Erratum: Simple Proof of Equivalence between Adiabatic Quantum Computation and the Circuit Model [Phys. Rev. Lett. 99, 070502 (2007)].

This corrects the article DOI: 10.1103/PhysRevLett.99.070502.

Entanglement versus gap, quantum teleportation, and the AKLT model.

Quantum-mechanical entanglement is notoriously volatile because of its susceptibility to external disturbances. However, entanglement can be stabilized if it is present in the non-degenerate ground state of a gapped, time-independent Hamiltonian. In this paper, we devise a spin-chain Hamiltonian whose ground state contains a Bell pair, with one member of the pair at each end of the chain. We study the Hamiltonian numerically, using full numerical diagonalization and a carefully tailored mean-field theory, to show that it is gapped. Whenever the Hamiltonian is tuned to increase its gap, the fidelity of its Bell pair decreases, manifesting a fundamental contention. The form of the Hamiltonian is motivated by quantum teleportation. Comparing it to the canonical Affleck, Kennedy, Lieb, and Tasaki (AKLT) model, we find that the AKLT model exhibits a sort of 'failed quantum teleportation'.

Critically damped quantum search.

Although measurement and unitary processes can accomplish any quantum evolution in principle, thinking in terms of dissipation and damping can be powerful. We propose a modification of Grover's algorithm in which the idea of damping plays a natural role. Remarkably, we find that there is a critical damping value that divides between the quantum O(sqrt[N]) and classical O(N) search regimes. In addition, by allowing the damping to vary in a fashion we describe, one obtains a fixed-point quantum search algorithm in which ignorance of the number of targets increases the number of oracle queries only by a factor of 1.5.

Simple proof of equivalence between adiabatic quantum computation and the circuit model.

We prove the equivalence between adiabatic quantum computation and quantum computation in the circuit model. An explicit adiabatic computation procedure is given that generates a ground state from which the answer can be extracted. The amount of time needed is evaluated by computing the gap. We show that the procedure is computationally efficient.

Controlled flow of spin-entangled electrons via adiabatic quantum pumping.

We propose a method to dynamically generate and control the flow of spin-entangled electrons, each belonging to a spin singlet, by means of adiabatic quantum pumping. The pumping cycle functions by periodic time variation of localized two-body interactions. We develop a generalized approach to adiabatic quantum pumping as traditional methods based on a scattering matrix in one dimension cannot be applied here. We specifically compute the flow of spin-entangled electrons within a Hubbard-like model of quantum dots, discuss possible implementations, and identify parameters that can be used to control the singlet flow.

Signatures of quantum behavior in single-qubit weak measurements.

With the recent surge of interest in quantum computation, it has become very important to develop clear experimental tests for "quantum behavior" in a system. This issue has been addressed in the past in the form of the inequalities due to Bell and those due to Leggett and Garg. These inequalities concern the results of ideal projective measurements, however, which are experimentally difficult to perform in many proposed qubit designs, especially in many solid-state qubit systems. Here, we show that weak continuous measurements, which are often practical to implement experimentally, can yield particularly clear signatures of quantum coherence, both in the measured correlation functions and in the measured power spectrum.

Nonlinear coupling of nanomechanical resonators to josephson quantum circuits.

We propose a technique to couple the position operator of a nanomechanical resonator to a SQUID device by modulating its magnetic flux bias. By tuning the magnetic field properly, either linear or quadratic couplings can be realized, with a discretely adjustable coupling strength. This provides a way to realize coherent nonlinear effects in a nanomechanical resonator by coupling it to a Josephson quantum circuit. As an example, we show how squeezing of the nanomechanical resonator state can be realized with this technique. We also propose a simple method to measure the uncertainty in the position of the nanomechanical resonator without quantum state tomography.

Three- and four-body interactions in spin-based quantum computers.

In the effort to design and to construct a quantum computer, several leading proposals make use of spin-based qubits. These designs generally assume that spins undergo pairwise interactions. We point out that, when several spins are engaged mutually in pairwise interactions, the quantitative strengths of the interactions can change and qualitatively new terms can arise in the Hamiltonian, including four-body interactions. In parameter regimes of experimental interest, these coherent effects are large enough to interfere with computation and may require new error correction or avoidance techniques.

Quantum-classical reentrant relaxation crossover in Dy2Ti2O7 spin ice.

We have studied spin relaxation in the spin ice compound Dy2Ti2O7 through measurements of the ac magnetic susceptibility. While the characteristic spin-relaxation time (tau) is thermally activated at high temperatures, it becomes almost temperature independent below T(cross) approximately 13 K. This behavior, combined with nonmonotonic magnetic field dependence of tau, indicates that quantum tunneling dominates the relaxational process below that temperature. As the low-entropy spin ice state develops below T(ice) approximately 4 K, tau increases sharply with decreasing temperature, suggesting the emergence of a collective degree of freedom for which thermal relaxation processes again become important as the spins become strongly correlated.