503 research outputs found
Quantum Cellular Automata, Tensor Networks, and Area Laws
No full textQuantum cellular automata are unitary maps that preserve locality and respect causality. We identify them, in any dimension, with simple tensor networks (projected entangled pair unitary) whose bond dimension does not grow with the system size. As a result, they satisfy an area law for the entanglement entropy they can create. We define other classes of nonunitary maps, the so-called quantum channels, that either respect causality or preserve locality. We show that, whereas the latter obey an area law for the number of quantum correlations they can create, as measured by the quantum mutual information, the former may violate it. We also show that neither of them can be expressed as tensor networks with a bond dimension that is independent of the system size
Toma de Posesión como Académico de Honor de D. Ignacio Cirac Sasturain.
No full textToma de Posesión como Académico de Honor de D. Ignacio Cirac Sasturain , Premio Príncipe de Asturias de Investigación Científica y Técnica 2006 y Premio Nacional de Investigación 2007 en Ciencias físicas, de los materiales y de la Tierra. Organiza: Academia de Ciencias de la Región de Murcia. Aula de Cultura Fundación Cajamurcia
Approximating Many-Body Quantum States with Quantum Circuits and Measurements
No full textWe introduce protocols to prepare many-body quantum states with quantum circuits assisted by local operations and classical communication. We show that by lifting the requirement of exact preparation, one can substantially save resources. In particular, the so-called W and, more generally, Dicke states require a circuit depth and number of ancillas per site that are independent of the system size. As a by-product of our work, we introduce an efficient scheme to implement certain nonlocal, non-Clifford unitary operators. We also discuss how similar ideas may be applied in the preparation of eigenstates of well-known spin models, both free and interacting
Claustre Obert: Ignacio Cirac 'La investigació: reptes, futur i política científica'
No full text'La investigació: reptes, futur i política científica' serà el tema a tractar hui dilluns 15 de juliol, a les 20 hores, a la Nau amb motiu de la celebració de la Biennal de Física que se celebra a la Universitat de València. Participen Eva Barreno, José Capmany, Ignacio Cirac, Eugenio Coronado, José Duato, Juan A. Fuster i Irene Higes. Modera Antonio Ariño i presenta Vicent J. Martínez
Quantum Physics Takes Free Will into Account
No full textIn this dialogue, the physicist Ignacio Cirac, director of the Theoretical Division of the Max Planck Institute for Quantum Optics, outlines why quantum physics has brought about a much greater change than that caused by Einstein’s theory of relativity, how quantum physics takes free will into account and how it combines with philosophy. He describes why quantum theory defines “everything else,” yet is unable to define itself. Explaining how, together with Peter Zoller, he developed and presented the first theoretical description of a quantum computing architecture based on trapped ions, and, how this quantum architecture will be viable and capable of performing calculations we cannot perform at present. Their quantum computer calculates in qubits, which would require at least 100,000 qubits to function, rising to 1,000,000 if error correction is implemented. It will be able to perform calculations previously unachievable and create encrypted messages impossible to decipher. Building a functional quantum computer still requires a huge technological change, which has yet to come about. Lastly, Cirac explains the differences between European and American visions of science and why mathematicians are even more conservative than physicists.</p
Topological Lower Bound on Quantum Chaos by Entanglement Growth
No full textA fundamental result in modern quantum chaos theory is the Maldacena-Shenker-Stanford upper bound on the growth of out-of-time-order correlators, whose infinite-temperature limit is related to the operator-space entanglement entropy of the evolution operator. Here we show that, for one-dimensional quantum cellular automata (QCA), there exists a lower bound on quantum chaos quantified by such entanglement entropy. This lower bound is equal to twice the index of the QCA, which is a topological invariant that measures the chirality of information flow, and holds for all the Renyi entropies, with its strongest Renyi-8 version being tight. The rigorous bound rules out the possibility of any sublinear entanglement growth behavior, showing in particular that many-body localization is forbidden for unitary evolutions displaying nonzero index. Since the Renyi entropy is measurable, our findings have direct experimental relevance. Our result is robust against exponential tails which naturally appear in quantum dynamics generated by local Hamiltonians
Quantum Circuits Assisted by Local Operations and Classical Communication: Transformations and Phases of Matter
No full textWe introduce deterministic state-transformation protocols between many-body quantum states that can be implemented by low-depth quantum circuits followed by local operations and classical communication. We show that this gives rise to a classification of phases in which topologically ordered states or other paradigmatic entangled states become trivial. We also investigate how the set of unitary operations is enhanced by local operations and classical communication in this scenario, allowing one to perform certain large-depth quantum circuits in terms of low-depth ones
Irreversibility in asymptotic manipulations of a distillable entangled state
No full textWe provide an example of a distillable bipartite mixed state such that, even in the asymptotic limit, more pure-state entanglement is required to create it than can be distilled from it. Thus, we show that the irreversibility in the processes of formation and distillation of bipartite states, recently proved in [G. Vidal and J. I. Cirac, Phys. Rev. Lett. 86, 5803 (2001)], is not limited to bound-entangled states
Fermionic quantum cellular automata and generalized matrix-product unitaries
No full textIn this paper, we study matrix-product unitary operators (MPUs) for fermionic one-dimensional chains. In stark contrast to the case of 1D qudit systems, we show that (i) fermionic MPUs (fMPUs) do not necessarily feature a strict causal cone and (ii) not all fermionic quantum cellular automata (QCA) can be represented as fMPUs. We then introduce a natural generalization of the latter, obtained by allowing for an additional operator acting on their auxiliary space. We characterize a family of such generalized MPUs that are locality-preserving, and show that, up to appending inert ancillary fermionic degrees of freedom, any representative of this family is a fermionic QCA (fQCA) and vice versa. Finally, we prove an index theorem for generalized MPUs, recovering the recently derived classification of fQCA in one dimension. As a technical tool for our analysis, we also introduce a graded canonical form for fermionic matrix product states, proving its uniqueness up to similarity transformations
Exact dynamics in dual-unitary quantum circuits
No full textWe consider the class of dual-unitary quantum circuits in 1 + 1 dimensions and introduce a notion of “solvable” matrix product states (MPSs), defined by a specific condition which allows us to tackle their time evolution analytically. We provide a classification of the latter, showing that they include certain MPSs of arbitrary bond dimension, and study analytically different aspects of their dynamics. For these initial states, we show that while any subsystem of size l reaches infinite temperature after a time t ∝ l, irrespective of the presence of conserved quantities, the light cone of two-point correlation functions displays qualitatively different features depending on the ergodicity of the quantum circuit, defined by the behavior of infinite-temperature dynamical correlation functions. Furthermore, we study the entanglement spreading from such solvable initial states, providing a closed formula for the time evolution of the entanglement entropy of a connected block. This generalizes recent results obtained in the context of the self-dual kicked Ising model. By comparison, we also consider a family of nonsolvable initial mixed states depending on one real parameter β, which, as β is varied from zero to infinity, interpolate between the infinite-temperature density matrix and arbitrary initial pure product states. We study analytically their dynamics for small values of β, and highlight the differences from the case of solvable MPSs
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