Qubit Regularization of Asymptotic Freedom

Bhattacharya, Tanmoy; Buser, Alexander J.; Chandrasekharan, Shailesh; Gupta, Rajan; Singh, Hersh

doi:10.1103/physrevlett.126.172001

Cited by 50 publications

(25 citation statements)

References 45 publications

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“…An interesting related question is whether we can reproduce the same continuum physics with a single layer model by further exploring the model space. This was realized for the O(3) model where an interesting critical Hamiltonian model was identified [34]. Discovering a spacetime symmetric qubit-regularized model, however, remains an interesting challenge for both the O(3) and O(4) cases.…”

Section: Qubit Regularization As An Eftmentioning

confidence: 99%

Space-time symmetric qubit regularization of the asymptotically free two-dimensional O(4) model

Zhou,

Singh,

Bhattacharya

et al. 2021

Preprint

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We explore if space-time symmetric lattice field theory models with a finite Hilbert space per lattice site can reproduce asymptotic freedom in the two-dimensional O(4) model. We focus on a simple class of such models with a five dimensional local Hilbert space. We demonstrate how even the simplest model reproduces asymptotic freedom within the D-theory formalism but at the cost of increasing the size of the Hilbert space through coupling several layers of a two-dimensional lattice. We then argue that qubit regularization can be viewed as an effective field theory (EFT) even if the continuum limit cannot be reached, as long as we can tune the model close enough to the continuum limit where perturbation theory, or other analytical techniques, become viable. We construct a simple lattice model on a single layer with a four dimensional local Hilbert space that acts like an excellent EFT of the original theory.

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Section: Qubit Regularization As An Eftmentioning

confidence: 99%

Space-time symmetric qubit regularization of the asymptotically free two-dimensional O(4) model

Zhou,

Singh,

Bhattacharya

et al. 2021

Preprint

Self Cite

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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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“…Although this infinity does not make calculations singular, it does create challenges for simulating quantum field theories on a quantum computer, whose local Hilbert space is finite dimensional. The procedure of regularizing this infinite dimensional local Hilbert space to a finite dimensional one is what we call "qubit regularization", which has been proposed as a first step in simulating quantum field theories using a quantum computer [38][39][40][41][42].…”

Section: Introductionmentioning

confidence: 99%

“…There is strong evidence that conformal field theories that emerge at Wilson-Fisher fixed points can be recovered using fixed finite dimensional local Hilbert spaces [39,59,60]. We have also recently discovered that some asymptotically free theories can also be recovered in this way [41]. In fact, D-theory suggests that one can recover many traditional lattice theories with infinite dimensional Hilbert spaces within acceptable errors, by using simple qubit regularized models.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, when sign problems are absent, quantum Monte Carlo methods similar to the ones used to solve traditional models can also be designed for qubit regularized models. Such a method led to the discovery of a two-qubit model that reproduces the asymptotically free two-dimensional O(3) model [41]. Methods based on tensor networks also seem promising and currently being developed for a variety of lattice field theories [24,64].…”

Section: Introductionmentioning

confidence: 99%

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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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Qubit Regularization of Asymptotic Freedom

Cited by 50 publications

References 45 publications

Space-time symmetric qubit regularization of the asymptotically free two-dimensional O(4) model

Space-time symmetric qubit regularization of the asymptotically free two-dimensional O(4) model

Simulating Effective QED on Quantum Computers

Qubit Regularization and Qubit Embedding Algebras

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