Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information ...technologies. While one long-term goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog quantum simulators, and ultimately of scalable universal quantum computers. In this manuscript, recent results and new tools from a quantum science approach to study lattice gauge theories are reviewed. Two new complementary approaches are discussed: first, tensor network methods are presented – a classical simulation approach – applied to the study of lattice gauge theories together with some results on Abelian and non-Abelian lattice gauge theories. Then, recent proposals for the implementation of lattice gauge theory quantum simulators in different quantum hardware are reported, e.g., trapped ions, Rydberg atoms, and superconducting circuits. Finally, the first proof-of-principle trapped ions experimental quantum simulations of the Schwinger model are reviewed.
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Quantum computing and simulation Cirac, Juan Ignacio
Nanophotonics (Berlin, Germany),
01/2021, Volume:
10, Issue:
1
Journal Article
Peer reviewed
Open access
Quantum computers and simulators can have an extraordinary impact on our society. Despite the extraordinary progress they have made in recent years, there are still great challenges to be met and new ...opportunities to be discovered.
Quantum computing and simulation Cirac, Juan Ignacio
Nanophotonics (Berlin, Germany),
01/2020, Volume:
10, Issue:
1
Journal Article
Peer reviewed
Open access
Abstract
Quantum computers and simulators can have an extraordinary impact on our society. Despite the extraordinary progress they have made in recent years, there are still great challenges to be ...met and new opportunities to be discovered.
Projected entangled pair states (PEPS) are used in practice as an efficient parametrization of the set of ground states of quantum many body systems. The aim of this paper is to present, for a broad ...mathematical audience, some mathematical questions about PEPS.
Quantum computation with cold bosonic atoms in an optical lattice José García-Ripoll, Juan; Ignacio Cirac, Juan
Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences,
07/2003, Volume:
361, Issue:
1808
Journal Article
Peer reviewed
Open access
We analyse an implementation of a quantum computer using bosonic atoms in an optical lattice. We show that, even though the number of atoms per site and the tunnelling rate between neighbouring sites ...is unknown, one may operate a universal set of gates by means of adiabatic passage.
How to Manipulate Cold Atoms Cirac, Juan Ignacio; Zoller, Peter
Science (American Association for the Advancement of Science),
07/2003, Volume:
301, Issue:
5630
Journal Article
Peer reviewed
The authors discuss the observation of strong correlation effects with cold atomic gases in the field of Bose-Einstein condensates.
Many-body open quantum systems, described by Lindbladian master equations, are a rich class of physical models that display complex equilibrium and out-of-equilibrium phenomena which remain to be ...understood. In this paper, we theoretically analyze noisy analogue quantum simulation of geometrically local open quantum systems and provide evidence that this problem is both hard to simulate on classical computers and could be approximately solved on near-term quantum devices. First, given a noiseless quantum simulator, we show that the dynamics of local observables and the fixed-point expectation values of rapidly-mixing local observables in geometrically local Lindbladians can be obtained to a precision of \(\varepsilon\) in time that is \(\text{poly}(\varepsilon^{-1})\) and uniform in system size. Furthermore, we establish that the quantum simulator would provide an exponential advantage, in run-time scaling with respect to the target precision and either the evolution time (when simulating dynamics) or the Lindbladian's decay rate (when simulating fixed-points) over any classical algorithm for these problems unless BQP = BPP. We then consider the presence of noise in the quantum simulator in the form of additional geometrically-local Linbdladian terms. We show that the simulation tasks considered in this paper are stable to errors, i.e. they can be solved to a noise-limited, but system-size independent, precision. Finally, we establish that there are stable geometrically local Lindbladian simulation problems such that as the noise rate on the simulator is reduced, classical algorithms must take time exponentially longer in the inverse noise rate to attain the same precision unless BQP = BPP.
The discovery of topological materials has challenged our understanding of condensed matter physics and led to novel and unusual phenomena. This has motivated recent developments to export ...topological concepts into photonics to make light behave in exotic ways. Here, we predict several unconventional quantum optical phenomena that occur when quantum emitters interact with a topological waveguide QED bath, namely, the photonic analogue of the Su-Schrieffer-Hegger model. When the emitters frequency lies within the topological band-gap, a chiral bound state emerges, which is located at just one side (right or left) of the emitter. In the presence of several emitters, it mediates topological, long-range tunable interactions between them, that can give rise to exotic phases such as double Néel ordered states. On the contrary, when the emitters' optical transition is resonant with the bands, we find unconventional scattering properties and different super/subradiant states depending on the band topology. We also investigate the case of a bath with open boundary conditions to understand the role of topological edge states. Finally, we propose several implementations where these phenomena can be observed with state-of-the-art technology.
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