Variational neural network ansatz for steady states in open quantum systems

We present a general variational approach to determine the steady state of open quantum lattice systems via a neural network approach. The steady-state density matrix of the lattice system is constructed via a purified neural network ansatz in an extended Hilbert space with ancillary degrees of freedom. The variational minimization of cost functions associated to the master equation can be performed using a Markov chain Monte Carlo sampling. As a first application and proof-of-principle, we apply the method to the dissipative quantum transverse Ising model.Comment: 6 pages, 4 figures, 54 references, 5 pages of Supplemental Information

Variational dynamics of open quantum systems in phase space

We present a method to simulate the dynamics of large driven-dissipative many-body open quantum systems using a variational encoding of the Wigner or Husimi-Q quasi-probability distributions. The method relies on Monte-Carlo sampling to maintain a polynomial computational complexity while allowing for several quantities to be estimated efficiently. As a first application, we present a proof of principle investigation into the physics of the driven-dissipative Bose-Hubbard model with weak nonlinearity, providing evidence for the high efficiency of the phase space variational approach.Comment: 7 pages, 5 figure

Embedding Classical Variational Methods in Quantum Circuits

We introduce a novel quantum-classical variational method that extends the quantum devices capabilities to approximate ground states of interacting quantum systems. The proposed method enhances parameterized quantum circuit ansatzes implemented on quantum devices with classical variational functions, such as neural-network quantum states. The quantum hardware is used as a high-accuracy solver on the most correlated degrees of freedom, while the remaining contributions are treated on a classical device. Our approach is completely variational, providing a well-defined route to systematically improve the accuracy by increasing the number of variational parameters, and performs a global optimization of the two partitions at the same time. We demonstrate the effectiveness of the protocol on spin chains and small molecules and provide insights into its accuracy and computational cost. We prove that our method is able to converge to exact diagonalization results via the addition of classical degrees of freedom, while the quantum circuit is kept fixed in both depth and width.Comment: 11 pages, 6 figure

An efficient quantum algorithm for the time evolution of parameterized circuits

We introduce a novel hybrid algorithm to simulate the real-time evolution of quantum systems using parameterized quantum circuits. The method, named "projected - Variational Quantum Dynamics" (p-VQD) realizes an iterative, global projection of the exact time evolution onto the parameterized manifold. In the small time-step limit, this is equivalent to the McLachlan's variational principle. Our approach is efficient in the sense that it exhibits an optimal linear scaling with the total number of variational parameters. Furthermore, it is global in the sense that it uses the variational principle to optimize all parameters at once. The global nature of our approach then significantly extends the scope of existing efficient variational methods, that instead typically rely on the iterative optimization of a restricted subset of variational parameters. Through numerical experiments, we also show that our approach is particularly advantageous over existing global optimization algorithms based on the time-dependent variational principle that, due to a demanding quadratic scaling with parameter numbers, are unsuitable for large parameterized quantum circuits.Comment: 7+4 pages, 8 figures; Manuscript revised for publication. Method: added Section 2.2, Results: added Figure 6, Appendix: added Appendix E with Figure

Learning ground states of gapped quantum Hamiltonians with Kernel Methods

Neural network approaches to approximate the ground state of quantum hamiltonians require the numerical solution of a highly nonlinear optimization problem. We introduce a statistical learning approach that makes the optimization trivial by using kernel methods. Our scheme is an approximate realization of the power method, where supervised learning is used to learn the next step of the power iteration. We show that the ground state properties of arbitrary gapped quantum hamiltonians can be reached with polynomial resources under the assumption that the supervised learning is efficient. Using kernel ridge regression, we provide numerical evidence that the learning assumption is verified by applying our scheme to find the ground states of several prototypical interacting many-body quantum systems, both in one and two dimensions, showing the flexibility of our approach

From Tensor Network Quantum States to Tensorial Recurrent Neural Networks

We show that any matrix product state (MPS) can be exactly represented by a recurrent neural network (RNN) with a linear memory update. We generalize this RNN architecture to 2D lattices using a multilinear memory update. It supports perfect sampling and wave function evaluation in polynomial time, and can represent an area law of entanglement entropy. Numerical evidence shows that it can encode the wave function using a bond dimension lower by orders of magnitude when compared to MPS, with an accuracy that can be systematically improved by increasing the bond dimension.Comment: 14 pages, 10 figure

Unbiasing time-dependent Variational Monte Carlo by projected quantum evolution

We analyze the accuracy and sample complexity of variational Monte Carlo approaches to simulate the dynamics of many-body quantum systems classically. By systematically studying the relevant stochastic estimators, we are able to: (i) prove that the most used scheme, the time-dependent Variational Monte Carlo (tVMC), is affected by a systematic statistical bias or exponential sample complexity when the wave function contains some (possibly approximate) zeros, an important case for fermionic systems and quantum information protocols; (ii) show that a different scheme based on the solution of an optimization problem at each time step is free from such problems; (iii) improve the sample complexity of this latter approach by several orders of magnitude with respect to previous proofs of concept. Finally, we apply our advancements to study the high-entanglement phase in a protocol of non-Clifford unitary dynamics with local random measurements in 2D, first benchmarking on small spin lattices and then extending to large systems

Assessment of immunostimulatory responses to the antimiR-22 oligonucleotide compound RES-010 in human peripheral blood mononuclear cells

microRNA-22 (miR-22) is a key regulator of lipid and energy homeostasis and represents a promising therapeutic target for NAFLD and obesity. We have previously identified a locked nucleic acid (LNA)-modified antisense oligonucleotide compound complementary to miR-22, designated as RES-010 that mediated robust inhibition of miR-22 function in cultured cells and in vivo. In this study we investigated the immune potential of RES-010 in human peripheral blood mononuclear cells (PBMCs). We treated fresh human peripheral blood mononuclear cells isolated from six healthy volunteers with different concentrations of the RES-010 compound and assessed its proinflammatory effects by quantifying IL-1β, IL-6, IFN-γ, TNF-α, IFN-α2a, IFN-β, IL-10, and IL-17A in the supernatants collected 24 h of treatment with RES-010. The T-cell activation markers, CD69, HLA-DR, and CD25 were evaluated by flow cytometry after 24 and 144 h of treatment, respectively, whereas cell viability was assessed after 24 h of treatment with RES-010. Our results show that RES-010 compound does not induce any significant immunostimulatory responses in human PBMCs in vitro compared to controls, implying that the proinflammatory potential of RES-010 is low.</p