Free-fermionic systems are a valuable, but limited, class of many-body problems efficiently simulable on a classical computer. We examine how classical simulability of noninteracting fermions is modified in the presence of Markovian dissipation described by quadratic Lindblad operators, including, for example, incoherent transitions or pair losses. On the one hand, we establish three broad classes of Markovian dynamics that are efficiently simulable classically, by devising efficient algorithms. On the other hand, we demonstrate that, in the worst case, simulating Markovian dynamics with quadratic Lindblad operators is at least as hard as simulating universal quantum circuits. This result is applicable to an experimentally relevant setting in cold atomic systems, where magnetic Feshbach resonances can be used to engineer the desired dissipation. For such systems, our hardness result provides a direct scheme for dissipation-assisted quantum computing with a potential significant advantage in the speed of two-qubit gates and, therefore, in error tolerance.Free-fermionic systems are a valuable, but limited, class of many-body problems efficiently simulable on a classical computer. We examine how classical simulability of noninteracting fermions is modified in the presence of Markovian dissipation described by quadratic Lindblad operators, including, for example, incoherent transitions or pair losses. On the one hand, we establish three broad classes of Markovian dynamics that are efficiently simulable classically, by devising efficient algorithms. On the other hand, we demonstrate that, in the worst case, simulating Markovian dynamics with quadratic Lindblad operators is at least as hard as simulating universal quantum circuits. This result is applicable to an experimentally relevant setting in cold atomic systems, where magnetic Feshbach resonances can be used to engineer the desired dissipation. For such systems, our hardness result provides a direct scheme for dissipation-assisted quantum computing with a potential significant advantage in the speed of two-qubit gates and, therefore, in error tolerance.

May 21, 20200 citations

Dissipation in finite Fermi systems

Sudhir R. Jain

arXiv:nucl-th/9912062Nuclear Physics AJun 1, 20007 citations

Energy diffusion in weakly interacting chains with fermionic dissipation assisted operator evolution

En-Jui Kuo, Brayden Ware, Peter Lunts +2 more

Interacting lattice Hamiltonians at high temperature generically give rise to energy transport governed by the classical diffusion equation; however, predicting the rate of diffusion requires numerical simulation of the microscopic quantum dynamics. For the purpose of predicting such transport properties, computational time evolution methods must be paired with schemes to control the growth of entanglement to tractably simulate for sufficiently long times. One such truncation scheme---dissipation-assisted operator evolution (DAOE)---controls entanglement by damping out components of operators with large Pauli weight. In this paper, we generalize DAOE to treat fermionic systems. Our method instead damps out components of operators with large fermionic weight. We investigate the performance of DAOE, the new fermionic DAOE (FDAOE), and another simulation method, density matrix truncation (DMT), in simulating energy transport in an interacting one-dimensional Majorana chain. The chain is found to have a diffusion coefficient scaling like interaction strength to the fourth power, contrary to naive expectations based on Fermi's Golden rule---but consistent with recent predictions based on the theory of weak integrability breaking. In the weak interaction regime where the fermionic nature of the system is most relevant, FDAOE is found to simulate the system more efficiently than DAOE.Interacting lattice Hamiltonians at high temperature generically give rise to energy transport governed by the classical diffusion equation; however, predicting the rate of diffusion requires numerical simulation of the microscopic quantum dynamics. For the purpose of predicting such transport properties, computational time evolution methods must be paired with schemes to control the growth of entanglement to tractably simulate for sufficiently long times. One such truncation scheme---dissipation-assisted operator evolution (DAOE)---controls entanglement by damping out components of operators with large Pauli weight. In this paper, we generalize DAOE to treat fermionic systems. Our method instead damps out components of operators with large fermionic weight. We investigate the performance of DAOE, the new fermionic DAOE (FDAOE), and another simulation method, density matrix truncation (DMT), in simulating energy transport in an interacting one-dimensional Majorana chain. The chain is found to have a diffusion coefficient scaling like interaction strength to the fourth power, contrary to naive expectations based on Fermi's Golden rule---but consistent with recent predictions based on the theory of weak integrability breaking. In the weak interaction regime where the fermionic nature of the system is most relevant, FDAOE is found to simulate the system more efficiently than DAOE.

arXiv:2311.17148Physical review. B./Physical review. BAug 26, 20246 citations

Weakly interacting fermionic Gibbs states are Gaussian mixtures and classically simulable

Zhengyi Han, Yuanchen Zhao, Zi-Wen Liu

Identifying regimes in which interacting fermionic systems admit efficient classical simulation is a crucial task in quantum many-body physics. In this work, we rigorously establish the Gaussianity and classical simulability of sufficiently weakly interacting fermions. For the Gibbs state of a local interacting fermionic Hamiltonian $H=H_0+V$ at any finite temperature and in any spatial dimension, where $H_0$ is quadratic and $V$ is the interaction term, we show that there exists a positive interaction strength below which the Gibbs state is a convex mixture of fermionic Gaussian states. Moreover, based on this structure, we construct a polynomial-time classical sampler for the Gibbs state via Metropolis updates on a tree whose leaves are Gaussian states.Identifying regimes in which interacting fermionic systems admit efficient classical simulation is a crucial task in quantum many-body physics. In this work, we rigorously establish the Gaussianity and classical simulability of sufficiently weakly interacting fermions. For the Gibbs state of a local interacting fermionic Hamiltonian $H=H_0+V$ at any finite temperature and in any spatial dimension, where $H_0$ is quadratic and $V$ is the interaction term, we show that there exists a positive interaction strength below which the Gibbs state is a convex mixture of fermionic Gaussian states. Moreover, based on this structure, we construct a polynomial-time classical sampler for the Gibbs state via Metropolis updates on a tree whose leaves are Gaussian states.

quant-pharXiv:2609.35159Sep 29, 20260 citations

Complexity of Fermionic Dissipative Interactions and Applications to Quantum Computing

Oles Shtanko, Abhinav Deshpande, Paul S. Julienne +1 more

Interactions between particles are usually a resource for quantum computing, making quantum manybody systems intractable by any known classical algorithm.In contrast, noise is typically considered as being inimical to quantum many-body correlations, ultimately leading the system to a classically tractable state.This work shows that noise represented by two-body processes, such as pair loss, plays the same role as many-body interactions and makes otherwise classically simulable systems universal for quantum computing.We analyze such processes in detail and establish a complexity transition between simulable and nonsimulable systems as a function of a tuning parameter.We determine important classes of simulable and nonsimulable two-body dissipation.Finally, we show how using resonant dissipation in cold atoms can enhance the performance of two-qubit gates.Interactions between particles are usually a resource for quantum computing, making quantum manybody systems intractable by any known classical algorithm.In contrast, noise is typically considered as being inimical to quantum many-body correlations, ultimately leading the system to a classically tractable state.This work shows that noise represented by two-body processes, such as pair loss, plays the same role as many-body interactions and makes otherwise classically simulable systems universal for quantum computing.We analyze such processes in detail and establish a complexity transition between simulable and nonsimulable systems as a function of a tuning parameter.We determine important classes of simulable and nonsimulable two-body dissipation.Finally, we show how using resonant dissipation in cold atoms can enhance the performance of two-qubit gates.

arXiv:2005.10840PRX QuantumSep 24, 202112 citations

H=H_0+V

at any finite temperature and in any spatial dimension, where

H_0

is quadratic and

V

is the interaction term, we show that there exists a positive interaction strength below which the Gibbs state is a convex mixture of fermionic Gaussian states. Moreover, based on this structure, we construct a polynomial-time classical sampler for the Gibbs state via Metropolis updates on a tree whose leaves are Gaussian states.