Top (quantum mechanics is unrealistic ← 10/11/2024 )
Grover algorithm is useless, not faster at all.
(Fig.1) No quantum advantage in (deceptive) hybrid computer which is just a classical computer.
Contrary to an incredibly large amount of overhyped news, all the present quantum computers are unable to give right answers or 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 )."
The so-called quantum supremacy or advantage is fake, because today's error-prone quantum computers can give just random meaningless numbers, which is completely useless with No advantage over ordinary classical computers ( this p.1-left-last-paragraph ).
Today's quantum computers are too error-prone and having too small numbers of bits or qubits (= only 2 ~ 20 qubits, each qubit can take only 0 or 1 state ) to calculate any meaningful values or energies, contrary to hypes.
A really useful quantum computer capable of calculating molecular energies is said to need more than millions of qubits, which is impossible to achieve forever ( this 4th-paragraph ).
So the current error-prone quantum computers have to rely on practical classical computers (= with billions of errorless bits ) for seemingly 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."
(Fig.2) Hybrid variational quantum eigensolver (= VQE ) depends on parameters or energies calculated by a classical computer, and an error-prone useless quantum computer can do nothing.
Today's error-prone hopeless quantum computers called noisy intermediate scale quantum (NISQ) computing with only small number of qubits cannot calculate any meaningful values such as molecular energies.
So physicist have to rely on ordinary practical classical computers as a (deceptive) hybrid quantum-classical computer which is actually a classical computer (= Not a quantum computer ).
Hybrid computing algorithms for calculating molecular energies are known as quantum variational eigensolver (= VQE ) and quantum approximate optimization algorithm (= QAOA ).
In this hybrid computing methods, an ordinary classical computer must conduct almost all complicated calculations and find the solutions by updating parameters called ansatz ( this p.7-Figure.1, this p.16 ).
The useless quantum computer with only small numbers of qubits (= just 2 ~ 20 qubits, one qubit can take only 0 or 1 state, which is still Not a computer, this p.2-Fig.1, this p.3-right-A. ) just manipulated and measured qubits based on parameters chosen by the classical computer (= so classical computers actually calculate everything ).
↑ A practical quantum computer for molecular energy calculation is said to need more than millions of qubits, which is impossible to realize forever.
↑ It is impossible for today's quantum computer with a small number of error-prone qubits to calculate any molecular energies.
This p.2-left-8th-sentences~ say
"Practically,
however, as the numbers of qubits and gates of a noisy quantum
computer increase, the fidelity starts to drop rapidly and the VQE
algorithm does Not achieve the desired accuracy"
They have to prepare the impractical simpler version of energy equation called Hamiltonian (= Not actual complicated molecular Hamiltonian energy equation ) for such an useless quantum computer with a few qubits through artificial methods called Jordan-Wigner transformation ( this Hamiltonian mapping, this p.2-right, this p.1-(1) ).
This p.4-left prepared just 4 qubit-Hamiltonian energy (= just 4 qubis or 4 bitstring = 0101 cannot calculate any actual complicated molecular Hamiltonian energies ) for a impractical quantum computer.
Even small numbers of qubits of the hybrid computer are unable to give right answers due to errors, so researchers often use "quantum simulators" that are just classical computers simulating quantum qubits (= which means "classical computers" ) also in quantum computer's part ( this p.1-right ).
This p.6-Fig.6 (= hybrid VQE method ) shows only IBM noiseless classical computer's simulator with no errors could give exact energy value, while quantum hardware (= impractical quantum computer ) with errors or noisy simulator gave wrong energy.
↑ Even today's hybrid quantum-classical computer cannot give right answers due to the small numbers of error-prone qubits.
It is impossible to achieve quantum advantage or supremacy also in these hybrid computers.
This p.2-left-1st-paragraph says
"We conclude that substantial quantum advantage in VQE based quantum chemistry is unlikely, unless gate-errors are
significantly reduced, or error-corrected hardware is realized" ← this quantum error correction is hopeless, impossible forever.
This abstract says
"However, it is not yet clear whether such algorithms (= hybrid VQE ), even in the absence of device error, could actually achieve quantum advantage"
Quantum advantage needing memories exceeding a classical computer's capacity can Not be achieved by the hybrid computer heavily relying on the classical computer for adjusting parameters and finding right solutions.
Whether the hybrid computer can calculate molecular energies faster or not depends on parameters called ansatz (= chosen initial states ) chosen or optimized by the classical computer ( this p.3-left-ansatz, this p.10-left-2nd-paragraph, )
This What are the challenges.. in VQAs ? says
"One of the main challenges is the noise and errors that are prevalent in today’s quantum computers. This noise can cause the quantum part of the algorithm to produce incorrect results"
"The choice of ansatz (= input parameters ) can have a significant impact on the performance of the algorithm, and finding the best ansatz for a given problem is a topic of ongoing research."
This recent paper ↓
p.2-left-1st-paragraph says "using an ansatz defined by a set of parameters that constitutes a trial measurement which is fed into a classical optimiser that iteratively updates the ansatz parameters"
p.5-right-last-paragraph says "Choosing the most optimal ansatz (= artificially-chosen parameters ) for a VQE simulation is of great importance and can considerably change the final result"
↑ So hybrid computer's calculation of molecular energies is affected by what parameters (= or ansatz ) are chosen ( by classical computer or optimizer ), which is irrelevant to quantum computer's calculation or 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 cannot 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 cannot calculate any values.
"While this model of BeH2 can be simulated on a classical computer (= quantum computer was unnecessary )"
↑ Each qubit can take only 0 or 1, so 6 qubits or 6 bitstring can express only 26 = 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 26 = 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 ).
(Fig.G) Hybrid computer is a classical computer, and its quantum computer with only 2 ~ 6 error-prone qubits (= only 2 ~ 6 bitstring ) is still Not a computer.
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 "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.
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.
(Fig.M) Quantum computer is useless, still Not a computer.
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 cannot 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 fantasy 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.
10/24/2024 updated. Feel free to link to this site.
