Physics-Inspired Quantum Simulation of Resonating Valence Bond States─A Prototypical Template for a Spin-Liquid Ground State.

Spin liquids─an emergent, exotic collective phase of matter─have garnered enormous attention in recent years. While experimentally many prospective candidates have been proposed and realized, theoretically modeling real materials that display such behavior may pose serious challenges due to the inherently high correlation content of such phases. Over the last few decades, the second-quantum revolution has been the harbinger of a novel computational paradigm capable of initiating a foundational evolution in computational physics. In this report, we strive to use the power of the latter to study a prototypical model, a spin-1/2-unit cell of a Kagome antiferromagnet. Extended lattices of such unit cells are known to possess a magnetically disordered spin-liquid ground state. We employ robust classical numerical techniques such as the density-matrix renormalization group (DMRG) to identify the nature of the ground state through a matrix-product state (MPS) formulation. We subsequently use the gained insight to construct an auxiliary Hamiltonian with reduced measurables and also design an ansatz that is modular and gate-efficient. With robust error-mitigation strategies, we are able to demonstrate that the said ansatz is capable of accurately representing the target ground state even on a real IBMQ backend within 1% accuracy in energy. Since the protocol is linearly scaling O(n) in the number of unit cells, gate requirements, and the number of measurements, it is straightforwardly extendable to larger Kagome lattices that can pave the way for efficient construction of spin-liquid ground states on a quantum device.

Hamiltonian Learning from Time Dynamics Using Variational Algorithms.

The Hamiltonian of a quantum system governs the dynamics of the system via the Schrodinger equation. In this paper, the Hamiltonian is reconstructed in the Pauli basis using measurables on random states forming a time series data set. The time propagation is implemented through Trotterization and optimized variationally with gradients computed on the quantum circuit. We validate our output by reproducing the dynamics of unseen observables on a randomly chosen state not used for the optimization. Unlike existing techniques that try and exploit the structure/properties of the Hamiltonian, our scheme is general and provides freedom with regard to what observables or initial states can be used while still remaining efficient with regard to implementation. We extend our protocol to doing quantum state learning where we solve the reverse problem of doing state learning given time series data of observables generated against several Hamiltonian dynamics. We show results on Hamiltonians involving XX, ZZ couplings along with transverse field Ising Hamiltonians and propose an analytical method for the learning of Hamiltonians consisting of generators of the SU(3) group. This paper is likely to pave the way toward using Hamiltonian learning for time series prediction within the context of quantum machine learning algorithms.

Magnetic phases of spatially modulated spin-1 chains in Rydberg excitons: Classical and quantum simulations.

In this work, we study the magnetic phases of a spatially modulated chain of spin-1 Rydberg excitons. Using the Density Matrix Renormalization Group (DMRG) technique, we study various magnetic and topologically nontrivial phases using both single-particle properties, such as local magnetization and quantum entropy, and many-body ones, such as pair-wise Néel and long-range string correlations. In particular, we investigate the emergence and robustness of the Haldane phase, a topological phase of anti-ferromagnetic spin-1 chains. Furthermore, we devise a hybrid quantum algorithm employing restricted Boltzmann machine to simulate the ground state of such a system that shows very good agreement with the results of exact diagonalization and DMRG.

Variational approach to quantum state tomography based on maximal entropy formalism.

Quantum state tomography is an integral part of quantum computation and offers the starting point for the validation of various quantum devices. One of the central tasks in the field of state tomography is to reconstruct, with high fidelity, the quantum states of a quantum system. From an experiment on a real quantum device, one can obtain the mean measurement values of different operators. With such data as input, in this report we employ the maximal entropy formalism to construct the least biased mixed quantum state that is consistent with the given set of expectation values. Even though, in principle, the reported formalism is quite general and should work for an arbitrary set of observables, in practice we shall demonstrate the efficacy of the algorithm on an informationally complete (IC) set of Hermitian operators. Such a set possesses the advantage of uniquely specifying a single quantum state from which the experimental measurements have been sampled and hence renders the rare opportunity not only to construct a least-biased quantum state but even replicate the exact state prepared experimentally within a preset tolerance. The primary workhorse of the algorithm is reconstructing an energy function which we designate as the effective Hamiltonian of the system, and parameterizing it with Lagrange multipliers, according to the formalism of maximal entropy. These parameters are thereafter optimized variationally so that the reconstructed quantum state of the system converges to the true quantum state within an error threshold. To this end, we employ a parameterized quantum circuit and a hybrid quantum-classical variational algorithm to obtain such a target state, making our recipe easily implementable on a near-term quantum device.

Quantum machine learning for chemistry and physics.

Machine learning (ML) has emerged as a formidable force for identifying hidden but pertinent patterns within a given data set with the objective of subsequent generation of automated predictive behavior. In recent years, it is safe to conclude that ML and its close cousin, deep learning (DL), have ushered in unprecedented developments in all areas of physical sciences, especially chemistry. Not only classical variants of ML, even those trainable on near-term quantum hardwares have been developed with promising outcomes. Such algorithms have revolutionized materials design and performance of photovoltaics, electronic structure calculations of ground and excited states of correlated matter, computation of force-fields and potential energy surfaces informing chemical reaction dynamics, reactivity inspired rational strategies of drug designing and even classification of phases of matter with accurate identification of emergent criticality. In this review we shall explicate a subset of such topics and delineate the contributions made by both classical and quantum computing enhanced machine learning algorithms over the past few years. We shall not only present a brief overview of the well-known techniques but also highlight their learning strategies using statistical physical insight. The objective of the review is not only to foster exposition of the aforesaid techniques but also to empower and promote cross-pollination among future research in all areas of chemistry which can benefit from ML and in turn can potentially accelerate the growth of such algorithms.

Quantum Machine-Learning for Eigenstate Filtration in Two-Dimensional Materials.

Quantum machine-learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure calculations of molecular systems and spin models in magnetic systems. However, the discussion in all these recipes focuses specifically on targeting the ground state. Herein we demonstrate a quantum algorithm that can filter any energy eigenstate of the system based on either symmetry properties or a predefined choice of the user. The workhorse of our technique is a shallow neural network encoding the desired state of the system with the amplitude computed by sampling the Gibbs-Boltzmann distribution using a quantum circuit and the phase information obtained classically from the nonlinear activation of a separate set of neurons. We show that the resource requirements of our algorithm are strictly quadratic. To demonstrate its efficacy, we use state filtration in monolayer transition metal dichalcogenides which are hitherto unexplored in any flavor of quantum simulations. We implement our algorithm not only on quantum simulators but also on actual IBM-Q quantum devices and show good agreement with the results procured from conventional electronic structure calculations. We thus expect our protocol to provide a new alternative in exploring the band structures of exquisite materials to usual electronic structure methods or machine-learning techniques that are implementable solely on a classical computer.

Conductance Switching in an Organometallic Single-Electron Transistor Using Current-Constrained Reduced-Density Matrix Theory.

We report switching of molecular conductance at finite bias in a binuclear organometallic complex and its cation which were previously experimentally analyzed at low voltages to see the signature of Kondo resonance. The variational reduced density matrix theory is applied to show that the system is strongly multireferenced especially in its charged form. We also study the molecular conductance of both forms using recently developed current-constrained two-electron reduced density matrix theory which is capable of handling strong electronic correlation. We compare the results against an uncorrelated 1-electron reduced density matrix version of conductance calculations using Hartree-Fock molecular orbitals. We observe that despite quantitative disagreements, the qualitative trend in the conductance is correctly predicted to be favorable for the cationic partner by both methods. We explain the results using the inherently high density of states for the low-lying excited states in the cationic partner which is also replicable from uncorrelated electronic structure methods. Our results not only indicate that the low-bias conductance trend is maintained even beyond the Kondo regime and produces quantitative agreement with that of the experiment but also identifies important physical markers that are responsible for the high conductance of the charged species.

Implementation of Quantum Machine Learning for Electronic Structure Calculations of Periodic Systems on Quantum Computing Devices.

Quantum machine learning algorithms, the extensions of machine learning to quantum regimes, are believed to be more powerful as they leverage the power of quantum properties. Quantum machine learning methods have been employed to solve quantum many-body systems and have demonstrated accurate electronic structure calculations of lattice models, molecular systems, and recently periodic systems. A hybrid approach using restricted Boltzmann machines and a quantum algorithm to obtain the probability distribution that can be optimized classically is a promising method due to its efficiency and ease of implementation. Here, we implement the benchmark test of the hybrid quantum machine learning on the IBM-Q quantum computer to calculate the electronic structure of typical two-dimensional crystal structures: hexagonal-boron nitride and graphene. The band structures of these systems calculated using the hybrid quantum machine learning approach are in good agreement with those obtained by the conventional electronic structure calculations. This benchmark result implies that the hybrid quantum machine learning method, empowered by quantum computers, could provide a new way of calculating the electronic structures of quantum many-body systems.

Fabrication of a material assembly of silver nanoparticles using the phase gradients of optical tweezers.

Optical matter can be created using the intensity gradient and electrodynamic (e.g., optical binding) forces that nano- and microparticles experience in focused optical beams. Here we show that the force associated with phase gradient is also important. In fact, in optical line traps the phase gradient force is crucial in determining the structure and stability of optical matter arrays consisting of Ag nanoparticles (NPs). NP lattices can be repeatedly assembled and disassembled simply by changing the sign of the phase gradient. The phase gradient creates a compressive force (and thus a stress) in the optically bound Ag NP lattices, causing structural transitions (a stress response) from 1D "chains" to 2D lattices, and even to amorphous structures. The structural transitions and dynamics of driven transport are well described by electrodynamics simulations and modeling using a drift-diffusion Langevin equation.

Anisotropic dynamics of guest molecules in aerosol OT lamellar structures.

The present work is focused on developing a description of an anisotropic microheterogeneous medium, exploiting the dynamics of a guest molecule. The medium in question is the lamellar structures formed in the aqueous layer of ternary mixtures containing aerosol OT (AOT), water and n-heptane. The guest used in this study is the fluorescent probe, coumarin 153 (C153). The dynamics of this molecule, within the lamellar structure, have been studied using a combination of steady state and time resolved fluorescence, as well as fluorescence correlation spectroscopy (FCS). The fluorophore is strongly solvatochromatic and so, the wavelength of excitation can be tuned so as to selectively excite fluorescent molecules residing in different regions of the microheterogeneous media, even if the spatial separation between these regions is below the diffraction limit. The excitation wavelength in the present experiments is chosen so as to exclusively excite those C153 molecules that reside in the hydrophobic region of the lamellar structures. This triggers two different modes of diffusion, one along and the other perpendicular to the bilayers of the AOT. Thus, the dynamics of the fluorescent probe provide an elegant manifestation of the anisotropy of the host medium.

Nanoconfinement of water layers in lamellar structures prepared in the presence and absence of organic solvent.

An attempt is made to draw a line of comparison between the extent of rigidity of the hydration layers bound to the interfacial region of lamellar structures of Aerosol OT (AOT, sodium bis(2-ethylhexyl) sulfosuccinate) in water, in the presence and absence of an organic solvent using POM, SAXS, cryo-TEM, and time-resolved fluorescence spectroscopy. These systems are ternary mixtures of AOT, water, and n-heptane containing lamellar structures in an aqueous layer at higher w(0) values (w(0) = 300 and 150) and a binary solution of 20 and 50% AOT in neat water (w/w). The solvation shells residing at the vicinity of these lamellar structures are monitored using two different coumarin probes (C153 and C500). It is intended to envisage a comparative solvation dynamics study of the restricted aqueous region confined in lamellar structures formed in ternary mixture and binary solution. Though steady state measurements show a similar microenvironment probed by the fluorophores in lamellar structures formed in the two different aqueous phases, temporal evolution of the solvent correlation function C(t) unveils the existence of lamellar structures with different degrees of confinement of water layers in these two systems. A slower relaxation of the restricted aqueous region in lamellar structures of binary solution signifies the presence of more rigid interfacially bound water layers at the lamellar interface than in the ternary mixture having a similar weight percentage of AOT in water. The present investigation concludes that the lamellar structures formed under two different conditions provide a similar hydrophobic environment with different extents of localized water populations at the lamellar interface as manifested by the solvent relaxation time in agreement with SAXS and cryo-TEM images.