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Register a new userStrategies for quantum computing molecular energies using the unitary coupled cluster ansatz
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Added by
Jonathan Romero Fontalvo
Publication date
2017
fields
Physics
and research's language is
English
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The variational quantum eigensolver (VQE) algorithm combines the ability of quantum computers to efficiently compute expectation values with a classical optimization routine in order to approximate ground state energies of quantum systems. In this paper, we study the application of VQE to the simulation of molecular energies using the unitary coupled cluster (UCC) ansatz. We introduce new strategies to reduce the circuit depth for the implementation of UCC and improve the optimization of the wavefunction based on efficient classical approximations of the cluster amplitudes. Additionally, we propose an analytical method to compute the energy gradient that reduces the sampling cost for gradient estimation by several orders of magnitude compared to numerical gradients. We illustrate our methodology with numerical simulations for a system of four hydrogen atoms that exhibit strong correlation and show that the circuit depth of VQE using a UCC ansatz can be reduced without introducing significant loss of accuracy in the final wavefunctions and energies.
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Neural-Network Quantum State (NQS) has attracted significant interests as a powerful wave-function ansatz to model quantum phenomena. In particular, a variant of NQS based on the restricted Boltzmann machine (RBM) has been adapted to model the ground state of spin lattices and the electronic structures of small molecules in quantum devices. Despite these progresses, significant challenges remain with the RBM-NQS based quantum simulations. In this work, we present a state-preparation protocol to generate a specific set of complex-valued RBM-NQS, that we name the unitary-coupled RBM-NQS, in quantum circuits. This is a crucial advancement as all prior works deal exclusively with real-valued RBM-NQS for quantum algorithms. With this novel scheme, we achieve (1) modeling complex-valued wave functions, (2) using as few as one ancilla qubit to simulate $M$ hidden spins in an RBM architecture, and (3) avoiding post-selections to improve scalability.
In classical computational chemistry, the coupled-cluster ansatz is one of the most commonly used $ab~initio$ methods, which is critically limited by its non-unitary nature. The unitary modification as an ideal solution to the problem is, however, extremely inefficient in classical conventional computation. Here, we provide the first experimental evidence that indeed the unitary version of the coupled cluster ansatz can be reliably performed in physical quantum system, a trapped ion system. We perform a simulation on the electronic structure of a molecular ion (HeH$^+$), where the ground-state energy surface curve is probed, energies of excited-states are studied and the bond-dissociation is simulated non-perturbatively. Our simulation takes advantages from quantum computation to overcome the intrinsic limitations in classical computation and our experimental results indicate that the method is promising for preparing molecular ground-states for quantum simulation.
Quantum computation represents a revolutionary means for solving problems in quantum chemistry. However, due to the limited coherence time and relatively low gate fidelity in the current noisy intermediate-scale quantum (NISQ) devices, realization of quantum algorithms for large chemical systems remains a major challenge. In this work, we demonstrate how the circuit depth of the unitary coupled cluster ansatz in the algorithm of variational quantum eigensolver can be significantly reduced by an energy-sorting strategy. Specifically, subsets of excitation operators are pre-screened from the unitary coupled-cluster singles and doubles (UCCSD) operator pool according to its contribution to the total energy. The procedure is then iteratively repeated until the convergence of the final energy to within the chemical accuracy. For demonstration, this method has been sucessfully applied to systems of molecules and periodic hydrogen chain. Particularly, a reduction up to 14 times in the number of operators is observed while retaining the accuracy of the origin UCCSD operator pools. This method can be widely extended to other variational ansatz other than UCC.
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.
Let $H_1, H_2$ be Hilbert spaces of the same finite dimension $ge2$, and $C$ an arbitrary quantum circuit with (principal) input state in $H_1$ and (principal) output state in $H_2$. $C$ may use ancillas and produce garbage which is traced out. $C$ may employ classical channels and measurement gates. If $C$ computes, for each computation path $mu$ through the circuit, a unitary transformation $U_mu: H_1 to H_2$ then, for each $mu$, the probability that a computation takes path $mu$ is independent of the input.
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