transitive Graphs by Lackadaisical Quantum Walk
Mason L. Rhodes, Thomas G. Wong
The lackadaisical quantum walk is a discrete-time, coined quantum walk on a graph with a weighted self-loop at each vertex. It uses a generalized Grover coin and the flip-flop shif…
Isolated Vertices in Continuous-Time Quantum Walks on Dynamic Graphs
Thomas G. Wong
It was recently shown that continuous-time quantum walks on dynamic graphs, i.e., sequences of static graphs whose edges change at specific times, can implement a universal set of…
Search by Lackadaisical Quantum Walk with Nonhomogeneous Weights
Mason L. Rhodes, Thomas G. Wong
The lackadaisical quantum walk, which is a quantum walk with a weighted self-loop at each vertex, has been shown to speed up dispersion on the line and improve spatial search on th…
Quantum Walk Search on the Complete Bipartite Graph
Mason L. Rhodes, Thomas G. Wong
The coined quantum walk is a discretization of the Dirac equation of relativistic quantum mechanics, and it is the basis of many quantum algorithms. We investigate how it searches…
Optimal Quantum Walk Search on Kronecker Graphs with Dominant or Fixed Regular Initiators
Adam Glos, Thomas G. Wong
In network science, graphs obtained by taking the Kronecker or tensor power of the adjacency matrix of an initiator graph are used to construct complex networks. In this paper, we…
Quantum Walk Search on Kronecker Graphs
Thomas G. Wong, Konstantin Wünscher, Joshua Lockhart +1
Kronecker graphs, obtained by repeatedly performing the Kronecker product of the adjacency matrix of an "initiator" graph with itself, have risen in popularity in network science d…
Faster Search by Lackadaisical Quantum Walk
Thomas G. Wong
In the typical model, a discrete-time coined quantum walk searching the 2D grid for a marked vertex achieves a success probability of in steps, w…
Coined Quantum Walks on Weighted Graphs
Thomas G. Wong
We define a discrete-time, coined quantum walk on weighted graphs that is inspired by Szegedy's quantum walk. Using this, we prove that many lackadaisical quantum walks, where each…
Equivalence of Szegedy's and Coined Quantum Walks
Thomas G. Wong
Szegedy's quantum walk is a quantization of a classical random walk or Markov chain, where the walk occurs on the edges of the bipartite double cover of the original graph. To sear…
Exceptional Quantum Walk Search on the Cycle
Thomas G. Wong, Raqueline A. M. Santos
Quantum walks are standard tools for searching graphs for marked vertices, and they often yield quadratic speedups over a classical random walk's hitting time. In some exceptional…
Stationary States in Quantum Walk Search
Krišjānis Prūsis, Jevgēnijs Vihrovs, Thomas G. Wong
When classically searching a database, having additional correct answers makes the search easier. For a discrete-time quantum walk searching a graph for a marked vertex, however, a…
Full Characterization of Oscillatory Localization of Quantum Walks
Andris Ambainis, Krišjānis Prūsis, Jevgēnijs Vihrovs +1
Discrete-time quantum walks are well-known for exhibiting localization, a quantum phenomenon where the walker remains at its initial location with high probability. In companion wi…
Oscillatory Localization of Quantum Walks Analyzed by Classical Electric Circuits
Andris Ambainis, Krišjānis Prūsis, Jevgēnijs Vihrovs +1
We examine an unexplored quantum phenomenon we call oscillatory localization, where a discrete-time quantum walk with Grover's diffusion coin jumps back and forth between two verti…
Engineering the Success of Quantum Walk Search Using Weighted Graphs
Thomas G. Wong, Pascal Philipp
Continuous-time quantum walks are natural tools for spatial search, where one searches for a marked vertex in a graph. Sometimes, the structure of the graph causes the walker to ge…
Irreconcilable Difference Between Quantum Walks and Adiabatic Quantum Computing
Thomas G. Wong, David A. Meyer
Continuous-time quantum walks and adiabatic quantum evolution are two general techniques for quantum computing, both of which are described by Hamiltonians that govern their evolut…
Quantum Walk Search on Johnson Graphs
Thomas G. Wong
The Johnson graph is defined by symbols, where vertices are -element subsets of the symbols, and vertices are adjacent if they differ in exactly one symbol. In part…
Laplacian versus Adjacency Matrix in Quantum Walk Search
Thomas G. Wong, Luís Tarrataca, Nikolay Nahimov
A quantum particle evolving by Schrödinger's equation contains, from the kinetic energy of the particle, a term in its Hamiltonian proportional to Laplace's operator. In discrete s…
Doubling the Success of Quantum Walk Search Using Internal-State Measurements
Krišjānis Prūsis, Jevgēnijs Vihrovs, Thomas G. Wong
In typical discrete-time quantum walk algorithms, one measures the position of the walker while ignoring its internal spin/coin state. Rather than neglecting the information in thi…
Quantum Walk on the Line through Potential Barriers
Thomas G. Wong
Quantum walks are well-known for their ballistic dispersion, traveling away in steps, which is quadratically faster than a classical random walk's diffusive spreading. I…