Trailhead for quantum simulation of SU(3) Yang-Mills lattice gauge theory in the local multiplet basis

Ciavarella, Anthony N.; Klco, Natalie; Savage, Martin J.

doi:10.1103/physrevd.103.094501

Cited by 166 publications

(90 citation statements)

References 123 publications

(171 reference statements)

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“…Of course, the ambitious goal of quantum simulating the SM is presently rather far away, given that only noisy intermediate-scale quantum (NISQ) computers are currently available. Still, first quantum simulations of gauge theories in lower dimensions showing some of the relevant features of the SM have already been successfully performed [18][19][20][21][22][23][24][25][26][27]. In addition, resource efficient formulations of gauge theories for quantum computations have been developed [28][29][30][31][32][33], and the Hamiltonian formulation of the CP-violating topological θ-terms in three spatial dimensions has been derived [34].…”

Section: Introductionmentioning

confidence: 99%

Towards quantum simulations in particle physics and beyond on noisy intermediate-scale quantum devices

Funcke

Hartung

Jansen

et al. 2021

Phil. Trans. R. Soc. A.

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We review two algorithmic advances that bring us closer to reliable quantum simulations of model systems in high-energy physics and beyond on noisy intermediate-scale quantum (NISQ) devices. The first method is the dimensional expressivity analysis of quantum circuits, which allows for constructing minimal but maximally expressive quantum circuits. The second method is an efficient mitigation of readout errors on quantum devices. Both methods can lead to significant improvements in quantum simulations, e.g. when variational quantum eigensolvers are used. This article is part of the theme issue ‘Quantum technologies in particle physics’.

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Section: Introductionmentioning

confidence: 99%

Towards quantum simulations in particle physics and beyond on noisy intermediate-scale quantum devices

Funcke

Hartung

Jansen

et al. 2021

Phil. Trans. R. Soc. A.

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show abstract

“…We can extend the above calculations to SU(3) lattice gauge theory, which is interesting from the perspective of QCD and is already being explored on a quantum computer [62]. In this case, P Q is again of the form…”

Section: Su(3) Lattice Gauge Theorymentioning

confidence: 99%

“…This is an important question to address in the noisy intermediate-scale quantum (NISQ) era, when large reliable quantum computers will not be available. For example, in the context of gauge theories, can we reduce the Hilbert space dramatically by implementing the Gauss law constraint [62,63]? However, before we can compare various qubit regularized models, we first need to identify which models are worth comparing by searching for those that contain the correct quantum critical point.…”

Section: Introductionmentioning

confidence: 99%

Qubit Regularization and Qubit Embedding Algebras

Liu

Chandrasekharan

2022

Symmetry

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Qubit regularization is a procedure to regularize the infinite dimensional local Hilbert space of bosonic fields to a finite dimensional one, which is a crucial step when trying to simulate lattice quantum field theories on a quantum computer. When the qubit-regularized lattice quantum fields preserve important symmetries of the original theory, qubit regularization naturally enforces certain algebraic structures on these quantum fields. We introduce the concept of qubit embedding algebras (QEAs) to characterize this algebraic structure associated with a qubit regularization scheme. We show a systematic procedure to derive QEAs for the (N) lattice spin models and the SU(N) lattice gauge theories. While some of the QEAs we find were discovered earlier in the context of the D-theory approach, our method shows that QEAs are far richer. A more complete understanding of the QEAs could be helpful in recovering the fixed points of the desired quantum field theories.

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“…Finally, digital and stroboscopic implementations offer various ways to impose gauge invariance: when the simulation does not involve a mapping of the Hamiltonian but rather an implementation of the time evolution by short-time pulses implementing different interactions and Hamiltonian terms separately (trotterization), possibly using auxiliary degrees of freedom, there are more options to enforce the symmetry. These range from tailoring gauge invariant interactions with an ancilla (an auxiliary degree of freedom) [20,[52][53][54][55][56] to developing tools to encode the symmetries on quantum computer algorithms [21,[57][58][59][60][61]. The effect of trotterization on gauge invariance has to be addressed, e.g.…”

Section: Gauge Fieldsmentioning

confidence: 99%

“…In completely digital approaches, not covered by this article, one can map these interactions to efficient quantum computer gates, as in, for example [60,61].…”

Section: The Hamiltonianmentioning

confidence: 99%

Quantum simulation of lattice gauge theories in more than one space dimension—requirements, challenges and methods

Zohar

2021

Phil. Trans. R. Soc. A.

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Over recent years, the relatively young field of quantum simulation of lattice gauge theories, aiming at implementing simulators of gauge theories with quantum platforms, has gone through a rapid development process. Nowadays, it is not only of interest to the quantum information and technology communities. It is also seen as a valid tool for tackling hard, non-perturbative gauge theory problems by particle and nuclear physicists. Along the theoretical progress, nowadays more and more experiments implementing such simulators are being reported, manifesting beautiful results, but mostly on 1 + 1 dimensional physics. In this article, we review the essential ingredients and requirements of lattice gauge theories in more dimensions and discuss their meanings, the challenges they pose and how they could be dealt with, potentially aiming at the next steps of this field towards simulating challenging physical problems in analogue, or analogue-digital ways. This article is part of the theme issue ‘Quantum technologies in particle physics’.

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Trailhead for quantum simulation of SU(3) Yang-Mills lattice gauge theory in the local multiplet basis

Cited by 166 publications

References 123 publications

Towards quantum simulations in particle physics and beyond on noisy intermediate-scale quantum devices

Towards quantum simulations in particle physics and beyond on noisy intermediate-scale quantum devices

Qubit Regularization and Qubit Embedding Algebras

Quantum simulation of lattice gauge theories in more than one space dimension—requirements, challenges and methods

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