Quantum computation of scattering amplitudes in scalar quantum electrodynamics

Yeter-Aydeniz, Kübra; Siopsis, George

doi:10.1103/physrevd.97.036004

Cited by 16 publications

(14 citation statements)

References 39 publications

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“…1. The scalar field digitization techniques of Jordan-Preskill-Lee [6-9, 34, 36, 50], a momentum-space mode expansion [42] and a harmonic oscillator basis are relevant for NISQ-era hardware implementations. The number of qubits per site needed to reduce the digitization and discretization systematic errors below near-term hardware noise levels are n Q ∼ 4 for potentials with m 2 > 0 and n Q > ∼ 6 for potentials with m 2 < 0.…”

Section: Discussionmentioning

confidence: 99%

“…In numerical computations of non-perturbative field theories, such as LQCD, the system is typically defined with regard to fields in position space, while components of calculations involve determining eigenvectors of the Dirac operator in the presence of a particular configuration of gauge fields. In the study of systems with few sites in each spatial direction, it is likely the case that calculating with the momentum-space modes is efficient [42]. First implementation of this quantization procedure on quantum devices has been completed by an ORNL team [87].…”

Section: +1 Dimensional λφ 4 Scalar Field Theorymentioning

confidence: 99%

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Digitization of scalar fields for quantum computing

2019

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Qubit, operator and gate resources required for the digitization of lattice λφ 4 scalar field theories onto quantum computers are considered, building upon the foundational work by Jordan, Lee and Preskill, with a focus towards noisy intermediate-scale quantum (NISQ) devices. The Nyquist-Shannon sampling theorem, introduced in this context by Macridin, Spentzouris, Amundson and Harnik building on the work of Somma, provides a guide with which to evaluate the efficacy of two field-space bases, the eigenstates of the field operator, as used by Jordan, Lee and Preskill, and eigenstates of a harmonic oscillator, to describe 0 + 1-and d + 1-dimensional scalar field theory. We show how techniques associated with improved actions, which are heavily utilized in Lattice QCD calculations to systematically reduce lattice-spacing artifacts, can be used to reduce the impact of the field digitization in λφ 4 , but are found to be inferior to a complete digitization-improvement of the Hamiltonian using a Quantum Fourier Transform. When the Nyquist-Shannon sampling theorem is satisfied, digitization errors scale as | log | log | dig ||| ∼ n Q (number of qubits describing the field at a given spatial site) for the low-lying states, leaving the familiar power-law lattice-spacing and finite-volume effects that scale as | log | latt || ∼ N Q (total number of qubits in the simulation). For localized(delocalized) field-space wavefunctions, it is found that n Q ∼ 4(7) qubits per spatial lattice site are sufficient to reduce theoretical digitization errors below error contributions associated with approximation of the time-evolution operator and noisy implementation on near-term quantum devices. 1 1 Only classical computing resources have been used to obtain the results presented in this work.

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Section: Discussionmentioning

confidence: 99%

Section: +1 Dimensional λφ 4 Scalar Field Theorymentioning

confidence: 99%

Digitization of scalar fields for quantum computing

2019

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“…The choice of scalar field is inspired by its simplicity, ubiquity, unique status of having a thoroughly examined qubit digitization [32][33][34][35][36], and having been proven to be BQP (bounded-error quantum polynomial time) complete [37]. The latter of these motivating factors indicates that any efficient quantum calculation, of fields or otherwise, can be transformed with polynomial resources to a scattering process of the interacting scalar field through the manipulation of classical external sources.…”

Section: Introductionmentioning

confidence: 99%

Geometric quantum information structure in quantum fields and their lattice simulation

Klco

Savage

2021

Phys. Rev. D

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An upper limit to distillable entanglement between two disconnected regions of massless noninteracting scalar field theory has an exponential decay defined by a geometric decay constant. When regulated at short distances with a spatial lattice, this entanglement abruptly vanishes beyond a dimensionless separation, defining a negativity sphere. In two spatial dimensions, we determine this geometric decay constant between a pair of disks and the growth of the negativity sphere toward the continuum through a series of lattice calculations. Making the connection to quantum field theories in three-spatial dimensions, assuming such quantum information scales appear also in quantum chromodynamics (QCD), a new relative scale may be present in effective field theories describing the low-energy dynamics of nucleons and nuclei. We highlight potential impacts of the distillable entanglement structure on effective field theories, lattice QCD calculations and future quantum simulations.

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“…We first evolve the wavepacket with the free Hamiltonian H 0 , which is diagonal in the momentum representation. This is followed by a squeezing operation (analogous to that performed in quantum optics [90,91]), a quantum Fourier transformation [92] from momentum space to position space, and lastly, an implementation of the interaction term in position space, where it is local.…”

Section: Quantum Algorithmmentioning

confidence: 99%

Single-particle digitization strategy for quantum computation of a $ϕ^4$ scalar field theory

Barata,

Mueller,

Tarasov

et al. 2020

Preprint

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Motivated by the parton picture of high energy quantum chromodynamics, we develop a singleparticle digitization strategy for the efficient quantum simulation of relativistic scattering processes in a d+1 dimensional scalar φ 4 field theory. We work out quantum algorithms for initial state preparation, time evolution and final state measurements. We outline a non-perturbative renormalization strategy in this single-particle framework.

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Quantum computation of scattering amplitudes in scalar quantum electrodynamics

Cited by 16 publications

References 39 publications

Digitization of scalar fields for quantum computing

Digitization of scalar fields for quantum computing

Geometric quantum information structure in quantum fields and their lattice simulation

Single-particle digitization strategy for quantum computation of a $ϕ^4$ scalar field theory

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