Mystery, Myth, Reality and Truth about quantum computer

Physical Review A, 1996

We describe an array of quantum gates implementing Shor's algorithm for prime factorization in a quantum computer. The array includes a circuit for modular exponentiation with several subcomponents (such as controlled multipliers, adders, etc) which are described in terms of elementary Toffoli gates.

Fluctuations and Noise in Photonics and Quantum Optics, 2003

The principal obstacle to quantum information processing with many qubits is decoherence. One source of decoherence is spontaneous emission which causes loss of energy and information. Inability to control system parameters with high precision is another possible source of error. Strategies aimed at overcoming one kind of error typically increase sensitivity to others. As a solution we propose quantum computing with dissipationassisted quantum gates. These can be run relatively fast while achieving fidelities close to one. The success rate of each gate operation can, at least in principle, be arbitrary close to one.

Physical Review Letters, 2000

We propose a new approach to the implementation of quantum gates in which decoherence during the gate operations is strongly reduced. This is achieved by making use of an environment induced quantum Zeno effect that confines the dynamics effectively to a decoherence-free subspace.

Journal of Physics: Conference Series, 2009

In spite of the quantum-mechanical nature of the electron and photon dynamics in the core region of typical solidstate nanodevices, the overall behavior of such quantum systems is often characterized by a non-trivial interplay between phase coherence and energy relaxation/dephasing phenomena. 1,2 This fundamental topic is getting more and more critical in the last years, due to the continuous downscaling in size that state-of-the-art technology allows for. The proper modelling of, e.g., charge-carrier dynamics in cascade nanodevices, 3,4 rather than of spin/chargebased implementations of quantum-computation algorithms in solid-state logic gates, 5,6 are just a couple of examples demanding for a unitary microscopic description. Not to forget the still unsolved issue represented by the effects due to the presence of spatial boundaries (contacts). 7

2012

Dissipative engineering constitutes a framework within which quantum information processing protocols are powered by system-environment interaction rather than by unitary dynamics alone. This framework embraces noise as a resource, and consequently, offers a number of advantages compared to one based on unitary dynamics alone, e.g., that the protocols are typically independent of the initial state of the system. However, the time independent nature of this scheme makes it difficult to imagine precisely timed sequential operations, conditional measurements or error correction. In this work, we provide a path around these challenges, by introducing basic dissipative gadgets which allow us to precisely initiate, trigger and time dissipative operations, while keeping the system Liouvillian time-independent. These gadgets open up novel perspectives for thinking of timed dissipative quantum information processing. As an example, we sketch how measurement based computation can be simulated in the dissipative setting. arXiv:1205.0985v2 [quant-ph]

Physical Review A, 2011

Pointer states are long-lasting high-fidelity states in open quantum systems. We show how any pure state in a non-Markovian open quantum system can be made to behave as a pointer state by suitably engineering the coupling to the environment via open-loop periodic control. Engineered pointer states are constructed as approximate fixed points of the controlled open-system dynamics, in such a way that they are guaranteed to survive over a long time with a fidelity determined by the relative precision with which the dynamics is engineered. We provide quantitative minimumfidelity bounds by identifying symmetry and ergodicity conditions that the decoherence-inducing perturbation must obey in the presence of control, and develop explicit pulse sequences for engineering any desired set of orthogonal states as pointer states. These general control protocols are validated through exact numerical simulations as well as semi-classical approximations in realistic single-and two-qubit dissipative systems. We also examine the role of control imperfections, and show that while pointer-state engineering protocols are highly robust in the presence of systematic pulse errors, the latter can also lead to unintended pointer-state generation in dynamical decoupling implementations, explaining the initial-state selectivity observed in recent experiments.

Annals of Physics, 1992

We discuss some aspects of dissipation in quantum field theory starting from the example of the quantum mechanical damped harmonic oscillator. We show that the set of states of the system splits into unitarily inequivalent representations of the canonical commutation relations. At quantum level the irreversibility of time evolution is expressed as tunneling among the unitarily inequivalent representations. Statistical and thermodynamical properties of the formalism are analysed and canonical quantization is shown to lead to time dependent SU( 1, 1) coherent states, well known in high energy physics as well as in quantum optics and thermal field theory. $0

New Journal of Physics, 2017

We introduce and study the adiabatic dynamics of free-fermion models subject to a local Lindblad bath and in the presence of a time-dependent Hamiltonian. The merit of these models is that they can be solved exactly, and will help us to study the interplay between non-adiabatic transitions and dissipation in many-body quantum systems. After the adiabatic evolution, we evaluate the excess energy (average value of the Hamiltonian) as a measure of the deviation from reaching the target final ground state. We compute the excess energy in a variety of different situations, where the nature of the bath and the Hamiltonian is modified. We find a robust evidence of the fact that an optimal working time for the quantum annealing protocol emerges as a result of the competition between the non-adiabatic effects and the dissipative processes. We compare these results with matrix-product-operator simulations of an Ising system and show that the phenomenology we found applies also for this more realistic case.

Semiconductor Science and Technology, 2009

We shall revisit the conventional adiabatic or Markov approximation, which-contrary to the semiclassical case-does not preserve the positive-definite character of the corresponding density matrix, thus leading to highly non-physical results. To overcome this serious limitation, originally pointed out and partially solved by Davies and co-workers almost three decades ago, we shall propose an alternative more general adiabatic procedure, which (i) is physically justified under the same validity restrictions of the conventional Markov approach, (ii) in the semiclassical limit reduces to the standard Fermi's golden rule, and (iii) describes a genuine Lindblad evolution, thus providing a reliable/robust treatment of energy-dissipation and dephasing processes in electronic quantum devices. Unlike standard master-equation formulations, the dependence of our approximation on the specific choice of the subsystem (that include the common partial trace reduction) does not threaten positivity, and quantum scattering rates are well defined even in case the subsystem is infinitely extended/has continuous spectrum.

Nature, in the form of dissipation, inevitably intervenes in our efforts to control a quantum system. In this talk we show that although we cannot, in general, compensate for dissipation by coherent control of the system, such effects are not always counterproductive; for example, the transformation from a thermal (mixed) state to a cold condensed (pure state) can only be achieved by non-unitary effects such as population and phase relaxation.