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arXiv:quant-ph/0104034 · Physical Review A

Simple pulses for universal quantum computation with a Heisenberg ABAB chain

Simon C. Benjamin

Published Oct 18, 2001• 49 citations
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Abstract

Recently, Levy has shown that quantum computation may be performed using an $\mathrm{ABAB}\dots{}$ chain of spin-1/2 systems with nearest-neighbor Heisenberg interactions. Levy notes that all necessary elementary computational ``gates'' may be achieved purely by manipulating the spin-spin interaction: he proposes using ``spin-resonance'' techniques involving modulating the interaction strength at high frequency. Here, we establish an alternative: it is possible to perform the elementary gates via simple, nonoscillatory switching of the interaction strength. This approach removes a time ``bottle neck'' in Levy's scheme, so that all elementary operations may now be performed within a time scale of order $\ensuremath{\Elzxh}{/(E}_{A}\ensuremath{-}{E}_{B}).$

DOI
10.1103/physreva.64.054303

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Recently, Levy has shown that quantum computation may be performed using an ABAB…\mathrm{ABAB}\dots{}ABAB… chain of spin-1/2 systems with nearest-neighbor Heisenberg interactions. Levy notes that all necessary elementary computational gates'' may be achieved purely by manipulating the spin-spin interaction: he proposes using spin-resonance'' techniques involving modulating the interaction strength at high frequency. Here, we establish an alternative: it is possible to perform the elementary gates via simple, nonoscillatory switching of the interaction strength. This approach removes a time ``bottle neck'' in Levy's scheme, so that all elementary operations may now be performed within a time scale of order \ensuremath\Elzxh/(EA\ensuremath−EB).\ensuremath{\Elzxh}{/(E}_{A}\ensuremath{-}{E}_{B}).\ensuremath\Elzxh/(EA​\ensuremath−EB​).
Heisenberg spin chains can act as quantum wires transferring quantum states either perfectly or with high fidelity. Gaussian packets of excitations passing through dual rails can encode the two states of a logical qubit, depending on which rail is empty and which rail is carrying the packet. With extra interactions in one or between different chains, one can introduce interaction zones in arrays of such chains, where specific one- or two-qubit gates act on any qubit which passes through these interaction zones. Therefore, universal quantum computation is made possible in a static way where no external control is needed. This scheme will then pave the way for a scalable way of quantum computation where specific hardware can be connected to make large quantum circuits. Our scheme is an improvement of a recent scheme where we borrowed an idea from quantum electrodynamics to replace nonlocal interactions between spin chains with local interactions mediated by an ancillary chain.
The effective Heisenberg interaction is generated by weakly interacting qubits with two strongly coupled chains. The system of two coupled chains can be regarded as a quantum bus. Universal quantum computation is enabled by restricting the bus to its ground state. The effective interaction is primarily determined by the energy spectrum of the bus. The interactions alternate between antiferromagnetic and ferromagnetic ones. The long-range interaction can also be attained in coupled chains with infinite size. The quantum gate operations with high precision can be realized when the quantum fluctuations are taken into account.
If the interaction between qubits is not diagonal in the computational basis (e.g., the Heisenberg interaction), then one must be able to "switch it off" in order to prevent uncontrolled propagation of states. Therefore, schemes for quantum computing typically demand local control of the interaction strength between each pair of neighboring qubits. Here we demonstrate that this degree of control is not necessary: it suffices to switch the interaction collectively, something that can in principle be achieved by global fields rather than with local manipulations. This observation may offer a significant simplification for various implementations, including solid state and optical lattice schemes.
Abstract. Quantum processors that combine the long decoherence times of spin qubits together with fast optical manipulation of excitons have recently been the subject of several proposals. I show here that arbitrary single- and entangling twoqubit gates can be performed in a chain of perpetually coupled spin qubits solely by using laser pulses to excite higher lying states. It is also demonstrated that universal quantum computing is possible even if these pulses are applied globally to a chain; by employing a repeating pattern of four distinct qubit units the need for individual qubit addressing is removed. Some current experimental qubit systems would lend themselves to implementing this idea. PACS numbers: 03.67.-a, 03.67.Lx, 78.67.HcGlobal Optical Control of a Quantum Spin Chain 2 1.