Quantum Algorithms for Quantum Field Theories

Jordan, Stephen P.; Lee, Keith S. M.; Preskill, John

doi:10.1126/science.1217069

Cited by 439 publications

(503 citation statements)

References 74 publications

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“…This is one example; now that quantum computers appear to be increasingly realistic, computer scientists and physicists will find efficient quantum algorthims for an array of problems. Many of these will be physical (e.g., quantum field theory 140 and many-body localisation are attractive targets 141 ), but even areas distant from physics are seeing quantum advances. Deep learning has had a dramatic impact on machine learning in the last few years, [142][143][144][145] but there is a computational bottleneck: computation of the true gradient of L, where L is the 'log-likelihood function', is classically intractable, leading to classical methods that can efficiently only approximate ∇L.…”

Section: Discussionmentioning

confidence: 99%

Majorana zero modes and topological quantum computation

2015

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We provide a current perspective on the rapidly developing field of Majorana zero modes (MZMs) in solid-state systems. We emphasise the theoretical prediction, experimental realisation and potential use of MZMs in future information processing devices through braiding-based topological quantum computation (TQC). Well-separated MZMs should manifest non-Abelian braiding statistics suitable for unitary gate operations for TQC. Recent experimental work, following earlier theoretical predictions, has shown specific signatures consistent with the existence of Majorana modes localised at the ends of semiconductor nanowires in the presence of superconducting proximity effect. We discuss the experimental findings and their theoretical analyses, and provide a perspective on the extent to which the observations indicate the existence of anyonic MZMs in solid-state systems. We also discuss fractional quantum Hall systems (the 5/2 state), which have been extensively studied in the context of non-Abelian anyons and TQC. We describe proposed schemes for carrying out braiding with MZMs as well as the necessary steps for implementing TQC. INTRODUCTIONTopological quantum computation 1,2 is an approach to faulttolerant quantum computation in which the unitary quantum gates result from the braiding of certain topological quantum objects called 'anyons'. Anyons braid non-trivially: two counterclockwise exchanges do not leave the state of the system invariant, unlike in the cases of bosons or fermions. Anyons can arise in two ways: as localised excitations of an interacting quantum Hamiltonian 3 or as defects in an ordered system.

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Section: Discussionmentioning

confidence: 99%

Majorana zero modes and topological quantum computation

2015

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“…As usual for quantum systems, by repeating identically prepared experiments many times, one obtains physical results by averaging over them. Quantum simulator constructions already exist for several bosonic [34][35][36] and fermionic [37][38][39][40] field theories. Quantum simulators have also been constructed for quantum particles interacting with classical gauge fields.…”

Section: Introductionmentioning

confidence: 99%

Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories

2013

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Abelian and non-Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, Abelian U(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information theory, Kitaev's toric code is a Z(2) lattice gauge theory. In particle physics, Quantum Chromodynamics (QCD), the non-Abelian SU(3) gauge theory of the strong interactions between quarks and gluons, is nonperturbatively regularized on a lattice. Quantum link models extend the concept of lattice gauge theories beyond the Wilson formulation, and are well suited for both digital and analog quantum simulation using ultracold atomic gases in optical lattices. Since quantum simulators do not suffer from the notorious sign problem, they open the door to studies of the real-time evolution of strongly coupled quantum systems, which are impossible with classical simulation methods. A plethora of interesting lattice gauge theories suggests itself for quantum simulation, which should allow us to address very challenging problems, ranging from confinement and deconfinement, or chiral symmetry breaking and its restoration at finite baryon density, to color superconductivity and the real-time evolution of heavy-ion collisions, first in simpler model gauge theories and ultimately in QCD.

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“…Proposals for quantum simulator constructions already exist for some simple bosonic [26,27,28] and fermionic [29,30,31,32] field theories. Hence it is natural to ask whether our understanding of strongly coupled systems in nuclear and particle physics may benefit from quantum simulation.…”

Section: Introductionmentioning

confidence: 99%

Towards quantum simulating QCD

Wiese

2014

Nuclear Physics A

100

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Quantum link models provide an alternative non-perturbative formulation of Abelian and non-Abelian lattice gauge theories. They are ideally suited for quantum simulation, for example, using ultracold atoms in an optical lattice. This holds the promise to address currently unsolvable problems, such as the real-time and high-density dynamics of strongly interacting matter, first in toy-model gauge theories, and ultimately in QCD.

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Quantum Algorithms for Quantum Field Theories

Cited by 439 publications

References 74 publications

Majorana zero modes and topological quantum computation

Majorana zero modes and topological quantum computation

Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories

Towards quantum simulating QCD

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