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Zache TV, González-Cuadra D, Zoller P. Quantum and Classical Spin-Network Algorithms for q-Deformed Kogut-Susskind Gauge Theories. PHYSICAL REVIEW LETTERS 2023; 131:171902. [PMID: 37955498 DOI: 10.1103/physrevlett.131.171902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2023] [Revised: 08/10/2023] [Accepted: 09/25/2023] [Indexed: 11/14/2023]
Abstract
Treating the infinite-dimensional Hilbert space of non-Abelian gauge theories is an outstanding challenge for classical and quantum simulations. Here, we employ q-deformed Kogut-Susskind lattice gauge theories, obtained by deforming the defining symmetry algebra to a quantum group. In contrast to other formulations, this approach simultaneously provides a controlled regularization of the infinite-dimensional local Hilbert space while preserving essential symmetry-related properties. This enables the development of both quantum as well as quantum-inspired classical spin-network algorithms for q-deformed gauge theories. To be explicit, we focus on SU(2)_{k} gauge theories with k∈N that are controlled by the deformation parameter q=e^{2πi/(k+2)}, a root of unity, and converge to the standard SU(2) Kogut-Susskind model as k→∞. In particular, we demonstrate that this formulation is well suited for efficient tensor network representations by variational ground-state simulations in 2D, providing first evidence that the continuum limit can be reached with k=O(10). Finally, we develop a scalable quantum algorithm for Trotterized real-time evolution by analytically diagonalizing the SU(2)_{k} plaquette interactions. Our work gives a new perspective for the application of tensor network methods to high-energy physics and paves the way for quantum simulations of non-Abelian gauge theories far from equilibrium where no other methods are currently available.
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Affiliation(s)
- Torsten V Zache
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria and Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria
| | - Daniel González-Cuadra
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria and Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria
| | - Peter Zoller
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria and Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria
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Davoudi Z, Mueller N, Powers C. Towards Quantum Computing Phase Diagrams of Gauge Theories with Thermal Pure Quantum States. PHYSICAL REVIEW LETTERS 2023; 131:081901. [PMID: 37683176 DOI: 10.1103/physrevlett.131.081901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2022] [Revised: 02/27/2023] [Accepted: 06/01/2023] [Indexed: 09/10/2023]
Abstract
The phase diagram of strong interactions in nature at finite temperature and chemical potential remains largely theoretically unexplored due to inadequacy of Monte-Carlo-based computational techniques in overcoming a sign problem. Quantum computing offers a sign-problem-free approach, but evaluating thermal expectation values is generally resource intensive on quantum computers. To facilitate thermodynamic studies of gauge theories, we propose a generalization of the thermal-pure-quantum-state formulation of statistical mechanics applied to constrained gauge-theory dynamics, and numerically demonstrate that the phase diagram of a simple low-dimensional gauge theory is robustly determined using this approach, including mapping a chiral phase transition in the model at finite temperature and chemical potential. Quantum algorithms, resource requirements, and algorithmic and hardware error analysis are further discussed to motivate future implementations. Thermal pure quantum states, therefore, may present a suitable candidate for efficient thermal simulations of gauge theories in the era of quantum computing.
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Affiliation(s)
- Zohreh Davoudi
- Maryland Center for Fundamental Physics and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
- Institute for Robust Quantum Simulation, University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Niklas Mueller
- Maryland Center for Fundamental Physics and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Connor Powers
- Maryland Center for Fundamental Physics and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
- Institute for Robust Quantum Simulation, University of Maryland, College Park, Maryland 20742, USA
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González-Cuadra D, Zache TV, Carrasco J, Kraus B, Zoller P. Hardware Efficient Quantum Simulation of Non-Abelian Gauge Theories with Qudits on Rydberg Platforms. PHYSICAL REVIEW LETTERS 2022; 129:160501. [PMID: 36306768 DOI: 10.1103/physrevlett.129.160501] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2022] [Revised: 07/12/2022] [Accepted: 09/27/2022] [Indexed: 05/02/2023]
Abstract
Non-Abelian gauge theories underlie our understanding of fundamental forces in nature, and developing tailored quantum hardware and algorithms to simulate them is an outstanding challenge in the rapidly evolving field of quantum simulation. Here we take an approach where gauge fields, discretized in spacetime, are represented by qudits and are time evolved in Trotter steps with multiqudit quantum gates. This maps naturally and hardware efficiently to an architecture based on Rydberg tweezer arrays, where long-lived internal atomic states represent qudits, and the required quantum gates are performed as holonomic operations supported by a Rydberg blockade mechanism. We illustrate our proposal for a minimal digitization of SU(2) gauge fields, demonstrating a significant reduction in circuit depth and gate errors in comparison to a traditional qubit-based approach, which puts simulations of non-Abelian gauge theories within reach of NISQ devices.
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Affiliation(s)
- Daniel González-Cuadra
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria
| | - Torsten V Zache
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria
| | - Jose Carrasco
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria
| | - Barbara Kraus
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria
| | - Peter Zoller
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria
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Carena M, Lamm H, Li YY, Liu W. Improved Hamiltonians for Quantum Simulations of Gauge Theories. PHYSICAL REVIEW LETTERS 2022; 129:051601. [PMID: 35960555 DOI: 10.1103/physrevlett.129.051601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2022] [Revised: 05/08/2022] [Accepted: 07/08/2022] [Indexed: 06/15/2023]
Abstract
Quantum simulations of lattice gauge theories for the foreseeable future will be hampered by limited resources. The historical success of improved lattice actions in classical simulations strongly suggests that Hamiltonians with improved discretization errors will reduce quantum resources, i.e., require ≳2^{d} fewer qubits in quantum simulations for lattices with d-spatial dimensions. In this work, we consider O(a^{2})-improved Hamiltonians for pure gauge theories and design the corresponding quantum circuits for its real-time evolution in terms of primitive gates. An explicit demonstration for Z_{2} gauge theory is presented including exploratory tests using the ibm_perth device.
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Affiliation(s)
- Marcela Carena
- Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
- Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA
- Kavli Institute for Cosmological Physics, University of Chicago, Chicago, Illinois 60637, USA
- Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - Henry Lamm
- Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
| | - Ying-Ying Li
- Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
| | - Wanqiang Liu
- Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
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Zohar E. Quantum simulation of lattice gauge theories in more than one space dimension-requirements, challenges and methods. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210069. [PMID: 34923840 PMCID: PMC8886423 DOI: 10.1098/rsta.2021.0069] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2021] [Accepted: 08/18/2021] [Indexed: 05/17/2023]
Abstract
Over recent years, the relatively young field of quantum simulation of lattice gauge theories, aiming at implementing simulators of gauge theories with quantum platforms, has gone through a rapid development process. Nowadays, it is not only of interest to the quantum information and technology communities. It is also seen as a valid tool for tackling hard, non-perturbative gauge theory problems by particle and nuclear physicists. Along the theoretical progress, nowadays more and more experiments implementing such simulators are being reported, manifesting beautiful results, but mostly on [Formula: see text] dimensional physics. In this article, we review the essential ingredients and requirements of lattice gauge theories in more dimensions and discuss their meanings, the challenges they pose and how they could be dealt with, potentially aiming at the next steps of this field towards simulating challenging physical problems in analogue, or analogue-digital ways. This article is part of the theme issue 'Quantum technologies in particle physics'.
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Affiliation(s)
- Erez Zohar
- Racah Institute of Physics, The Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel
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Abstract
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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Armon T, Ashkenazi S, García-Moreno G, González-Tudela A, Zohar E. Photon-Mediated Stroboscopic Quantum Simulation of a Z_{2} Lattice Gauge Theory. PHYSICAL REVIEW LETTERS 2021; 127:250501. [PMID: 35029424 DOI: 10.1103/physrevlett.127.250501] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2021] [Accepted: 11/15/2021] [Indexed: 06/14/2023]
Abstract
Quantum simulation of lattice gauge theories, aiming at tackling nonperturbative particle and condensed matter physics, has recently received a lot of interest and attention, resulting in many theoretical proposals as well as several experimental implementations. One of the current challenges is to go beyond 1+1 dimensions, where four-body (plaquette) interactions, not contained naturally in quantum simulating devices, appear. In this Letter, we propose a method to obtain them based on a combination of stroboscopic optical atomic control and the nonlocal photon-mediated interactions appearing in nanophotonic or cavity QED setups. We illustrate the method for a Z_{2} lattice gauge theory. We also show how to prepare the ground state and measure Wilson loops using state-of-the-art techniques in atomic physics.
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Affiliation(s)
- Tsafrir Armon
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Shachar Ashkenazi
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Gerardo García-Moreno
- Institute of Fundamental Physics IFF-CSIC, Calle Serrano 113b, 28006 Madrid, Spain, Departamento de Física Teórica and IPARCOS, Universidad Complutense de Madrid, 28040 Madrid, Spain, and Instituto de Astrofísica de Andalucía (IAA-CSIC), Glorieta de la Astronomía, 18008 Granada, Spain
| | | | - Erez Zohar
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
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Lacroix D. Symmetry-Assisted Preparation of Entangled Many-Body States on a Quantum Computer. PHYSICAL REVIEW LETTERS 2020; 125:230502. [PMID: 33337171 DOI: 10.1103/physrevlett.125.230502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2020] [Revised: 09/08/2020] [Accepted: 10/27/2020] [Indexed: 06/12/2023]
Abstract
Starting from the quantum-phase-estimate (QPE) algorithm, a method is proposed to construct entangled states that describe correlated many-body systems on quantum computers. Using operators for which the discrete set of eigenvalues is known, the QPE approach is followed by measurements that serve as projectors on the entangled states. These states can then be used as inputs for further quantum or hybrid quantum-classical processing. When the operator is associated with a symmetry of the Hamiltonian, the approach can be seen as a quantum-computer formulation of symmetry breaking followed by symmetry restoration. The method, called discrete spectra assisted, is applied to superfluid systems. By using the blocking technique adapted to qubits, the full spectra of a pairing Hamiltonian is obtained.
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Affiliation(s)
- Denis Lacroix
- Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France
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Meurice Y. Discrete aspects of continuous symmetries in the tensorial formulation of Abelian gauge theories. Int J Clin Exp Med 2020. [DOI: 10.1103/physrevd.102.014506] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Mueller N, Tarasov A, Venugopalan R. Deeply inelastic scattering structure functions on a hybrid quantum computer. Int J Clin Exp Med 2020. [DOI: 10.1103/physrevd.102.016007] [Citation(s) in RCA: 29] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Klco N, Savage MJ, Stryker JR. SU(2) non-Abelian gauge field theory in one dimension on digital quantum computers. Int J Clin Exp Med 2020. [DOI: 10.1103/physrevd.101.074512] [Citation(s) in RCA: 71] [Impact Index Per Article: 17.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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