Experimental implementation of the Deutsch-Jozsa algorithm for three-qubit functions using pure coherent molecular superpositions

Vala, Jiří; Amitay, Zohar; Zhang, Bo; Leone, Stephen R.; Kosloff, Ronnie

doi:10.1103/physreva.66.062316

Cited by 82 publications

(73 citation statements)

References 28 publications

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“…23 It seems quite feasible to create in the experiment a system of few vibrational qubits, fully entangled and well separated from the environment. 4 Such prototype systems by themselves also could be used in the fundamental studies of quantum control, noise effects, decoherence, etc. For these small-scale (or test-bed) applications, the quantum beat approach to the readout, discussed in this paper, is also quite appropriate.…”

Section: Introductionmentioning

confidence: 99%

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On readout of vibrational qubits using quantum beats

Shyshlov

Berrios

Gruebele

et al. 2014

The Journal of Chemical Physics

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Readout of the final states of qubits is a crucial step towards implementing quantum computation in experiment. Although not scalable to large numbers of qubits per molecule, computational studies show that molecular vibrations could provide a significant (factor 2-5 in the literature) increase in the number of qubits compared to two-level systems. In this theoretical work, we explore the process of readout from vibrational qubits in thiophosgene molecule, SCCl 2 , using quantum beat oscillations. The quantum beats are measured by first exciting the superposition of the qubit-encoding vibrational states to the electronically excited readout state with variable time-delay pulses. The resulting oscillation of population of the readout state is then detected as a function of time delay. In principle, fitting the quantum beat signal by an analytical expression should allow extracting the values of probability amplitudes and the relative phases of the vibrational qubit states. However, we found that if this procedure is implemented using the standard analytic expression for quantum beats, a non-negligible phase error is obtained. We discuss the origin and properties of this phase error, and propose a new analytical expression to correct the phase error. The corrected expression fits the quantum beat signal very accurately, which may permit reading out the final state of vibrational qubits in experiments by combining the analytic fitting expression with numerical modelling of the readout process. The new expression is also useful as a simple model for fitting any quantum beat experiments where more accurate phase information is desired. © 2014 AIP Publishing LLC.

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Section: Introductionmentioning

confidence: 99%

“…In one type of implementation, a set of 2 n vibrational eigenstates in a molecule can represent n qubits that are inherently entangled, 4 encoding several qubits on a single molecule, as shown in Fig. 1.…”

Section: Introductionmentioning

confidence: 99%

On readout of vibrational qubits using quantum beats

Shyshlov

Berrios

Gruebele

et al. 2014

The Journal of Chemical Physics

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“…We show how a TFRCARS interference experiment can use the molecular vibrational level structure to solve the Deutsch-Jozsa (DJ) problem [5]. The DJ problem has become a benchmark for demonstrations of algorithms on prototypes of quantum computers; having so far been used in NMR [6][7][8][9][10][11], linear optics [12], ro-vibrational molecular wavepackets in a pump-probe experiment [13], and excitons in semiconductor quantum dots [14].…”

Section: Introductionmentioning

confidence: 99%

An implementation of the Deutsch–Jozsa algorithm on molecular vibronic coherences through four-wave mixing: a theoretical study

Bihary

Glenn

Lidar

et al. 2002

Chemical Physics Letters

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Time-Frequency Resolved Coherent Anti-Stokes Raman Scattering (TFRCARS) was recently proposed as a means to implement quantum logic using the molecular ro-vibrational manifold as a quantum register [R. Zadoyan et al., Chem. Phys. 266, (2001) 323]. We give a concrete example of how this can be accomplished through an illustrative algorithm that solves the Deutsch-Jozsa problem. We use realistic molecular parameters to recognize that, as the problem size expands, shaped pulses must be tailored to maintain fidelity of the algorithm.

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“…It is the case that one could, although not so easily for a molecule with a high vibrational frequency as HCl, prepare a coherent superposition of the ϭ 0 and ϭ 1 states of a molecule. One certainly can prepare a coherent superposition of different rotational states and such rovibrational coherent superpositions have been proposed for molecule-based quantum computing (12,13). But on a longer time scale molecular states decohere quite rapidly.…”

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confidence: 99%

Quasiclassical computation

Remacle

Levine

2004

Proc. Natl. Acad. Sci. U.S.A.

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The chemical kinetic description of time evolution where the phase is random but the states are discrete is discussed as a basis for a computational approach. This proposed scheme uses numbers in the entire range of 0 to 1 to represent Boolean propositions. In the implementation by chemical kinetics these numbers are the mole fractions of different species. Vibrational relaxation in a mixture of HCl and DCI is the physical system that is used to illustrate the approach. Energy exchange in such a mixture corresponds to two strongly coupled two-level systems. A search problem, previously discussed in the quantum computing literature, is solved as an example. The solution requires the same number of function evaluations as in the quantal case. The action of the oracle is described in detail.T he basic element of current logic devices is a switch. It is either on or off. This corresponds to the two possible values, say 0 and 1 or true and false, of a Boolean variable. The values of physical observables are not usually either 0 or 1. A molecule is not easily made to act as a switch. On the other hand, molecules exhibit a rich dynamical behavior that we would like to take advantage of so as to perform logic operations.In this article we focus on what is, to us, a rather common characteristic of molecules. It is that molecules can be classified into discrete alternatives. The simplest such distinction is the very idea of a chemical species. The operational definition of a molecule is made possible by the (relative) stability of the entities we know as atoms and by the atoms combining into molecules in simple and definite proportions. Thereby a molecule can be identified to be, say, HCl and not HBr or any other diatomic one. A finer but still operationally fully viable resolution is that molecules of a given chemical species can be identified to occupy definite quantum states (or groups of states). Except for special circumstances it is typical of molecules that the quantum mechanical phase of its states is random. So the different states of molecules act as discrete and mutually exclusive classical alternatives. This state of affairs is what we mean by quasiclassical. We want to perform logic operations by taking advantage of the probabilities of occupancy of the different quantum states that are resolvable in an experiment. By the end of this article we intend to show, by an explicit example, that this is possible.To implement our program we need input from several directions. In this introduction we review the different ideas that we intend to invoke. Then we describe a solution of a particular problem with special reference to what is the logic problem that we claim to solve, what is the physical system that is used, and how we set up the interface between them.We do not use the phase of the quantum mechanical state because we propose to operate under conditions where this phase is random. Starting with the work of Deutsch (1, 2), there is an extensive current literature emphasizing the critical computational advant...

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Experimental implementation of the Deutsch-Jozsa algorithm for three-qubit functions using pure coherent molecular superpositions

Cited by 82 publications

References 28 publications

On readout of vibrational qubits using quantum beats

On readout of vibrational qubits using quantum beats

An implementation of the Deutsch–Jozsa algorithm on molecular vibronic coherences through four-wave mixing: a theoretical study

Quasiclassical computation

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