Verification of the Quantum Jarzynski Equality on Digital Quantum Computers
The quantum Jarzynski equality and the Crooks relation are fundamental laws connecting equilibrium processes with nonequilibrium fluctuations. While they are well established theoretically and also experimental realizations for simple few-body systems already exist, a verification in the quantum many-body regime is still missing. Here, we present results for nonequilibrium protocols in systems with up to Read more…
jVMC: Versatile and performant variational Monte Carlo leveraging automated differentiation and GPU acceleration
The introduction of Neural Quantum States (NQS) has recently given a new twist to variational Monte Carlo (VMC). The ability to systematically reduce the bias of the wave function ansatz renders the approach widely applicable. However, performant implementations are crucial to reach the numerical state of the art. Here, we present a Python codebase that Read more…
Quantum phase transition dynamics in the two-dimensional transverse-field Ising model
The quantum Kibble-Zurek mechanism (QKZM) predicts universal dynamical behavior in the vicinity of quantum phase transitions (QPTs). It is now well understood for one-dimensional quantum matter. Higher-dimensional systems, however, remain a challenge, complicated by fundamental differences of the associated QPTs and their underlying conformal field theories. In this work, we take the first steps towards Read more…
Time-dependent variational principle for open quantum systems with artificial neural networks
We develop a variational approach to simulating the dynamics of open quantum many-body systems using deep autoregressive neural networks. The parameters of a compressed representation of a mixed quantum state are adapted dynamically according to the Lindbald master equation by employing a time-dependent variational principle. We illustrate our approach by solving the dissipative quantum Heisenberg Read more…
From observations to complexity of quantum states via unsupervised learning
The vast complexity is a daunting property of generic quantum states that poses a significant challenge for theoretical treatment, especially in nonequilibrium setups. Therefore, it is vital to recognize states which are locally less complex and thus describable with (classical) effective theories. We use unsupervised learning with autoencoder neural networks to detect the local complexity Read more…
Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape
Strongly interacting quantum systems described by non-stoquastic Hamiltonians exhibit rich low-temperature physics. Yet, their study poses a formidable challenge, even for state-of-the-art numerical techniques. Here, we investigate systematically the performance of a class of universal variational wave-functions based on artificial neural networks, by considering the frustrated spin-1/2 J_1−J_2 Heisenberg model on the square lattice. Focusing Read more…
Variational classical networks for dynamics in interacting quantum matter
Dynamics in correlated quantum matter is a hard problem, as its exact solution generally involves a computational effort that grows exponentially with the number of constituents. While a remarkable progress has been witnessed in recent years for one-dimensional systems, much less has been achieved for interacting quantum models in higher dimensions, since they incorporate an Read more…
Discrete truncated Wigner approach to dynamical phase transitions in Ising models after a quantum quench
By means of the discrete truncated Wigner approximation we study dynamical phase transitions arising in the steady state of transverse-field Ising models after a quantum quench. Starting from a fully polarized ferromagnetic initial condition these transitions separate a phase with nonvanishing magnetization along the ordering direction from a symmetric phase upon increasing the transverse field. Read more…
Disorder-free localization in an interacting two-dimensional lattice gauge theory
Disorder-free localization has been recently introduced as a mechanism for ergodicity breaking in low-dimensional homogeneous lattice gauge theories caused by local constraints imposed by gauge invariance. We show that also genuinely interacting systems in two spatial dimensions can become nonergodic as a consequence of this mechanism. Specifically, we prove nonergodic behavior in the quantum link Read more…
Quantum many-body dynamics in two dimensions with artificial neural networks
The efficient numerical simulation of nonequilibrium real-time evolution in isolated quantum matter constitutes a key challenge for current computational methods. This holds in particular in the regime of two spatial dimensions, whose experimental exploration is currently pursued with strong efforts in quantum simulators. In this work we present a versatile and efficient machine learning inspired Read more…
