Displaying items by tag: Quantum chemistry

A prospective application of quantum computing is solving quantum chemistry problems, however, obtaining exact solutions is difficult due to the lack of general method of obtaining such solutions. Typically the solution lies in finding the ground state energy, even though the energy is not descriptive enough to fully characterize all desired properties of a system. In order to find such properties, many measurements of the wavefunction are required. These measurements are expensive, because the wavefunction cannot be copied and must often be re-prepared before a second measurement is performed. Finding the full wavefunction would require exponentially many measurements, so one option would be to encode many solutions into one measurement by using a machine learned (ML) model. Training of the ML model requires finding exact quantities at several different external potentials. Besides that, one can use density functional theory (DFT), to replace the wavefunction with the one-body density, n(r), which has fewer variables. When DFT is used, instead of the Hamiltonian, the universal functional, F[n], must be found. The quantities required for the classical user to find self-consistent solutions are the exact functional (determining the energy) and the functional derivative. So, in addition to finding F[n], one also must find some other quantity such as the density, n(r), or the Kohn-Sham(KS) potential, vs(r). With these components, one can fully characterize a quantum ground state and solve for other measurable quantities.

The authors propose an algorithm that finds the ML model for F[n] on the quantum computer if a ground-state wavefunction is available. The algorithm leaves the wavefunction largely undisturbed so it can be used as the starting state for another system, greatly reducing the pre-factor required to solve other systems through a quantum counting algorithm to extract descriptive quantities such as the density. Most of this algorithm is kept entirely on the quantum computer to motivate future improvements for speed, but the counting algorithm does allow for information to be output classically. Moreover, the authors demonstrate that the exact Kohn-Sham potential can be solved in a faster way with a gradient evaluated on a cost function for the Kohn-Sham system.

The novelty of the proposed algorithm suggested in this work is the limitation of the number of measurements and re-preparations of the wavefunction especially in the case of time-dependent quantities. Since there is no algorithm for the general case that is exponentially better than the proposed algorithm, limiting the number of measurements and re-preparations of the wavefunction is as best as one can achieve. The proposed algorithm is a combination of several known algorithms including quantum phase estimation, quantum amplitude estimation, and quantum gradient methods that are iteratively used to train a machine learned model.
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In this arXiv submission by Qu & Co and Covestro, a well-known approximation in classical computational methods for quantum chemistry is applied to a quantum computing scheme for simulating molecular chemistry efficiently on near-term quantum devices. The restricted mapping allows for a polynomial reduction in both the quantum circuit depth and the total number of measurements required, as compared to the conventional variational approaches based on near-term quantum simulation of molecular chemistry, such as UCCSD. This enables faster runtime convergence of the variational algorithm to a potentially higher accuracy by using a larger basis set allowed by the restricted mapping. The latter is shown via an example simulation of the disassociation curve of lithium hydride. These results open up a new direction for efficient near-term quantum chemistry simulation, as well as decreasing the effective quantum resource requirements for future fault-tolerant quantum computing schemes.

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In this article by McKinsey & Co, a strategy consulting firm, Florian Budde and Daniel Volz state that the chemical companies must act now to capture the benefits of quantum computing. Of course we at Qu & Co are a bit biased on this topic, but we do agree with the authors that the chemical sector is likely to be an early beneficiary of the vastly expanded modeling and computational capabilities, which is promised to be unlocked by quantum computing.

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Thus far, quantum chemistry quantum algorithms have been experimentally demonstrated only on gate-based quantum computers. Efforts have been made to also map the chemistry problem Fermionic Hamiltonian to an Ising Hamiltonian in order to solve it on a quantum annealer.  However, the number of qubits required still scales exponentially with the problem size (the number of orbitals considered in the electronic structure problem). As an alternative, this paper presents a different approach exploiting the efficiency at which quantum annealers can solve discrete optimization problems, and mapping a qubit coupled cluster method to this form. They simulate their method on an ideal Ising machine and on a D-Wave 2000Q system, and find promising success rates for smaller molecules. However, further investigation would be necessary to investigate the usability for larger or more complex systems, as the scaling of their folding technique with the number of local minima is unknown. In addition, it is unclear from the experimental data whether the limitations of the D-Wave system  as compared to a perfect Ising machine could hinder expected performance gains for more complex systems.

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Most near-term quantum-computational chemistry experiments have so-far been implemented by applying the Variational Quantum Eigensolver (VQE) classical-quantum hybrid algorithm as an alternative to Quantum Phase Estimation (QPE). This is due to the fact that QPE requires many orders of magnitude more quantum gates than is feasible with typical coherence times of current and near-term quantum-processors. As an alternative, in this paper, Paesani et al. report experimental results of a recently proposed adaptive Bayesian approach to quantum phase estimation and use it to simulate molecular energies on a Silicon quantum photonic device. The approach is verified to be well suited for NISQ quantum-processors by investigating its superior robustness to noise and decoherence compared to the iterative phase estimation algorithm. There results shows a promising route to unlock the power of QPE much sooner than previously believed possible.

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Quantum computers can be used to address molecular structure, materials science and condensed matter physics problems, which currently stretch the limits of existing high-performance computing resources. Finding exact numerical solutions to these interacting fermion problems has exponential cost, while Monte Carlo methods are plagued by the fermionic sign problem. In Quantum Computational Chemistry solutions, the Variational Quantum Eigensolver (VQE) algorithm offers a hybrid classical-quantum, and thus low quantum circuit depth, alternative to the Phase Estimation algorithm used to measure the ground-state energy of a molecular Hamiltonian. In VQE the quantum computer is used to prepare variational trial states that depend on a set of parameters. Then, the expectation value of the energy is estimated and used by a classical optimizer to generate a new set of improved parameters. The advantage of VQE over classical simulation methods is that in VQE one can prepare trial states that are not amenable to efficient classical numerics. In this paper, Kandala et al. demonstrate the experimental results for determining the ground state energy for molecules of increasing size, up to BeH2 using the VQE algorithm.

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Quantum Computational Chemistry is one of the most promising applications for both near-term and large scale fault-tolerant quantum-computers. In this paper, McClean et al. present Open Fermion (www.openfermion.org), an open-source software library written largely in Python, aimed at enabling the simulation of fermionic models and quantum chemistry problems on quantum hardware. Without such a library, developing and studying algorithms for these problems is be difficult due to the prohibitive amount of domain knowledge required in both the area of chemistry and quantum algorithms. Beginning with an interface to common electronic structure packages, it simplifies the translation between a molecular specification and a quantum circuit for solving or studying the electronic structure problem on a quantum computer, minimizing the amount of domain expertise required to enter the field.

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Recently, promising experimental results have been shown for quantum-chemistry calculations using small, noisy quantum processors. As full scale fault-tolerant error correction is still many years away, near-term quantum computers will have a limited number of qubits, and each qubit will be noisy. Methods that reduce noise and correct errors without doing full error correction on every qubit will help extend the range of interesting problems that can be solved in the near-term. In this paper Otten et al. present a scheme for accounting (and removal) of errors in observables determined from quantum algorithms and apply this scheme to the variational quantum eigensolver algorithm, simulating the calculation of the ground state energy of equilibrium H2 and LiH in the presence of several noise sources, including amplitude damping, dephasing, thermal noise, and correlated noise. They show that their scheme provides a decrease in the needed quality of the qubits by up to two orders of magnitude.

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This report by Olson et al. summarizes the resuts of an NSF Workshop on Quantum Computational Chemistry held in November 2016. The workshop was attended by a wide range of experts from directly quantum-oriented fields such as algorithms, chemistry, machine learning, optics, simulation, and metrology, as well as experts in related fields such as condensed matter physics, biochemistry, physical chemistry, inorganic and organic chemistry, and spectroscopy. The goal of the workshop was to summarize recent progress in research at the interface of quantum information science and chemistry as well as to discuss the promising research challenges and opportunities in the field.

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Efficient quantum simulations of classically intractable instances of the associated electronic structure problem promise breakthroughs in our understanding of basic chemistry and could revolutionize research into new materials, pharmaceuticals, and industrial catalysts. In Quantum Computational Chemistry solutions, the Variational Quantum Eigensolver (VQE) algorithm offers a hybrid classical-quantum, and thus low quantum circuit depth, alternative to the Phase Estimation algorithm used to measure the ground-state energy of a molecular Hamiltonian. In this paper, Hempel et al. use a digital quantum simulator based on trapped ions to experimentally investigate the VQE algorithm for the calculation of molecular ground state energies of two simple molecules  (H2 and LiH) and experimentally demonstrate and compare different encoding methods using up to four qubits. 

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