Whaley Group Publications

Another way to approach zero entropy for a finite system of atoms

Authors: D. S. Weiss and J. Vala and A. V. Thapliyal and S. Myrgren and U. Vazirani and K. B. Whaley

Phys.\ Rev.\ A 70

We propose a way to manifestly reduce the entropy of a finite system of atoms to arbitrarily small values. First, the locations of vacancies of laser-cooled atoms in a deep optical lattice are measured. Then, the distribution is efficiently compacted using a combination of site-specific atomic state flips and state-sensitive lattice site translations. In the final state, the central region of the lattice has exactly one atom per site in its vibrational ground state. This is a good initial state for a quantum computer. The process can be understood to be an experimentally viable Maxwell demon with a memory.

Deterministic optical Fock-state generation

Authors: K. R. Brown and K. M. Dani and D. M. Stamper-Kurn and K. B. Whaley

Phys.\ Rev.\ A 67 043818

We present a scheme for the deterministic generation of N-photon Fock states from N three-level atoms in a high-finesse optical cavity. The method applies an external laser pulse that generates an N-photon output state while adiabatically keeping the atom-cavity system within a subspace of optically dark states. We present analytical estimates of the error due to amplitude leakage from these dark states for general N, and compare it with explicit results of numerical simulations for N 5. The method is shown to provide a robust source of N-photon states under a variety of experimental conditions and is suitable for experimental implementation using a cloud of cold atoms magnetically trapped in a cavity. The resulting N-photon states have potential applications in fundamental studies of nonclassical states and in quantum information processing.

Encoded Universality from a Single Physical Interaction

Authors: J. Kempe and D. Bacon and D. P. DiVincenzo and K. B. Whaley

quant-ph/0112013

We present a theoretical analysis of the paradigm of encoded universality, using a Lie algebraic analysis to derive specific conditions under which physical interactions can provide universality. We discuss the significance of the tensor product structure in the quantum circuit model and use this to define the conjoining of encoded qudits. The construction of encoded gates between conjoined qudits is discussed in detail. We illustrate the general procedures with several examples from exchange-only quantum computation. In particular, we extend our earlier results showing universality with the isotropic exchange interaction to the derivation of encoded universality with the anisotropic exchange interaction, i.e., to the XY model. In this case the minimal encoding for universality is into qutrits rather than into qubits as was the case for isotropic (Heisenberg) exchange. We also address issues of fault-tolerance, leakage and correction of encoded qudits.

Generation of quantum logic operations from physical Hamiltonians

Authors: J. Zhang and K. B. Whaley

Phys.\ Rev.\ A 71 052317

We provide a systematic analysis of the physical generation of single- and two-qubit quantum operations from Hamiltonians available in various quantum systems for scalable quantum information processing. We show that generation of single-qubit operations can be transformed into a steering problem on the Bloch sphere, which represents all Rz-equivalence classes of single-qubit operations, whereas the two-qubit problem can be generally transformed into a steering problem in a tetrahedron representing all the local-equivalence classes of two-qubit operations the Weyl chamber . We use this approach to investigate several physical examples for the generation of two-qubit operations. The steering approach provides useful guidance for the realization of various quantum computation schemes.

Perfect pattern formation of neutral in an addressable optical lattice

Authors: J. Vala and A. V. Thapliyal and S. Myrgren and U. Vazirani and D. S. Weiss and K. B. Whaley

Phys.\ Rev.\ A 71

We propose a physical scheme for formation of an arbitrary pattern of neutral atoms in an addressable optical lattice. We focus specifically on the generation of a perfect optical lattice of simple orthorhombic structure with unit occupancy, as required for initialization of a neutral atom quantum computer. The scheme employs a compacting process that is accomplished by sequential application of two types of operations: a flip operator that changes the internal state of the atoms, and a shift operator that selectively moves the atoms in one internal state along the lattice principal axis. Realizations of these elementary operations and their physical limitations are analyzed. The complexity of the compacting scheme is analyzed and we show that this scales linearly with the number of lattice sites per row of the lattice.

Quantum Error Correction of a Qubit Loss in an Addressable Atomic System

Authors: J. Vala and K. B. Whaley and D. S. Weiss

arXiv:quant-ph/0510021

We present a scheme for correcting qubit loss error while quantum computing with neutral atoms in an addressable optical lattice. The qubit loss is first detected using a quantum non-demolition measurement and then transformed into a standard qubit error by inserting a new atom in the vacated lattice site. The logical qubit, encoded here into four physical qubits with the Grassl-BethPellizzari code, is reconstructed via a sequence of one projective measurement, two single-qubit gates, and three controlled-NOT operations. No ancillary qubits are required. Both quantum non-demolition and projective measurements are implemented using a cavity QED system which can also detect a general leakage error and thus allow qubit loss to be corrected within the same framework. The scheme can also be applied in quantum computation with trapped ions or with photons.

Scalable Ion Trap Quantum Computation with Pairwise Interactions Only

Authors: K. R. Brown and J. Vala and K. B. Whaley

Universal ion trap computation on Decoherence Free Subspaces (DFS) using only two qubit operations is presented. The DFS is constructed for the collective dephasing model. Encoded single and two-qubit logical operations are implemented via the Sorensen-Molmer interaction. Alternation of the effective Hamiltonians for two particular phase configurations of control fields approximates an anisotropic exchange interaction. This is universal over suitable encodings of one logical qubit into three physical qubits which are also DFS under collective decoherence.