arXiv subjects

Panagiotis Kl. Barkoutsos

Publications and source records attributed to Panagiotis Kl. Barkoutsos.

32 records · Page 2Linked to original sources

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.

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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 $c = 1.31 {\rm{\pm}}0.13$.

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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.

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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.

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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.

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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.

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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.

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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.

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arXiv2019

Variational Quantum Simulation of Ultrastrong Light-Matter Coupling

We propose the simulation of quantum-optical systems in the ultrastrong-coupling regime using a variational quantum algorithm. More precisely, we introduce a short-depth variational form to prepare the groundstate of the multimode Dicke model on a quantum processor and present proof-of-principle results obtained via cloud access to an IBM device. We moreover provide an algorithm for characterizing the groundstate by Wigner state tomography. Our work is a first step towards digital quantum simulation of quantum-optical systems with potential applications to the spin-boson, Kondo and Jahn-Teller models.

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arXiv2019

Resource-Efficient Quantum Algorithm for Protein Folding

Predicting the three-dimensional (3D) structure of a protein from its primary sequence of amino acids is known as the protein folding (PF) problem. Due to the central role of proteins' 3D structures in chemistry, biology and medicine applications (e.g., in drug discovery) this subject has been intensively studied for over half a century. Although classical algorithms provide practical solutions, sampling the conformation space of small proteins, they cannot tackle the intrinsic NP-hard complexity of the problem, even reduced to its simplest Hydrophobic-Polar model. While fault-tolerant quantum computers are still beyond reach for state-of-the-art quantum technologies, there is evidence that quantum algorithms can be successfully used on Noisy Intermediate-Scale Quantum (NISQ) computers to accelerate energy optimization in frustrated systems. In this work, we present a model Hamiltonian with $\mathcal{O}(N^4)$ scaling and a corresponding quantum variational algorithm for the folding of a polymer chain with $N$ monomers on a tetrahedral lattice. The model reflects many physico-chemical properties of the protein, reducing the gap between coarse-grained representations and mere lattice models. We use a robust and versatile optimisation scheme, bringing together variational quantum algorithms specifically adapted to classical cost functions and evolutionary strategies (genetic algorithms), to simulate the folding of the 10 amino acid Angiotensin peptide on 22 qubits. The same method is also successfully applied to the study of the folding of a 7 amino acid neuropeptide using 9 qubits on an IBM Q 20-qubit quantum computer. Bringing together recent advances in building gate-based quantum computers with noise-tolerant hybrid quantum-classical algorithms, this work paves the way towards accessible and relevant scientific experiments on real quantum processors.

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arXiv2018

Gate-efficient simulation of molecular eigenstates on a quantum computer

A key requirement to perform simulations of large quantum systems on near-term quantum hardware is the design of quantum algorithms with short circuit depth that finish within the available coherence time. A way to stay within the limits of coherence is to reduce the number of gates by implementing a gate set that matches the requirements of the specific algorithm of interest directly in hardware. Here, we show that exchange-type gates are a promising choice for simulating molecular eigenstates on near-term quantum devices since these gates preserve the number of excitations in the system. Complementing the theoretical work by Barkoutsos et al. [PRA 98, 022322 (2018)], we report on the experimental implementation of a variational algorithm on a superconducting qubit platform to compute the eigenstate energies of molecular hydrogen. We utilize a parametrically driven tunable coupler to realize exchange-type gates that are configurable in amplitude and phase on two fixed-frequency superconducting qubits. With gate fidelities around 95% we are able to compute the eigenstates within an accuracy of 50 mHartree on average, a limit set by the coherence time of the tunable coupler.

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arXiv2018

Quantum algorithms for electronic structure calculations: particle/hole Hamiltonian and optimized wavefunction expansions

In this work we investigate methods to improve the efficiency and scalability of quantum algorithms for quantum chemistry applications. We propose a transformation of the electronic structure Hamiltonian in the second quantization framework into the particle-hole (p/h) picture, which offers a better starting point for the expansion of the trial wavefunction. The state of the molecular system at study is parametrized in a way to efficiently explore the sector of the molecular Fock space that contains the desired solution. To this end, we explore several trial wavefunctions to identify the most efficient parameterization of the molecular ground state. Taking advantage of known post-Hartree Fock quantum chemistry approaches and heuristic Hilbert space search quantum algorithms, we propose a new family of quantum circuits based on exchange-type gates that enable accurate calculations while keeping the gate count (i.e., the circuit depth) low. The particle-hole implementation of the Unitary Coupled Cluster (UCC) method within the Variational Quantum Eigensolver approach gives rise to an efficient quantum algorithm, named q-UCC , with important advantages compared to the straightforward 'translation' of the classical Coupled Cluster counterpart. In particular, we show how a single Trotter step can accurately and efficiently reproduce the ground state energies of simple molecular systems.

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arXiv2018

Entanglement generation in superconducting qubits using holonomic operations

We investigate a non-adiabatic holonomic operation that enables us to entangle two fixed-frequency superconducting transmon qubits attached to a common bus resonator. Two coherent microwave tones are applied simultaneously to the two qubits and drive transitions between the first excited resonator state and the second excited state of each qubit. The cyclic evolution within this effective 3-level $Λ$-system gives rise to a holonomic operation entangling the two qubits. Two-qubit states with 95\% fidelity, limited mainly by charge-noise of the current device, are created within $213~\rm{ns}$. This scheme is a step toward implementing a SWAP-type gate directly in an all-microwave controlled hardware platform. By extending the available set of two-qubit operations in the fixed-frequency qubit architecture, the proposed scheme may find applications in near-term quantum applications using variational algorithms to efficiently create problem-specific trial states.

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arXiv2017

Fermionic Hamiltonians for quantum simulations: a general reduction scheme

Many-body fermionic quantum calculations performed on analog quantum computers are restricted by the presence of k-local terms, which represent interactions among more than two qubits. These originate from the fermion-to-qubit mapping applied to the electronic Hamiltonians. Current solutions to this problem rely on perturbation theory in an enlarged Hilbert space. The main challenge associated with this technique is that it relies on coupling constants with very different magnitudes. This prevents its implementation in currently available architectures. In order to resolve this issue, we present an optimization scheme that unfolds the k-local terms into a linear combination of 2-local terms, while ensuring the conservation of all relevant physical properties of the original Hamiltonian, with several orders of magnitude smaller variation of the coupling constants.

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