Daniel Burgarth

Non-Markovian dynamics in a spin star system: Exact solution and approximation techniques

The reduced dynamics of a central spin coupled to a bath of

Conclusive and arbitrarily perfect quantum-state transfer using parallel spin-chain channels

N

Local controllability of quantum networks

spin-

Scalable quantum computation via local control of only two qubits

\frac{1}{2}

Zero Forcing, Linear and Quantum Controllability for Systems Evolving on Networks

particles arranged in a spin star configuration is investigated. The exact time evolution of the reduced density operator is derived, and an analytical solution is obtained in the limit

Indirect Hamiltonian identification through a small gateway

N\ensuremath{\rightarrow}\ensuremath{\infty}

Indirect quantum tomography of quadratic Hamiltonians

of an infinite number of bath spins, where the model shows complete relaxation and partial decoherence. It is demonstrated that the dynamics of the central spin cannot be treated within the Born-Markov approximation. The Nakajima-Zwanzig and the time-convolutionless projection operator technique are applied to the spin star system. The performance of the corresponding perturbation expansions of the non-Markovian equations of motion is examined through a comparison with the exact solution.

Coupling strength estimation for spin chains despite restricted access

We suggest a protocol for perfect quantum communication through spin-chain channels. By combining a dual-rail encoding with measurements only at the receiving end, we can get conclusively perfect state transfer, whose probability of success can be made arbitrarily close to unity. As an example of such an amplitude-delaying channel, we show how two parallel Heisenberg spin chains can be used as quantum wires. Perfect state transfer with a probability of failure lower than P in a Heisenberg chain of N spin-(1/2) particles can be achieved in a timescale of the order of (0.33({Dirac_h}/2{pi})/J)N{sup 1.7} vertical bar ln P vertical bar. We demonstrate that our scheme is more robust to decoherence and nonoptimal timing than any scheme using single spin chains.

Dynamics of nonequilibrium thermal entanglement

We give a sufficient criterion that guarantees that a many-body quantum system can be controlled by properly manipulating the (local) Hamiltonian of one of its subsystems. The method can be applied to a wide range of systems: it does not depend on the details of the couplings but only on their associated topology. As a special case, we prove that Heisenberg and Affleck-Kennedy-Lieb-Tasaki chains can be controlled by operating on one of the spins at their ends. In principle, arbitrary quantum algorithms can be performed on such chains by acting on a single qubit.

Improved transfer of quantum information using a local memory.

We apply quantum control techniques to a long spin chain by acting only on two qubits at one of its ends, thereby implementing universal quantum computation by a combination of quantum gates on these qubits and indirect swap operations across the chain. It is shown that the control sequences can be computed and implemented efficiently. We discuss the application of these ideas to physical systems such as superconducting qubits in which full control of long chains is challenging.