Quantum computing using Cirq and OpenFermion with application to quantum chemistry

A Full Quantum Eigensolver for Quantum Chemistry Simulations

Research ◽

10.34133/2020/1486935 ◽

2020 ◽

Vol 2020 ◽

pp. 1-11 ◽

Cited By ~ 7

Author(s):

Shijie Wei ◽

Hang Li ◽

GuiLu Long

Keyword(s):

Quantum Computing ◽

Quantum Chemistry ◽

Gradient Descent ◽

Materials Science ◽

Hybrid Methods ◽

Quantum Computer ◽

Rapid Development ◽

System Size ◽

Near Term ◽

Full Quantum

Quantum simulation of quantum chemistry is one of the most compelling applications of quantum computing. It is of particular importance in areas ranging from materials science, biochemistry, and condensed matter physics. Here, we propose a full quantum eigensolver (FQE) algorithm to calculate the molecular ground energies and electronic structures using quantum gradient descent. Compared to existing classical-quantum hybrid methods such as variational quantum eigensolver (VQE), our method removes the classical optimizer and performs all the calculations on a quantum computer with faster convergence. The gradient descent iteration depth has a favorable complexity that is logarithmically dependent on the system size and inverse of the precision. Moreover, the FQE can be further simplified by exploiting a perturbation theory for the calculations of intermediate matrix elements and obtaining results with a precision that satisfies the requirement of chemistry application. The full quantum eigensolver can be implemented on a near-term quantum computer. With the rapid development of quantum computing hardware, the FQE provides an efficient and powerful tool to solve quantum chemistry problems.

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Quantum Computing for Quantum Chemistry

10.21236/ada534093 ◽

2010 ◽

Cited By ~ 1

Author(s):

Alan Aspuru-Guzik

Keyword(s):

Quantum Computing ◽

Quantum Chemistry

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Compilation by stochastic Hamiltonian sparsification

Quantum ◽

10.22331/q-2020-02-27-235 ◽

2020 ◽

Vol 4 ◽

pp. 235 ◽

Cited By ~ 3

Author(s):

Yingkai Ouyang ◽

David R. White ◽

Earl T. Campbell

Keyword(s):

Electronic Structure ◽

Quantum Computing ◽

Probability Distribution ◽

Quantum Chemistry ◽

Error Bounds ◽

Simulation Methods ◽

Physical Systems ◽

First Order ◽

Convex Optimisation ◽

Principal Application

Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the effect of each term during time-evolution is individually computed. For many physical systems, the Hamiltonian has a large number of terms, constraining the scalability of established simulation methods. To address this limitation we introduce a new scheme that approximates the actual Hamiltonian with a sparser Hamiltonian containing fewer terms. By stochastically sparsifying weaker Hamiltonian terms, we benefit from a quadratic suppression of errors relative to deterministic approaches. Relying on optimality conditions from convex optimisation theory, we derive an appropriate probability distribution for the weaker Hamiltonian terms, and compare its error bounds with other probability ansatzes for some electronic structure Hamiltonians. Tuning the sparsity of our approximate Hamiltonians allows our scheme to interpolate between two recent random compilers: qDRIFT and randomized first order Trotter. Our scheme is thus an algorithm that combines the strengths of randomised Trotterisation with the efficiency of qDRIFT, and for intermediate gate budgets, outperforms both of these prior methods.

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