Table 1 Overview of potential application areas for quantum algorithms alongside with information about relevant physical target quantities, underlying theoretical foundations, and some of the traditional algorithms to compete with
Applications | Molecular structure prediction & exploration | Biochemical processes (e.g. drug-molecule protein docking) | Ground state chemistry (e.g. catalysis) | Photochemistry (e.g. photosynthesis) | Complex dynamics (e.g. charge dynamics) | Cheminformatics |
|---|---|---|---|---|---|---|
Chemical physics | Forces on atom | Thermodynamics | Kinetics | Spectroscopy | Electronic & nuclear dynamics | Data-driven, physics-inspired, cost-function optimization |
Physical quantity to be calculated | Energy gradient | Free energy (difference) | Reaction & activation energies | Excitation energies | Autocorrelation functions | Universal applicability |
Accuracy (Hartree atomic units) | 10−3∼10−4 | 10−3∼10−4 | 10−3∼10−4 | 10−3 | purpose dependent | purpose dependent |
Mechanical theory | Effectively classical dynamics of nuclei/ions | Effectively classical dynamics of nuclei/ions | Electronic Schrödinger equation for ground states | Electronic Schrödinger equation for excited states | Time-dependent electronic and nuclear Schrödinger equations | Agnostic to the underlying mechanical theory |
State-of-the-art traditional competitors | DFT, QM/MM | FF,DFT,QM/MM | CCSD(T), CASSCF, DMRG-CI/SCF, FCIQMC/SCF, MR-PT2, MRCI+Q | EOM-CC/LR-CC, DMRG-CI/SCF, MR-PT2, MRCI+Q, | MCTDH | Neural Network |
Routine traditional competitor | DFT, FF | FF | DFT, MP2 | TD-DFT, ADC(2) | Surface hopping | |
Quantum algorithms | Quantum search | Quantum Metropolis-Hastings | QPE, VQE | QPE, VQE | Hamiltonian simulation | Quantum Machine Learning |
Quantum speedup | Quadratic | Polynomial | Exponential | Exponential | Exponential | Unknown |