Single-particle digitization strategy for quantum computation of a 
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 scalar field theory

Barata, João; Mueller, Niklas; Tarasov, Andrey; Venugopalan, Raju

doi:10.1103/physreva.103.042410

Cited by 50 publications

(17 citation statements)

References 137 publications

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“…In an actual implementation, one would have to consider signed values, since, in general, there is no condition that physically constrains the system to positive values. 9 In principle, signed values can be dealt with by, for example, including an extra qubit that stores the sign of the state (similar to the encoding used in [25]) or using a two's complement encoding. This caveat requires one to modify circuits we detail in the main text to accommodate for the new encodings.…”

Section: Discussionmentioning

confidence: 99%

“…However, including a localized initial state distribution might be important for certain digitizations where one can not prepare the state | p = 0 exactly or if one is simply interested in studying how different production mechanisms influence the final state. Several strategies to prepare |ψ 0 from an integrable template distributions can be found in the literature [25][26][27][28]. Depending exactly on what |ψ 0 one wants to prepare, in principle, one can devise a routine which only requires O(n Q ) basic quantum gate operations.…”

Section: Initial State Preparationmentioning

confidence: 99%

“…with μ an infrared (model dependent) regulator, related to the medium Debye mass; typically μ ∼ O(0.1 − 1 GeV) [25,44,45] and we used the previous estimates to reduce the problem to the ratio between the soft and hard scales at play. Recalling that N s = 2 n Q , we obtain…”

Section: Numerical Estimates For the Circuit Parametersmentioning

confidence: 99%

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A quantum strategy to compute the jet quenching parameter $$\hat{q}$$

Barata

Salgado

2021

Eur. Phys. J. C

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Jet quenching, the modification of the properties of a QCD jet when the parton cascade takes place inside a medium, is an intrinsically quantum process, where color coherence effects play an essential role. Despite a very significant progress in the last years, the simulation of a full quantum medium induced cascade remains inaccessible to classical Monte Carlo parton showers. In this situation, alternative formulations are worth being tried and the fast developments in quantum computing provide a very promising direction. The goal of this paper is to introduce a strategy to quantum simulate single particle momentum broadening, the simplest building block of jet quenching. Momentum broadening is the modification of the quark or gluon transverse momentum due interactions with the underlying medium, modeled as a QCD background field. At the lowest order in $$\alpha _s$$ α s that we consider here, momentum broadening does not involve parton splittings and particle number is conserved, greatly simplifying the quantum algorithmic implementation. This quantity is, however, very relevant for the phenomenology of RHIC, LHC or the future EIC.

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Section: Discussionmentioning

confidence: 99%

Section: Initial State Preparationmentioning

confidence: 99%

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A quantum strategy to compute the jet quenching parameter $$\hat{q}$$

Barata

Salgado

2021

Eur. Phys. J. C

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“…Much work has been done on the quantum simulation of relativistic field theories including but not limited to the simulation of scalar field theories [15][16][17][18][19][20][21][22][23], fermionic field theories [24][25][26], lattice gauge theories , superstring theory [81], σ models [82][83][84][85] and light front QFTs [86,87] (which are known to have many similarities with quantum chemistry as noted by Kenneth Wilson [88]). However, the absence of relativity from the majority of existing quantum chemistry simulation algorithms raises both practical and theoretical questions.…”

Section: Introductionmentioning

confidence: 99%

Simulating Effective QED on Quantum Computers

Stetina

Ciavarella

et al. 2022

Quantum

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In recent years simulations of chemistry and condensed materials has emerged as one of the preeminent applications of quantum computing, offering an exponential speedup for the solution of the electronic structure for certain strongly correlated electronic systems. To date, most treatments have ignored the question of whether relativistic effects, which are described most generally by quantum electrodynamics (QED), can also be simulated on a quantum computer in polynomial time. Here we show that effective QED, which is equivalent to QED to second order in perturbation theory, can be simulated in polynomial time under reasonable assumptions while properly treating all four components of the wavefunction of the fermionic field. In particular, we provide a detailed analysis of such simulations in position and momentum basis using Trotter-Suzuki formulas. We find that the number of T-gates needed to perform such simulations on a 3D lattice of ns sites scales at worst as O(ns3/ϵ)1+o(1) in the thermodynamic limit for position basis simulations and O(ns4+2/3/ϵ)1+o(1) in momentum basis. We also find that qubitization scales slightly better with a worst case scaling of O~(ns2+2/3/ϵ) for lattice eQED and complications in the prepare circuit leads to a slightly worse scaling in momentum basis of O~(ns5+2/3/ϵ). We further provide concrete gate counts for simulating a relativistic version of the uniform electron gas that show challenging problems can be simulated using fewer than 1013 non-Clifford operations and also provide a detailed discussion of how to prepare multi-reference configuration interaction states in effective QED which can provide a reasonable initial guess for the ground state. Finally, we estimate the planewave cutoffs needed to accurately simulate heavy elements such as gold.

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“…Classical simulations of scalar fields are limited to only small size systems since the memory requirement increases exponentially with system size. Because of this computational difficulty in classical computers, there have been proposals to study field theory simulations on qubit based quantum computers [3][4][5][6][7][8]. The other path forward for studying the dynamics of field theories is to utilize cold atoms in optical lattices and simulate the field in an actual quantum environment [9].…”

Section: Introductionmentioning

confidence: 99%

Quantum simulation of $ϕ^4$ theories in qudit systems

Kürkçüoğlu¹,

Alam²,

Job³

et al. 2021

Preprint

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We discuss the implementation of quantum algorithms for lattice Φ 4 theory on circuit quantum electrodynamics (cQED) system. The field is represented on qudits in a discretized field amplitude basis. The main advantage of qudit systems is that its multi-level characteristic allows the field interaction to be implemented only with diagonal single-qudit gates. Considering the set of universal gates formed by the single-qudit phase gate and the displacement gate, we address initial state preparation and single-qudit gate synthesis with variational methods.

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Single-particle digitization strategy for quantum computation of a ϕ4 scalar field theory

Cited by 50 publications

References 137 publications

A quantum strategy to compute the jet quenching parameter $$\hat{q}$$

A quantum strategy to compute the jet quenching parameter $$\hat{q}$$

Simulating Effective QED on Quantum Computers

Quantum simulation of $ϕ^4$ theories in qudit systems

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