arXiv subjects

Ivano Tavernelli

Publications and source records attributed to Ivano Tavernelli.

At least 91 records · Page 5Linked to original sources

arXiv2021

Molecular spin qudits for quantum simulation of light-matter interactions

We show that molecular spin qudits provide an ideal platform to simulate the quantum dynamics of photon fields strongly interacting with matter. The basic unit of the proposed molecular quantum simulator can be realized by a simple dimer of a spin 1/2 and a spin $S$ transition metal ion, solely controlled by microwave pulses. The spin $S$ ion is exploited to encode the photon field in a flexible architecture, which enables the digital simulation of a wide range of spin-boson models much more efficiently than by using a multi-qubit register. The effectiveness of our proposal is demonstrated by numerical simulations using realistic molecular parameters, whose prerequisites delineating possible chemical approaches are also discussed.

quant-ph↗

arXiv2021

Variational learning for quantum artificial neural networks

In the last few years, quantum computing and machine learning fostered rapid developments in their respective areas of application, introducing new perspectives on how information processing systems can be realized and programmed. The rapidly growing field of Quantum Machine Learning aims at bringing together these two ongoing revolutions. Here we first review a series of recent works describing the implementation of artificial neurons and feed-forward neural networks on quantum processors. We then present an original realization of efficient individual quantum nodes based on variational unsampling protocols. We investigate different learning strategies involving global and local layer-wise cost functions, and we assess their performances also in the presence of statistical measurement noise. While keeping full compatibility with the overall memory-efficient feed-forward architecture, our constructions effectively reduce the quantum circuit depth required to determine the activation probability of single neurons upon input of the relevant data-encoding quantum states. This suggests a viable approach towards the use of quantum neural networks for pattern classification on near-term quantum hardware.

quant-ph↗

arXiv2021

Deterministic Algorithms for Compiling Quantum Circuits with Recurrent Patterns

Current quantum processors are noisy, have limited coherence and imperfect gate implementations. On such hardware, only algorithms that are shorter than the overall coherence time can be implemented and executed successfully. A good quantum compiler must translate an input program into the most efficient equivalent of itself, getting the most out of the available hardware. In this work, we present novel deterministic algorithms for compiling recurrent quantum circuit patterns in polynomial time. In particular, such patterns appear in quantum circuits that are used to compute the ground state properties of molecular systems using the variational quantum eigensolver (VQE) method together with the RyRz heuristic wavefunction Ansatz. We show that our pattern-oriented compiling algorithms, combined with an efficient swapping strategy, produces - in general - output programs that are comparable to those obtained with state-of-art compilers, in terms of CNOT count and CNOT depth. In particular, our solution produces unmatched results on RyRz circuits.

quant-ph↗

arXiv2021

Improved accuracy on noisy devices by non-unitary Variational Quantum Eigensolver for chemistry applications

We propose a modification of the Variational Quantum Eigensolver algorithm for electronic structure optimization using quantum computers, named non-unitary Variational Quantum Eigensolver (nu-VQE), in which a non-unitary operator is combined with the original system Hamiltonian leading to a new variational problem with a simplified wavefunction Ansatz. In the present work, we use, as non-unitary operator, the Jastrow factor, inspired from classical Quantum Monte Carlo techniques for simulation of strongly correlated electrons. The method is applied to prototypical molecular Hamiltonians for which we obtain accurate ground state energies with shallower circuits, at the cost of an increased number of measurements. Finally, we also show that this method achieves an important error mitigation effect that drastically improves the quality of the results for VQE optimizations on today's noisy quantum computers. The absolute error in the calculated energy within our scheme is one order of magnitude smaller than the corresponding result using traditional VQE methods, with the same circuit depth.

quant-ph↗

arXiv2021

Gravitational quantum dynamics: a geometrical perspective

We present a gravitational quantum dynamics theory that combines quantum field theory for particle dynamics in space-time with classical Einstein's general relativity in a non-Riemannian Finsler space. This approach is based on the geometrization of quantum mechanics proposed in ref. [1] and combines quantum and gravitational effects into a global curvature of the Finsler space induced by the quantum potential associated to the matter quantum fields. In order to make this theory compatible with general relativity, the quantum effects are described in the framework of quantum field theory, where a covariant definition of `simultaneity' for many-body systems is introduced through the definition of a suited foliation of space-time. As in Einstein's gravitation theory, the particle dynamics is finally described by means of a geodesic equation in a curved space-time manifold.

gr-qc↗

arXiv2020

Probing molecular excited states by atomic force microscopy

By employing single charge injections with an atomic force microscope, we investigated redox reactions of a molecule on a multilayer insulating film. First, we charged the molecule positively by attaching a single hole. Then we neutralized it by attaching an electron and observed three channels for the neutralization. We rationalize that the three channels correspond to transitions to the neutral ground state, to the lowest energy triplet excited states and to the lowest energy singlet excited states. By single-electron tunneling spectroscopy we measured the energy differences between the transitions obtaining triplet and singlet excited state energies. The experimental values are compared with density functional theory calculations of the excited state energies. Our results show that molecules in excited states can be prepared and that energies of optical gaps can be quantified by controlled single-charge injections. Our work demonstrates the access to, and provides insight into, ubiquitous electron-attachment processes related to excited-state transitions important in electron transfer and molecular optoelectronics phenomena on surfaces.

cond-mat.mes-hall↗

arXiv2020

Entanglement Production and Convergence Properties of the Variational Quantum Eigensolver

We perform a systematic investigation of variational forms (wave function Ansätze), to determine the ground state energies and properties of two-dimensional model fermionic systems on triangular lattices (with and without periodic boundary conditions), using the Variational Quantum Eigensolver (VQE) algorithm. In particular, we focus on the nature of the entangler blocks which provide the most efficient convergence to the system ground state inasmuch as they use the minimal number of gate operations, which is key for the implementation of this algorithm in NISQ computers. Using the concurrence measure, the amount of entanglement of the register qubits is monitored during the entire optimization process, illuminating its role in determining the efficiency of the convergence. Finally, we investigate the scaling of the VQE circuit depth as a function of the desired energy accuracy. We show that the number of gates required to reach a solution within an error $\varepsilon$ follows the Solovay-Kitaev scaling, $\mathcal{O}(\log^c(1/\varepsilon))$, with an exponent $c = 1.31 {\rm{\pm}}0.13$.

quant-ph↗

arXiv2020

Quantum Orbital-Optimized Unitary Coupled Cluster Methods in the Strongly Correlated Regime: Can Quantum Algorithms Outperform their Classical Equivalents?

The Coupled Cluster (CC) method is used to compute the electronic correlation energy in atoms and molecules and often leads to highly accurate results. However, due to its single-reference nature, standard CC in its projected form fails to describe quantum states characterized by strong electronic correlations and multi-reference projective methods become necessary. On the other hand, quantum algorithms for the solution of many-electron problems have also emerged recently. The quantum UCC with singles and doubles (q-UCCSD) is a popular wavefunction Ansatz for the Variational Quantum Eigensolver (VQE) algorithm. The variational nature of this approach can lead to significant advantages compared to its classical equivalent in the projected form, in particular for the description of strong electronic correlation. However, due to the large number of gate operations required in q-UCCSD, approximations need to be introduced in order to make this approach implementable in a state-of-the-art quantum computer. In this work, we evaluate several variants of the standard q-UCCSD Ansatz in which only a subset of excitations is included. In particular, we investigate the singlet and pair q-UCCD approaches combined with orbital optimization. We show that these approaches can capture the dissociation/distortion profiles of challenging systems such as H$_4$, H$_2$O and N$_2$ molecules, as well as the one-dimensional periodic Fermi-Hubbard chain. These results promote the future use of q-UCC methods for the solution of challenging electronic structure problems in quantum chemistry.

quant-ph↗

arXiv2020

Quantum HF/DFT-Embedding Algorithms for Electronic Structure Calculations: Scaling up to Complex Molecular Systems

In the near future, material and drug design may be aided by quantum computer assisted simulations. These have the potential to target chemical systems intractable by the most powerful classical computers. However, the resources offered by contemporary quantum computers are still limited, restricting the chemical simulations to very simple molecules. In order to rapidly scale up to more interesting molecular systems, we propose the embedding of the quantum electronic structure calculation into a classically computed environment obtained at the Hartree-Fock (HF) or Density Functional Theory (DFT) level of theory. We achieve this by constructing an effective Hamiltonian that incorporates a mean field potential describing the action of the inactive electrons on a selected Active Space (AS). The ground state of the AS Hamiltonian is determined by means of the Variational Quantum Eigensolver (VQE) algorithm. With the proposed iterative DFT embedding scheme we are able to obtain energy correction terms for a single pyridine molecule that outperform the Complete Active Space Self Consistent Field (CASSCF) results regardless of the chosen AS.

quant-ph↗

arXiv2020

Microcanonical and finite temperature ab initio molecular dynamics simulations on quantum computers

Ab initio molecular dynamics (AIMD) is a powerful tool to predict properties of molecular and condensed matter systems. The quality of this procedure is based on accurate electronic structure calculations. The development of quantum processors has shown great potential for the efficient evaluation of accurate ground and excited state energies of molecular systems, opening up new avenues for molecular dynamics simulations. In this work we address the use of variational quantum algorithms for the calculation of accurate atomic forces to be used in AIMD. In particular, we provide solutions for the alleviation of the statistical noise associated to the measurements of the expectation values of energies and forces, as well as schemes for the mitigation of the hardware noise sources (in particular, gate infidelities, qubit decoherence and readout errors). Despite the relative large error in the calculation of the potential energy, our results show that the proposed algorithms can provide reliable MD trajectories in the microcanonical (constant energy) ensemble. Further, exploiting the intrinsic noise arising from the quantum measurement process, we also propose a Langevin dynamics algorithm for the simulation of canonical, i.e., constant temperature, dynamics. Both algorithms (microcanonical and canonical) are applied to the simulation of simple molecular systems such as H2 and H3+. Finally, we also provide results for the dynamics of H2 obtained with IBM quantum computer ibmq_athens.

quant-ph↗

arXiv2020

Quantum equation of motion for computing molecular excitation energies on a noisy quantum processor

The computation of molecular excitation energies is essential for predicting photo-induced reactions of chemical and technological interest. While the classical computing resources needed for this task scale poorly, quantum algorithms emerge as promising alternatives. In particular, the extension of the variational quantum eigensolver algorithm to the computation of the excitation energies is an attractive option. However, there is currently a lack of such algorithms for correlated molecular systems that is amenable to near-term, noisy hardware. In this work, we propose an extension of the well-established classical equation of motion approach to a quantum algorithm for the calculation of molecular excitation energies on noisy quantum computers. In particular, we demonstrate the efficiency of this approach in the calculation of the excitation energies of the LiH molecule on an IBM Quantum computer.

quant-ph↗

arXiv2020

Quantum algorithm for alchemical optimization in material design

The development of tailored materials for specific applications is an active field of research in chemistry, material science and drug discovery. The number of possible molecules that can be obtained from a set of atomic species grow exponentially with the size of the system, limiting the efficiency of classical sampling algorithms. On the other hand, quantum computers can provide an efficient solution to the sampling of the chemical compound space for the optimization of a given molecular property. In this work we propose a quantum algorithm for addressing the material design problem with a favourable scaling. The core of this approach is the representation of the space of candidate structures as a linear superposition of all possible atomic compositions. The corresponding `alchemical' Hamiltonian drives then the optimization in both the atomic and electronic spaces leading to the selection of the best fitting molecule, which optimizes a given property of the system, e.g., the interaction with an external potential in drug design. The quantum advantage resides in the efficient calculation of the electronic structure properties together with the sampling of the exponentially large chemical compound space. We demonstrate both in simulations and in IBM Quantum hardware the efficiency of our scheme and highlight the results in a few test cases. These preliminary results can serve as a basis for the development of further material design quantum algorithms for near-term quantum computers.

quant-ph↗

arXiv2020

Quantum-optimal-control-inspired ansatz for variational quantum algorithms

A central component of variational quantum algorithms (VQA) is the state-preparation circuit, also known as ansatz or variational form. This circuit is most commonly designed to respect the symmetries of the problem Hamiltonian and, in this way, constrain the variational search to a subspace of interest. Here, we show that this approach is not always advantageous by introducing ansätze that incorporate symmetry-breaking unitaries. This class of ansätze, that we call Quantum-Optimal-Control-inspired Ansätze (QOCA), is inspired by the theory of quantum optimal control and leads to an improved convergence of VQAs for some important problems. Indeed, we benchmark QOCA against popular ansätze applied to the Fermi-Hubbard model at half-filling and show that our variational circuits can approximate the ground state of this model with significantly higher accuracy and for larger systems. We also show how QOCA can be used to find the ground state of the water molecule and compare the performance of our ansatz against other common choices used for chemistry problems. This work constitutes a first step towards the development of a more general class of symmetry-breaking ansätze with applications to physics and chemistry problems.

quant-ph↗

arXiv2020

Non-adiabatic molecular quantum dynamics with quantum computers

The theoretical investigation of non-adiabatic processes is hampered by the complexity of the coupled electron-nuclear dynamics beyond the Born-Oppenheimer approximation. Classically, the simulation of such reactions is limited by the unfavourable scaling of the computational resources as a function of the system size. While quantum computing exhibits proven quantum advantage for the simulation of real-time dynamics, the study of quantum algorithms for the description of non-adiabatic phenomena is still unexplored. In this work, we propose a quantum algorithm for the simulation of fast non-adiabatic chemical processes together with an initialization scheme for quantum hardware calculations. In particular, we introduce a first-quantization method for the time evolution of a wavepacket on two coupled harmonic potential energy surfaces (Marcus model). In our approach, the computational resources scale polynomially in the system dimensions, opening up new avenues for the study of photophysical processes that are classically intractable.

quant-ph↗

arXiv2020

Toward scalable simulations of Lattice Gauge Theories on quantum computers

The simulation of real-time dynamics in lattice gauge theories is particularly hard for classical computing due to the exponential scaling of the required resources. On the other hand, quantum algorithms can potentially perform the same calculation with a polynomial dependence on the number of degrees of freedom. A precise estimation is however particularly challenging for the simulation of lattice gauge theories in arbitrary dimensions, where, gauge fields are dynamical variables, in addition to the particle fields. Moreover, there exist several choices for discretizing particles and gauge fields on a lattice, each of them coming at different prices in terms of qubit register size and circuit depth. Here we provide a resource counting for real-time evolution of $U(1)$ gauge theories, such as Quantum Electrodynamics, on arbitrary dimension using the Wilson fermion representation for the particles, and the Quantum Link Model approach for the gauge fields. We study the phenomena of flux-string breaking up to a genuine bi-dimensional model using classical simulations of the quantum circuits, and discuss the advantages of our discretization choice in simulation of more challenging $SU(N)$ gauge theories such as Quantum Chromodynamics.

quant-ph↗

arXiv2020

Improving Variational Quantum Optimization using CVaR

Hybrid quantum/classical variational algorithms can be implemented on noisy intermediate-scale quantum computers and can be used to find solutions for combinatorial optimization problems. Approaches discussed in the literature minimize the expectation of the problem Hamiltonian for a parameterized trial quantum state. The expectation is estimated as the sample mean of a set of measurement outcomes, while the parameters of the trial state are optimized classically. This procedure is fully justified for quantum mechanical observables such as molecular energies. In the case of classical optimization problems, which yield diagonal Hamiltonians, we argue that aggregating the samples in a different way than the expected value is more natural. In this paper we propose the Conditional Value-at-Risk as an aggregation function. We empirically show -- using classical simulation as well as quantum hardware -- that this leads to faster convergence to better solutions for all combinatorial optimization problems tested in our study. We also provide analytical results to explain the observed difference in performance between different variational algorithms.

quant-ph↗

arXiv2020

Hardware Efficient Quantum Algorithms for Vibrational Structure Calculations

We introduce a framework for the calculation of ground and excited state energies of bosonic systems suitable for near-term quantum devices and apply it to molecular vibrational anharmonic Hamiltonians. Our method supports generic reference modal bases and Hamiltonian representations, including the ones that are routinely used in classical vibrational structure calculations. We test different parametrizations of the vibrational wave function, which can be encoded in quantum hardware, based either on heuristic circuits or on the bosonic Unitary Coupled Cluster Ansatz. In particular, we define a novel compact heuristic circuit and demonstrate that it provides the best compromise in terms of circuit depth, optimization costs, and accuracy. We evaluate the requirements, number of qubits and circuit depth, for the calculation of vibrational energies on quantum hardware and compare them with state-of-the-art classical vibrational structure algorithms for molecules with up to seven atoms.

quant-ph↗

arXiv2019

Quantum implementation of an artificial feed-forward neural network

Artificial intelligence algorithms largely build on multi-layered neural networks. Coping with their increasing complexity and memory requirements calls for a paradigmatic change in the way these powerful algorithms are run. Quantum computing promises to solve certain tasks much more efficiently than any classical computing machine, and actual quantum processors are now becoming available through cloud access to perform experiments and testing also outside of research labs. Here we show in practice an experimental realization of an artificial feed-forward neural network implemented on a state-of-art superconducting quantum processor using up to 7 active qubits. The network is made of quantum artificial neurons, which individually display a potential advantage in storage capacity with respect to their classical counterpart, and it is able to carry out an elementary classification task which would be impossible to achieve with a single node. We demonstrate that this network can be equivalently operated either via classical control or in a completely coherent fashion, thus opening the way to hybrid as well as fully quantum solutions for artificial intelligence to be run on near-term intermediate-scale quantum hardware.

quant-ph↗