Top (quantum mechanics is unrealistic)
Grover algorithm is useless, not faster at all.
(Fig.1) Hybrid variational quantum eigensolver (= VQE ) depends on classical computer for finding atomic lowest ground-state energy, and quantum computer with a small number of qubits is useless, doing almost nothing.
Contrary to an incredibly large amount of overhyped news, all the present quantum computers are unable to give right answers and calculate any molecular energies because of their too high error rates and inability to correct errors.
This 1 introduction-4th-paragraph (and 1.3-3rd-paragraph ) says
"there are still No known use cases where a quantum computer has simulated something that could not be simulated on a classical computer, much less so for a chemistry with practical applications"
"although simple molecules can already be simulated on real quantum hardware, the possible system sizes are still small enough to also be modeled using classical computers.. there is still a wide gap between current hardware and required error rates (= still error-prone useless quantum computers )."
Today's quantum computers are too error-prone and having too small numbers of bits or qubits to calculate any meaningful values or energies.
So the current error-prone quantum computers have to rely on practical classical computers for calculating molecular energies as (deceptive) hybrid quantum-classical computers where quantum computers can do almost nothing.
This 3~4th paragraphs say
"The long story short version is that our quantum hardware isn't nearly as good as it should be (ie, lots of noise, decoherence…)"
".. So, in the meantime, we're using quantum computer terms as the NISQ ( noisy intermediate-scale quantum ) era quantum devices. They don't have a huge amount of qubits and also don't have an amazingly low error rate."
Quantum computers are useless and deadend.
So physicists needed to create a (confusing) concept called hybrid classical-quantum computer that can use the classical computer's power to mask the uselessness of quantum computer.
This (deceptive) hybrid classical-quantum computing method relying on ordinary classical computers for almost all their calculations of molecular energies is called variational quantum eigensolver (= VQE ).
Quantum mechanics cannot predict any atomic or molecular energies except for one-electron hydrogen atom, because all multi-electron Schrödinger equations are unsolvable.
So physicists use variational methods where they just artificially choose fake trial wavefunctions or basis sets with arbitrary numbers of freely-adjustable parameters to get energies close to experimental values.
In the hybrid variational quantum eigensolver (= VQE ), they rely on ordinary classical computers for almost all calculations including finding the true lowest atomic or molecular energies by adjusting variational energy parameters.
So the hybrid classical-quantum computer is substantially a classical computer, because the classical computer is used to find and calculate actual molecular energies, and the quantum computer with a tiny number of error-prone qubits can do almost nothing.
The current quantum computers are too error-prone to calculate any values correctly.
They can use only a very small number of qubits (= 2 ~ 20 qubits = just 2 ~ 20 bitstring ) as quantum computers (= still Not computers ) for the quantum calculation part of this hybrid variaitonal quantum eigensolver method in order to avoid increasing errors caused by use of large numbers of qubits.
↑ Of course, it is impossible to calculate complicated molecular energy just by less than 20 qubits or 20 bitstring (= each qubit can take only 1 or 0 value ).
It is impossible for just a small number of qubits (= 2 ~ 20 qubits ) to express and calculate complicated molecular energies using ordinary energy equation or Hamiltonian.
So physicists have to artificially prepare pseudo-molecular energy or Hamiltonian (= H ) equation consisting only of a small numbers of bits for the present impractical quantum computers with only small numbers of qubits.
This artificially transformation from ordinary complicated Hamiltonian energy equation into fake simplified Hamiltonian consisting of a small numbers of qubits and coefficients that are calculated by classical computers is called Jordan-Wigner transformation or mapping ( this p.1-right-(1)-last-paragraph, footnote ).
For example, some researches used only two qubits or two bitstring (= 01 ) to express (fake) Hamiltonian energy for a H2 molecule.
Another recent paper used the (fake) Hamiltonian for H2 molecular energy expressed by only 4 impractical qubits ( this p.4-C. p.6-right-coefficient parameters chosen beforehand ).
This simplified (fake) Hamiltonian energy equation consists of several qubit operators (= each qubit operator can take only 0 or 1 value ) and coefficients (= different in different molecular energies ) that must be calculated by classical computers beforehand ( this-middle, this p.2-right-(4), this p.29-4.6 ).
In this hybrid variational quantum eigensolver (= VQE ) method, ordinary classical computer has to choose and determine the crucial molecular energy parameters as classical optimizers.
↑ So the most important calculations for finding the true lowest ground-state energies of atoms and molecules (= optimization ) rely on ordinary classical computers ( this p.16, this p.7-Figure.1, this-4. this 1.-5th-paragraph ) instead of the present impractical quantum computers.
This abstract & p.2-left-2nd-paragraph say
"the accuracy of the molecular properties predicted by most
of the quantum computations nowadays is still far off (not within chemical accuracy)..
the classical computer performing the parameter optimization."
The impractical quantum computer with a tiny number of qubits can do nothing but change their qubits based on parameters chosen by classical computer for the artificially-created simplified pseudo-Hamiltonian energy equation.
The 1st, 4th, 6-7th paragraphs This website say ↓
"The Variational Quantum Eigensolver (VQE) is a hybrid classical-quantum algorithm that,.. can find the ground state energy of various quantum systems..
Although true quantum speedups in computational chemistry are still far off and dependant on the development of large fault-tolerant quantum computers (= still error-prone quantum computers )"
"variationally updating these parameters on a classical computer to find a tight upper bound to the ground state. "
"2. A quantum measurement circuit estimates the energy expectation in this trial state (= this vague "estimate" does Not mean "calculate" nor "predict energy" )."
"3. The
This 3rd-paragraph says
"Notably, VQE is a hybrid quantum-classical algorithm,.. The quantum device "encodes" a trial molecular wave function into an assembly of qubits and estimates the wave function's energy by performing measurements on the qubits (= just using the words "estimate" and "measurement", which have nothing to do with "quantum computer calculating molecular energy" ).
".. The classical processor then minimizes the estimated energy by adjusting the trial-wave-function parameters (= classical computer has to do the most important part of finding the true lowest ground-state energy of the molecule and changing its parameter )."
As a result, in this (deceptive) hybrid quantum-classical method for molecular energy calculation, the quantum computer is useless, meaningless, doing almost nothing except for slightly changing qubits based on parameters determined by classical computers.
Quantum computer advantage is impossible in the current error-prone quantum computers with only small numbers of qubits.
This abstract says
"However, it is Not yet clear whether such algorithms, even in the absence of device error, could actually achieve quantum advantage for systems of practical interest (= No quantum computer advantage )"
IBM research on calculating energies of small molecules H2, LiH and BeH2 used only 2 ~ 6 impractical qubits as part of hybrid classical-quantum variational quantum eigensolver (= VQE ) method.
This 1st, 4th paragraphs say
"IBM yesterday reported in Nature Communications the use of a novel algorithm to simulate BeH2 (beryllium-hydride) on a quantum computer. This is the largest molecule so far simulated on a quantum computer. The technique, which used six qubits of a seven-qubit system"
"While this model of BeH2 can be simulated on a classical computer (= quantum computer was necessary )"
↑ Each qubit can take only 0 or 1, so 6 qubits or 6 bitstring can express only 26 = 64 numbers which number is too small to calculate complicated molecular energy.
It means the ordinary classical computer did almost all the molecular energy calculation.
↑ This IBM research paper ( this ↓ )
p.2-Fig.1, p.4-Fig.3 used only less than 6 (superconducting) qubits (= this is still Not a computer nor able to calculate molecular energy ).
p.20-Fig.S9-b,d showed calculation results where even this very small number of qubits (= green, red, blue dotted lines ) caused errors, disagreed with the exact energy values (= black dotted lines ). depth (= d ) meant the number of qubit operations.
↑ Six qubits can express only 26 = 64 numbers (= one qubit takes 0 or 1 values ), which is too small number to calculate any molecular energies.
As a result, in the current alleged quantum computer calculation of molecular energy in the confusing hybrid method (= ex. VQE ), the ordinary classical computer actually has to calculate the molecular energy, and the quantum computer can do nothing useful.
Also in IBM's research on the hybrid classical-quantum variational quantum eigensolver (= VQE ) in 2021, they used only up to 8 (impractical) error-prone qubits, and almost all important molecular energy calculations must be done by ordinary errorless classical computers ( this p.4-Fig.1, p.6-Fig.5 ).
In this Google, Harvard research on hybrid VQE calculation of H2 molecular energy in 2016, they used only 2 impractical qubits or 2 bitstring (= 00, 01, 11 ) as a quantum computer. ← just 2 bits can Not calculate anything.
See this p.3-Fig.1, p.9-left-Appendix-C
The 5th, 7-8th paragraphs of this recent news on hybrid computer says
"There is still a way to go before quantum computers can achieve what the researchers are aiming for. This field of research is still young (= quantum computers are still impractical )"
"..The method is called Reference-State Error Mitigation (REM) and works by correcting for the errors that occur due to noise by utilizing the calculations from both a quantum computer and a conventional (= classical ) computer."
"The difference between the two computers' solutions for the reference problem can then be used to correct the solution for the original, more complex, problem when it is run on the quantum processor (= by using the difference between the correct classical computer's result and the erroneous quantum computer's result to correct errors of other quantum computer's result )."
"the researchers have succeeded in calculating the intrinsic energy of small example molecules such as hydrogen and lithium hydride. Equivalent calculations can be carried out more quickly on a conventional (classical) computer (= classical computer could more quickly calculate these molecular energies than the useless quantum computer )"
↑ This original paper ↓
p.3-left-3rd paragraph says "Eexact is the exact solution for the reference state, evaluated on a classical
computer.
EVQE (= hybrid VQE ) refers to the energy evaluated from
measurements on a quantum computer"
↑ ΔEREM was the difference between erroneous quantum computer's result in VQE and the exact errorless classical computer's result.
p.5-Table 2 used only 2 ~ 6 qubits, which is Not a computer and can Not calculate any meaningful energy values.
As a result, also in this research, a conventional classical computer performed almost all calculations of molecular energy and error-correction, and the quantum computer with a very small number of qubits (= 2~6 qubits ) did nothing but generate errors.
Google and other researchers tried to use another (deceptive) hybrid quantum-classical method called quantum Monte-Carlo (= QMC ).
Also in this quantum Monte-Carlo hybrid method, they used only tiny numbers of qubits (= up to 16 qubits, this 2nd, 4th--paragraphs ) for allegedly calculating molecular energies of H4 (= 8 qubits ), N2 (= 12 qubits ), diamond (= 16 qubits ).
↑ Just 16 qubits or 16 bitstring (= 0011010110111010 ) can Not calculate any meaningful molecular energies (= 16 qubits can express only 216 = 65536 numbers which can be easily calculated by ordinary classical computers )
Quantum computers (= with only tiny numbers of error-prone qubits ) were useless, doing almost nothing, and classical computers had to perform almost all molecular energy calculations.
In this hybrid QMC, classical computers have to choose and determine the key atomic or molecular wavefunctions (= the true ground-state atomic wavefunction and a variable atomic wavefunction gradually approaching the true wavefunction ) and energy parameters.
Quantum computers just vaguely estimate the similarity (or overlap ) between these atomic wavefunctions chosen by classical computers without conducting any quantum computation of molecular energies.
Classical computers repeatedly change and update the variable atomic wavefunction's parameters, so that it gradually approaches the (chosen) true atomic ground state wavefunction.
↑ So what these quantum computers did was meaningless.
This 5~6th-paragraphs say
"QMC (= quantum Monte-Carlo ) refers to a class of stochastic (= random guess ) methods that sample from the wavefunction"
"..We focus on auxiliary-field QMC (AFQMC) which represents the target wavefunction as a linear combination of Slater determinant wavefunctions,.. referred to as ‘walker states.’ The walker states, |φl〉, can be efficiently manipulated using classical computers. "
"..AFQMC is driven by importance sampling from a trial state |ψT〉 , that approximates the true ground state. This is achieved by computing the overlaps 〈φl|ψT〉 and local energies 〈φl|H|ψT〉 between the trial wavefunction and the walker states, at each step of the algorithm. The accuracy of AFQMC depends on the quality of the trial state."
↑ This QMC has to know the true ground (trial) state in advance, and let (impractical) quantum computer's tiny number of qubits estimate the vague similarity or overlap between this already-known true energy and the changeable walker state that are manipulated by ordinary classical computer.
↑ This Google's research paper ↓
p.1-right-1st-paragraph says "s. We do not attempt to represent the ground-state wavefunction using our quantum processor (= that couldn't calculate the true ground state energy ), choosing instead to use it to guide a quantum Monte Carlo (QMC) calculation performed on a classical coprocessor"
p.1-right-last-paragraph, p.2-Fig.1-a show the initial state (= ψ or φ ) gradually changed into the final true energy state of ψ
p.2-Fig.1-c,d show the classical computer manipulated, changed the initial wavefunction state (= φ ), and chose the final true energy state of ψ.
↑ Quantum computer's part with only 16 qubits just estimated the overlap between these two artificially-chosen trial wavefunctions of ψ and φ (= No quantum computer calculation of molecular energy ).
p.3-Fig.2-a shows only 8 qubits for H4 molecular energy calculation where quantum computer's qubit operation includes "offline orbital rotation" meaning classical computer's post-processing (= a quantum computer alone was useless, the classical computer had to help calculating it ).
p.4-right-last says "Although we have yet to achieve practical quantum advantage over available classical algorithms (= No quantum computer's advantage )"
Even the latest research in 2024 on the hybrid quantum Monte Carlo used only 5 impractical qubits ( this paper ↓ ).
p.7-left-3rd-paragraph says "We applied the pseudo-Hadamard test technique to the HTN+QMC (= classical tensor network + quantum Monte Carlo ) calculations on a real device ibmq_kolkata for the hydrogen plane model with ID 3 and MABI. The best trial wave function was selected from 100 seeds of HTN+VQE (= which heavily relies on classical computer ) runs under the constraint, where at most five qubits (= just 5 impractical qubits !) including an ancilla qubit, are used in the overlap calculation"
p.9-right-Methods say "Here, a trial wave function is generated by a quantum circuit with variational parameters θ, which is repeatedly updated using the classical computer until a termination condition is satisfied."
↑ Even this latest hybrid quantum-classical Monte-Carlo method used only 5 impractical qubits (= just 5 bitstring, 00110 ), which can Not calculate any meaningful molecular energy calculation.
So they relied on practical classical computer for finding and calculating true molecular energy by updating parameters.
Quantum computer with a tiny number of qubits (= just 5 qubits ) is unable to calculate any molecular energy, contrary to hypes.
This abstract lower mentions "numerically test (= classical simulate ) the method using 12 ~ 16 qubits."
↑ It is impossible to simulate or calculate complicated molecular energy by only less than 20 qubits or 20 bitstring.
So "quantum computers have the potential to calculate molecular energies quickly or discover drugs" is just an overhyped fake news.
They have to rely on practical classical computers (= errorless ) in almost all important molecular energy calculations after all.
(Fig.2) Quantum computer Grover's search algorithm is Not "searching", because "answer" or location they want to search for must be already known beforehand and earmarked.
Grover's search algorithm is often misleadingly said to be potentially one of examples of quantum computer's advantage or speed-up in the task of finding the "marked target (← this is trick. The "marked" means they need to already know the target answer )" among multiple objects faster than classical computer.
In fact, this Grover's search algorithm has nothing to do with quantum computer advantage or speed-up, because Grover algorithm is Not a method of searching for unknown answers, but just a method of marking and picking up the already-known answer (= "10" bitstring in the upper case ) that they want.
This dubious Grover's search algorithm is unable to "search" for an object whose location or value is unknown, so meaningless and useless ( this p.1 ) except for quantum computer physicists' political tool.
For example, think about the case when there are multiple closed boxes and one of those boxes is supposed to include the target item-A that we want to find.
We have to open all boxes one by one to find the target item-A, which may take much time, and the quantum Grover's search algorithm is said to find this item-A faster using (fantasy) quantum mechanical parallel worlds or superposition, though this is Not true.
For the Grover's search algorithm to find the target item-A, first, we have to mark the box including the target item-A with negative sign (= this operation is called "oracle", this figure.4 ), which means we must already know which box or location (= "10" bitstring in the upper figure ) contains the target item-A. ← So Grover's search algorithm is Not searching for unknown target in unknown location but just a meaningless concept just marking the (already-known) target in already-known location.
In the upper figure, there are two quantum bits or two qubits-1 and 2, and each qubit can take 0 or 1 bit state.
Quantum computer theory unrealistically claims that each qubit can take 0 and 1 state using fantansy quantum superposition or parallel worlds simultaneously just by applying (classical) light wave pulse on them, which operation is called Hadamard gate (= H, this middle ).
↑ So two qubits are said to be able to take four different states "00 (= qubit-1 is 0 and qubit-2 is 0 )", "01 (= qubit-1 is 0 and qubit-2 is 1 )", "10", "11" at the same time using fantasy parallel worlds and superposition.
Of course, these quantum superposition or parallel worlds are baseless and unobservable, because quantum mechanics claims when we try to look at these parallel worlds, they would suddenly collapse into only one state that is observed.
In Grover's search algorithm, when physicists want to "search" for "10 (= qubit-1 is 1 and qubit-2 is 0 state )" out of these four different superposition or parallel-world states, first, they have to (ear)mark only this "10" state with negative sign (= this artificial marking operation is called "oracle", this step1:mirroring Frodo trying to find "11" bitstring as final answer ).
This 2nd paragraph says
"The idea behind Grover’s algorithm is to first use an oracle to mark the correct answer by applying a negative to the correct answer (= which means "correct answer" must be already known )... It essentially checks the input to see if it is the “correct answer” (the item that the algorithm is searching for) and if it is, it changes the amplitude to negative."
↑ The fact that marking the target state is possible means physicists must already find and know the final answer of "10" state that can be manipulated by "marking (= oracle)", so Grover's algorithm is a meaningless junk science that cannot search for unknown targets, because unknown targets or answers cannot be marked ( this p.9, this middle-step-2, this Grover's algorithm and amplitude amplification ).
After artificially marking the already-known answer or target (= "10" bitstring is the final answer or target in the upper case ), the next operation tries to amplify only the probability of this (ear)marked "10" state, and eliminate all other states (= other unmarked 00, 01, 11 states are eliminated by artificial manipulation ), hence, eventually, they claim physicists find only "10" state out of four superposition states of two qubits.
↑ As you notice, this Grover's search algorithm is doing a meaningless thing just finding the already-known answer or target state that can be artificially marked, which can Not prove any substantial quantum computer's advantage or speed-up.
This p.1-left-2nd-paragraph says
"to our best knowledge,
those are Not a practical one in the above sense; that
is, there has been No proposal to implement the “practical Grover algorithm".
↑ If the current dubious quantum supremacy and advantage were true, those quantum computers would have already replaced our ordinary (classical) computers or laptops. But the quantum computers are still completely useless, far from practical computers.
This means all the alleged quantum computer's supremacy and advantage are just illusion or media-hype.
2023/3/27 updated. Feel free to link to this site.
