75 research outputs found
Quantum Walks, Weyl equation and the Lorentz group
Quantum cellular automata and quantum walks provide a framework for the
foundations of quantum field theory, since the equations of motion of free
relativistic quantum fields can be derived as the small wave-vector limit of
quantum automata and walks starting from very general principles. The intrinsic
discreteness of this framework is reconciled with the continuous Lorentz
symmetry by reformulating the notion of inertial reference frame in terms of
the constants of motion of the quantum walk dynamics. In particular, among the
symmetries of the quantum walk which recovers the Weyl equation--the so called
Weyl walk--one finds a non linear realisation of the Poincar\'e group, which
recovers the usual linear representation in the small wave-vector limit. In
this paper we characterise the full symmetry group of the Weyl walk which is
shown to be a non linear realization of a group which is the semidirect product
of the Poincar\'e group and the group of dilations.Comment: 9 pages, 2 figure
Memory cost of quantum protocols
In this paper we consider the problem of minimizing the ancillary systems
required to realize an arbitrary strategy of a quantum protocol, with the
assistance of classical memory. For this purpose we introduce the notion of
memory cost of a strategy, which measures the resources required in terms of
ancillary dimension. We provide a condition for the cost to be equal to a given
value, and we use this result to evaluate the cost in some special cases. As an
example we show that any covariant protocol for the cloning of a unitary
transformation requires at most one ancillary qubit. We also prove that the
memory cost has to be determined globally, and cannot be calculated by
optimizing the resources independently at each step of the strategy.Comment: 9 page
Cloning of a quantum measurement
We analyze quantum algorithms for cloning of a quantum measurement. Our aim
is to mimic two uses of a device performing an unknown von Neumann measurement
with a single use of the device. When the unknown device has to be used before
the bipartite state to be measured is available we talk about 1 -> 2 learning
of the measurement, otherwise the task is called 1 -> 2 cloning of a
measurement. We perform the optimization for both learning and cloning for
arbitrary dimension of the Hilbert space. For 1 -> 2 cloning we also propose a
simple quantum network that realizes the optimal strategy.Comment: 10 pages, 1 figur
Solutions of a two-particle interacting quantum walk
We study the solutions of the interacting Fermionic cellular automaton
introduced in Ref. [Phys Rev A 97, 032132 (2018)]. The automaton is the
analogue of the Thirring model with both space and time discrete. We present a
derivation of the two-particles solutions of the automaton, which exploits the
symmetries of the evolution operator. In the two-particles sector, the
evolution operator is given by the sequence of two steps, the first one
corresponding to a unitary interaction activated by two-particle excitation at
the same site, and the second one to two independent one-dimensional Dirac
quantum walks. The interaction step can be regarded as the discrete-time
version of the interacting term of some Hamiltonian integrable system, such as
the Hubbard or the Thirring model. The present automaton exhibits scattering
solutions with nontrivial momentum transfer, jumping between different regions
of the Brillouin zone that can be interpreted as Fermion-doubled particles, in
stark contrast with the customary momentum-exchange of the one dimensional
Hamiltonian systems. A further difference compared to the Hamiltonian model is
that there exist bound states for every value of the total momentum, and even
for vanishing coupling constant. As a complement to the analytical derivations
we show numerical simulations of the interacting evolution.Comment: 16 pages, 6 figure
Phase-Based Binocular Perception of Motion in Depth: Cortical-Like Operators and Analog VLSI Architectures
We present a cortical-like strategy to obtain reliable estimates of the motions of objects in a scene toward/away from the observer (motion in depth), from local measurements of binocular parameters derived from direct comparison of the results of monocular spatiotemporal filtering operations performed on stereo image pairs. This approach is suitable for a hardware implementation, in which such parameters can be gained via a feedforward computation (i.e., collection, comparison, and punctual operations) on the outputs of the nodes of recurrent VLSI lattice networks, performing local computations. These networks act as efficient computational structures for embedded analog filtering operations in smart vision sensors. Extensive simulations on both synthetic and real-world image sequences prove the validity of the approach that allows to gain high-level information about the 3D structure of the scene, directly from sensorial data, without resorting to explicit scene reconstruction
Scattering and perturbation theory for discrete-time dynamics
We present a systematic treatment of scattering processes for quantum systems
whose time evolution is discrete. First we define and show some general
properties of the scattering operator, in particular the conservation of
quasi-energy which is defined only modulo . Then we develop two
perturbative techniques for the power series expansion of the scattering
operator, the first one analogous to the iterative solution of the
Lippmann-Schwinger equation, the second one to the Dyson series of perturbative
Quantum Field Theory. Our framework can be applied to a wide class of quantum
simulators, like quantum walks and quantum cellular automata. As a case study
we analyse the scattering properties of a one-dimensional cellular automaton
with locally interacting fermions.Comment: 11 pages, 1 figur
- …