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1. Classical trajectory simulations on a D-Wave quantum annealer

   Gayday I.; Babikov D.; Teplukhin A.; Kendrick B. K.; Mniszewski S.; Zhang Y.; Tretiak S.; Dub P. A. (August 2022, https://acs.digitellinc.com/p/s/classical-trajectory-simulations-on-a-d-wave-quantum-annealer-516515)

   We report the first-ever formulation of the molecular dynamics problem as a Quadratic Unconstrained Binary Optimization (QUBO) problem and demonstrate its successful solution on a D-Wave quantum annealer. This methodology, named a Quantum Differential Equation (QDE) solver, is applied to propagate trajectories for the vibrational motion of hydrogen molecule, H2, in three different energy regimes: nearly harmonic, highly anharmonic, and above dissociation threshold. The results obtained using the D-Wave 2000Q quantum annealer are mutually consistent and quickly converge to the exact solution. Several alternative strategies for such calculations are explored and it is shown that the most accurate result and the best efficiency are obtained by combining quantum annealer with classical post-processing (known as “greedy” algorithm). Importantly, the QDE framework developed here is entirely general and can be applied to solve any system of first-order ordinary nonlinear differential equations using a quantum annealer. 

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2. Molecular dynamics on quantum annealers

   https://doi.org/10.1038/s41598-022-21163-x  

   Gaidai, Igor; Babikov, Dmitri; Teplukhin, Alexander; Kendrick, Brian K.; Mniszewski, Susan M.; Zhang, Yu; Tretiak, Sergei; Dub, Pavel A. (October 2022, Scientific Reports)

   Abstract In this work we demonstrate a practical prospect of using quantum annealers for simulation of molecular dynamics. A methodology developed for this goal, dubbed Quantum Differential Equations (QDE), is applied to propagate classical trajectories for the vibration of the hydrogen molecule in several regimes: nearly harmonic, highly anharmonic, and dissociative motion. The results obtained using the D-Wave 2000Q quantum annealer are all consistent and quickly converge to the analytical reference solution. Several alternative strategies for such calculations are explored and it was found that the most accurate results and the best efficiency are obtained by combining the quantum annealer with classical post-processing (greedy algorithm). Importantly, the QDE framework developed here is entirely general and can be applied to solve any system of first-order ordinary nonlinear differential equations using a quantum annealer. 

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3. Automatically Translating Quantum Programs from a Subset of Common Gates to an Adiabatic Representation

   https://doi.org/10.1007/978-3-030-21500-2_9  

   Regan M., Eastwood B. (May 2019, nternational Conference on Reversible Computation (RC), Springer LNCS)

   Adiabatic computing with two degrees of freedom of 2-local Hamiltonians has been theoretically shown to be equivalent to the gate model of universal quantum computing. But today’s quantum annealers, namely D-Wave’s 2000Q platform, only provide a 2-local Ising Hamiltonian abstraction with a single degree of freedom. This raises the question what subset of gate programs can be expressed as quadratic unconstrained binary problems (QUBOs) on the D-Wave. The problem is of interest because gate-based quantum platforms are currently limited to 20 qubits while D-Wave provides 2,000 qubits. However, when transforming entire gate circuits into QUBOs, additional qubits will be required. The objective of this work is to determine a subset of quantum gates suitable for transformation into single-degree 2-local Ising Hamiltonians under a common qubit base representation such that they comprise a compound circuit suitable for pure quantum computation, i.e., without having to switch between classical and quantum computing for different bases. To this end, this work contributes, for the first time, a fully automated method to translate quantum gate circuits comprised of a subset of common gates expressed as an IBM Qiskit program to single-degree 2-local Ising Hamiltonians, which are subsequently embedded in the D-Wave 2000Q chimera graph. These gate elements are placed in the chimera graph and augmented by constraints that enforce inter-gate logical relationships, resulting in an annealer embedding that completely characterizes the overall gate circuit. Annealer embeddings for several example quantum gate circuits are then evaluated on D-Wave 2000Q hardware. 

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4. A universal variational quantum eigensolver for non-Hermitian systems

   https://doi.org/10.1038/s41598-023-49662-5  

   Zhao, Huanfeng; Zhang, Peng; Wei, Tzu-Chieh (December 2023, Scientific Reports)

   Abstract Many quantum algorithms are developed to evaluate eigenvalues for Hermitian matrices. However, few practical approach exists for the eigenanalysis of non-Hermintian ones, such as arising from modern power systems. The main difficulty lies in the fact that, as the eigenvector matrix of a general matrix can be non-unitary, solving a general eigenvalue problem is inherently incompatible with existing unitary-gate-based quantum methods. To fill this gap, this paper introduces a Variational Quantum Universal Eigensolver (VQUE), which is deployable on noisy intermediate scale quantum computers. Our new contributions include: (1) The first universal variational quantum algorithm capable of evaluating the eigenvalues of non-Hermitian matrices—Inspired by Schur’s triangularization theory, VQUE unitarizes the eigenvalue problem to a procedure of searching unitary transformation matrices via quantum devices; (2) A Quantum Process Snapshot technique is devised to make VQUE maintain the potential quantum advantage inherited from the original variational quantum eigensolver—With additional$$O(log_{2}{N})$$ $O\left(lo{g}_{2}N\right)$quantum gates, this method efficiently identifies whether a unitary operator is triangular with respect to a given basis; (3) Successful deployment and validation of VQUE on a real noisy quantum computer, which demonstrates the algorithm’s feasibility. We also undertake a comprehensive parametric study to validate VQUE’s scalability, generality, and performance in realistic applications. 

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5. Quantum Social Computing Approaches for Influence Maximization

   https://doi.org/10.1109/GLOBECOM48099.2022.10000698  

   Dinh, Thang; Nguyen, An; Nguyen, Uyen; Nguyen, Giang (January 2023, GLOBECOM 2022 - 2022 IEEE Global Communications Conference)

   Influence Maximization (IM), which seeks a small set of important nodes that spread the influence widely into the network, is a fundamental problem in social networks. It finds applications in viral marketing, epidemic control, and assessing cascading failures within complex systems. Despite the huge amount of effort, finding near-optimal solutions for IM is difficult due to its NP-completeness. In this paper, we propose the first social quantum computing approaches for IM, aiming to retrieve near-optimal solutions. We propose a two-phase algorithm that 1) converts IM into a Max-Cover instance and 2) provides efficient quadratic unconstrained binary optimization formulations to solve the Max-Cover instance on quantum annealers. Our experiments on the state-of-the-art D-Wave annealer indicate better solution quality compared to classical simulated annealing, suggesting the potential of applying quantum annealing to find high-quality solutions for IM. 

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