Author
Zak Webb
Bio: Zak Webb is an academic researcher from University of Waterloo. The author has contributed to research in topics: Classical XY model & Quantum walk. The author has an hindex of 6, co-authored 12 publications receiving 502 citations.
Papers
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TL;DR: The construction of a scalable quantum computer architecture based on multiple interacting quantum walkers could, in principle, be used as an architecture for building a scaled quantum computer with no need for time-dependent control.
Abstract: A quantum walk is a time-homogeneous quantum-mechanical process on a graph defined by analogy to classical random walk. The quantum walker is a particle that moves from a given vertex to adjacent vertices in quantum superposition. We consider a generalization to interacting systems with more than one walker, such as the Bose-Hubbard model and systems of fermions or distinguishable particles with nearest-neighbor interactions, and show that multiparticle quantum walk is capable of universal quantum computation. Our construction could, in principle, be used as an architecture for building a scalable quantum computer with no need for time-dependent control.
413 citations
TL;DR: This article showed that the Clifford group is a 3-design, showing that it is a better approximation to Haar-random unitaries than previously expected, and showed that it does not form a 4-design unless the dimension of the qudit is a power of 2.
Abstract: Unitary $k$-designs are finite ensembles of unitary matrices that approximate the Haar distribution over unitary matrices. Several ensembles are known to be 2-designs, including the uniform distribution over the Clifford group, but no family of ensembles was previously known to form a 3-design. We prove that the Clifford group is a 3-design, showing that it is a better approximation to Haar-random unitaries than previously expected. Our proof strategy works for any distribution of unitaries satisfying a property we call Pauli 2-mixing and proceeds without the use of heavy mathematical machinery. We also show that the Clifford group does not form a 4-design, thus characterizing how well random Clifford elements approximate Haar-random unitaries. Additionally, we show that the generalized Clifford group for qudits is not a 3-design unless the dimension of the qudit is a power of 2.
85 citations
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TL;DR: It is proved that the Clifford group is a 3-design, showing that it is a better approximation to Haar-random unitaries than previously expected and characterizing how well random Clifford elements approximateHaar- random unitaries.
Abstract: Unitary $k$-designs are finite ensembles of unitary matrices that approximate the Haar distribution over unitary matrices. Several ensembles are known to be 2-designs, including the uniform distribution over the Clifford group, but no family of ensembles was previously known to form a 3-design. We prove that the Clifford group is a 3-design, showing that it is a better approximation to Haar-random unitaries than previously expected. Our proof strategy works for any distribution of unitaries satisfying a property we call Pauli 2-mixing and proceeds without the use of heavy mathematical machinery. We also show that the Clifford group does not form a 4-design, thus characterizing how well random Clifford elements approximate Haar-random unitaries. Additionally, we show that the generalized Clifford group for qudits is not a 3-design unless the dimension of the qudit is a power of 2.
55 citations
TL;DR: A short working distance (SWD) multicrystal x-ray spectrometer is constructed and tested in good agreement with prior work for measurements of the Mn Kbeta x- Ray emission and resonant inelastic x-Ray scattering for MnO, and also for measurement of the x-rays absorption near-edge structure for Dy metal using Lalpha(2) partial-fluorescence yield detection.
Abstract: For x-ray spot sizes of a few tens of microns or smaller, a millimeter-sized flat analyzer crystal placed ∼1 cm from the sample will exhibit high energy resolution while subtending a collection solid angle comparable to that of a typical spherically bent crystal analyzer (SBCA) at much larger working distances. Based on this observation and a nonfocusing geometry for the analyzer optic, we have constructed and tested a short working distance (SWD) multicrystal x-ray spectrometer. This prototype instrument has a maximum effective collection solid angle of 0.14 sr, comparable to that of 17 SBCA at 1 m working distance. We find good agreement with prior work for measurements of the Mn Kβ x-ray emission and resonant inelastic x-ray scattering for MnO, and also for measurements of the x-ray absorption near-edge structure for Dy metal using Lα2 partial-fluorescence yield detection. We discuss future applications at third- and fourth-generation light sources. For concentrated samples, the extremely large collect...
33 citations
08 Jul 2014
TL;DR: This work proves that approximating the ground energy of the Bose-Hubbard model on a graph at fixed particle number is QMA-complete, and obtains a related result for a class of 2-local Hamiltonians defined by graphs that generalizes the XY model.
Abstract: The Bose-Hubbard model is a system of interacting bosons that live on the vertices of a graph. The particles can move between adjacent vertices and experience a repulsive on-site interaction. The Hamiltonian is determined by a choice of graph that specifies the geometry in which the particles move and interact. We prove that approximating the ground energy of the Bose-Hubbard model on a graph at fixed particle number is QMA-complete. In our QMA-hardness proof, we encode the history of an n-qubit computation in the subspace with at most one particle per site (i.e., hard-core bosons). This feature, along with the well-known mapping between hard-core bosons and spin systems, lets us prove a related result for a class of 2-local Hamiltonians defined by graphs that generalizes the XY model. By avoiding the use of perturbation theory in our analysis, we circumvent the need to multiply terms in the Hamiltonian by large coefficients.
31 citations
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TL;DR: In this paper, the equivalence of the adiabatic and circuit models of quantum computation has been proved, and the placement of quantum computations in the more general classification of computational complexity theory is discussed.
Abstract: The simple act of slowly varying the parameters of a quantum system so that it remains always in its ground state is extremely rich from an information processing point of view. For an ideal, closed system, this adiabatic evolution is equivalent to full quantum computation, and it is convenient for establishing quantum algorithms for optimization. This review presents adiabatic quantum algorithms, proves the closed-system equivalence of the adiabatic and circuit models of quantum computation, reviews the placement of adiabatic quantum computation in the more general classification of computational complexity theory, and discusses the case of ``stoquastic'' quantum evolutions.
800 citations
TL;DR: It is argued that physical intuition can lead to optimal simulation methods by showing that a focus on simple single-qubit rotations elegantly furnishes an optimal algorithm for Hamiltonian simulation, a universal problem that encapsulates all the power of quantum computation.
Abstract: The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly simulation of physical systems. Surprisingly, this has been challenging, with current Hamiltonian simulation algorithms remaining abstract and often the result of sophisticated but unintuitive constructions. We contend that physical intuition can lead to optimal simulation methods by showing that a focus on simple single-qubit rotations elegantly furnishes an optimal algorithm for Hamiltonian simulation, a universal problem that encapsulates all the power of quantum computation. Specifically, we show that the query complexity of implementing time evolution by a d-sparse Hamiltonian H[over ^] for time-interval t with error e is O[td∥H[over ^]∥_{max}+log(1/e)/loglog(1/e)], which matches lower bounds in all parameters. This connection is made through general three-step "quantum signal processing" methodology, comprised of (i) transducing eigenvalues of H[over ^] into a single ancilla qubit, (ii) transforming these eigenvalues through an optimal-length sequence of single-qubit rotations, and (iii) projecting this ancilla with near unity success probability.
543 citations
TL;DR: In this article, spontaneous parity and topological edge states are observed in a photonic non-Hermitian system with a quantum walk interferometer, where topological parity is achieved by time symmetry breaking.
Abstract: Spontaneous parity–time-symmetry breaking and topological edge states are observed in a photonic non-Hermitian system — a quantum walk interferometer.
511 citations
TL;DR: Using interacting bosonic atoms in an optical lattice, this work directly observed fundamental effects such as the emergence of correlations in two-particle quantum walks, as well as strongly correlated Bloch oscillations in tilted optical lattices.
Abstract: Full control over the dynamics of interacting, indistinguishable quantum particles is an important prerequisite for the experimental study of strongly correlated quantum matter and the implementation of high-fidelity quantum information processing. We demonstrate such control over the quantum walk-the quantum mechanical analog of the classical random walk-in the regime where dynamics are dominated by interparticle interactions. Using interacting bosonic atoms in an optical lattice, we directly observed fundamental effects such as the emergence of correlations in two-particle quantum walks, as well as strongly correlated Bloch oscillations in tilted optical lattices. Our approach can be scaled to larger systems, greatly extending the class of problems accessible via quantum walks.
403 citations
TL;DR: In this article, a fully programmable two-qubit quantum processor is presented, which enables universal quantum information processing in optics, using large-scale silicon photonic circuits to implement an extension of the linear combination of quantum operators scheme.
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 93.2 ± 4.5%), 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.
403 citations