129,865 research outputs found
Simulation of Quantum Search Algorithm
The rapid progress of computer science has been accompanied by a corresponding evolution of computation, from classical computation to quantum computation. As quantum computing is on its way to becoming an established discipline of computing science, much effort is being put into the development of new quantum algorithms. One of quantum algorithms is Grover\u27s algorithm, which is used for searching an element in an unstructured list of N elements with quadratic speed-up over classical algorithms. In this work, Quantum Computer Language (QCL) is used to make a Grover\u27s quantum search simulation in a classical computer document
Deterministic constant-temperature dynamics for dissipative quantum systems
A novel method is introduced in order to treat the dissipative dynamics of
quantum systems interacting with a bath of classical degrees of freedom. The
method is based upon an extension of the Nos\`e-Hoover chain (constant
temperature) dynamics to quantum-classical systems. Both adiabatic and
nonadiabatic numerical calculations on the relaxation dynamics of the
spin-boson model show that the quantum-classical Nos\`e-Hoover chain dynamics
represents the thermal noise of the bath in an accurate and simple way.
Numerical comparisons, both with the constant energy calculation and with the
quantum-classical Brownian motion treatment of the bath, show that the
quantum-classical Nos\`e-Hoover Chain dynamics can be used to introduce
dissipation in the evolution of a quantum subsystem even with just one degree
of freedom for the bath. The algorithm can be computationally advantageous in
modeling, within computer simulation, the dynamics of a quantum subsystem
interacting with complex molecular environments.Comment: Revised versio
Using the qubus for quantum computing
In this thesis I explore using the qubus for quantum computing. The qubus is an architecture of quantum computing, where a continuous variable ancilla is used to generate operations between matter qubits. I concentrate on using the qubus for two purposes - quantum simulation, and
generating cluster states.
Quantum simulation is the idea of using a quantum computer to simulate a quantum system. I focus on conducting a simulation of the BCS Hamiltonian. I demonstrate how to perform the necessary two qubit operations in a controlled fashion using the qubus. In particular I demonstrate an O(N3) saving over an implementation on an NMR computer, and a factor of 2 saving over a naıve technique. I also discuss how to perform the quantum Fourier transform on the qubus quantum computer. I show that it is possible to perform the quantum Fourier transform using just, 24âN/2â + 7N â 6, this is an O(N) saving over a naıve method.
In the second part of the thesis, I move on, and consider generating cluster states using the qubus. A cluster state, is a universal resource for one-way or measurement-based computation. In one-way computation, the pre-generated, entangled resource is used to perform calculations, which only require local corrections and measurement. I demonstrate that the qubus can generate cluster states deterministically, and in a relatively short time. I discuss several techniques of cluster state generation, one of which is optimal, given the physical architecture we are using. This can generate an n Ă m cluster in only 3nm â 2n â 2m + 4 operations. The alternative techniques look at generating a cluster using layers or columns, allowing it to be built dynamically, while the cluster is used to perform calculations. I then move on, and discuss problems with error accumulation in the generation process
3+1 Dimension Schwinger Pair Production with Quantum Computers
Real-time quantum simulation of quantum field theory in (3+1)D requires large
quantum computing resources. With a few-qubit quantum computer, we develop a
novel algorithm and experimentally study the Schwinger effect, the
electron-positron pair production in a strong electric field, in (3+1)D. The
resource reduction is achieved by treating the electric field as a background
field, working in Fourier space transverse to the electric field direction, and
considering parity symmetry, such that we successfully map the three spatial
dimension problems into one spatial dimension problems. We observe that the
rate of pair production of electrons and positrons is consistent with the
theoretical predication of the Schwinger effect. Our work paves the way towards
exploring quantum simulation of quantum field theory beyond one spatial
dimension.Comment: 7 pages, 2 figures, 7 pages supplemental, 1 figure supplementa
Qdensity - a Mathematica Quantum Computer Simulation
This Mathematica 5.2 package~\footnote{QDENSITY is available at
http://www.pitt.edu/~tabakin/QDENSITY} is a simulation of a Quantum Computer.
The program provides a modular, instructive approach for generating the basic
elements that make up a quantum circuit. The main emphasis is on using the
density matrix, although an approach using state vectors is also implemented in
the package. The package commands are defined in {\it Qdensity.m} which
contains the tools needed in quantum circuits, e.g. multiqubit kets,
projectors, gates, etc. Selected examples of the basic commands are presented
here and a tutorial notebook, {\it Tutorial.nb} is provided with the package
(available on our website) that serves as a full guide to the package. Finally,
application is made to a variety of relevant cases, including Teleportation,
Quantum Fourier transform, Grover's search and Shor's algorithm, in separate
notebooks: {\it QFT.nb}, {\it Teleportation.nb}, {\it Grover.nb} and {\it
Shor.nb} where each algorithm is explained in detail. Finally, two examples of
the construction and manipulation of cluster states, which are part of ``one
way computing" ideas, are included as an additional tool in the notebook {\it
Cluster.nb}. A Mathematica palette containing most commands in QDENSITY is also
included: {\it QDENSpalette.nb} .Comment: The Mathematica 5+ package is available at:
http://www.pitt.edu/~tabakin/QDENSITY/QDENSITY.htm Minor corrections,
accepted in Computer Physics Communication
Variational quantum simulation of the quantum critical regime
The quantum critical regime marks a zone in the phase diagram where quantum
fluctuation around the critical point plays a significant role at finite
temperatures. While it is of great physical interest, simulation of the quantum
critical regime can be difficult on a classical computer due to its intrinsic
complexity. In this paper, we propose a variational approach, which minimizes
the variational free energy, to simulate and locate the quantum critical regime
on a quantum computer. The variational quantum algorithm adopts an ansatz by
performing an unitary operator on a product of a single-qubit mixed state, in
which the entropy can be analytically obtained from the initial state, and thus
the free energy can be accessed conveniently. With numeral simulation, we show,
using the one-dimensional Kitaev model as a demonstration, the quantum critical
regime can be identified by accurately evaluating the temperature crossover
line. Moreover, the dependence of both the correlation length and the phase
coherence time with the temperature are evaluated for the thermal states. Our
work suggests a practical way as well as a first step for investigating quantum
critical systems at finite temperatures on quantum devices with few qubits
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