Implementation of conditional phase-shift gate for quantum information processing by NMR, using transition-selective pulses

Das, Ranabir; Mahesh, T. S.; Kumar, Anil

doi:10.1016/s1090-7807(02)00009-5

Cited by 18 publications

(21 citation statements)

References 32 publications

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“…Alternatively, it is also possible to implement them by selective irradiation of individual transitions in coupled multi-qubit systems (see, e.g., Refs. [41][42][43][44][45][46][47][48][49][50][51][52][53]). As an example, a transition-selective π-pulse applied to the transition between the states |10 ↔ |11 implements the operation [50]:…”

Section: Multi-qubit Quantum Gate Operationsmentioning

confidence: 99%

Spin qubits for quantum simulations

Peng

Suter

2009

Front. Phys. China

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The investigation of quantum mechanical systems mostly concentrates on single elementary particles. If we combine such particles into a composite quantum system, the number of degrees of freedom of the combined system grows exponentially with the number of particles. This is a major difficulty when we try to describe the dynamics of such a system, since the computational resources required for this task also grow exponentially. In the context of quantum information processing, this difficulty becomes the main source of power: in some situations, information processors based in quantum mechanics can process information exponentially faster than classical systems. From the perspective of a physicist, one of the most interesting applications of this type of information processing is the simulation of quantum systems. We call a quantum information processor that simulates other quantum systems a quantum simulator.This review discusses a specific type of quantum simulator, based on nuclear spin qubits, and using nuclear magnetic resonance for processing. We review the basics of quantum information processing by nuclear magnetic resonance (NMR) as well as the fundamentals of quantum simulation and describe some simple applications that can readily be realized by today's quantum computers. In particular, we discuss the simulation of quantum phase transitions: the qualitative changes that the ground states of some quantum mechanical systems exhibit when some parameters in their Hamiltonians change through some critical points. As specific examples, we consider quantum phase transitions where the relevant ground states are entangled. Chains of spins coupled by Heisenberg interactions represent an ideal system for studying these effects: depending on the type and strength of interactions, the ground states can be product states or they can be maximally entangled states representing different types of entanglement.

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Section: Multi-qubit Quantum Gate Operationsmentioning

confidence: 99%

Spin qubits for quantum simulations

Peng

Suter

2009

Front. Phys. China

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“…Transition selective (p)-pulse has a narrow bandwidth and when tuned to the resonance frequency of a specific transition in the spectrum, it exchanges the amplitudes of the two eigenstates which are connected by that transition [24]. Such pulses have already been used to simplify the implementation of several logical operations for quantum information processing [10,12,17,21,22,[31][32][33][34].…”

Section: Het-z-cosymentioning

confidence: 99%

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

Das

Bhattacharyya

Kumar

2004

Journal of Magnetic Resonance

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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.

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“…Three-and four-qubit gates were experimentally realized early on in NMR quantum computing by several groups [20][21][22][23]. The Toffoli gate has been experimentally implemented using trapped ions [24] and circuit QED [25] and superconducting qubits [26,27].…”

Section: Introductionmentioning

confidence: 99%

Efficient experimental design of high-fidelity three-qubit quantum gates via genetic programming

Devra

Prabhu

Singh

et al. 2018

Quantum Inf Process

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We have designed efficient quantum circuits for the three-qubit Toffoli (controlled-controlled NOT) and the Fredkin (controlled-SWAP) gate, optimized via genetic programming methods. The gates thus obtained were experimentally implemented on a three-qubit NMR quantum information processor, with a high fidelity. Toffoli and Fredkin gates in conjunction with the single-qubit Hadamard gates form a universal gate set for quantum computing, and are an essential component of several quantum algorithms. Genetic algorithms are stochastic search algorithms based on the logic of natural selection and biological genetics and have been widely used for quantum information processing applications. The numerically optimized rf pulse profiles of the three-qubit quantum gates achieve > 99% fidelity. The optimization was performed under the constraint that the experimentally implemented pulses are of short duration and can be implemented with high fidelity. Therefore the gate implementations do not suffer from the drawbacks of rf offset errors or debilitating effects of decoherence during gate action. We demonstrate the advantage of our pulse sequences by comparing our results with existing experimental schemes.

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Implementation of conditional phase-shift gate for quantum information processing by NMR, using transition-selective pulses

Cited by 18 publications

References 32 publications

Spin qubits for quantum simulations

Spin qubits for quantum simulations

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

Efficient experimental design of high-fidelity three-qubit quantum gates via genetic programming

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