852 research outputs found
Physics as Quantum Information Processing: Quantum Fields as Quantum Automata
Can we reduce Quantum Field Theory (QFT) to a quantum computation? Can
physics be simulated by a quantum computer? Do we believe that a quantum field
is ultimately made of a numerable set of quantum systems that are unitarily
interacting? A positive answer to these questions corresponds to substituting
QFT with a theory of quantum cellular automata (QCA), and the present work is
examining this hypothesis. These investigations are part of a large research
program on a "quantum-digitalization" of physics, with Quantum Theory as a
special theory of information, and Physics as emergent from the same
quantum-information processing. A QCA-based QFT has tremendous potential
advantages compared to QFT, being quantum "ab-initio" and free from the
problems plaguing QFT due to the continuum hypothesis. Here I will show how
dynamics emerges from the quantum processing, how the QCA can reproduce the
Dirac-field phenomenology at large scales, and the kind of departures from QFT
that that should be expected at a Planck-scale discreteness. I will introduce
the notions of linear field quantum automaton and local-matrix quantum
automaton, in terms of which I will provide the solution to the Feynman's
problem about the possibility of simulating a Fermi field with a quantum
computer.Comment: This version: further improvements in notation. Added reference. Work
presented at the conference "Foundations of Probability and Physics-6" (FPP6)
held on 12-15 June 2011 at the Linnaeus University, Vaaxjo, Sweden. Many new
results, e.g. Feynman problem of qubit-ization of Fermi fields solved
A Graph Theory Approach for Regional Controllability of Boolean Cellular Automata
Controllability is one of the central concepts of modern control theory that
allows a good understanding of a system's behaviour. It consists in
constraining a system to reach the desired state from an initial state within a
given time interval. When the desired objective affects only a sub-region of
the domain, the control is said to be regional. The purpose of this paper is to
study a particular case of regional control using cellular automata models
since they are spatially extended systems where spatial properties can be
easily defined thanks to their intrinsic locality. We investigate the case of
boundary controls on the target region using an original approach based on
graph theory. Necessary and sufficient conditions are given based on the
Hamiltonian Circuit and strongly connected component. The controls are obtained
using a preimage approach
A single-shot measurement of the energy of product states in a translation invariant spin chain can replace any quantum computation
In measurement-based quantum computation, quantum algorithms are implemented
via sequences of measurements. We describe a translationally invariant
finite-range interaction on a one-dimensional qudit chain and prove that a
single-shot measurement of the energy of an appropriate computational basis
state with respect to this Hamiltonian provides the output of any quantum
circuit. The required measurement accuracy scales inverse polynomially with the
size of the simulated quantum circuit. This shows that the implementation of
energy measurements on generic qudit chains is as hard as the realization of
quantum computation. Here a ''measurement'' is any procedure that samples from
the spectral measure induced by the observable and the state under
consideration. As opposed to measurement-based quantum computation, the
post-measurement state is irrelevant.Comment: 19 pages, transition rules for the CA correcte
Physics Without Physics: The Power of Information-theoretical Principles
David Finkelstein was very fond of the new information-theoretic paradigm of
physics advocated by John Archibald Wheeler and Richard Feynman. Only recently,
however, the paradigm has concretely shown its full power, with the derivation
of quantum theory (Chiribella et al., Phys. Rev. A 84:012311, 2011; D'Ariano et
al., 2017) and of free quantum field theory (D'Ariano and Perinotti, Phys. Rev.
A 90:062106, 2014; Bisio et al., Phys. Rev. A 88:032301, 2013; Bisio et al.,
Ann. Phys. 354:244, 2015; Bisio et al., Ann. Phys. 368:177, 2016) from
informational principles. The paradigm has opened for the first time the
possibility of avoiding physical primitives in the axioms of the physical
theory, allowing a refoundation of the whole physics over logically solid
grounds. In addition to such methodological value, the new
information-theoretic derivation of quantum field theory is particularly
interesting for establishing a theoretical framework for quantum gravity, with
the idea of obtaining gravity itself as emergent from the quantum information
processing, as also suggested by the role played by information in the
holographic principle (Susskind, J. Math. Phys. 36:6377, 1995; Bousso, Rev.
Mod. Phys. 74:825, 2002). In this paper I review how free quantum field theory
is derived without using mechanical primitives, including space-time, special
relativity, Hamiltonians, and quantization rules. The theory is simply provided
by the simplest quantum algorithm encompassing a countable set of quantum
systems whose network of interactions satisfies the three following simple
principles: homogeneity, locality, and isotropy. The inherent discrete nature
of the informational derivation leads to an extension of quantum field theory
in terms of a quantum cellular automata and quantum walks. A simple heuristic
argument sets the scale to the Planck one, and the observed regime is that of
small wavevectors ...Comment: 34 pages, 8 figures. Paper for in memoriam of David Finkelstei
Spin-1/2 particles moving on a 2D lattice with nearest-neighbor interactions can realize an autonomous quantum computer
What is the simplest Hamiltonian which can implement quantum computation
without requiring any control operations during the computation process? In a
previous paper we have constructed a 10-local finite-range interaction among
qubits on a 2D lattice having this property. Here we show that
pair-interactions among qutrits on a 2D lattice are sufficient, too, and can
also implement an ergodic computer where the result can be read out from the
time average state after some post-selection with high success probability.
Two of the 3 qutrit states are given by the two levels of a spin-1/2 particle
located at a specific lattice site, the third state is its absence. Usual
hopping terms together with an attractive force among adjacent particles induce
a coupled quantum walk where the particle spins are subjected to spatially
inhomogeneous interactions implementing holonomic quantum computing. The
holonomic method ensures that the implemented circuit does not depend on the
time needed for the walk.
Even though the implementation of the required type of spin-spin interactions
is currently unclear, the model shows that quite simple Hamiltonians are
powerful enough to allow for universal quantum computing in a closed physical
system.Comment: More detailed explanations including description of a programmable
version. 44 pages, 12 figures, latex. To appear in PR
Quantum Cellular Automata
Quantum cellular automata (QCA) are reviewed, including early and more recent
proposals. QCA are a generalization of (classical) cellular automata (CA) and
in particular of reversible CA. The latter are reviewed shortly. An overview is
given over early attempts by various authors to define one-dimensional QCA.
These turned out to have serious shortcomings which are discussed as well.
Various proposals subsequently put forward by a number of authors for a general
definition of one- and higher-dimensional QCA are reviewed and their properties
such as universality and reversibility are discussed.Comment: 12 pages, 3 figures. To appear in the Springer Encyclopedia of
Complexity and Systems Scienc
Physical portrayal of computational complexity
Computational complexity is examined using the principle of increasing
entropy. To consider computation as a physical process from an initial instance
to the final acceptance is motivated because many natural processes have been
recognized to complete in non-polynomial time (NP). The irreversible process
with three or more degrees of freedom is found intractable because, in terms of
physics, flows of energy are inseparable from their driving forces. In
computational terms, when solving problems in the class NP, decisions will
affect subsequently available sets of decisions. The state space of a
non-deterministic finite automaton is evolving due to the computation itself
hence it cannot be efficiently contracted using a deterministic finite
automaton that will arrive at a solution in super-polynomial time. The solution
of the NP problem itself is verifiable in polynomial time (P) because the
corresponding state is stationary. Likewise the class P set of states does not
depend on computational history hence it can be efficiently contracted to the
accepting state by a deterministic sequence of dissipative transformations.
Thus it is concluded that the class P set of states is inherently smaller than
the set of class NP. Since the computational time to contract a given set is
proportional to dissipation, the computational complexity class P is a subset
of NP.Comment: 16, pages, 7 figure
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