An implementation of the Deutsch–Jozsa algorithm on a three-qubit NMR quantum computer

Controlling NMR spin systems for quantum computation

Nuclear magnetic resonance is arguably both the best available quantum technology for implementing simple quantum computing experiments and the worst technology for building large scale quantum computers that has ever been seriously put forward. After a few years of rapid growth, leading to an implementation of Shor's quantum factoring algorithm in a seven-spin system, the field started to reach its natural limits and further progress became challenging. Rather than pursuing more complex algorithms on larger systems, interest has now largely moved into developing techniques for the precise and efficient manipulation of spin states with the aim of developing methods that can be applied in other more scalable technologies and within conventional NMR. However, the user friendliness of NMR implementations means that they remain popular for proof-of-principle demonstrations of simple quantum information protocols.

A tutorial on regularized partial correlation networks

Recent years have seen an emergence of network modeling applied to moods, attitudes, and problems in the realm of psychology. In this framework, psychological variables are understood to directly affect each other rather than being caused by an unobserved latent entity. In this tutorial, we introduce the reader to estimating the most popular network model for psychological data: the partial correlation network. We describe how regularization techniques can be used to efficiently estimate a parsimonious and interpretable network structure in psychological data. We show how to perform these analyses in R and demonstrate the method in an empirical example on posttraumatic stress disorder data. In addition, we discuss the effect of the hyperparameter that needs to be manually set by the researcher, how to handle non-normal data, how to determine the required sample size for a network analysis, and provide a checklist with potential solutions for problems that can arise when estimating regularized partial correlation networks. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond

The nitrogen-vacancy defect center (N-V center) is a promising candidate for quantum information processing due to the possibility of coherent manipulation of individual spins in the absence of the cryogenic requirement. We report a room-temperature implementation of the Deutsch-Jozsa algorithm by encoding both a qubit and an auxiliary state in the electron spin of a single N-V center. By thus exploiting the specific S=1 character of the spin system, we demonstrate how even scarce quantum resources can be used for test-bed experiments on the way towards a large-scale quantum computing architecture.

Implementation of controlled phase shift gates and Collins version of Deutsch-Jozsa algorithm on a quadrupolar spin-7/2 nucleus using non-adiabatic geometric phases

In this work controlled phase shift gates are implemented on a qaudrupolar system, by using non-adiabatic geometric phases. A general procedure is given, for implementing controlled phase shift gates in an 'N' level system. The utility of such controlled phase shift gates, is demonstrated here by implementing 3-qubit Deutsch-Jozsa algorithm on a spin-7/2 quadrupolar nucleus oriented in a liquid crystal matrix.

A study of the relaxation dynamics in a quadrupolar NMR system using Quantum State Tomography

This article reports a relaxation study in an oriented system containing spin 3/2 nuclei using quantum state tomography (QST). The use of QST allowed evaluating the time evolution of all density matrix elements starting from several initial states. Using an appropriated treatment based on the Redfield theory, the relaxation rate of each density matrix element was measured and the reduced spectral densities that describe the system relaxation were determined. All the experimental data could be well described assuming pure quadrupolar relaxation and reduced spectral densities corresponding to a superposition of slow and fast motions. The data were also analyzed in the context of Quantum Information Processing, where the coherence loss of each qubit of the system was determined using the partial trace operation.

Indirect detection of selective nuclear spin-spin interactions in a hostile environment

We present a number of techniques which may be used to obtain precise values of selective spin-spin interactions between two nuclear spins in a hostile environment. Such an environment may be characterized by very fast relaxation and decoherence, e.g. due to the strong coupling of the two spins of interest to electron spins in their vicinity as well as other nuclei. Here, we used dilute paramagnetic Ce(3+) centers hosted in a single crystal of CaF(2). Selected (19)F internuclear interactions were measured indirectly by applying different electron nuclear double resonance (ENDOR) pulse sequences.

Use of non-adiabatic geometric phase for quantum computing by NMR

Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled dynamics of qubits. In controlled dynamics, one qubit undergoes coherent evolution and acquires appropriate phase, depending on the state of other qubits. If the evolution is geometric, then the phase acquired depend only on the geometry of the path executed, and is robust against certain types of error. This phenomenon leads to an inherently fault-tolerant quantum computation. Here we suggest a technique of using non-adiabatic geometric phase for quantum computation, using selective excitation. In a two-qubit system, we selectively evolve a suitable subsystem where the control qubit is in state |1, through a closed circuit. By this evolution, the target qubit gains a phase controlled by the state of the control qubit. Using the non-adiabatic geometric phase we demonstrate implementation of Deutsch-Jozsa algorithm and Grover's search algorithm in a two-qubit system.

Quantum information processing by NMR using a 5-qubit system formed by dipolar coupled spins in an oriented molecule

Quantum information processing by NMR with small number of qubits is well established. Scaling to higher number of qubits is hindered by two major requirements (i) mutual coupling among qubits and (ii) qubit addressability. It has been demonstrated that mutual coupling can be increased by using residual dipolar couplings among spins by orienting the spin system in a liquid crystalline matrix. In such a case, the heteronuclear spins are weakly coupled, but the homonuclear spins often become strongly coupled. In such circumstances, the strongly coupled spins, which yield second order spectra, can no longer be individually treated as qubits. However, it has been demonstrated elsewhere, that the 2(N) energy levels of a strongly coupled N spin-1/2 system can be treated as an N-qubit system. For this purpose the various transitions have to be identified to well defined energy levels. This paper consists of two parts. In the first part, the energy level diagram of a heteronuclear 5-spin system is obtained by using a newly developed heteronuclear z-cosy (HET-Z-COSY) experiment. In the second part, implementation of logic gates, preparation of pseudopure states, creation of entanglement, and entanglement transfer is demonstrated, validating the use of such systems for quantum information processing.

A simple method for the preparation of pseudopure states in nuclear magnetic resonance quantum information processing

The use of nuclear magnetic resonance (NMR) to carry out quantum information processing (QIP) often requires the preparation, transformation, and detection of pseudopure states. In our previous work, it was shown that the use of pairs of pseudopure states (POPS) as a basis for QIP is very convenient because of the simplicity in experimental execution. It is now further demonstrated that the product of the NMR spectra corresponding to two sets of POPS that share a common pseudopure state has the same peak frequencies as those of the common (single) pseudopure state. Examples of applying two different quantum logic gates to a 5-qubit system are given.

Fiber-optics implementation of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms with three qubits

We report on a fiber-optics implementation of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms for 8-point functions. The measured visibility of the 8-path interferometer is about 97.5%. Potential applications of our setup to quantum communication or cryptographic protocols using several qubits are discussed.

Approximate quantum cloning with nuclear magnetic resonance

Here we describe a nuclear magnetic resonance (NMR) experiment that uses a three qubit NMR device to implement the one-to-two approximate quantum cloning network of Buzek et al. [Phys. Rev. A 56, 3446 (1997)]. As expected the experimental results indicate that the network clones all input states with similar fidelities, but as a result of decoherence and incoherent evolution arising from B(1) inhomogeneity the total fidelity achieved does not exceed the measurement bound.

Quantum algorithms for Josephson networks

We analyze possible implementations of quantum algorithms in a system of (macroscopic) Josephson charge qubits. System layout and parameters to realize the Deutsch algorithm with up to three qubits are provided. Special attention is paid to the necessity of entangled states in the various implementations. Further, we demonstrate explicitly that the gates to implement the Bernstein-Vazirani algorithm can be realized by using a system of uncoupled qubits.

Preparation of entangled states by adiabatic passage

We propose a novel technique for the creation of entangled pairs of two-state systems based upon adiabatic passage induced by a suitably crafted time-dependent external field.

Implementing logic gates and the Deutsch-Jozsa quantum algorithm by two-dimensional NMR using spin- and transition-selective pulses

Quantum logical operations using two-dimensional NMR have recently been described using the scalar coupling evolution technique [J. Chem. Phys. 109, 10603 (1998)]. In the present paper, we describe the implementation of quantum logical operations using two-dimensional NMR, with the help of spin- and transition-selective pulses. A number of logic gates are implemented using two and three qubits with one extra observer spin. Some many-in-one gates (or Portmanteau gates) are also implemented. Toffoli gate (or AND/NAND gate) and OR/NOR gates are implemented on three qubits. The Deutsch-Jozsa quantum algorithm for one and two qubits, using one extra work qubit, has also been implemented using spin- and transition-selective pulses after creating a coherent superposition state in the two-dimensional methodology.

Quantum information and computation

In information processing, as in physics, our classical world view provides an incomplete approximation to an underlying quantum reality. Quantum effects like interference and entanglement play no direct role in conventional information processing, but they can--in principle now, but probably eventually in practice--be harnessed to break codes, create unbreakable codes, and speed up otherwise intractable computations.