Towards quantum simulating QCD

Wiese, U.‐J.

doi:10.1016/j.nuclphysa.2014.09.102

Cited by 104 publications

(85 citation statements)

References 58 publications

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“…Since the different parts of the Hamiltonian cannot be implemented simultaneously, they are split up in the digitized simulation scheme. Hence, for the computation of the Trotter error we divide the Hamiltonian into these individual pieces, according to the Trotterized time evolution given in (38). Generalizing to d dimensions:…”

Section: Error Bounds For Trotterized Time Evolutions In Lattice Gaugmentioning

confidence: 99%

“…We briefly want to look at the scaling of these errors. We consider a small perturbation h j to one of the Hamiltonians H j which is realized during the implementation of the Trotter sequence (38). The difference of the time evolution t…”

Section: Errorsmentioning

confidence: 99%

“…There are also differences in the proposed simulation scheme: the first one is the analogue approach, where not only the degrees of freedom of the simulated system are mapped to those of the simulating one: by appropriately tailoring the interactions of the simulator, its Hamiltonian is exactly or approximately mapped to the desired one (which can be adiabatically changed). Quantum simulations of this type have been proposed, mostly using ultracold atoms [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44], as well as trapped ions [45,46] and superconducting qubits [47,48]. Another approach-the digital one-is based on an idea of Feynman [49], to use a quantum computer (i.e.…”

Section: Introductionmentioning

confidence: 99%

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Digital quantum simulation of lattice gauge theories in three spatial dimensions

et al. 2018

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In the present work, we propose a scheme for the digital formulation of lattice gauge theories with dynamical fermions in 3+1 dimensions. All interactions are obtained as a stroboscopic sequence of two-body interactions with an auxiliary system. This enables quantum simulations of lattice gauge theories where the magnetic four-body interactions arising in two and more spatial dimensions are obtained without the use of perturbation theory, thus resulting in stronger interactions compared with analogue approaches. The simulation scheme is applicable to lattice gauge theories with either compact or finite gauge groups. The required bounds on the digitization errors in lattice gauge theories, due to the sequential nature of the stroboscopic time evolution, are provided. Furthermore, an implementation of a lattice gauge theory with a non-abelian gauge group, the dihedral group D 3 , is proposed employing the aforementioned simulation scheme using ultracold atoms in optical lattices.

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Section: Error Bounds For Trotterized Time Evolutions In Lattice Gaugmentioning

confidence: 99%

Section: Errorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Digital quantum simulation of lattice gauge theories in three spatial dimensions

et al. 2018

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“…The idea is to simulate the real time evolution of an arbitrary Hamiltonian, including the evolution of non-abelian gauge fields [5]. At present a number of schemes for implementing abelian or nonabelian gauge fields have been tested in small systems, but the experiments typically do not realize dynamical gauge fields, and mostly explorer systems in reduced numbers of dimensions.…”

Section: Introductionmentioning

confidence: 99%

Round table: What can we learn about confinement and anoma-lous effects in QCD using analog systems?

et al. 2017

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“…With the recent advent of quantum technologies [8][9][10][11][12], it is then natural to consider multiqubit systems that encode a dual gravity theory via quantum simulation. Currently, four-dimensional gauge theories such as the aforementioned N = 4 theory appear out of reach (see, however, [13] for work on QCD in this context). Instead, we start by looking elsewhere for simpler models which nevertheless have a holographic interpretation.…”

mentioning

confidence: 99%

Digital Quantum Simulation of MinimalAdS/CFT

García-Álvarez¹,

Egusquiza²,

Lamata³

et al. 2017

Phys. Rev. Lett.

162

121

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We propose the digital quantum simulation of a minimal AdS/CFT model in controllable quantum platforms. We consider the Sachdev-Ye-Kitaev model describing interacting Majorana fermions with randomly distributed all-to-all couplings, encoding nonlocal fermionic operators onto qubits to efficiently implement their dynamics via digital techniques. Moreover, we also give a method for probing non-equilibrium dynamics and the scrambling of information. Finally, our approach serves as a protocol for reproducing a simplified low-dimensional model of quantum gravity in advanced quantum platforms as trapped ions and superconducting circuits.Holographic duality [1] posits the equivalence, subject to certain conditions, of quantum gravity and ordinary quantum field theories. The most celebrated such correspondence is conjectured to exist between N = 4 supersymmetric YangMills theory in four dimensions and type IIB string theory on AdS 5 × S 5 . Such dualities offer the exciting prospect of probing quantum gravity effects by studying the well-defined equivalent quantum field theory. Nevertheless, this is still a hard problem because the semiclassical gravity regime is located at strong coupling and for a large number of local degrees of freedom N 1. Furthermore, a fully nonperturbative understanding of the dual field theory is likely necessary in order to resolve the most puzzling aspects of quantum black holes, such as the famous information loss paradox [2]. We may therefore opt for studying the dual field theory on the lattice, by rewriting the problem in terms of a quantum many-body system suitable for simulation on a classical computer [3,4]. Even this powerful technique faces important challenges and limitations, such as the sign problem [5], and the inapplicability of Euclidean lattice methods for intrinsically Lorentzian physics. It is precisely the latter kind of problem one needs to understand in order to describe black hole formation [6] and evaporation.It is essential to develop alternative avenues of dealing with strongly coupled quantum many-body systems; both for their own sake, as well as with an eye on quantum gravity. As pointed out originally by Feynman [7], quantum systems themselves are vastly more computationally efficient at solving many-body Hamiltonians than classical computer simulations. With the recent advent of quantum technologies [8][9][10][11][12], it is then natural to consider multiqubit systems that encode a dual gravity theory via quantum simulation. Currently, four-dimensional gauge theories such as the aforementioned N = 4 theory appear out of reach (see, however, [13] for work on QCD in this context). Instead, we start by looking elsewhere for simpler models which nevertheless have a holographic interpretation.In this Letter, we propose the digital quantum simulation of the simplest known AdS/CFT duality, namely the SachdevYe-Kitaev (SYK) model [14][15][16]. We consider different variants of the model, two in terms of Majorana fermions, and two with complex fermions. We then propose dig...

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Towards quantum simulating QCD

Cited by 104 publications

References 58 publications

Digital quantum simulation of lattice gauge theories in three spatial dimensions

Digital quantum simulation of lattice gauge theories in three spatial dimensions

Round table: What can we learn about confinement and anoma-lous effects in QCD using analog systems?

Digital Quantum Simulation of MinimalAdS/CFT

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