Compiling gate networks on an Ising quantum computer

Here we describe a simple mechanical procedure for compiling a quantum gate network into the natural gates (pulses and delays) for an Ising quantum computer. The aim is not necessarily to generate the most efficient pulse sequence, but rather to develop an efficient compilation algorithm that can be easily implemented in large spin systems. The key observation is that it is not always necessary to refocus all the undesired couplings in a spin system. Instead the coupling evolution can simply be tracked and then corrected at some later time. Although described within the language of NMR the algorithm is applicable to any design of quantum computer based on Ising couplings.Comment: 5 pages RevTeX4 including 4 figures. Will submit to PR

Quantum Simulations on a Quantum Computer

We present a general scheme for performing a simulation of the dynamics of one quantum system using another. This scheme is used to experimentally simulate the dynamics of truncated quantum harmonic and anharmonic oscillators using nuclear magnetic resonance. We believe this to be the first explicit physical realization of such a simulation.Comment: 4 pages, 2 figures (\documentstyle[prl,aps,epsfig,amscd]{revtex}); to appear in Phys. Rev. Let

Principles of Control for Decoherence-Free Subsystems

Decoherence-Free Subsystems (DFS) are a powerful means of protecting quantum information against noise with known symmetry properties. Although Hamiltonians theoretically exist that can implement a universal set of logic gates on DFS encoded qubits without ever leaving the protected subsystem, the natural Hamiltonians that are available in specific implementations do not necessarily have this property. Here we describe some of the principles that can be used in such cases to operate on encoded qubits without losing the protection offered by the DFS. In particular, we show how dynamical decoupling can be used to control decoherence during the unavoidable excursions outside of the DFS. By means of cumulant expansions, we show how the fidelity of quantum gates implemented by this method on a simple two-physical-qubit DFS depends on the correlation time of the noise responsible for decoherence. We further show by means of numerical simulations how our previously introduced "strongly modulating pulses" for NMR quantum information processing can permit high-fidelity operations on multiple DFS encoded qubits in practice, provided that the rate at which the system can be modulated is fast compared to the correlation time of the noise. The principles thereby illustrated are expected to be broadly applicable to many implementations of quantum information processors based on DFS encoded qubits.Comment: 12 pages, 7 figure

Measurement of persistence in 1-D diffusion

Using a novel NMR scheme we observed persistence in 1-D gas diffusion. Analytical approximations and numerical simulations have shown that for an initially random array of spins undergoing diffusion, the probability p(t) that the average spin orientation in a given region has not changed sign (i.e., ``persists'') up to time t follows a power law t^{-\theta}, where \theta depends on the dimensionality of the system. The large nuclear spin polarization of laser-polarized 129Xe gas allowed us both to prepare an initial ``quasi-random'' 1-D array of spin orientations and then to perform real-time NMR imaging to monitor the spin diffusion. Our measurements are consistent with theoretical and numerical predictions of \theta ~ 0.12. We also observed finite size effects for long time gas diffusion

Practical Spectrophotometric Assay for the \u3cem\u3edapE\u3c/em\u3e-Encoded \u3cem\u3eN\u3c/em\u3e-Succinyl-L,L-Diaminopimelic Acid Desuccinylase, a Potential Antibiotic Target

A new enzymatic assay for the bacterial enzyme succinyl-diaminopimelate desuccinylase (DapE, E.C. 3.5.1.18) is described. This assay employs N6-methyl-N2-succinyl-L,L-diaminopimelic acid (N6-methyl-L,L-SDAP) as the substrate with ninhydrin used to detect cleavage of the amide bond of the modified substrate, wherein N6-methylation enables selective detection of the primary amine enzymatic product. Molecular modeling supported preparation of the mono-N6-methylated-L,L-SDAP as an alternate substrate for the assay, given binding in the active site of DapE predicted to be comparable to the endogenous substrate. The alternate substrate for the assay, N6-methyl-L,L-SDAP, was synthesized from the tert-butyl ester of Boc-L-glutamic acid employing a Horner-Wadsworth-Emmons olefination followed by an enantioselective reduction employing Rh(I)(COD)(S,S)-Et-DuPHOS as the chiral catalyst. Validation of the new ninhydrin assay was demonstrated with known inhibitors of DapE from Haemophilus influenza (HiDapE) including captopril (IC50 = 3.4 [± 0.2] μM, 3-mercaptobenzoic acid (IC50 = 21.8 [±2.2] μM, phenylboronic acid (IC50 = 316 [± 23.6] μM, and 2-thiopheneboronic acid (IC50 = 111 [± 16] μM. Based on these data, this assay is simple and robust, and should be amenable to high-throughput screening, which is an important step forward as it opens the door to medicinal chemistry efforts toward the discovery of DapE inhibitors that can function as a new class of antibiotics

Experimental Implementation of Logical Bell State Encoding

Liquid phase NMR is a general purpose test-bed for developing methods of coherent control relevant to quantum information processing. Here we extend these studies to the coherent control of logical qubits and in particular to the unitary gates necessary to create entanglement between logical qubits. We report an experimental implementation of a conditional logical gate between two logical qubits that are each in decoherence free subspaces that protect the quantum information from fully correlated dephasing.Comment: 9 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

Quantum Reed-Solomon Codes

After a brief introduction to both quantum computation and quantum error correction, we show how to construct quantum error-correcting codes based on classical BCH codes. With these codes, decoding can exploit additional information about the position of errors. This error model - the quantum erasure channel - is discussed. Finally, parameters of quantum BCH codes are provided.Comment: Summary only (2 pages), for the full version see: Proceedings Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC-13), Lecture Notes in Computer Science 1719, Springer, 199

Dynamics of a Quantum Control-Not Gate for an Ensemble of Four-Spin Molecules at Room Temperature

We investigate numerically a single-pulse implementation of a quantum Control-Not (CN) gate for an ensemble of Ising spin systems at room temperature. For an ensemble of four-spin ``molecules'' we simulate the time-evolution of the density matrix, for both digital and superpositional initial conditions. Our numerical calculations confirm the feasibility of implementation of quantum CN gate in this system at finite temperature, using electromagnetic $\pi$-pulse.Comment: 7 pages 3 figure

Local Realistic Model for the Dynamics of Bulk-Ensemble NMR Information Processing

We construct a local realistic hidden-variable model that describes the states and dynamics of bulk-ensemble NMR information processing up to about 12 nuclear spins. The existence of such a model rules out violation of any Bell inequality, temporal or otherwise, in present high-temperature, liquid-state NMR experiments. The model does not provide an efficient description in that the number of hidden variables grows exponentially with the number of nuclear spins.Comment: REVTEX, 7 page