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 “evidence for H1” in one condition and bayesian “evidence for H0” 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 × 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