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arXiv:2301.02592 · SciPost Physics

Adaptive variational quantum minimally entangled typical thermal states for finite temperature simulations

João C. Getelina, Niladri Gomes, Thomas Iadecola, Peter P. Orth, Yongxin Yao

Published Sep 19, 2023• 21 citations
arXivHTMLPDF

Abstract

Scalable quantum algorithms for the simulation of quantum many-body systems in thermal equilibrium are important for predicting properties of quantum matter at finite temperatures. Here we describe and benchmark a quantum computing version of the minimally entangled typical thermal states (METTS) algorithm for which we adopt an adaptive variational approach to perform the required quantum imaginary time evolution. The algorithm, which we name AVQMETTS, dynamically generates compact and problem-specific quantum circuits, which are suitable for noisy intermediate-scale quantum (NISQ) hardware. We benchmark AVQMETTS on statevector simulators and perform thermal energy calculations of integrable and nonintegrable quantum spin models in one and two dimensions and demonstrate an approximately linear system-size scaling of the circuit complexity. We further map out the finite-temperature phase transition line of the two-dimensional transverse field Ising model. Finally, we study the impact of noise on AVQMETTS calculations using a phenomenological noise model.

DOI
10.21468/scipostphys.15.3.102

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Scalable quantum algorithms for the simulation of quantum many-body systems in thermal equilibrium are important for predicting properties of quantum matter at finite temperatures. Here we describe and benchmark a quantum computing version of the minimally entangled typical thermal states (METTS) algorithm for which we adopt an adaptive variational approach to perform the required quantum imaginary time evolution. The algorithm, which we name AVQMETTS, dynamically generates compact and problem-specific quantum circuits, which are suitable for noisy intermediate-scale quantum (NISQ) hardware. We benchmark AVQMETTS on statevector simulators and perform thermal energy calculations of integrable and nonintegrable quantum spin models in one and two dimensions and demonstrate an approximately linear system-size scaling of the circuit complexity. We further map out the finite-temperature phase transition line of the two-dimensional transverse field Ising model. Finally, we study the impact of noise on AVQMETTS calculations using a phenomenological noise model.
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Simulating strongly coupled gauge theories at finite temperature and density is a longstanding challenge in nuclear and high-energy physics that also has fundamental implications for condensed matter physics. In this work, we use minimally entangled typical thermal state (METTS) approaches to facilitate both classical and quantum computational studies of such systems. METTS techniques combine classical random sampling with imaginary time evolution, which can be performed on either a classical or a quantum computer, to estimate thermal averages of observables. We study 1+1-dimensional Z2\mathbb{Z}_2Z2​ gauge theory coupled to spinless fermionic matter, which maps onto a local quantum spin chain. We benchmark both a classical matrix-product-state implementation of METTS and a recently proposed adaptive variational approach that is a promising candidate for implementation on near-term quantum devices, focusing on the equation of state as well as on various measures of fermion confinement. Of particular importance is the choice of basis for obtaining new METTS samples, which impacts both the classical sampling complexity (a key factor in both classical and quantum simulation applications) and complexity of circuits used in the quantum computing approach. Our work sets the stage for future studies of strongly coupled gauge theories with both classical and quantum hardware.
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Abstract Simulating strongly coupled gauge theories at finite temperature and density is a longstanding challenge in nuclear and high-energy physics with fundamental implications for condensed matter physics. Here, we simulate such systems using minimally entangled typical thermal state (METTS) approaches, which combine classical random sampling with imaginary-time evolution, implementable on either classical or quantum computers, to estimate thermal averages of observables. We study 1+1-dimensional Z2{{\mathbb{Z}}}_{2}Z2​ Z 2 gauge theory coupled to spinless fermionic matter, which maps onto a local quantum spin chain. We benchmark both a classical matrix-product-state implementation of METTS and a recently proposed adaptive variational approach for near-term quantum devices, focusing on the equation of state and measures of fermion confinement. Of particular importance is the choice of basis for METTS sampling, which impacts both the sampling overhead and quantum circuit complexity. Our work sets the stage for future studies of strongly coupled gauge theories using classical and quantum hardware.
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Variational methods are a common approach for computing properties of ground states but have not yet found analogous success in finite-temperature calculations. In this work, we develop a new variational finite-temperature algorithm (VAFT), which combines ideas from minimally entangled typical thermal states (METTS), variational Monte Carlo (VMC) optimization, and path integral Monte Carlo (PIMC). This allows us to define an implicit variational density matrix to estimate finite-temperature properties in two and three dimensions. We benchmark the algorithm on the bipartite Heisenberg model and compare to exact results.
We extend White's minimally entangled typically thermal states approach (METTS) to allow Abelian and non-Ablian symmetries to be exploited when computing finite-temperature response functions in one-dimensional (1D) quantum systems. Our approach, called SYMETTS, starts from a METTS sample of states that are not symmetry eigenstates, and generates from each a symmetry eigenstate. These symmetry states are then used to calculate dynamic response functions. SYMETTS is ideally suited to determine the low-temperature spectra of 1D quantum systems with high resolution. We employ this method to study a generalized diamond chain model for the natural mineral azurite Cu3(CO3)2(OH)2\mathrm{Cu}{}_{3}(\mathrm{CO}{}_{3}{)}_{2}({\mathrm{OH})}_{2}Cu3​(CO3​)2​(OH)2​, which features a plateau at 13\frac{1}{3}31​ in the magnetization curve at low temperatures. Our calculations provide new insight into the effects of temperature on magnetization and excitation spectra in the plateau phase, which can be fully understood in terms of the microscopic model.