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Register a new userCalculation of molecular vibrational spectra on a quantum annealer
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Added by
Alexander Teplukhin
Publication date
2018
fields
Physics
and research's language is
English
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Quantum computers are ideal for solving chemistry problems due to their polynomial scaling with system size in contrast to classical computers which scale exponentially. Until now molecular energy calculations using quantum computing hardware have been limited to quantum simulators. In this paper, a new methodology is presented to calculate the vibrational spectrum of a molecule on a quantum annealer. The key idea of the method is a mapping of the ground state variational problem onto an Ising or quadratic unconstrained binary optimization (QUBO) problem by expressing the expansion coefficients using spins or qubits. The algorithm is general and represents a new revolutionary approach for solving the real symmetric eigenvalue problem on a quantum annealer. The method is applied to two chemically important molecules: O$_2$ (oxygen) and O$_3$ (ozone). The lowest two vibrational states of these molecules are computed using both a hardware quantum annealer and a software based classical annealer.
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The possibility of using quantum computers for electronic structure calculations has opened up a promising avenue for computational chemistry. Towards this direction, numerous algorithmic advances have been made in the last five years. The potential of quantum annealers, which are the prototypes of adiabatic quantum computers, is yet to be fully explored. In this work, we demonstrate the use of a D-Wave quantum annealer for the calculation of excited electronic states of molecular systems. These simulations play an important role in a number of areas, such as photovoltaics, semiconductor technology and nanoscience. The excited states are treated using two methods, time-dependent Hartree-Fock (TDHF) and time-dependent density-functional theory (TDDFT), both within a commonly used Tamm-Dancoff approximation (TDA). The resulting TDA eigenvalue equations are solved on a D-Wave quantum annealer using the Quantum Annealer Eigensolver (QAE), developed previously. The method is shown to reproduce a typical basis set convergence on the example H$_2$ molecule and is also applied to several other molecular species. Characteristic properties such as transition dipole moments and oscillator strengths are computed as well. Three potential energy profiles for excited states are computed for NH$_3$ as a function of the molecular geometry. Similar to previous studies, the accuracy of the method is dependent on the accuracy of the intermediate meta-heuristic software called qbsolv.
Harnessing the full power of nascent quantum processors requires the efficient management of a limited number of quantum bits with finite lifetime. Hybrid algorithms leveraging classical resources have demonstrated promising initial results in the efficient calculation of Hamiltonian ground states--an important eigenvalue problem in the physical sciences that is often classically intractable. In these protocols, a Hamiltonian is parsed and evaluated term-wise with a shallow quantum circuit, and the resulting energy minimized using classical resources. This reduces the number of consecutive logical operations that must be performed on the quantum hardware before the onset of decoherence. We demonstrate a complete implementation of the Variational Quantum Eigensolver (VQE), augmented with a novel Quantum Subspace Expansion, to calculate the complete energy spectrum of the H2 molecule with near chemical accuracy. The QSE also enables the mitigation of incoherent errors, potentially allowing the implementation of larger-scale algorithms without complex quantum error correction techniques.
We demonstrate that a quantum annealer can be used to solve the NP-complete problem of graph partitioning into subgraphs containing Hamiltonian cycles of constrained length. We present a method to find a partition of a given directed graph into Hamiltonian subgraphs with three or more vertices, called vertex 3-cycle cover. We formulate the problem as a quadratic unconstrained binary optimisation and run it on a D-Wave Advantage quantum annealer. We test our method on synthetic graphs constructed by adding a number of random edges to a set of disjoint cycles. We show that the probability of solution is independent of the cycle length, and a solution is found for graphs up to 4000 vertices and 5200 edges, close to the number of physical working qubits available on the quantum annealer.
The recent availability of quantum annealers has fueled a new area of information technology where such devices are applied to address practically motivated and computationally difficult problems with hardware that exploits quantum mechanical phenomena. D-Wave annealers are promising platforms to solve these problems in the form of quadratic unconstrained binary optimization. Here we provide a formulation of the Chinese postman problem that can be used as a tool for probing the local connectivity of graphs and networks. We treat the problem classically with a tabu algorithm and using a D-Wave device. We systematically analyze computational parameters associated with the specific hardware. Our results clarify how the interplay between the embedding due to limited connectivity of the Chimera graph, the definition of logical qubits, and the role of spin-reversal controls the probability of reaching the expected solution.
The performance of a D-Wave Vesuvius quantum annealer was recently compared to a suite of classical algorithms on a class of constraint satisfaction instances based on frustrated loops. However, the construction of these instances leads the maximum coupling strength to increase with problem size. As a result, larger instances are subject to amplified analog control error, and are effectively annealed at higher temperatures in both hardware and software. We generate similar constraint satisfaction instances with limited range of coupling strength and perform a similar comparison to classical algorithms. On these instances the D-Wave Vesuvius processor, run with a fixed 20$mu$s anneal time, shows a scaling advantage over the software solvers for the hardest regime studied. This scaling advantage opens the possibility of quantum speedup on these problems. Our results support the hypothesis that performance of D-Wave Vesuvius processors is heavily influenced by analog control error, which can be reduced and mitigated as the technology matures.
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