Quantum chemistry beyond Born-Oppenheimer approximation on a quantum computer: A simulated phase estimation study

2016 ◽  
Vol 116 (18) ◽  
pp. 1328-1336 ◽  
Author(s):  
Libor Veis ◽  
Jakub Višňák ◽  
Hiroaki Nishizawa ◽  
Hiromi Nakai ◽  
Jiří Pittner
Keyword(s):  
Quantum Chemistry ◽  
Quantum Computer ◽  
Phase Estimation ◽  
Oppenheimer Approximation

Quantum algorithm for measuring the energy of n qubits with unknown pair-interactions

2002 ◽  
Vol 2 (3) ◽  
pp. 198-207
Author(s):  
D. Janzing
Keyword(s):  
Quantum State ◽  
Quantum Computer ◽  
Quantum Algorithm ◽  
Pair Interaction ◽  
Phase Estimation ◽  
Solid States ◽  
Energy Gaps ◽  
Large N ◽  
Conditional Transformation ◽  
Essential Assumption

The well-known algorithm for quantum phase estimation requires that the considered unitary is available as a conditional transformation depending on the quantum state of an ancilla register. We present an algorithm converting an unknown n-qubit pair-interaction Hamiltonian into a conditional one such that standard phase estimation can be applied to measure the energy. Our essential assumption is that the considered system can be brought into interaction with a quantum computer. For large n the algorithm could still be applicable for estimating the density of energy states and might therefore be useful for finding energy gaps in solid states.

scholarly journals Qubit Coupled Cluster Method: A Systematic Approach to Quantum Chemistry on a Quantum Computer

2018 ◽  
Vol 14 (12) ◽  
pp. 6317-6326 ◽  
Author(s):  
Ilya G. Ryabinkin ◽  
Tzu-Ching Yen ◽  
Scott N. Genin ◽  
Artur F. Izmaylov
Keyword(s):  
Quantum Chemistry ◽  
Systematic Approach ◽  
Quantum Computer ◽  
Cluster Method ◽  
Coupled Cluster ◽  
Coupled Cluster Method

scholarly journals Quantum simulation of chemistry with sublinear scaling in basis size

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Ryan Babbush ◽  
Dominic W. Berry ◽  
Jarrod R. McClean ◽  
Hartmut Neven
Keyword(s):  
Electronic Structure ◽  
Plane Wave ◽  
Quantum Chemistry ◽  
Plane Waves ◽  
Quantum Algorithm ◽  
Discretization Error ◽  
Rotating Frame ◽  
Interaction Picture ◽  
Basis Size ◽  
Oppenheimer Approximation

Abstract We present a quantum algorithm for simulating quantum chemistry with gate complexity $$\tilde {\cal{O}}(N^{1/3}\eta ^{8/3})$$ O ̃ ( N 1 ∕ 3 η 8 ∕ 3 ) where η is the number of electrons and N is the number of plane wave orbitals. In comparison, the most efficient prior algorithms for simulating electronic structure using plane waves (which are at least as efficient as algorithms using any other basis) have complexity $$\tilde {\cal{O}}(N^{8/3}{\mathrm{/}}\eta ^{2/3})$$ O ̃ ( N 8 ∕ 3 ∕ η 2 ∕ 3 ) . We achieve our scaling in first quantization by performing simulation in the rotating frame of the kinetic operator using interaction picture techniques. Our algorithm is far more efficient than all prior approaches when N ≫ η, as is needed to suppress discretization error when representing molecules in the plane wave basis, or when simulating without the Born-Oppenheimer approximation.

scholarly journals A Full Quantum Eigensolver for Quantum Chemistry Simulations

Research ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
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.

Quantum Chemistry on a Quantum Computer: First Steps and Prospects

2009 ◽  
Author(s):  
B. P. Lanyon ◽  
J. D. Whitfield ◽  
G. G. Gillett ◽  
M. E. Goggin ◽  
M. P. Almeida ◽  
...  
Keyword(s):  
Quantum Chemistry ◽  
Quantum Computer

scholarly journals Corrected quantum walk for optimal Hamiltonian simulation

2016 ◽  
Vol 16 (15&16) ◽  
pp. 1295-1317
Author(s):  
Dominic Berry ◽  
Leonardo Novo
Keyword(s):  
Lower Bound ◽  
Quantum Chemistry ◽  
Taylor Series ◽  
Quantum Computer ◽  
Quantum Walk ◽  
Query Complexity ◽  
Hamiltonian Simulation ◽  
Hamiltonian Evolution

We describe a method to simulate Hamiltonian evolution on a quantum computer by repeatedly using a superposition of steps of a quantum walk, then applying a correction to the weightings for the numbers of steps of the quantum walk. This correction enables us to obtain complexity which is the same as the lower bound up to doublelogarithmic factors for all parameter regimes. The scaling of the query complexity is given. This technique should also be useful for improving the scaling of the Taylor series approach to simulation, which is relevant to applications such as quantum chemistry.

Quantum algorithm for measuring the eigenvalues of UÄU-1 for a black-box unitary transformation U

2002 ◽  
Vol 2 (3) ◽  
pp. 192-197
Author(s):  
D. Janzing ◽  
T. Beth
Keyword(s):  
Energy Spectrum ◽  
Quantum System ◽  
Autocorrelation Function ◽  
Unitary Transformation ◽  
Quantum Computer ◽  
Quantum Algorithm ◽  
Black Box ◽  
Phase Estimation

Estimating the eigenvalues of a unitary transformation U by standard phase estimation requires the implementation of controlled-U-gates which are not available if U is only given as a black box. We show that a simple trick allows to measure eigenvalues of U\otimesU^\deggar even in this case. Running the algorithm several times allows therefore to estimate the autocorrelation function of the density of eigenstates of U. This can be applied to find periodicities in the energy spectrum of a quantum system with unknown Hamiltonian if it can be coupled to a quantum computer.

scholarly journals Evaluating Energy Differences on a Quantum Computer with Robust Phase Estimation

2021 ◽  
Vol 126 (21) ◽  
Author(s):  
A. E. Russo ◽  
K. M. Rudinger ◽  
B. C. A. Morrison ◽  
A. D. Baczewski
Keyword(s):  
Quantum Computer ◽  
Phase Estimation
Sign in / Sign up

Export Citation Format

Share Document