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arXiv:quant-ph/0609111 · Physical Review Letters

Quantum Logic via the Exchange Blockade in Ultracold Collisions

David Hayes, Paul S. Julienne, Ivan Deutsch

Published Feb 14, 2007• 116 citations
arXivHTMLPDF

Abstract

A nuclear spin can act as a quantum switch that turns on or off ultracold collisions between atoms even when there is neither interaction between nuclear spins nor between the nuclear and electron spins. This "exchange blockade" is a new mechanism for implementing quantum logic gates that arises from the symmetry of composite identical particles, rather than direct coupling between qubits. We study the implementation of the entangling sqrt SWAP gate based on this mechanism for a model system of two atoms, each with ground electronic configuration 1S0, spin 1/2 nuclei, and trapped in optical tweezers. We evaluate a proof-of-principle protocol based on adiabatic evolution of a one-dimensional double Gaussian well, calculating fidelities of operation as a function of interaction strength, gate time, and temperature.

DOI
10.1103/physrevlett.98.070501

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We describe how to implement quantum logic operations in a silicon-based quantum computer with phosphorus atoms serving as qubits. The information is stored in the states of nuclear spins and the conditional logic operations are implemented through the electron spins using nuclear–electron hyperfine and electron–electron exchange interactions. The electrons in our computer should stay coherent only during implementation of one Controlled-NOT gate. The exchange interaction is constant, and selective excitations are provided by a magnetic field gradient. The quantum logic operations are implemented by rectangular radio-frequency pulses. This architecture is scalable and does not require manufacturing nanoscale electronic gates. As shown in this paper, parameters of a quantum protocol can be derived analytically even for a computer with a large number of qubits using our perturbation approach. We present the protocol for initialization of the nuclear spins and the protocol for creation of entanglement. All analytical results are tested numerically using a two-qubit system.
The use of nuclear spins for quantum computation is limited by the difficulty in creating genuine quantum entanglement between distant nuclei. Current demonstrations of nuclear entanglement in semiconductors rely on coupling the nuclei to a common electron, which is not a scalable strategy. In this work, we demonstrated a two-qubit controlled-Z logic operation between the nuclei of two phosphorus atoms in a silicon device, separated by up to 20 nanometers. Each atom binds separate electrons, whose exchange interaction mediates the nuclear two-qubit gate. We prepared and measured a nuclear Bell state with a fidelity of [Formula: see text] and a concurrence of [Formula: see text]. With this method, future progress in scaling up semiconductor spin qubits can be extended to the development of nuclear spin-based quantum computers.
We describe how to implement quantum logic operations in a silicon-based quantum computer with phosphorus atoms serving as qubits. The information is stored in the states of nuclear spins and the conditional logic operations are implemented through the electron spins using nuclear-electron hyperfine and electron-electron exchange interactions. The electrons in our computer should stay coherent only during implementation of one Control-Not gate. The exchange interaction is constant and selective excitations are provided by a magnetic field gradient. The quantum logic operations are implemented by rectangular radio-frequency pulses. This architecture is scalable and does not require manufacturing nanoscale electronic gates. As shown in this paper parameters of a quantum protocol can be derived analytically even for a computer with a large number of qubits using our perturbation approach. We present the protocol for initialization of the nuclear spins and the protocol for creation of entanglement. All analytical results are tested numerically using a two-qubit system.
A two-electron system confined in two coupled semiconductor quantum dots is investigated as a candidate for performing quantum logic operations with spin qubits. We study different processes of swapping the electron spins by a controlled switching on and off of the exchange interaction. The resulting spin swap corresponds to an elementary operation in quantum-information processing. We perform direct simulations of the time evolution of the two-electron system. Our results show that, in order to obtain the full interchange of spins, the exchange interaction should change smoothly in time. The presence of jumps and spikes in the time characteristics of the confinement potential leads to a considerable increase of the spin-swap time. We propose several mechanisms to modify the exchange interaction by changing the confinement potential profile and discuss their advantages and disadvantages.
We propose an implementation for quantum logic and computing using trapped atomic spins of two different species, interacting via direct magnetic spin-spin interaction. In this scheme, the spins (electronic or nuclear) of distantly spaced trapped neutral atoms serve as the qubit arrays for quantum information processing and storage, and the controlled interaction between two spins, as required for universal quantum computing, is implemented in a three-step process that involves state swapping with a movable auxiliary spin.
We propose a scheme to implement the two-qubit gates between the nuclear spins of the encapsulated atoms in endohedral fullerenes 15N@C60^{15}\mathrm{N}@{\mathrm{C}}_{60}15N@C60​ or 31P@C60^{31}\mathrm{P}@{\mathrm{C}}_{60}31P@C60​, within today's magnetic resonance techniques. Since there is no interaction between the nuclear spins, this scheme employs the electronic spins as medium and two swap operations are proposed to transfer the information between the nuclear spin 12\frac{1}{2}21​ and the electronic spin 32\frac{3}{2}23​, and between two electronic spins 32\frac{3}{2}23​. These two-qubit gates, along with the single-qubit rotation gates, compose a universal set of quantum gates in fullerene-based quantum computation.