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arXiv:quant-ph/0610168 · Physical Review A

Local operations in qubit arrays via global periodic manipulation

Zheng-Wei Zhou, Yong‐Jian Han, Guang‐Can Guo

Published Nov 27, 2006• 11 citations
arXivHTMLPDF

Abstract

We provide a scheme for quantum computation in lattice systems via global but periodic manipulation, in which only effective periodic magnetic fields and global nearest-neighbor interactions are required. All operations in our scheme are attainable in optical-lattice or solid-state systems. We also investigate universal quantum operations and quantum simulation of two-dimensional lattices. We find that global manipulations are superior in simulating some nontrivial many-body Hamiltonians.

DOI
10.1103/physreva.74.052334

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We provide a scheme for quantum computation in lattice systems via global but periodic manipulation, in which only effective periodic magnetic fields and global nearest-neighbor interactions are required. All operations in our scheme are attainable in optical-lattice or solid-state systems. We also investigate universal quantum operations and quantum simulation of two-dimensional lattices. We find that global manipulations are superior in simulating some nontrivial many-body Hamiltonians.
A scheme for globally addressing a quantum computer is presented along with its realization in an optical lattice set-up of one, two or three dimensions. The required resources are mainly those necessary for performing quantum simulations of spin systems with optical lattices, circumventing the necessity for single qubit addressing. We present the control procedures, in terms of laser manipulations, required to realize universal quantum computation. Error avoidance with the help of the quantum Zeno effect is presented and a scheme for globally addressed error correction is given. The latter does not require measurements during the computation, facilitating its experimental implementation. As an illustrative example, the pulse sequence for the factorization of the number 15 is given.
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.
Typical quantum computing schemes require transformations (gates) to be targeted at specific elements (qubits). In many physical systems, direct targeting is difficult to achieve; an alternative is to encode local gates into globally applied transformations. Here we demonstrate the minimum physical requirements for such an approach: a one-dimensional array composed of two alternating ``types'' of two-state system. Each system need be sensitive only to the net state of its nearest neighbors, i.e. the number in state $``\ensuremath{\uparrow}''$ minus the number in $``\ensuremath{\downarrow}.''$ Additionally, we show that all such arrays can perform quite general parallel operations. A broad range of physical systems and interactions is suitable: we highlight two examples.
We propose the use of quantum optical systems to perform universal simulation of quantum dynamics. Two specific implementations that require present technology are put forward for illustrative purposes. The first scheme consists of neutral atoms stored in optical lattices, while the second scheme consists of ions stored in an array of micro--traps. Each atom (ion) supports a two--level system, on which local unitary operations can be performed through a laser beam. A raw interaction between neighboring two--level systems is achieved by conditionally displacing the corresponding atoms (ions). Then, average Hamiltonian techniques are used to achieve evolutions in time according to a large class of Hamiltonians.
We propose the use of quantum optical systems to perform universal simulation of quantum dynamics. Two specific implementations that require present technology are put forward for illustrative purposes. The first scheme consists of neutral atoms stored in optical lattices, while the second scheme consists of ions stored in an array of micro--traps. Each atom (ion) supports a two--level system, on which local unitary operations can be performed through a laser beam. A raw interaction between neighboring two--level systems is achieved by conditionally displacing the corresponding atoms (ions). Then, average Hamiltonian techniques are used to achieve evolutions in time according to a large class of Hamiltonians.
We propose the use of quantum optical systems to perform universal simulation of quantum dynamics. Two specific implementations that require present technology are put forward for illustrative purposes. The first scheme consists of neutral atoms stored in optical lattices, while the second scheme consists of ions stored in an array of micro--traps. Each atom (ion) supports a two--level system, on which local unitary operations can be performed through a laser beam. A raw interaction between neighboring two--level systems is achieved by conditionally displacing the corresponding atoms (ions) Then, average Hamiltonian techniques are used to achieve evolutions in time according to a large class of Hamiltonians.