arXiv subjects

Diego de Falco

Publications and source records attributed to Diego de Falco.

11 recordsLinked to original sources

arXiv2012

Noise-assisted quantum transport and computation

The transmission of an excitation along a spin chain can be hindered by the presence of small fixed imperfections that create trapping regions where the excitation may get caught (Anderson localization). A certain degree of noise, ensuing from the interaction with a thermal bath, allows to overcome localization (noise-assisted transport). In this paper we investigate the relation between noise-assisted transport and (quantum) computation. In particular we prove that noise does assist classical computation on a quantum computing device but hinders the possibility of creating entanglement.

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arXiv2011

Time-dependent density functional theory for open spin chains

The application of methods of time-dependent density functional theory (TDDFT) to systems of qubits provided the interesting possibility of simulating an assigned Hamiltonian evolution by means of an auxiliary Hamiltonian having different two-qubit interactions and hence a possibly simpler wave function evolution. In this note we extend these methods to some instances of Lindblad evolution of a spin chain.

quant-ph↗

arXiv2011

An introduction to quantum annealing

Quantum Annealing, or Quantum Stochastic Optimization, is a classical randomized algorithm which provides good heuristics for the solution of hard optimization problems. The algorithm, suggested by the behaviour of quantum systems, is an example of proficuous cross contamination between classical and quantum computer science. In this survey paper we illustrate how hard combinatorial problems are tackled by quantum computation and present some examples of the heuristics provided by Quantum Annealing. We also present preliminary results about the application of quantum dissipation (as an alternative to Imaginary Time Evolution) to the task of driving a quantum system toward its state of lowest energy.

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arXiv2011

Dissipative dynamics of a spin system with three-body interaction

In this note we explicitly solve the Lindblad equation for a system of three spins with a three-body interaction, coupled to the environment by bath operators that inject or absorb spin carriers. We exemplify the properties of this solution in the context of a simple instance of Feynman's quantum computer in which a two-qubit program line is executed, applying the $\sqrt{NOT}$ primitive to a one-qubit register.

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arXiv2008

Quantum annealing and the Schrödinger-Langevin-Kostin equation

We show, in the context of quantum combinatorial optimization, or quantum annealing, how the nonlinear Schrödinger-Langevin-Kostin equation can dynamically drive the system toward its ground state. We illustrate, moreover, how a frictional force of Kostin type can prevent the appearance of genuinely quantum problems such as Bloch oscillations and Anderson localization which would hinder an exhaustive search.

quant-ph↗

arXiv2008

Dynamical kickback and non commuting impurities in a spin chain

In an interacting continuous time quantum walk, while the walker (the cursor) is moving on a graph, computational primitives (unitary operators associated with the edges) are applied to ancillary qubits (the register). The model with one walker was originally proposed by R. Feynman, who thus anticipated many features of the Continuous Time Quantum Walk (CTWQ) computing paradigm. In this note we examine the behaviour of an interacting CTQW with two walkers and examine the interaction of the walkers with noncommuting primitives. We endow such a walk with a notion of trajectory, in the sense of sample path of an associated Markov process, in order to use such notions as sojourn time and first passage time as heuristic tools for gaining intuition about its behaviour.

quant-ph↗

arXiv2008

Quantum walks: a Markovian perspective

For a continuous-time quantum walk on a line the variance of the position observable grows quadratically in time, whereas, for its classical counterpart on the same graph, it exhibits a linear, diffusive, behaviour. A quantum walk, thus, propagates at a rate which is linear in time, as compared to the square root rate for a classical random walk. Indeed, it has been suggested that there are graphs that can be traversed by a quantum walker exponentially faster than by the classical random analogue. In this note we adopt the approach of exploring the conditions to impose on a Markov process in order to emulate its quantum counterpart: the central issue that emerges is the problem of taking into account, in the numerical generation of each sample path, the causative effect of the ensemble of trajectories to which it belongs. How to deal numerically with this problem is shown in a paradigmatic example.

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arXiv2006

Entropy generation in a model of reversible computation

We present a model in which, due to the quantum nature of the signals controlling the implementation time of successive unitary computational steps, \emph{physical} irreversibility appears in the execution of a \emph{logically} reversible computation.

cs.CC↗

arXiv2006

Grover's algorithm on a Feynman computer

We present an implementation of Grover's algorithm in the framework of Feynman's cursor model of a quantum computer. The cursor degrees of freedom act as a quantum clocking mechanism, and allow Grover's algorithm to be performed using a single, time-independent Hamiltonian. We examine issues of locality and resource usage in implementing such a Hamiltonian. In the familiar language of Heisenberg spin-spin coupling, the clocking mechanism appears as an excitation of a basically linear chain of spins, with occasional controlled jumps that allow for motion on a planar graph: in this sense our model implements the idea of "timing" a quantum algorithm using a continuous-time random walk. In this context we examine some consequences of the entanglement between the states of the input/output register and the states of the quantum clock.

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arXiv2006

Speed and entropy of an interacting continuous time quantum walk

We present some dynamic and entropic considerations about the evolution of a continuous time quantum walk implementing the clock of an autonomous machine. On a simple model, we study in quite explicit terms the Lindblad evolution of the clocked subsystem, relating the evolution of its entropy to the spreading of the wave packet of the clock. We explore possible ways of reducing the generation of entropy in the clocked subsystem, as it amounts to a deficit in the probability of finding the target state of the computation. We are thus lead to examine the benefits of abandoning some classical prejudice about how a clocking mechanism should operate.

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arXiv2005

Quantum Timing and Synchronization Problems

Feynman's model of a quantum computer provides an example of a continuous-time quantum walk. Its clocking mechanism is an excitation of a basically linear chain of spins with occasional controlled jumps which allow for motion on a planar graph. The spreading of the wave packet poses limitations on the probability of ever completing the $s$ elementary steps of a computation: an additional amount of storage space $δ$ is needed in order to achieve an assigned completion probability. In this note we study the END instruction, viewed as a measurement of the position of the clocking excitation: a $π$-pulse indefinitely freezes the contents of the input/output register, with a probability depending only on the ratio $δ/s$.

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