Fast Quantum Search Algorithms in Protein Sequence Comparison - Quantum Biocomputing

Quantum search algorithms are considered in the context of protein sequence comparison in biocomputing. Given a sample protein sequence of length m (i.e m residues), the problem considered is to find an optimal match in a large database containing N residues. Initially, Grover's quantum search algorithm is applied to a simple illustrative case - namely where the database forms a complete set of states over the 2^m basis states of a m qubit register, and thus is known to contain the exact sequence of interest. This example demonstrates explicitly the typical O(sqrt{N}) speedup on the classical O(N) requirements. An algorithm is then presented for the (more realistic) case where the database may contain repeat sequences, and may not necessarily contain an exact match to the sample sequence. In terms of minimizing the Hamming distance between the sample sequence and the database subsequences the algorithm finds an optimal alignment, in O(sqrt{N}) steps, by employing an extension of Grover's algorithm, due to Boyer, Brassard, Hoyer and Tapp for the case when the number of matches is not a priori known.Comment: LaTeX, 5 page

NMR quantum computation with indirectly coupled gates

An NMR realization of a two-qubit quantum gate which processes quantum information indirectly via couplings to a spectator qubit is presented in the context of the Deutsch-Jozsa algorithm. This enables a successful comprehensive NMR implementation of the Deutsch-Jozsa algorithm for functions with three argument bits and demonstrates a technique essential for multi-qubit quantum computation.Comment: 9 pages, 2 figures. 10 additional figures illustrating output spectr

Scaling issues in ensemble implementations of the Deutsch-Jozsa algorithm

We discuss the ensemble version of the Deutsch-Jozsa (DJ) algorithm which attempts to provide a "scalable" implementation on an expectation-value NMR quantum computer. We show that this ensemble implementation of the DJ algorithm is at best as efficient as the classical random algorithm. As soon as any attempt is made to classify all possible functions with certainty, the implementation requires an exponentially large number of molecules. The discrepancies arise out of the interpretation of mixed state density matrices.Comment: Minor changes, reference added, replaced with publised versio

Implementation of a Deutsch-like quantum algorithm utilizing entanglement at the two-qubit level, on an NMR quantum information processor

We describe the experimental implementation of a recently proposed quantum algorithm involving quantum entanglement at the level of two qubits using NMR. The algorithm solves a generalisation of the Deutsch problem and distinguishes between even and odd functions using fewer function calls than is possible classically. The manipulation of entangled states of the two qubits is essential here, unlike the Deutsch-Jozsa algorithm and the Grover's search algorithm for two bits.Comment: 4 pages, two eps figure

Solid-State Nuclear Spin Quantum Computer Based on Magnetic Resonance Force Microscopy

We propose a nuclear spin quantum computer based on magnetic resonance force microscopy (MRFM). It is shown that an MRFM single-electron spin measurement provides three essential requirements for quantum computation in solids: (a) preparation of the ground state, (b) one- and two- qubit quantum logic gates, and (c) a measurement of the final state. The proposed quantum computer can operate at temperatures up to 1K.Comment: 16 pages, 5 figure

An NMR-based nanostructure switch for quantum logic

We propose a nanostructure switch based on nuclear magnetic resonance (NMR) which offers reliable quantum gate operation, an essential ingredient for building a quantum computer. The nuclear resonance is controlled by the magic number transitions of a few-electron quantum dot in an external magnetic field.Comment: 4 pages, 2 separate PostScript figures. Minor changes included. One reference adde

The Majorization Arrow in Quantum Algorithm Design

We apply majorization theory to study the quantum algorithms known so far and find that there is a majorization principle underlying the way they operate. Grover's algorithm is a neat instance of this principle where majorization works step by step until the optimal target state is found. Extensions of this situation are also found in algorithms based in quantum adiabatic evolution and the family of quantum phase-estimation algorithms, including Shor's algorithm. We state that in quantum algorithms the time arrow is a majorization arrow.Comment: REVTEX4.b4 file, 4 color figures (typos corrected.

Limits to clock synchronization induced by completely dephasing communication channels

Clock synchronization procedures are analyzed in the presence of imperfect communications. In this context we show that there are physical limitations which prevent one from synchronizing distant clocks when the intervening medium is completely dephasing, as in the case of a rapidly varying dispersive medium.Comment: 6 Pages. Revised version as published in PR

Experimental requirements for Grover's algorithm in optical quantum computation

The field of linear optical quantum computation (LOQC) will soon need a repertoire of experimental milestones. We make progress in this direction by describing several experiments based on Grover's algorithm. These experiments range from a relatively simple implementation using only a single non-scalable CNOT gate to the most complex, requiring two concatenated scalable CNOT gates, and thus form a useful set of early milestones for LOQC. We also give a complete description of basic LOQC using polarization-encoded qubits, making use of many simplifications to the original scheme of Knill, Laflamme, and Milburn.Comment: 9 pages, 8 figure

A Lorentz-invariant look at quantum clock synchronization protocols based on distributed entanglement

Recent work has raised the possibility that quantum information theory techniques can be used to synchronize atomic clocks nonlocally. One of the proposed algorithms for quantum clock synchronization (QCS) requires distribution of entangled pure singlets to the synchronizing parties. Such remote entanglement distribution normally creates a relative phase error in the distributed singlet state which then needs to be purified asynchronously. We present a fully relativistic analysis of the QCS protocol which shows that asynchronous entanglement purification is not possible, and, therefore, that the proposed QCS scheme remains incomplete. We discuss possible directions of research in quantum information theory which may lead to a complete, working QCS protocol.Comment: 5 pages; typeset in RevTe