Qubitization strategies for bosonic field theories

Alexandru, Andrei; Bedaque, Paulo F.; Carosso, Andrea; Cervia, Michael J.; Sheng, Andy

doi:10.1103/physrevd.107.034503

Cited by 9 publications

(5 citation statements)

References 30 publications

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“…Another interesting approach that can be studied by Monte Carlo is the use of non-commutative geometry. For example, [7,32] studied the truncation of the target space of the O(3) nonlinear sigma model by fuzzy sphere.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…The Hilbert space for bosons is infinite-dimensional. To simulate bosons on a qubit-or qudit-based quantum computer, one has to introduce a finite-dimensional approximation of the theory by truncating the Hilbert space [1][2][3][4][5][6][7][8]. Sometimes this truncation is referred to as digitization and it is one of the necessary steps in the construction of efficient quantum algorithms to simulate quantum gauge theories [9][10][11][12][13], and to estimate quantum resources [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

“…Some errors associated with digitization are inevitable, and one needs to know how big they can be. While previous studies on truncated bosonic Hilbert spaces [1][2][3][4][5][6][7][8] have looked at the scaling of the errors with the digitization spacing (or equivalently, the number of qubits), this does not seem to be a straightforward task in general. In fact, when the bosonic systems investigated are too large, one would need to run the digitized theory on a good (noiseless) quantum computer and also efficiently compute the same observable with classical algorithms in order to benchmark the result.…”

Section: Introductionmentioning

confidence: 99%

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Estimating truncation effects of quantum bosonic systems using sampling algorithms

Hanada,

Liu,

Rinaldi

et al. 2023

Mach. Learn.: Sci. Technol.

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To simulate bosons on a qubit- or qudit-based quantum computer, one has to regularize the theory by truncating infinite-dimensional local Hilbert spaces to finite dimensions. In the search for practical quantum applications, it is important to know how big the truncation errors can be. In general, it is not easy to estimate errors unless we have a good quantum computer. In this paper, we show that traditional sampling methods on classical devices, specifically Markov Chain Monte Carlo, can address this issue for a rather generic class of bosonic systems with a reasonable amount of computational resources available today. As a demonstration, we apply this idea to the scalar field theory on a two-dimensional lattice, with a size that goes beyond what is achievable using exact diagonalization methods. This method can be used to estimate the resources needed for realistic quantum simulations of bosonic theories, and also, to check the validity of the results of the corresponding quantum simulations.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Estimating truncation effects of quantum bosonic systems using sampling algorithms

Hanada,

Liu,

Rinaldi

et al. 2023

Mach. Learn.: Sci. Technol.

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“…In this conference paper, we discuss how to express the 𝑂 (3) model in the oscillator basis using the Schwinger boson approach and comment on the possibility of whether this is realistic to achieve using current state-of-the-art methods in photonic quantum hardware1. The 𝑂 (3) model has been the subject of many investigations recently for efficient time evolution using fuzzy qubitization methods [5] and for preparation of ground states using cold atoms [6]. In addition, the Schwinger boson approach has also been used in Ref.…”

Section: Introductionmentioning

confidence: 99%

Quantum computations of the 𝑶(3) model using qumodes

Jha,

Ringer,

Siopsis

et al. 2024

Proceedings of the 40th International Symposium on Lattice Field Theory — PoS(LATTICE2023)

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We express the discrete 1+1-dimensional 𝑂 (3) non-linear sigma model (NL𝜎M) in a form wellsuited for the continuous variable approach to quantum computing. Within the Schwinger boson formulation, we need two qumodes (quantum-mechanical oscillators) at each lattice site. We envision that it might be possible to reach the scaling regime of this model and observe asymptotic freedom on near-term photonic quantum devices in the coming decade.

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“…Quantum computers can tackle high energy physics (HEP) problems beyond the reach of classical methods if noise can be controlled [1][2][3][4][5]. In particular the symmetry breaking by noise can spoil the predictive power of simulations by changing universality classes [6][7][8][9][10][11][12]. Thus sufficiently preserving these symmetries is crucial [13][14][15][16][17][18][19]; both in the current noisy era and the error-corrected future.…”

mentioning

confidence: 99%