Coherent quantum evolution via reservoir driven holonomies

Slow Dynamics and Thermodynamics of Open Quantum Systems

We develop a perturbation theory of quantum (and classical) master equations with slowly varying parameters, applicable to systems which are externally controlled on a time scale much longer than their characteristic relaxation time. We apply this technique to the analysis of finite-time isothermal processes in which, differently from quasistatic transformations, the state of the system is not able to continuously relax to the equilibrium ensemble. Our approach allows one to formally evaluate perturbations up to arbitrary order to the work and heat exchange associated with an arbitrary process. Within first order in the perturbation expansion, we identify a general formula for the efficiency at maximum power of a finite-time Carnot engine. We also clarify under which assumptions and in which limit one can recover previous phenomenological results as, for example, the Curzon-Ahlborn efficiency.

Holonomic Quantum Control with Continuous Variable Systems

Universal computation of a quantum system consisting of superpositions of well-separated coherent states of multiple harmonic oscillators can be achieved by three families of adiabatic holonomic gates. The first gate consists of moving a coherent state around a closed path in phase space, resulting in a relative Berry phase between that state and the other states. The second gate consists of "colliding" two coherent states of the same oscillator, resulting in coherent population transfer between them. The third gate is an effective controlled-phase gate on coherent states of two different oscillators. Such gates should be realizable via reservoir engineering of systems that support tunable nonlinearities, such as trapped ions and circuit QED.

Coherent quantum dynamics in steady-state manifolds of strongly dissipative systems

Recently, it has been realized that dissipative processes can be harnessed and exploited to the end of coherent quantum control and information processing. In this spirit, we consider strongly dissipative quantum systems admitting a nontrivial manifold of steady states. We show how one can enact adiabatic coherent unitary manipulations, e.g., quantum logical gates, inside this steady-state manifold by adding a weak, time-rescaled, Hamiltonian term into the system's Liouvillian. The effective long-time dynamics is governed by a projected Hamiltonian which results from the interplay between the weak unitary control and the fast relaxation process. The leakage outside the steady-state manifold entailed by the Hamiltonian term is suppressed by an environment-induced symmetrization of the dynamics. We present applications to quantum-computation in decoherence-free subspaces and noiseless subsystems and numerical analysis of nonadiabatic errors.

Exponential rise of dynamical complexity in quantum computing through projections

The ability of quantum systems to host exponentially complex dynamics has the potential to revolutionize science and technology. Therefore, much effort has been devoted to developing of protocols for computation, communication and metrology, which exploit this scaling, despite formidable technical difficulties. Here we show that the mere frequent observation of a small part of a quantum system can turn its dynamics from a very simple one into an exponentially complex one, capable of universal quantum computation. After discussing examples, we go on to show that this effect is generally to be expected: almost any quantum dynamics becomes universal once ‘observed’ as outlined above. Conversely, we show that any complex quantum dynamics can be ‘purified’ into a simpler one in larger dimensions. We conclude by demonstrating that even local noise can lead to an exponentially complex dynamics.

It is an old adage in quantum physics that the observation of a system changes its properties, as exemplified by the quantum Zeno effect. Now, Burgarth et al. show that such repeated measurement of a quantum system actually enriches its dynamics, letting it explore a much larger algebra than it did before.

Adiabatic markovian dynamics

We propose a theory of adiabaticity in quantum markovian dynamics based on a decomposition of the Hilbert space induced by the asymptotic behavior of the Lindblad semigroup. A central idea of our approach is that the natural generalization of the concept of eigenspace of the Hamiltonian in the case of markovian dynamics is a noiseless subsystem with a minimal noisy cofactor. Unlike previous attempts to define adiabaticity for open systems, our approach deals exclusively with physical entities and provides a simple, intuitive picture at the Hilbert-space level, linking the notion of adiabaticity to the theory of noiseless subsystems. As two applications of our theory, we propose a general framework for decoherence-assisted computation in noiseless codes and a dissipation-driven approach to holonomic computation based on adiabatic dragging of subsystems that is generally not achievable by nondissipative means.

Nonadiabatic coherent evolution of two-level systems under spontaneous decay

In this Letter we extend current perspectives in engineering reservoirs by producing a time-dependent master equation leading to a nonstationary superposition equilibrium state that can be nonadiabatically controlled by the system-reservoir parameters. Working with an ion trapped inside a nonideal cavity, we first engineer effective interactions, which allow us to achieve two classes of decoherence-free evolution of superpositions of the ground and excited ionic levels: those with a time-dependent azimuthal or polar angle. As an application, we generalize the purpose of an earlier study [Phys. Rev. Lett. 96, 150403 (2006)10.1103/PhysRevLett.96.150403], showing how to observe the geometric phases acquired by the protected nonstationary states even under nonadiabatic evolution.