Lian-Ao Wu

Quantum Phase Transitions and Bipartite Entanglement

We develop a general theory of the relation between quantum phase transitions (QPTs) characterized by nonanalyticities in the energy and bipartite entanglement. We derive a functional relation between the matrix elements of two-particle reduced density matrices and the eigenvalues of general two-body Hamiltonians of d-level systems. The ground state energy eigenvalue and its derivatives, whose nonanalyticity characterizes a QPT, are directly tied to bipartite entanglement measures. We show that first-order QPTs are signaled by density matrix elements themselves and second-order QPTs by the first derivative of density matrix elements. Our general conclusions are illustrated via several quantum spin models.

Reducing constraints on quantum computer design by encoded selective recoupling.

The requirement of performing both single-qubit and two-qubit operations in the implementation of universal quantum logic often leads to very demanding constraints on quantum computer design. We show here how to eliminate the need for single-qubit operations in a large subset of quantum computer proposals: those governed by isotropic and XXZ, XY-type anisotropic exchange interactions. Our method employs an encoding of one logical qubit into two physical qubits, while logic operations are performed using an analogue of the NMR selective recoupling method.

Polynomial-time simulation of pairing models on a quantum computer.

We propose a polynomial-time algorithm for simulation of the class of pairing Hamiltonians, e.g., the BCS Hamiltonian, on an NMR quantum computer. The algorithm adiabatically finds the low-lying spectrum in the vicinity of the gap between the ground and the first excited states and provides a test of the applicability of the BCS Hamiltonian to mesoscopic superconducting systems, such as ultrasmall metallic grains.

Holonomic Quantum Computation in Decoherence-Free Subspaces

We show how to realize, by means of non-Abelian quantum holonomies, a set of universal quantum gates acting on decoherence-free subspaces and subsystems. In this manner we bring together the quantum coherence stabilization virtues of decoherence-free subspaces and the fault tolerance of all-geometric holonomic control. We discuss the implementation of this scheme in the context of quantum information processing using trapped ions and quantum dots.

Linking entanglement and quantum phase transitions via density-functional theory

Density-functional theory (DFT) is shown to provide a conceptual and computational framework for entanglement in interacting many-body quantum systems. DFT can, in particular, shed light on the intriguing relationship between quantum phase transitions and entanglement. We use DFT concepts to express entanglement measures in terms of the first or second derivative of the ground-state energy. We illustrate the versatility of the DFT approach via a variety of analytically solvable models. As a further application we discuss entanglement and quantum phase transitions in the case of mean-field approximations for realistic models of many-body systems.

Fast ground-state cooling of mechanical resonators with time-dependent optical cavities

We propose a feasible scheme to cool down a mechanical resonator (MR) in a three-mirror cavity optomechanical system with controllable external optical driving fields. Under the Born-Oppenheimer approximation, the whole dynamics of the mechanical resonator and cavities is reduced to that of a time-dependent harmonic oscillator, whose effective frequency can be controlled through the optical driving fields. The fast cooling of the MR can be realized by controlling the amplitude of the optical driving fields. Significantly, we further show that the ground-state cooling may be achieved via the three-mirror cavity optomechanical system without the resolved sideband condition.

Consistency of the Adiabatic Theorem

We review the quantum adiabatic approximation for closed systems, and its recently introduced generalization to open systems (M.S. Sarandy and D.A. Lidar, eprint quant-ph/0404147). We also critically examine a recent argument claiming that there is an inconsistency in the adiabatic theorem for closed quantum systems (K.P. Marzlin and B.C. Sanders, Phys. Rev. Lett. 93, 160408 (2004).) and point out how an incorrect manipulation of the adiabatic theorem may lead one to obtain such an inconsistent result.PACS: 03.65.Ta, 03.65.Yz, 03.67.-a, 03.65.Vf.

Entanglement observables and witnesses for interacting quantum spin systems

We discuss the detection of entanglement in interacting quantum spin systems. First, thermodynamic Hamiltonian-based witnesses are computed for a general class of one-dimensional spin-1/2 models. Second, we introduce optimal bipartite entanglement observables. We show that a bipartite entanglement measure can generally be associated with a set of independent two-body spin observables whose expectation values can be used to witness entanglement. The number of necessary observables is ruled by the symmetries of the model. Illustrative examples are presented.

Qubits as Parafermions

We extend the results of Wu & Lidar, eprint quant-ph/0103039: By mapping qubits to parafermions we study the quantum computational power of a generic class of Hamiltonians. We discuss the immunity to decoherence of encoded qubits, symmetry and quantum statistical properties of qubits treated as identical parafermions.

Master Equation and Control of an Open Quantum System with Leakage

Given a multilevel system coupled to a bath, we use a Feshbach P, Q partitioning technique to derive an exact trace-nonpreserving master equation for a subspace S_{i} of the system. The resultant equation properly treats the leakage effect from S_{i} into the remainder of the system space. Focusing on a second-order approximation, we show that a one-dimensional master equation is sufficient to study problems of quantum state storage and is a good approximation, or exact, for several analytical models. It allows a natural definition of a leakage function and its control and provides a general approach to study and control decoherence and leakage. Numerical calculations on an harmonic oscillator coupled to a room temperature harmonic bath show that the leakage can be suppressed by the pulse control technique without requiring ideal pulses.