Experimental realization of a continuous version of the Grover algorithm

Ermakov, Vladimir L.; Fung, B. M.

doi:10.1103/physreva.66.042310

Cited by 43 publications

(31 citation statements)

References 23 publications

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“…The polynomial speed-up in the search process represents an advantage over the classical counterpart, O(N ). The algorithm belongs to the class of probabilistic quantum algorithms and a detailed description can be found elsewhere [9,23,[33][34][35][36]. The exposition here is restricted to the description of the two-qubit quantum circuit, which is represented in figure 3.…”

Section: (D) Grover's Algorithmmentioning

confidence: 99%

“…Using circularly polarized RF pulses combined with double quantum excitation, Possa et al [18] demonstrated the creation of two-qubit PPS and the implementation of the C-NOT gate in zero-field NQR of nuclei with I = 3 2 in an axially symmetric EFG, taking 35 Cl nuclei in a single crystal of KClO 3 as an illustrative example. The required pulse sequences were detailed, and the results of typical experiments were simulated using a numerical procedure.…”

Section: Nuclear Quadrupole Resonance Studiesmentioning

confidence: 99%

“…Furthermore, the number of substances suitable for quantum computing applications via NQR is much more limited than in the NMR case, because NQR is observable only for quadrupolar nuclei placed in a site with a non-vanishing EFG. Both zero-field NQR and Zeeman-perturbed NQR experiments are widely reported in the literature on quadrupolar nuclei, and more frequent examples involve the nuclides 35 Cl (I = 3 2 ) and 14 N (I = 1) [37]. In zero-field or pure NQR, the Hamiltonian given in equation (2.1), describing the interaction between a nucleus with spin quantum number I and the EFG tensor at the site of the nucleus, is the only static interaction acting on the nuclear spin (disregarding other internal local fields).…”

Section: Nuclear Quadrupole Resonance Studiesmentioning

confidence: 99%

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Quantum information processing by nuclear magnetic resonance on quadrupolar nuclei

Teles

deAzevedo

Freitas

et al. 2012

Phil. Trans. R. Soc. A.

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Nuclear magnetic resonance is viewed as an important technique for the implementation of many quantum information algorithms and protocols. Although the most straightforward approach is to use the two-level system composed of spin 1 2 nuclei as qubits, quadrupolar nuclei, which possess a spin greater than 1 2 , are being used as an alternative. In this study, we show some unique features of quadrupolar systems for quantum information processing, with an emphasis on the ability to execute efficient quantum state tomography (QST) using only global rotations of the spin system, whose performance is shown in detail. By preparing suitable states and implementing logical operations by numerically optimized pulses together with the QST method, we follow the stepwise execution of Grover's algorithm. We also review some work in the literature concerning the relaxation of pseudo-pure states in spin 3 2 systems as well as its modelling in both the Redfield and Kraus formalisms. These data are used to discuss differences in the behaviour of the quantum correlations observed for two-qubit systems implemented by spin 1 2 and quadrupolar spin 3 2 systems, also presented in the literature. The possibilities and advantages of using nuclear quadrupole resonance experiments for quantum information processing are also discussed.

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Section: (D) Grover's Algorithmmentioning

confidence: 99%

Section: Nuclear Quadrupole Resonance Studiesmentioning

confidence: 99%

Section: Nuclear Quadrupole Resonance Studiesmentioning

confidence: 99%

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Quantum information processing by nuclear magnetic resonance on quadrupolar nuclei

Teles

deAzevedo

Freitas

et al. 2012

Phil. Trans. R. Soc. A.

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“…A driving Hamiltonian is then con-structed, without any knowledge of the solution, to produce a Rabi-like half-cycle which populates the marked state in a time scaling as N 1/2 , thereby exhibiting the quadratic speedup. An experimental realization of this analog Grover algorithm has been performed by NMR [11] in a setting where a quadrupolar coupling makes a spin 3/2 nucleus a two-qubit system (N =4).…”

Section: Introductionmentioning

confidence: 99%

Analog Grover search by adiabatic passage in a cavity-laser-atom system

Daems

Guérin

2008

Phys. Rev. A

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A physical implementation of the adiabatic Grover search is theoretically investigated in a system of N identical three-level atoms trapped in a single mode cavity. Some of the atoms are marked through the presence of an energy gap between their two ground states. The search is controlled by two partially delayed lasers which allow a deterministic adiabatic transfer from an initially entangled state to the marked states. Pulse schemes are proposed to satisfy the Grover speedup either exactly or approximately, and the success rate of the search is calculated.

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“…Several quantum algorithms outperforming their classical analogs have been proposed and implemented more or less successfully. These algorithms, based on the quantum parallelism, target such problems like factoring large numbers into prime numbers 2 , optimization 3 , and search 4 . The incredible possibilities offered by quantum computers made the scientists invest a lot of efforts in this field.…”

mentioning

confidence: 99%

All optical controlled-NOT gate based on an exciton–polariton circuit

Solnyshkov

Bleu

Malpuech

2015

Superlattices and Microstructures

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We propose an implementation of a CNOT quantum gate for quantum computing based on a patterned microcavity polariton system, which can be manufactured using the modern technological facilities. The qubits are encoded in the spin of polaritons. The structure consists of two wire cavities oriented at 45 degrees with a micropillar between them. The polariton spin rotates due to the Longitudinal-Transverse splitting between polarisation eigenstates in the wires. In the pillar, the optically generated circularly polarised polariton macrooccupied state plays the role of the control qubit. Because of the spin-anisotropic polariton interaction, it induces an effective magnetic field along the Z-direction with a sign depending on the qubit value. Quantum computing has evolved a lot since the original idea of R. Feynmann 1 . Several quantum algorithms outperforming their classical analogs have been proposed and implemented more or less successfully. These algorithms, based on the quantum parallelism, target such problems like factoring large numbers into prime numbers 2 , optimization 3 , and search 4 . The incredible possibilities offered by quantum computers made the scientists invest a lot of efforts in this field. However, the implementation of these algorithms is haunted by serious obstacles, the most important one being the rapid decoherence of quantum bits (qubits). Various physical implementations of these algorithms have been proposed, the most important difference between them being the choice of the physical realization of the quantum states for encoding the qubits. The implementations can be based on discrete quantum states, such as the confined states of the quantum dots 5 , on the spin degree of freedom, as in liquid-state nuclear magnetic resonance 6 , or on different combinations of the states of Bose-Einstein condensates 7 . All these degrees of freedom can be combined to encode information if one decides to make use of quantum microcavities in the strong coupling regime, and the corresponding 2-dimensional quasiparticles -excitonpolaritons. These particles are a superposition of light (photons confined in the microcavity) and matter (excitons in the quantum wells) 8 . They can be easily crated, controlled, and detected using optical means, and their polarization (spin) degree of freedom is easy to manipulate and measure as well 9 . Their in-plane spatial confinement can be organized by patterning the microcavity 10-15 and/or by applying external potentials, which can be created optically 24 as a basis for qubit representation. This approach, however, is limited by the use of the strongly damped upper polariton branch, which leads to rapid decoherence of the qubit 25 , and by the difficulties with the control of the qubit state, requiring large energy shifts. We propose to use the polarization degree of freedom of polaritons to encode information. For example, the circular-polarized σ + state can be assigned a logical 0 (|0 ), and the σ − state can be assigned a logical 1 (|1 ). A generic qubit is a super...

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Experimental realization of a continuous version of the Grover algorithm

Cited by 43 publications

References 23 publications

Quantum information processing by nuclear magnetic resonance on quadrupolar nuclei

Quantum information processing by nuclear magnetic resonance on quadrupolar nuclei

Analog Grover search by adiabatic passage in a cavity-laser-atom system

All optical controlled-NOT gate based on an exciton–polariton circuit

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