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arXiv:quant-ph/0403052 · Journal of Modern Optics

Scalable quantum computation in systems with Bose-Hubbard dynamics

Guido Pupillo, Ana Maria Rey, Gavin K. Brennen, Carl J. Williams, Charles W. Clark

Published Nov 1, 2004• 9 citations
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Abstract

Several proposals for quantum computation utilize a lattice-type architecture with qubits trapped by a periodic potential. For systems undergoing many-body interactions described by the Bose-Hubbard Hamiltonian, the ground state carries number fluctuations that scale with the number of qubits. This process degrades the initialization of the quantum computer register. In an earlier manuscript we proposed a solution to this problem tailored to the loading of cold atoms into an optical lattice via the Mott insulator phase transition. It was shown that, by introducing an inhomogeneity to the lattice and performing a continuous measurement, the unit filled state suitable for a quantum computer register can be maintained. Here, we give a more rigorous derivation of the register fidelity in homogeneous and inhomogeneous lattices and provide evidence that the protocol is effective in the finite temperature regime.

DOI
10.1080/09500340408231798

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Several proposals for quantum computation utilize a lattice-type architecture with qubits trapped by a periodic potential. For systems undergoing many-body interactions described by the Bose-Hubbard Hamiltonian, the ground state carries number fluctuations that scale with the number of qubits. This process degrades the initialization of the quantum computer register. In an earlier manuscript we proposed a solution to this problem tailored to the loading of cold atoms into an optical lattice via the Mott insulator phase transition. It was shown that, by introducing an inhomogeneity to the lattice and performing a continuous measurement, the unit filled state suitable for a quantum computer register can be maintained. Here, we give a more rigorous derivation of the register fidelity in homogeneous and inhomogeneous lattices and provide evidence that the protocol is effective in the finite temperature regime.
Several proposals for quantum computation utilize a lattice-type architecture with qubits trapped by a periodic potential. For systems undergoing many-body interactions described by the Bose-Hubbard Hamiltonian, the ground state carries number fluctuations that scale with the number of qubits. This process degrades the initialization of the quantum computer register. In an earlier manuscript we proposed a solution to this problem tailored to the loading of cold atoms into an optical lattice via the Mott insulator phase transition. It was shown that, by introducing an inhomogeneity to the lattice and performing a continuous measurement, the unit filled state suitable for a quantum computer register can be maintained. Here, we give a more rigorous derivation of the register fidelity in homogeneous and inhomogeneous lattices and provide evidence that the protocol is effective in the finite temperature regime.
Several proposals for quantum computation utilize a lattice type architecture with qubits trapped by a periodic potential. For systems undergoing many body interactions described by the Bose-Hubbard Hamiltonian, the ground state of the system carries number fluctuations that scale with the number of qubits. This process degrades the initialization of the quantum computer register and can introduce errors during error correction. In [1] we proposed a solution to this problem tailored to the loading of cold atoms into an optical lattice via the Mott Insulator phase transition. It was shown that by adding an inhomogeneity to the lattice and performing a continuous measurement, the unit filled state suitable for a quantum computer register can be maintained. Here, we give a more rigorous derivation of the register fidelity in homogeneous and inhomogeneous lattices and provide evidence that the protocol is effective in the finite temperature regime. 1
The Mott insulator state created by loading an atomic Bose–Einstein condensate (BEC) into an optical lattice may be used as a means to prepare a register of atomic qubits in a quantum computer. Such architecture requires a lattice commensurately filled with atoms, which corresponds to the insulator state only in the limit of zero inter-well tunnelling. We show that a lattice with spatial inhomogeneity created by a quadratic magnetic trapping potential can be used to isolate a subspace in the centre which is impervious to hole-hoping. Components of the wavefunction with more than one atom in any well can be projected out by selective measurement on a molecular photo-associative transition. Maintaining the molecular coupling can sustain a commensurately filled register for the duration of a quantum computation.
The Mott insulator state created by loading an atomic Bose-Einstein condensate (BEC) into an optical lattice may be used as a means to prepare a register of atomic qubits in a quantum computer. Such architecture requires a lattice commensurately filled with atoms, which corresponds to the insulator state only in the limit of zero inter-well tunneling. We show that a lattice with spatial inhomogeneity created by a quadratic magnetic trapping potential can be used to isolate a subspace in the center which is impervious to hole-hoping. Components of the wavefunction with more than one atom in any well can be projected out by selective measurement on a molecular photo-associative transition. Maintaining the molecular coupling induces a quantum Zeno effect that can sustain a commensurately filled register for the duration of a quantum computation.
We propose a method for the fast generation of a quantum register of addressable qubits consisting of ultracold atoms stored in an optical lattice. Starting with a half filled lattice we remove every second lattice barrier by adiabatically switching on a superlattice potential which leads to a long wavelength lattice in the Mott insulator state with unit filling. The larger periodicity of the resulting lattice could make individual addressing of the atoms via an external laser feasible. We develop a Bose-Hubbard-like model for describing the dynamics of cold atoms in a lattice when doubling the lattice periodicity via the addition of a superlattice potential. The dynamics of the transition from a half filled to a commensurately filled lattice is analysed numerically with the help of the time evolving block decimation algorithm and analytically using the Kibble–Zurek theory. We show that the timescale for the whole process, i.e. creating the half filled lattice and subsequent doubling of the lattice periodicity, is significantly faster than adiabatic direct quantum-freezing of a superfluid into a Mott insulator for large lattice periods. Our method therefore provides a high-fidelity quantum register of addressable qubits on a fast timescale.
The Bose-Hubbard model describes the physics of a system of bosonic ultracold atoms in an optical lattice, in which a phase transition is present between a superfluid phase and a Mott insulator one. \nThe exact solution of this Hamiltonian is only feasible to find the ground-state of small systems, while other techniques (as mean-field schemes or quantum Monte Carlo) are necessary to study systems of larger size. \n \nAs a first application, we study the trapped model - relevant for the comparison with current experiments - through an inhomogeneous mean-field scheme. We describe some signatures of the phase crossover between superfluid and Mott insulator. In particular, the visibility of the quasimomentum distribution shows some kinks as a function of the lattice depth; we describe these features and we link them with the ones observed in other works in the literature. \n \nAs a second application, we use quantum Monte Carlo techniques to study the one-dimensional Bose-Hubbard model with long-range interactions and we focus on the appearance of the Haldane insulating phase, distinguishable from the Mott one through the presence of non-local hidden order. \nNon-local correlation functions are also used to describe the difference between the superfluid phase and the Mott insulator one.