Heisenberg Spin Bus as a Robust Transmission Line for Perfect State Transfer

We study the protocol known as quantum state transfer for a strongly coupled antiferromagnetic spin chain or ring (acting as a spin bus), with weakly coupled external qubits. By treating the weak coupling as a perturbation, we find that perfect state transfer (PST) is possible when second order terms are included in the expansion. We also show that PST is robust against variations in the couplings along the spin bus and between the bus and the qubits. As evidence of the quantum interference which mediates PST, we show that the optimal time for PST can be smaller with larger qubit separations, for an even-size chain or ring.Comment: 6 figures,submitte

Effect of Randomness on Quantum Data Buses of Heisenberg Spin Chains

A strongly coupled spin chain can mediate long-distance effective couplings or entanglement between remote qubits, and can be used as a quantum data bus. We study how the fidelity of a spin-1/2 Heisenberg chain as a spin bus is affected by static random exchange couplings and magnetic fields. We find that, while non-uniform exchange couplings preserve the isotropy of the qubit effective couplings, they cause the energy levels, the eigenstates, and the magnitude of the couplings to vary locally. On the other hand, random local magnetic fields lead to an avoided level crossing for the bus ground state manifold, and cause the effective qubit couplings to be anisotropic. Interestingly, the total magnetic moment of the ground state of an odd-size bus may not be parallel to the average magnetic field. Its alignment depends on both the direction of the average field and the field distribution, in contrast with the ground state of a single spin which always aligns with the applied magnetic field to minimize the Zeeman energy. Lastly, we calculate sensitivities of the spin bus to such local variations, which are potentially useful for evaluating decoherence when dynamical fluctuations in the exchange coupling or magnetic field are considered

Topology of Entanglement Evolution of Two Qubits

The dynamics of a two-qubit system is considered with the aim of a general categorization of the different ways in which entanglement can disappear in the course of the evolution, e.g., entanglement sudden death. The dynamics is described by the function ~n(t), where ~n is the 15-dimensional polarization vector. This representation is particularly useful because the components of ~n are direct physical observables, there is a meaningful notion of orthogonality, and the concurrence C can be computed for any point in the space. We analyze the topology of the space S of separable states (those having C = 0), and the often lower-dimensional linear dynamical subspace D that is characteristic of a specific physical model. This allows us to give a rigorous characterization of the four possible kinds of entanglement evolution. Which evolution is realized depends on the dimensionality of D and of D \cap S, the position of the asymptotic point of the evolution, and whether or not the evolution is "distance-Markovian", a notion we define. We give several examples to illustrate the general principles, and to give a method to compute critical points. We construct a model that shows all four behaviors.Comment: 15 pages, 11 figures, 2 tabl

Resonant Adiabatic Passage with Three Qubits

We investigate the non-adiabatic implementation of an adiabatic quantum teleportation protocol, finding that perfect fidelity can be achieved through resonance. We clarify the physical mechanisms of teleportation, for three qubits, by mapping their dynamics onto two parallel and mutually-coherent adiabatic passage channels. By transforming into the adiabatic frame, we explain the resonance by analogy with the magnetic resonance of a spin-1/2 particle. Our results establish a fast and robust method for transferring quantum states, and suggest an alternative route toward high precision quantum gates

Mediated gates between spin qubits

In a typical quantum circuit, nonlocal quantum gates are applied to nonproximal qubits. If the underlying physical interactions are short-range (e.g., exchange interactions between spins), intermediate swap operations must be introduced, thus increasing the circuit depth. Here we develop a class of "mediated" gates for spin qubits, which act on nonproximal spins via intermediate ancilla qubits. At the end of the operation, the ancillae return to their initial states. We show how these mediated gates can be used (1) to generate arbitrary quantum states and (2) to construct arbitrary quantum gates. We provide some explicit examples of circuits that generate common states [e.g., Bell, Greenberger-Horne-Zeilinger (GHZ), W, and cluster states] and gates (e.g.,square-root-SWAP, SWAP, CNOT, and Toffoli gates). We show that the depths of these circuits are often shorter than those of conventional swap-based circuits. We also provide an explicit experimental proposal for implementing a mediated gate in a triple-quantum-dot system.Comment: 12 pages, 8 figures, 2 table