Autoregressive Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation

Quasiprobabilistic state-overlap estimator for NISQ devices

“…In here, we have used a quasiprobabilistic representation specifically for estimating the fidelity between quantum states. However, these representations can be used to describe not only quantum states, but also quantum measurements, unitary evolution, and open system quantum dynamics [23][24][25][26]. Can they be efficiently used for classical simulations of quantum circuits?…”

jVMC: Versatile and performant variational Monte Carlo leveraging automated differentiation and GPU acceleration

“…One possibility is based on representing the density matrix in a purified form [27]. While implementing the purification approach is also within the scope of the jVMC codebase, we focus in the following on a method that relies on the Positive Operator Valued Measurements (POVM)-formalism [28,29,32,48,49] for a purely probabilistic formulation of quantum mechanics. Given a many-body POVM M a = M a 1 ⊗ .…”

“…The object of interest in an open quantum setting is the density matrix ρ, taking on the role of the wave-function ψ in a closed scenario. Different paths to variational approximations of ρ using neural networks have been explored [27][28][29], which were briefly introduced in Section 2.4. We here want to showcase results that were obtained in Ref.…”

“…It has been shown that NQS can be used to describe ground states of critical systems in two dimensions [11] or states with (chiral) topological order [12][13][14] and their suitability to study frustrated magnets is under investigation [15][16][17][18][19]. Moreover, various approaches have been developed for the simulation of non-equilibrium dynamics in closed [10,[20][21][22][23][24][25][26] and open quantum systems [27][28][29]. Other directions include the incorporation of NQS in quantum chemical simulations [30], quantum state tomography [31,32], and the simulation of quantum computation [33].…”

Gauge Invariant Autoregressive Neural Networks for Quantum Lattice Models

“…Autoregressive neural networks, such as recurrent neural networks (RNN) [29,30], pixel convolutional neural networks (pixelCNN) [31], and Transformers [32], have revolutionized the fields of computer vision and language translation and generation, among many others. Autoregressive neural networks quantum states have recently been introduced in quantum manybody physics [4,33,34] and shown to be capable of rep-resenting volume law states (as one generically needs in dynamics) with a number of parameters that scale sublinearly [35]. A central feature of AR-NN is their capability of exactly sampling configurations from them.…”