Simulating Gauge Theories With Variational Quantum Eigensolvers In Superconducting Microwave Cavities

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Jinglei Zhang^1,2, Ryan Ferguson^1,2, Stefan Kühn³, Jan F. Haase^1,2,4, C.M. Wilson^1,5, Karl Jansen⁶, and Christine A. Muschik^1,2,7

¹Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
²Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
³Computation-based Science and Technology Research Center,The Cyprus Institute, 20 Kavafi Street, 2121 Nicosia, Cyprus
⁴Institute of Theoretical Physics and IQST, Universität Ulm, Albert-Einstein-Allee 11, D-89069 Ulm, Germany
⁵Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
⁶NIC, DESY Zeuthen, Platanenallee 6, 15738 Zeuthen, Germany
⁷Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada

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Abstract

Quantum-enhanced computing methods are promising candidates to solve currently intractable problems. We consider here a variational quantum eigensolver (VQE), that delegates costly state preparations and measurements to quantum hardware, while classical optimization techniques guide the quantum hardware to create a desired target state. In this work, we propose a bosonic VQE using superconducting microwave cavities, overcoming the typical restriction of a small Hilbert space when the VQE is qubit based. The considered platform allows for strong nonlinearities between photon modes, which are highly customisable and can be tuned in situ, i.e. during running experiments. Our proposal hence allows for the realization of a wide range of bosonic ansatz states, and is therefore especially useful when simulating models involving degrees of freedom that cannot be simply mapped to qubits, such as gauge theories, that include components which require infinite-dimensional Hilbert spaces. We thus propose to experimentally apply this bosonic VQE to the U(1) Higgs model including a topological term, which in general introduces a sign problem in the model, making it intractable with conventional Monte Carlo methods.

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Popular summary

Gauge theories are a fundamental part of modern physics, in particular they constitute the theoretical foundation of the Standard Model, which is the best description we have to date of elementary particles and their interactions, except for gravity. One prominent success of the Standard Model is the Higgs mechanism, which explains how gauge bosons acquire their masses; this was experimentally confirmed by the discovery of the Higgs particle announced in 2013 at CERN. As gauge theories are quantum theories, quantum computers offer an exciting opportunity to understand them more deeply than what we have been able to do so far.

In this work, we propose to use photons in superconducting microwave cavities as a new quantum platform to study gauge theories. While many quantum computing platforms are based on qubits, which have two available states, the photons in a microwave cavity are a higher-dimensional system that can be exploited for the computation. This is particularly relevant because bosonic fields have intrinsically high-dimensional elements, and recent technological developments offer us an excellent level of control and variety of interactions between the microwave photons.

The theory we choose to study is called a U(1) Higgs model with a topological term. This theory contains rich and emblematic physics that we simulate via a hybrid quantum-classical algorithm called a variational quantum eigensolver (VQE). This protocol uses the quantum platform, in our case the microwave cavity, to perform evaluations that are classically hard, and a classical computer to perform a variational optimization that is robust to errors. We show that a VQE is able to compute the lowest-energy state of the model for a range of parameters, allowing us to study different phases of the system that have qualitatively different behaviour.

We discuss in detail and show that the quantum algorithm we developed is experimentally accessible, it studies a gauge theory that would not be accessible with classical methods alone, and it opens up many new possibilities to further develop quantum simulations for gauge theories.

► BibTeX data

@article{Zhang2023simulatinggauge, doi = {10.22331/q-2023-10-23-1148}, url = {https://doi.org/10.22331/q-2023-10-23-1148}, title = {Simulating gauge theories with variational quantum eigensolvers in superconducting microwave cavities}, author = {Zhang, Jinglei and Ferguson, Ryan and K{“{u}}hn, Stefan and Haase, Jan F. and Wilson, C.M. and Jansen, Karl and Muschik, Christine A.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {1148}, month = oct, year = {2023}<br /> }

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[1] Christian W. Bauer, Zohreh Davoudi, A. Baha Balantekin, Tanmoy Bhattacharya, Marcela Carena, Wibe A. de Jong, Patrick Draper, Aida El-Khadra, Nate Gemelke, Masanori Hanada, Dmitri Kharzeev, Henry Lamm, Ying-Ying Li, Junyu Liu, Mikhail Lukin, Yannick Meurice, Christopher Monroe, Benjamin Nachman, Guido Pagano, John Preskill, Enrico Rinaldi, Alessandro Roggero, David I. Santiago, Martin J. Savage, Irfan Siddiqi, George Siopsis, David Van Zanten, Nathan Wiebe, Yukari Yamauchi, Kübra Yeter-Aydeniz, and Silvia Zorzetti, “Quantum Simulation for High-Energy Physics”, PRX Quantum 4 2, 027001 (2023).

[2] He-Liang Huang, Xiao-Yue Xu, Chu Guo, Guojing Tian, Shi-Jie Wei, Xiaoming Sun, Wan-Su Bao, and Gui-Lu Long, “Near-term quantum computing techniques: Variational quantum algorithms, error mitigation, circuit compilation, benchmarking and classical simulation”, Science China Physics, Mechanics, and Astronomy 66 5, 250302 (2023).

[3] Roland C. Farrell, Ivan A. Chernyshev, Sarah J. M. Powell, Nikita A. Zemlevskiy, Marc Illa, and Martin J. Savage, “Preparations for quantum simulations of quantum chromodynamics in 1 +1 dimensions. I. Axial gauge”, Physical Review D 107 5, 054512 (2023).

[4] Roland C. Farrell, Ivan A. Chernyshev, Sarah J. M. Powell, Nikita A. Zemlevskiy, Marc Illa, and Martin J. Savage, “Preparations for quantum simulations of quantum chromodynamics in 1 +1 dimensions. II. Single-baryon β -decay in real time”, Physical Review D 107 5, 054513 (2023).

[5] Anthony N. Ciavarella and Ivan A. Chernyshev, “Preparation of the SU(3) lattice Yang-Mills vacuum with variational quantum methods”, Physical Review D 105 7, 074504 (2022).

[6] Zohreh Davoudi, Alexander F. Shaw, and Jesse R. Stryker, “General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory”, arXiv:2212.14030, (2022).

[7] A. Kan, L. Funcke, S. Kühn, L. Dellantonio, J. Zhang, J. F. Haase, C. A. Muschik, and K. Jansen, “3+1D theta-Term on the Lattice from the Hamiltonian Perspective”, The 38th International Symposium on Lattice Field Theory 112 (2022).

[8] G. Iannelli and K. Jansen, “Noisy Bayesian optimization for variational quantum eigensolvers”, The 38th International Symposium on Lattice Field Theory 251 (2022).

[9] Anthony N. Ciavarella, Stephan Caspar, Marc Illa, and Martin J. Savage, “State Preparation in the Heisenberg Model through Adiabatic Spiraling”, Quantum 7, 970 (2023).

[10] Judah F. Unmuth-Yockey, “Metropolis-style random sampling of quantum gates for the estimation of low-energy observables”, Physical Review D 105 3, 034515 (2022).

[11] Anthony N. Ciavarella, Stephan Caspar, Hersh Singh, and Martin J. Savage, “Preparation for quantum simulation of the (1 +1 ) -dimensional O(3) nonlinear σ model using cold atoms”, Physical Review A 107 4, 042404 (2023).

[12] Yiming Ding, Xiaopeng Cui, and Yu Shi, “Digital quantum simulation and pseudoquantum simulation of the Z<SUB>2</SUB> gauge-Higgs model”, Physical Review D 105 5, 054508 (2022).

The above citations are from SAO/NASA ADS (last updated successfully 2023-10-23 16:19:49). The list may be incomplete as not all publishers provide suitable and complete citation data.

Could not fetch Crossref cited-by data during last attempt 2023-10-23 16:19:47: Could not fetch cited-by data for 10.22331/q-2023-10-23-1148 from Crossref. This is normal if the DOI was registered recently.

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Source: https://quantum-journal.org/papers/q-2023-10-23-1148/

Time Stamp: October 23, 2023

Time Stamp: Oct 19, 2023

Simulating gauge theories with variational quantum eigensolvers in superconducting microwave cavities

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