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arXiv:2412.19599

Super-bath Quantum Eigensolver

Tianren Wang, Zongkang Zhang, Bing-Nan Lu, Mauro Cirio, Ying Li

Published Dec 27, 2024• 1 citation
arXivHTMLPDF

Abstract

The simulation of the dynamics of a system coupled to a low-temperature environment is a promising application of quantum computers to determine ground-state properties of physical systems. However, this approach requires not only the $\textit{existence}$ of an environment that allows the system to dissipate energy and evolve to its ground state, but also the $\textit{detailed knowledge}$ of the properties of the bath. In this paper, we propose a polynomial-time algorithm for ground state preparation which only relies on the $\textit{existence}$ of a physical bath which achieves the same task, while a detailed description of the environment may remain $\textit{unknown}$. In particular, we show that this ``super-bath quantum eigensolver algorithm'' prepares the ground state of the system by combining a Gaussian stabilization dephasing procedure with the simulation of the interaction between the system and a super-bath which only requires minimal knowledge of the physical environment. Based on our algorithmic framework, we establish a partial order relation among environments. Supported by experimental lifetime data of nuclear metastable states, we suggest that our algorithm is applicable to determine nuclear ground states in polynomial time. These results highlight the potential advantage of quantum computing in addressing ground state problems in real-world physical systems.

DOI
10.48550/arxiv.2412.19599

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The simulation of the dynamics of a system coupled to a low-temperature environment is a promising application of quantum computers to determine ground-state properties of physical systems. However, this approach requires not only the existence\textit{existence}existence of an environment that allows the system to dissipate energy and evolve to its ground state, but also the detailed knowledge\textit{detailed knowledge}detailed knowledge of the properties of the bath. In this paper, we propose a polynomial-time algorithm for ground state preparation which only relies on the existence\textit{existence}existence of a physical bath which achieves the same task, while a detailed description of the environment may remain unknown\textit{unknown}unknown. In particular, we show that this ``super-bath quantum eigensolver algorithm'' prepares the ground state of the system by combining a Gaussian stabilization dephasing procedure with the simulation of the interaction between the system and a super-bath which only requires minimal knowledge of the physical environment. Based on our algorithmic framework, we establish a partial order relation among environments. Supported by experimental lifetime data of nuclear metastable states, we suggest that our algorithm is applicable to determine nuclear ground states in polynomial time. These results highlight the potential advantage of quantum computing in addressing ground state problems in real-world physical systems.
Abstract The simulation of the dynamics of a system coupled to a low-temperature environment is a promising application of quantum computers to determine ground-state properties of physical systems. However, this approach requires not only the existence of an environment that allows the system to dissipate energy and evolve to its ground state, but also the detailed knowledge of the properties of the bath. In this paper, we propose a polynomial-time algorithm for ground state preparation which only relies on the existence of a physical bath which achieves the same task, while a detailed description of the environment may remain unknown . In particular, we show that this ''super-bath quantum eigensolver algorithm'' prepares the ground state of the system by combining a Gaussian stabilization dephasing procedure with the simulation of the interaction between the system and a super-bath which only requires minimal knowledge of the physical environment. Based on our algorithmic framework, we establish a partial order relation among environments. Supported by experimental lifetime data of nuclear metastable states, we suggest that our algorithm is applicable to determine nuclear ground states in polynomial time. These results highlight the potential advantage of quantum computing in addressing ground state problems in real-world physical systems.
Learning quantum interactions from finite-temperature many-body systems is a central task in emerging quantum platforms. Recently, the problem of learning from lattice quantum Gibbs states has found rigorous, efficient protocols. Nevertheless, exact Gibbs states, as the input premise, are in fact computationally intractable to prepare and may not faithfully represent generic finite-temperature quantum systems. In contrast, a system coupled to a heat bath can be stuck at an approximate stationary state (metastable state) long before it truly equilibrates. Here, we formulate a physically and algorithmically consistent alternative: learning from such metastable states of detailed-balanced master equations (Lindbladians) arising from system-bath interactions. We distill the algorithmic mechanism and structural condition underlying Gibbs-state learning and extend it in full to metastable states, attaining nearly optimal sample and computational complexity (in the system size and the precision). More broadly, we sharpen notions of metastability and develop a unified framework for finite-temperature learning.
Quantum impurity models are paradigmatic models of interacting quantum matter, as well as key computational primitives for modern electronic-structure methods. They describe a small subsystem of interacting fermions coupled to a large, noninteracting bath. We perform a comprehensive study of the computational complexity of simulating impurity models, delineating the boundary between classical and quantum tractability for this class of problems. Our main finding is that static properties of quantum impurity models can be calculated efficiently on a classical computer. Specifically, we give classical algorithms that (1) estimate the ground-state energy to additive precision δδδ in time poly(n,δ−1)\mathrm{poly}(n,δ^{-1})poly(n,δ−1), and (2) estimate the partition function at inverse temperature βββ to relative precision δδδ in time poly(n,β,δ−1)\mathrm{poly}(n,β,δ^{-1})poly(n,β,δ−1), where nnn is the system size. These results improve the previous best-known complexity for ground-state energy estimation from quasipolynomial to polynomial time, while establishing for the first time rigorous polynomial-time guarantees for simulating impurity models in thermal equilibrium. On the other hand, we find that simulating dynamical properties of impurity models is hard for classical computers but easy on a quantum computer. As a canonical example, we show that computing their nonequilibrium Green's functions captures the full power of quantum computation, even at finite temperature. Taken together, our results rule out superpolynomial quantum speedups for computing static properties, but provide an avenue for quantum advantage in simulating impurity physics out of equilibrium.
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Preparing the ground state of a system is an important task in physics. We propose a quantum algorithm for preparing the ground state of a physical system that can be simulated on a quantum computer. The system is coupled to an ancillary qubit, by introducing a resonance mechanism between the ancilla qubit and the system, and combined with measurements performed on the ancilla qubit, the system can be evolved to monotonically converge to its ground state through an iterative procedure. We have simulated the application of this algorithm for the Afflect-Kennedy-Lieb-Tasaki model, whose ground state can be used as resource state in one-way quantum computation.
Dissipative algorithms approach the problem of ground state preparation by mimicking the natural thermalization of a quantum system in contact with a large, low-temperature thermal environment. The environment can be efficiently simulated by a single ancilla qubit with a variable energy gap that is repeatedly coupled to the system qubits to generate a dissipative channel, and then reset after each interaction. Here we present an adaptive implementation of the dissipative algorithm, RL-Adapt, that uses single-shot reinforcement learning to optimize the selection of ancilla frequency and system-bath interaction operator to maximize energy dissipation without relying on a priori knowledge of the system spectrum. The adaptive implementation results in significantly reduced convergence times and can successfully find the ground state even for non-ideal operator pools that fail to converge using non-adaptive, uniform random operator and ancilla frequency selection.