Realization of logically labeled effective pure states for bulk quantum computation

We report the first use of "logical labeling" to perform a quantum computation with a room-temperature bulk system. This method entails the selection of a subsystem which behaves as if it were at zero temperature - except for a decrease in signal strength - conditioned upon the state of the remaining system. No averaging over differently prepared molecules is required. In order to test this concept, we execute a quantum search algorithm in a subspace of two nuclear spins, labeled by a third spin, using solution nuclear magnetic resonance (NMR), and employing a novel choice of reference frame to uncouple nuclei.Comment: PRL 83, 3085 (1999). Small changes made to improve readability and remove ambiguitie

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

Implementing universal multi-qubit quantum logic gates in three and four-spin systems at room temperature

In this paper, we present the experimental realization of multi-qubit gates $$ in macroscopic ensemble of three-qubit and four-qubit molecules. Instead of depending heavily on the two-bit universal gate, which served as the basic quantum operation in quantum computing, we use pulses of well-defined frequency and length that simultaneously apply to all qubits in a quantum register. It appears that this method is experimentally convenient when this procedure is extended to more qubits on some quantum computation, and it can also be used in other physical systems.Comment: 5 Pages, 2 Figure

Quantum entanglement in the NMR implementation of the Deutsch-Jozsa algorithm

A scheme to execute an n-bit Deutsch-Jozsa (D-J) algorithm using n qubits has been implemented for up to three qubits on an NMR quantum computer. For the one and two bit Deutsch problem, the qubits do not get entangled, hence the NMR implementation is achieved without using spin-spin interactions. It is for the three bit case, that the manipulation of entangled states becomes essential. The interactions through scalar J-couplings in NMR spin systems have been exploited to implement entangling transformations required for the three bit D-J algorithm.Comment: 4-pages in revtex with 5 eps figure included using psfi

Separability of very noisy mixed states and implications for NMR quantum computing

We give a constructive proof that all mixed states of N qubits in a sufficiently small neighborhood of the maximally mixed state are separable. The construction provides an explicit representation of any such state as a mixture of product states. We give upper and lower bounds on the size of the neighborhood, which show that its extent decreases exponentially with the number of qubits. We also discuss the implications of the bounds for NMR quantum computing.Comment: 4 pages, extensively revised, references adde

Experimental Implementation of Hogg's Algorithm on a Three-Quantum-bit NMR Quantum Computer

Using nuclear magnetic resonance (NMR) techniques with three-qubit sample, we have experimentally implemented the highly structured algorithm for the 1-SAT problem proposed by Hogg. A simplified temporal averaging procedure was employed to the three-qubit spin pseudo-pure state. The algorithm was completed with only a single evaluation of structure of the problem and the solutions were found with probability 100%, which outperform both unstructured quantum and the best classical search algorithm.Comment: Revtex, 14 pages and 1 table, 4 EPS figure

Realization of quantum process tomography in NMR

Quantum process tomography is a procedure by which the unknown dynamical evolution of an open quantum system can be fully experimentally characterized. We demonstrate explicitly how this procedure can be implemented with a nuclear magnetic resonance quantum computer. This allows us to measure the fidelity of a controlled-not logic gate and to experimentally investigate the error model for our computer. Based on the latter analysis, we test an important assumption underlying nearly all models of quantum error correction, the independence of errors on different qubits.Comment: 8 pages, 7 EPS figures, REVTe

Experimental Realization of A Two Bit Phase Damping Quantum Code

Using nuclear magnetic resonance techniques, we experimentally investigated the effects of applying a two bit phase error detection code to preserve quantum information in nuclear spin systems. Input states were stored with and without coding, and the resulting output states were compared with the originals and with each other. The theoretically expected result, net reduction of distortion and conditional error probabilities to second order, was indeed observed, despite imperfect coding operations which increased the error probabilities by approximately 5%. Systematic study of the deviations from the ideal behavior provided quantitative measures of different sources of error, and good agreement was found with a numerical model. Theoretical questions in quantum error correction in bulk nuclear spin systems including fidelity measures, signal strength and syndrome measurements are discussed.Comment: 21 pages, 17 figures, mypsfig2, revtex. Minor changes made to appear in PR

ROM-based quantum computation: Experimental explorations using Nuclear Magnetic Resonance, and future prospects

ROM-based quantum computation (QC) is an alternative to oracle-based QC. It has the advantages of being less ``magical'', and being more suited to implementing space-efficient computation (i.e. computation using the minimum number of writable qubits). Here we consider a number of small (one and two-qubit) quantum algorithms illustrating different aspects of ROM-based QC. They are: (a) a one-qubit algorithm to solve the Deutsch problem; (b) a one-qubit binary multiplication algorithm; (c) a two-qubit controlled binary multiplication algorithm; and (d) a two-qubit ROM-based version of the Deutsch-Jozsa algorithm. For each algorithm we present experimental verification using NMR ensemble QC. The average fidelities for the implementation were in the ranges 0.9 - 0.97 for the one-qubit algorithms, and 0.84 - 0.94 for the two-qubit algorithms. We conclude with a discussion of future prospects for ROM-based quantum computation. We propose a four-qubit algorithm, using Grover's iterate, for solving a miniature ``real-world'' problem relating to the lengths of paths in a network.Comment: 11 pages, 5 figure

Approximate quantum counting on an NMR ensemble quantum computer

We demonstrate the implementation of a quantum algorithm for estimating the number of matching items in a search operation using a two qubit nuclear magnetic resonance (NMR) quantum computer.Comment: 4 pages LaTeX/RevTex including 4 figures (3 LaTeX, 1 PostScript). Submitted to Physical Review Letter