Top (quantum mechanics is unrealistic ← 6/30/2024 )

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.*

- Quantum computer is useless for calculating molecular energy
- Hybrid method relies on classical computer, Not (useless) quantum computer
- IBM used only 6 impractical qubits that cannot calculate molecules.
- Google's just 16 impractical qubits showed No quantum advantage

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 ( which quantum mechanical methods cannot predict any values ).

Today's quantum computers, which have only small numbers of qubits, are too error-prone to calculate the (fake) molecular energies by this quantum mechanical variational method choosing artificial parameters and trial wavefunctions.

So "quantum computer for chemistry or molecular energy calculation" is **untrue** and just an overhyped fake news.

In order to use quantum variational method for calculating (fake) molecular energies, physicists have to use the method called (hybrid) variational quantum eigensolver (= VQE ) that relies 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 actually 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**.

But the overhyped news often tries to **wrongly** treat this (classical computer's) variational quantum eigensolver as "quantum computer's method for molecular energy calculation". ← nonsense

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 ).

This recent research paper on this hybrid computer (= actually a classical computer ) misleadingly treated as quantum computing for quantum chemistry ↓

p.6-Fig.1 used a **classical** computer for almost **all** calculations such as optimizing parameters or complicated energy calculation, and quantum computer just did vague "energy **estimation** (= **No** actual quantum computation )"

p.6-Table 1-qubit numbers used in this research were just **6 ~ 20** (= one qubit can take only 1 or 0, so just 6 ~ 20 bitstring, which is **Not** a computer ), which quantum computers with extremely small numbers of qubits alone cannot calculate any molecular energy.

Another recent research on hybrid quantum variational eigensolver used **only two** (photon) qubits = 00, this p.3-Figure 1, p.3-right-last-paragraph saying "one two-qubit gate", p.4-Figure 2a using only two qubits 00, which fake quantum computer can**not** calculate anything without the help of practical classical computer.

It is **impossible** for today's impractical quantum computer with 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 artificial 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 in advance 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.

This Hamiltonian Mapping section-3rd-paragraph says "The h terms are coefficients (= of fake simpler Hamiltonian energy for qubits ) known as the one- and two-electron integrals and can be calculated relatively efficiently in terms of a small set of orbital basis states on a **classical** computer. "

Another recent paper used the (fake) Hamiltonian for H2 molecular energy expressed by only 4 impractical qubits.

↑ This p.4-C used fake simpler Hamiltonian energy equation for (only) 4 qubits, and their coefficients c must be calculated by classical computer's open source called Qiskit's PySCF (= this-p.6-right )

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 using the original complicated molecular energy calculation equations 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**."

In the (deceptive) hybrid computer, the impractical quantum computer with a tiny number of qubits is said to only vaguely "evaluate or estimate energy" which just changes or measures their qubits a little based on parameters chosen by **classical** computer (= so **classical** computer instead of useless quantum computer calculates energy or controls qubits ) for the artificially-created simplified pseudo-Hamiltonian energy equation.

The 1st, 4th, 6-7th paragraphs of 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 **parameters** to (ideally) decrease the energy expectation of the next trial state"

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 )"

*(Fig.H) IBM's Hybrid quantum-classical computer for molecular energy calculation is just a classical computer with a fake quantum computer with only 6 error-prone useless qubits.*

IBM research on calculating energies of small molecules H2, LiH and BeH2 used only **2** ~ 6 impractical qubits (= each qubit can take only 0 or 1 values, so just 6 qubits can**not** calculate any molecular energies ) 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 (= false, today's useless quantum computers can simulate nothing ). The technique, which used **six** qubits of a seven-qubit system" ← Just **6** qubits can**not** calculate any values.

"While this model of BeH2 can be simulated on a classical computer (= quantum computer was **un**necessary )"

↑ Each qubit can take only 0 or 1, so 6 qubits or 6 bitstring can express only 2^{6} = only 1 ~ 64 numbers which number is too small to calculate complicated molecular energy.

It means the ordinary **classical** computer did almost all the complicated molecular energy calculation, contrary to overhyped news.

↑ 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.4-left-2nd-paragraph says "we search for the ground state energy of their
molecular Hamiltonians, using 2,4, and **6** qubits respectively" ← only **2 ~ 6** qubits cannot calculate anything.

p.9-last says "The energies measured in this way are then fed to a **classical** optimizer," ← A **classical** computer (with billions of bits) had to calculate almost all complicated molecular energies after all. So this research had **nothing** to do with quantum computers.

p.20-Fig.S9-a used only **4** qubits.

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 2^{6} = 1 ~ 64 numbers (= one qubit takes 0 or 1 values ), which is too small number to calculate any molecular energies, and the ordinary classical computer can easily express 1 ~ 64 different numbers, so the quantum computer was **unnecessary** for molecular energy calculation.

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** (~ 3 )impractical qubits or 2 bitstring (= 00, 01, 11 ) as a quantum computer. ← just 2 bits can Not calculate anything.

↑ this research paper ↓

p.3-Fig.1 used **only 2** qubits.

p.8-left-1st-paragraph says "We can use this symmetry to
scalably **reduce** the Hamiltonian of interest to the
following **effective** (= fake ) Hamiltonian which acts only on
**two qubits**" ← They artificially changed the original molecular energy Hamiltonian into the fake effective Hamiltonian (A6) usable for only 2 qubits or 2 bitstring (= 01 ), which is **Not** a quantum computer at all.

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 on Swedish research ↓

p.3-left-3rd paragraph says "E_{exact} is the **exact** solution for the reference state, evaluated on a **classical**
computer.

E_{VQE} (= hybrid VQE ) refers to the energy evaluated from
measurements on a quantum computer"

↑ ΔE_{REM} 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.

One of the new slightly-modified hybrid variational quantum eigensolver (= VQE ) methods is QSCI (= Quantum Selected Configuration Interaction ).

This **hybrid** QSCI method using **only 8** impractical qubits (= still Not a computer ) as a (fake) quantum computer ( this Figure 2 ) relied on the ordinary **classical** computer for the actual molecular energy calculation ( this p.5-Fig.1-classical computer, p.12-right-IV used **only 8** qubits ).

So the (error-prone) quantum computer for molecular energy calculation or drug discovery is just a baseless overhype.

This QSCI research p.1-abstract-last just says

"The proposed algorithms are **potentially** (= just speculation, still useless ) feasible to tackle some challenging
molecules by exploiting quantum devices with several tens of qubits, **assisted** by high-performance
**classical** computing resources for diagonalization"

↑ In all cases, ordinary **classical** computers were used for molecular energy calculations as (deceptive) hybrid computers where quantum computers are completely useless.

The 2nd, 4th, 6th, 8-9th last paragraphs of this Google's alleged quantum computer calculating molecular energy says

"the algorithm uses up to (only) **16** qubits on Sycamore, Google's 53-qubit computer, to calculate ground state energy, the lowest energy state of a molecule. These are the **largest** quantum chemistry calculations that have ever been done on a real quantum device,"

↑ Just 16 qubits or 16 bitstring (= each qubit can take only 0 or 1 state ) can **Not** calculate any molecular energy without the help of classical computer.

"The algorithm uses a quantum Monte Carlo (= just meaningless random number generation ), a system of methods for calculating probabilities when there are a large number of **random**, unknown variables at play, like in a game of roulette. Here, the researchers used their (hybrid) algorithm to determine the ground state energy of three molecules: heliocide (H4), using **eight** qubits for the calculation; molecular nitrogen (N2), using **12** qubits; and solid diamond, using **16** qubits"

↑ Just 8 ~ 16 qubits alone can **Not** calculate any actual molecular energies.

"Qubits, however, are fragile and error-prone: the more qubits used, the **less accurate** the final answer. Lee's algorithm harnesses the combined power of **classical** and quantum computers to solve chemistry equations more efficiently while minimizing the quantum computer's mistakes."

↑ **Classical** computer was **necessary** to calculate molecular energy or correct errors of the error-prone quantum computer after all.

"A **classical** computer can handle **most** of Lee's quantum Monte Carlo simulation" ← classical computer had to conduct almost **all** calculations.

"This gives us hope that quantum technologies that are being developed **will** (= uncertain future, still **unrealized** ) be practically useful."

↑ This Google research paper ↓

p.1-right-1st-paragraph says "We do **not** attempt to represent the
ground-state wavefunction using our quantum processor, choosing
instead to use it to guide a quantum Monte Carlo (QMC) calculation
performed on a **classical** coprocessor" ← Quantum computer alone can**not** calculate molecular energy.

p.2-Fig.1 used a **classical** computer to calculate molecular energy by choosing parameters, and the (useless) quantum computer with only 16 qubits just vaguely estimated (= did Not calculate ) something.

p.4-right-last says "Although we have **yet** to achieve
practical quantum advantage over available classical algorithms" ← **No** quantum computer 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 computer's simulation ) 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 (= optimization, this p.2-Figure 1 ) 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.