A bird's eye view of quantum computers

Quantum computers are discussed in the general framework of computation, the laws of physics and the foundations of quantum mechanics.Comment: 6 pages, 1 figur

Computing the distance between quantum channels: Usefulness of the Fano representation

The diamond norm measures the distance between two quantum channels. From an operational vewpoint, this norm measures how well we can distinguish between two channels by applying them to input states of arbitrarily large dimensions. In this paper, we show that the diamond norm can be conveniently and in a physically transparent way computed by means of a Monte-Carlo algorithm based on the Fano representation of quantum states and quantum operations. The effectiveness of this algorithm is illustrated for several single-qubit quantum channels.Comment: 8 pages, 7 figure

Non-perturbative interpretation of the Bloch vector's path beyond rotating wave approximation

The Bloch vector's path of a two-level system exposed to a monochromatic field exhibits, in the regime of strong coupling, complex corkscrew trajectories. By considering the infinitesimal evolution of the two-level system when the field is treated as a classical object, we show that the Bloch vector's rotation speed oscillates between zero and twice the rotation speed predicted by the rotating wave approximation. Cusps appear when the rotation speed vanishes. We prove analytically that in correspondence to cusps the curvature of the Bloch vector's path diverges. On the other hand, numerical data show that the curvature is very large even for a quantum field in the deep quantum regime with mean number of photons $\bar{n}\lesssim 1$. We finally compute numerically the typical error size in a quantum gate when the terms beyond rotating wave approximation are neglected.Comment: 9 pages, 8 figure

A Graphic Representation of States for Quantum Copying Machines

The aim of this paper is to introduce a new graphic representation of quantum states by means of a specific application: the analysis of two models of quantum copying machines. The graphic representation by diagrams of states offers a clear and detailed visualization of quantum information's flow during the unitary evolution of not too complex systems. The diagrams of states are exponentially more complex in respect to the standard representation and this clearly illustrates the discrepancy of computational power between quantum and classical systems. After a brief introductive exposure of the general theory, we present a constructive procedure to illustrate the new representation by means of concrete examples. Elementary diagrams of states for single-qubit and two-qubit systems and a simple scheme to represent entangled states are presented. Quantum copying machines as imperfect cloners of quantum states are introduced and the quantum copying machines of Griffiths and Niu and of Buzek and Hillery are analyzed, determining quantum circuits of easier interpretation. The method has indeed shown itself to be extremely successful for the representation of the involved quantum operations and it has allowed to point out the characteristic aspects of the quantum computations examined.Comment: 30 pages, 22 figure

Exotic States in the Dynamical Casimir Effect

We consider the interaction of a qubit with a single mode of the quantized electromagnetic field and show that, in the ultrastrong coupling regime and when the qubit-field interaction is switched on abruptly, the dynamical Casimir effect leads to the generation of a variety of exotic states of the field, which cannot be simply described as squeezed states. Such effect also appears when initially both the qubit and the field are in their ground state. The non-classicality of the obtained exotic states is characterized by means of a parameter based on the volume of the negative part of the Wigner function. A transition to non-classical states is observed by changing either the interaction strength or the interaction time. The observed phenomena appear as a general feature of nonadiabatic quantum gates, so that the dynamical Casimir effect can be the origin of a fundamental upper limit to the maximum speed of quantum computation and communication protocols.Comment: 5 pages, 4 figure

Gaussian wave packets in phase space: The Fermi g_F function

Any pure quantum state can be equivalently represented by means of its wave function psi(q) or of the Fermi function g_F(q,p), with q and p coordinates and conjugate momenta of the system under investigation.We show that a Gaussian wave packet can be conveniently visualized in phase space by means of the curve g_F(q,p)=0. The evolution in time of the g_F=0 curve is then computed for a Gaussian packet evolving freely or under a constant or a harmonic force. As a result, the spreading or shrinking of the packet is easily interpreted in phase space. Finally, we discuss a gedanken prism microscope experiment for measuring the position-momentum correlation. This gedanken experiment, together with the well-known Heisenberg microscope and von Neumann velocimeter, is sufficient to fully determine the state of a Gaussian packet.Comment: 7 pages, 4 figures, remarks adde

Dynamical Casimir Effect in Quantum Information Processing

We demonstrate, in the regime of ultrastrong matter-field coupling, the strong connection between the dynamical Casimir effect (DCE) and the performance of quantum information protocols. Our results are illustrated by means of a realistic quantum communication channel and show that the DCE is a fundamental limit for quantum computation and communication and that novel schemes are required to implement ultrafast and reliable quantum gates. Strategies to partially counteract the DCE are also discussed.Comment: 7 pages, 5 figure

Dynamical Casimir effect and minimal temperature in quantum thermodynamics

We study the fundamental limitations of cooling to absolute zero for a qubit, interacting with a single mode of the electromagnetic field. Our results show that the dynamical Casimir effect, which is unavoidable in any finite-time thermodynamic cycle, forbids the attainability of the absolute zero of temperature, even in the limit of an infinite number of cycles.Comment: 5 pages, 4 figure

Quantum simulation of the single-particle Schrodinger equation

The working of a quantum computer is described in the concrete example of a quantum simulator of the single-particle Schrodinger equation. We show that a register of 6-10 qubits is sufficient to realize a useful quantum simulator capable of solving in an efficient way standard quantum mechanical problems.Comment: 7 pages, 6 figures, added remarks and reference