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Quantum computers cannot calculate energy
Vatiational quantum eigensolver (= VQE ) is useless
(Fig.1) Quantum mechanics and quantum computers are useless, unable to predict atomic energy.
Quantum phase estimation (= QPE ) is said to estimate atomic energy by quantum computing (= actually classical computers disguised as hybrid-quantum computers are used ), which is untrue.
In this quantum phase estimation, physicists have to choose fake trial wavefunctions (= ψ = basis set functions ) close to ground-state energy in advance for unsolvable Schrödinger equations that cannot predict any multi-electron atomic energies.
This-p.7-2.2 says -- Choose fake wavefunction
"The choice of these basis functions has a critical impact on both the accuracy and
the computational cost of electronic structure calculations"
This-p.4-right-II says -- Artificial choice, No prediction
"the first step of this algorithm is to prepare the
system register in a state having good overlap with the
ground state of the Hamiltonian H."
Then, they use classical computers to calculate atomic total energy (= Hamiltonian H ) instead of today's error-prone useless quantum computers. That's all.
↑ Quantum mechanics is useless, unable to predict any multi-electron atomic energies due to the unsolvable Schrödinger equation.
Quantum computers are also useless, too error-prone to calculate anything.
Physicists have to artificially change the atomic energy (= H ) calculated by classical computers into very simple impractical Hamiltonian energy for very small numbers of qubits of today's impractical quantum computers.
After the artificially-chosen fake trial wavefunction (= ψ ) is changed into very simple version expressed by the quantum computer's qubits, they evolve the wavefunction by some qubit phase operators expressed as U =e-Ht (= atomic energy H must be computed by classical computers in advance, this-p.9-Fig.5 ), which is called time evolution ( this or this-p.2 ).
Then, they measure the resultant qubits' state to estimate the phase (= containing Hamiltonian H atomic energy ) that must be already known in advance by classical computers ( this or this-p.14, this or this-middle-0.-4. this or this-p.7 ).
↑ So this quantum phase estimation (= QPE ) and quantum computers are meaningless concepts for calculating atomic energies.
↑ Only classical computers and artificially-chosen fake trial wavefunctions determine the final atomic energy (= H or phase ).
This-paper on quantum phase estimation ↓
p.5-2nd~3rd-paragraphs says -- Classical computer needed
"IPEA (= iterative phase estimation algorithm ).."
"For our proof-of-principle demonstration,
all necessary molecular integrals are evaluated classically (= classical computers ) using the
Hartree- Fock procedure"
p.6-B. says -- Classical computers calculate energy
"Restricted Hartree-Fock calculations were carried out on a classical computer using the STO3G basis. The software used was the PyQuante quantum chemistry package version 1.6.
The molecular integrals from the Hartree-Fock procedure are used to evaluate the matrix
elements of the Hamiltonians H"
p.11-1st-paragraph says -- Just classical, No quantum
"the four single-electron spin-orbitals (i.e. |0 = occupied, |1 = unoccupied)."
" The ground state energies of the approximate unitary
propagators were obtained via direct diagonalization on a classical computer"
This or this-abstract, p.3-right-2nd-paragraph says
"Quantum phse estimation (= QPE)"
"orbital. hpq and hpqrs (of total Hamiltonian energy H of evolution operator of eHt in Fig.1, (7) ) are one- and two-electron integrals and
they are computed on classical computers prior to quantum
simulations"
This-p.2-left-4th-paragraph says
"After obtaining Hsim through this (typically) efficient
classical computation, we perform the quantum simulation of this molecule on a single-NV register, which consists of an electronic spin-1 and an associated 14N nuclear spin-1 forming a qutrit pair (= only two useless qubits 01 were used in this research-p.8-Figure 2, which is Not a quantum computer )... iterative phase estimation algorithm (IPEA)"
↑ So instead of useless quantum computers, ordinary classical computers need to be used to calculate (fake) atomic energy from artificially chosen fake trial wavefunctions in this QPE, which quantum mechanical methods cannot predict anything.
This other QPE paper ↓
p.1-abstract says -- Classical computer simulation
"We performed numerical simulations (= simulation means classical computer's simulation of fictional quantum computer qubits ) of QPE for the supramolecular
approach-based intermolecular interaction energy calculations of the hydrogen-bonded water dimer,"
p.3-right-2nd-paragraph says -- Choose some orbits
"Note that the QPE with active space approximation
returns the CASCI energy and therefore large part of
dynamical electron correlation effects are not taken into
account" ← Only a small number of orbitals were artificially chosen as active space = a target for calculations (= other orbitals were ignored due to taking too much time ), which cannot get right molecular energy.
p.4-right-2nd-paragraph says -- Using only classical computers
"The HF calculations (= hartree-fock calculation for unsolvable Schrodinger equation that cannot predict any energy ) and molecular orbital localizations were performed using PySCF (= PySCF is an ordinary classical computer's software, so No quantum computation )"
p.9-V. says -- Just 12 simulated qubits
"we have
successfully reduced the number of qubits required to
calculate the potential energy curve of hydrogen bonding quantitatively to 12 (= one qubit takes only 0 or 1 value, so just 12 qubits are Not a quantum computer, and these 12 qubits were simulated by a classical computer in this research )"
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