9,298 research outputs found
Programmable networks for quantum algorithms
The implementation of a quantum computer requires the realization of a large
number of N-qubit unitary operations which represent the possible oracles or
which are part of the quantum algorithm. Until now there are no standard ways
to uniformly generate whole classes of N-qubit gates. We have developed a
method to generate arbitrary controlled phase shift operations with a single
network of one-qubit and two-qubit operations. This kind of network can be
adapted to various physical implementations of quantum computing and is
suitable to realize the Deutsch-Jozsa algorithm as well as Grover's search
algorithm.Comment: 4 pages. Accepted version; Journal-ref. adde
Adiabatic Quantum Computation and Deutsch's Algorithm
We show that by a suitable choice of a time dependent Hamiltonian, Deutsch's
algorithm can be implemented by an adiabatic quantum computer. We extend our
analysis to the Deutsch-Jozsa problem and estimate the required running time
for both global and local adiabatic evolutions.Comment: 6 Pages, Revtex. Typos corrected, references added. Published versio
Logic programming as quantum measurement
The emphasis is made on the juxtaposition of (quantum~theorem) proving versus
quantum (theorem~proving). The logical contents of verification of the
statements concerning quantum systems is outlined. The Zittereingang (trembling
input) principle is introduced to enhance the resolution of predicate
satisfiability problem provided the processor is in a position to perform
operations with continuous input. A realization of Zittereingang machine by a
quantum system is suggested.Comment: 11 pages, latex, paper accepted for publication in the International
Journal of Theoretical Physic
Entangled Mixed States and Local Purification
Linden, Massar and Popescu have recently given an optimization argument to
show that a single two-qubit Werner state, or any other mixture of the
maximally entangled Bell states, cannot be purified by local operations and
classical communications. We generalise their result and give a simple
explanation. In particular, we show that no purification scheme using local
operations and classical communications can produce a pure singlet from any
mixed state of two spin-1/2 particles. More generally, no such scheme can
produce a maximally entangled state of any pair of finite-dimensional systems
from a generic mixed state. We also show that the Werner states belong to a
large class of states whose fidelity cannot be increased by such a scheme.Comment: 3 pages, Latex with Revtex. Small clarifications and reference adde
On Halting Process of Quantum Turing Machine
We prove that there is no algorithm to tell whether an arbitrarily
constructed Quantum Turing Machine has same time steps for different branches
of computation. We, hence, can not avoid the notion of halting to be
probabilistic in Quantum Turing Machine. Our result suggests that halting
scheme of Quantum Turing Machine and quantum complexity theory based upon the
existing halting scheme sholud be reexamined.Comment: 2 page
Quantum Analogue Computing
We briefly review what a quantum computer is, what it promises to do for us,
and why it is so hard to build one. Among the first applications anticipated to
bear fruit is quantum simulation of quantum systems. While most quantum
computation is an extension of classical digital computation, quantum
simulation differs fundamentally in how the data is encoded in the quantum
computer. To perform a quantum simulation, the Hilbert space of the system to
be simulated is mapped directly onto the Hilbert space of the (logical) qubits
in the quantum computer. This type of direct correspondence is how data is
encoded in a classical analogue computer. There is no binary encoding, and
increasing precision becomes exponentially costly: an extra bit of precision
doubles the size of the computer. This has important consequences for both the
precision and error correction requirements of quantum simulation, and
significant open questions remain about its practicality. It also means that
the quantum version of analogue computers, continuous variable quantum
computers (CVQC) becomes an equally efficient architecture for quantum
simulation. Lessons from past use of classical analogue computers can help us
to build better quantum simulators in future.Comment: 10 pages, to appear in the Visions 2010 issue of Phil. Trans. Roy.
Soc.
Simple scheme for implementing the Deutsch-Jozsa algorithm in thermal cavity
We present a simple scheme to implement the Deutsch-Jozsa algorithm based on
two-atom interaction in a thermal cavity. The photon-number-dependent parts in
the evolution operator are canceled with the strong resonant classical field
added. As a result, our scheme is immune to thermal field, and does not require
the cavity to remain in the vacuum state throughout the procedure. Besides,
large detuning between the atoms and the cavity is not necessary neither,
leading to potential speed up of quantum operation. Finally, we show by
numerical simulation that the proposed scheme is equal to demonstrate the
Deutsch-Jozsa algorithm with high fidelity.Comment: 7 pages, 4 figure
Why bayesian âevidence for H1â in one condition and bayesian âevidence for H0â in another condition does not mean good-enough bayesian evidence for a difference between the conditions
Psychologists are often interested in whether an independent variable has a different effect in condition A than in condition B. To test such a question, one needs to directly compare the effect of that variable in the two conditions (i.e., test the interaction). Yet many researchers tend to stop when they find a significant test in one condition and a nonsignificant test in the other condition, deeming this as sufficient evidence for a difference between the two conditions. In this Tutorial, we aim to raise awareness of this inferential mistake when Bayes factors are used with conventional cutoffs to draw conclusions. For instance, some researchers might falsely conclude that there must be good-enough evidence for the interaction if they find good-enough Bayesian evidence for the alternative hypothesis, H1, in condition A and good-enough Bayesian evidence for the null hypothesis, H0, in condition B. The case study we introduce highlights that ignoring the test of the interaction can lead to unjustified conclusions and demonstrates that the principle that any assertion about the existence of an interaction necessitates the direct comparison of the conditions is as true for Bayesian as it is for frequentist statistics. We provide an R script of the analyses of the case study and a Shiny app that can be used with a 2 Ă 2 design to develop intuitions on this issue, and we introduce a rule of thumb with which one can estimate the sample size one might need to have a well-powered design
Conditional Quantum Dynamics and Logic Gates
Quantum logic gates provide fundamental examples of conditional quantum
dynamics. They could form the building blocks of general quantum information
processing systems which have recently been shown to have many interesting
non--classical properties. We describe a simple quantum logic gate, the quantum
controlled--NOT, and analyse some of its applications. We discuss two possible
physical realisations of the gate; one based on Ramsey atomic interferometry
and the other on the selective driving of optical resonances of two subsystems
undergoing a dipole--dipole interaction.Comment: 5 pages, RevTeX, two figures in a uuencoded, compressed fil
The Measurement Calculus
Measurement-based quantum computation has emerged from the physics community
as a new approach to quantum computation where the notion of measurement is the
main driving force of computation. This is in contrast with the more
traditional circuit model which is based on unitary operations. Among
measurement-based quantum computation methods, the recently introduced one-way
quantum computer stands out as fundamental.
We develop a rigorous mathematical model underlying the one-way quantum
computer and present a concrete syntax and operational semantics for programs,
which we call patterns, and an algebra of these patterns derived from a
denotational semantics. More importantly, we present a calculus for reasoning
locally and compositionally about these patterns.
We present a rewrite theory and prove a general standardization theorem which
allows all patterns to be put in a semantically equivalent standard form.
Standardization has far-reaching consequences: a new physical architecture
based on performing all the entanglement in the beginning, parallelization by
exposing the dependency structure of measurements and expressiveness theorems.
Furthermore we formalize several other measurement-based models:
Teleportation, Phase and Pauli models and present compositional embeddings of
them into and from the one-way model. This allows us to transfer all the theory
we develop for the one-way model to these models. This shows that the framework
we have developed has a general impact on measurement-based computation and is
not just particular to the one-way quantum computer.Comment: 46 pages, 2 figures, Replacement of quant-ph/0412135v1, the new
version also include formalization of several other measurement-based models:
Teleportation, Phase and Pauli models and present compositional embeddings of
them into and from the one-way model. To appear in Journal of AC
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