Variational Quantum Computation of Excited States

@article{Higgott2019VariationalQC,
  title={Variational Quantum Computation of Excited States},
  author={Oscar Higgott and Daochen Wang and Stephen Brierley},
  journal={Quantum},
  year={2019}
}
The calculation of excited state energies of electronic structure Hamiltonians has many important applications, such as the calculation of optical spectra and reaction rates. While low-depth quantum algorithms, such as the variational quantum eigenvalue solver (VQE), have been used to determine ground state energies, methods for calculating excited states currently involve the implementation of high-depth controlled-unitaries or a large number of additional samples. Here we show how overlap… Expand

Figures from this paper

A method of determining molecular excited-states using quantum computation
A method is presented in which the ground-state subspace is projected out of a Hamiltonian representation. As a result of this projection, an effective Hamiltonian is constructed where itsExpand
Quantum Chemistry Calculations using Energy Derivatives on Quantum Computers
Quantum chemistry calculations such as the prediction of molecular properties and modeling of chemical reactions are a few of the critical areas where near-term quantum computers can showcase quantumExpand
Calculation of excited states via symmetry constraints in the variational quantum eigensolver
The variational quantum eigensolver (VQE) requires specification of symmetries that describe the system, e.g. spin and number of electrons. This opens the possibility of using VQE to obtain excitedExpand
Quantum simulations of excited states with active-space downfolded Hamiltonians.
TLDR
This letter study the effectiveness of the DUCC formalism in describing excited states, and views PE algorithms as an engine for verifying various hypotheses for excited-state processes and providing statistically meaningful results that correspond to the electronic state(s) with the largest overlap with a postulated configurational structure. Expand
Adaptive variational quantum eigensolvers for highly excited states
Highly excited states of quantum many-body systems are central objects in the study of quantum dynamics and thermalization that challenge classical computational methods due to their volumelawExpand
Practical quantum computation of chemical and nuclear energy levels using quantum imaginary time evolution and Lanczos algorithms
Various methods have been developed for the quantum computation of the ground and excited states of physical and chemical systems, but many of them require either large numbers of ancilla qubits orExpand
A variational quantum eigensolver for dynamic correlation functions
Recent practical approaches for the use of current generation noisy quantum devices in the simulation of quantum many-body problems have been dominated by the use of a variational quantum eigensolverExpand
Subspace-search variational quantum eigensolver for excited states
The variational quantum eigensolver (VQE), a variational algorithm to obtain an approximated ground state of a given Hamiltonian, is an appealing application of near-term quantum computers. TheExpand
A Quantum Algorithm to Calculate Band Structure at the EOM Level of Theory
Band structure is a cornerstone to understand electronic properties of materials. Accurate band structure calculations using a high-level quantum-chemistry theory can be computationally veryExpand
Theory of analytical energy derivatives for the variational quantum eigensolver
The variational quantum eigensolver (VQE) and its variants, which is a method for finding eigenstates and eigenenergies of a given Hamiltonian, are appealing applications of near-term quantumExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 82 REFERENCES
Variational quantum algorithms for discovering Hamiltonian spectra
Calculating the energy spectrum of a quantum system is an important task, for example to analyse reaction rates in drug discovery and catalysis. There has been significant progress in developingExpand
Scalable Quantum Simulation of Molecular Energies
We report the first electronic structure calculation performed on a quantum computer without exponentially costly precompilation. We use a programmable array of superconducting qubits to compute theExpand
Witnessing eigenstates for quantum simulation of Hamiltonian spectra
TLDR
The concept of an eigenstate witness is introduced and used to find energies of quantum systems with quantum computers and provides a new quantum approach that combines variational methods and phase estimation to approximate eigenvalues for both ground and excited states. Expand
Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz
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 approximateExpand
Progress towards practical quantum variational algorithms
The preparation of quantum states using short quantum circuits is one of the most promising near-term applications of small quantum computers, especially if the circuit is short enough and theExpand
Constrained Variational Quantum Eigensolver: Quantum Computer Search Engine in the Fock Space.
TLDR
The proposed constrained VQE can find an electronic state with a certain number of electrons, a certain spin, or any other property, and naturally removes unphysical kinks in potential energy surfaces (PESs), which frequently appeared in the regular V QE and required significant additional quantum resources for their removal. Expand
Simulated Quantum Computation of Molecular Energies
TLDR
Calculations of the water and lithium hydride molecular ground-state energies have been carried out on a quantum computer simulator using a recursive phase-estimation algorithm and mapping of the molecular wave function to the quantum bits are described. Expand
Quantum Simulation of Electronic Structure with Linear Depth and Connectivity.
TLDR
It is conjecture that no explicit Trotter step of the electronic structure Hamiltonian is possible with fewer entangling gates, even with arbitrary connectivities, which represents significant practical improvements on the cost of mostTrotter-based algorithms for both variational and phase-estimation-based simulation of quantum chemistry. Expand
Quantum optimization using variational algorithms on near-term quantum devices
TLDR
The quantum volume as a metric to compare the power of near-term quantum devices is discussed and simple error-mitigation schemes are introduced that could improve the accuracy of determining ground-state energies. Expand
Accelerated Variational Quantum Eigensolver.
TLDR
A generalized VQE algorithm is proposed that interpolates between these two regimes via a free parameter α∈[0,1], which can exploit quantum coherence over a circuit depth of O(1/ε^{α}) to reduce the number of samples to O( 1/ε-α) and give a new routine for expectation estimation under limited quantum resources that is of independent interest. Expand
...
1
2
3
4
5
...