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

AC-driven quantum spins: resonant enhancement of transverse DC magnetization

We consider s=1/2 spins in the presence of a constant magnetic field in z-direction and an AC magnetic field in the x-z plane. A nonzero DC magnetization component in y direction is a result of broken symmetries. A pairwise interaction between two spins is shown to resonantly increase the induced magnetization by one order of magnitude. We discuss the mechanism of this enhancement, which is due to additional avoided crossings in the level structure of the system.Comment: 7 pages, 7 figure

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

Decoherence and Programmable Quantum Computation

An examination of the concept of using classical degrees of freedom to drive the evolution of quantum computers is given. Specifically, when externally generated, coherent states of the electromagnetic field are used to drive transitions within the qubit system, a decoherence results due to the back reaction from the qubits onto the quantum field. We derive an expression for the decoherence rate for two cases, that of the single-qubit Walsh-Hadamard transform, and for an implementation of the controlled-NOT gate. We examine the impact of this decoherence mechanism on Grover's search algorithm, and on the proposals for use of error-correcting codes in quantum computation.Comment: submitted to Phys. Rev. A 35 double-spaced pages, 2 figures, in LaTe

Experimental Implementation of the Quantum Random-Walk Algorithm

The quantum random walk is a possible approach to construct new quantum algorithms. Several groups have investigated the quantum random walk and experimental schemes were proposed. In this paper we present the experimental implementation of the quantum random walk algorithm on a nuclear magnetic resonance quantum computer. We observe that the quantum walk is in sharp contrast to its classical counterpart. In particular, the properties of the quantum walk strongly depends on the quantum entanglement.Comment: 5 pages, 4 figures, published versio

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

Testing integrability with a single bit of quantum information

We show that deterministic quantum computing with a single bit (DQC1) can determine whether the classical limit of a quantum system is chaotic or integrable using O(N) physical resources, where $N$ is the dimension of the Hilbert space of the system under study. This is a square root improvement over all known classical procedures. Our study relies strictly on the random matrix conjecture. We also present numerical results for the nonlinear kicked top.Comment: Minor changes taking into account Howard Wiseman's comment: quant-ph/0305153. Accepted for publication in Phys. Rev.

Grover search with pairs of trapped ions

The desired interference required for quantum computing may be modified by the wave function oscillations for the implementation of quantum algorithms[Phys.Rev.Lett.84(2000)1615]. To diminish such detrimental effect, we propose a scheme with trapped ion-pairs being qubits and apply the scheme to the Grover search. It can be found that our scheme can not only carry out a full Grover search, but also meet the requirement for the scalable hot-ion quantum computing. Moreover, the ion-pair qubits in our scheme are more robust against the decoherence and the dissipation caused by the environment than single-particle qubits proposed before.Comment: RevTe