D-Wave annealing machines are useless, Not real quantum computers. Their overhyped quantum speed-up or supremacy is fake.

Quantum annealing machines are fake quantum computers slower than classical computers.

All the ( overhyped dubious ) quantum supremacy claims in quantum annealing or D-Wave are fake.  3/12/2025

(Fig.S)  Quantum supremacy of quantum annealing or D-Wave was fake, far slower, more error-prone than good classical computer's methods.

D-Wave quantum supremacy claim in 2025 was a lie, disproved.

Many overhyped claims that these annealing machines might be faster than ordinary classical computers are based on unfair comparison with bad classical methods (= good classical computer's methods easily outperformed quantum annealing or D-Wave ).

The 1st and 8th paragraphs of this recent article ( or this,  3/12/2025 ) say
"D-Wave's claim that its quantum computers can solve problems that would take hundreds of years on classical machines have been undermined by two separate research groups showing that even an ordinary (= classical ) laptop can perform similar calculations"

"his (classical computer's) tensor approach could easily scale further"

The 11th and 14th paragraphs of this article ( or this  3/12/2025 ) also say
"D-Wave’s quantum supremacy claim is also being disputed by physicists particularly those who say classical computers still have their place."
"Look, this one problem at this one time didn't beat classical computers. Try again ( this-last-paragraph )"

↑ This recent D-Wave quantum annealing supremacy claim was also overhyped, fake, as shown in D-Wave's recent bad business loss (= No practical use, though one year has already been passed since this fake supremacy paper was published in arxiv ).

Quantum supremacy turned out to be illusion also in quantum annealing or D-Wave that is far more error-prone than a classical computer.

This (or this )-1st and 3rd-last paragraphs (3/12/2025) say
"There's No clear quantum advantage yet in tests of real-world problems"
"our classical approach demonstrably outperforms other reported methods... we are also able to reach errors noticeably lower than the quantum annealing approach employed by the D-Wave Advantage2 system."

This-p.1-right-last-paragraph ~ p.2 (3/10/2025) says
"In the case of cylindrical and diamond lattices our ( classical computer's ) simulations reach accuracies well beyond those of the ( error-prone ) quantum annealer for large system sizes"

↑ Quantum annealing machines or D-Wave are too useless and error-prone, so D-Wave has to rely on ordinary classical computers as (deceptive) hybrid machines that also cannot match the current good classical computers' methods.

Even D-Wave admits quantum annealing is still useless (forever).

Actually, even this latest (fake supremacy) D-Wave paper's p.1-abstract-last just vaguely says
"Thus quantum annealers can answer questions of practical importance that may (= this uncertain phrase means D-Wave is still useless ) remain out of reach for classical computation (← D-Wave changed the expression from this paper's arxiv's abstract-last that didn't use 'may' )."

This-middle-The Controversy; skepticism says
"even D-Wave admits that solving practical business problems (e.g. in logistics, finance, etc.) on an annealer remains work for the future"
"These limitations lead some researchers to argue that quantum annealers face scaling challenges for truly complex, real-world instances"

Quantum annealing or D-Wave has No commercial practical use, contrary to hypes.

This-9th and last paragraphs (3/13/2025) say
"additional research is necessary to confirm whether practical application cases can be resolved in various fields"
"doubts remain as to whether quantum computers can solve problems that classical computers cannot"

This-lower-Limitations and future work (for this fake quantum supremacy's first application,  3/22/2025 ) says
"The system is still a prototype, and hurdles remain before a quantum blockchain could be deployed commercially."  ← Even D-Wave admits there is still No practical use of this (dubious) quantum supremacy.

This-5th-last ~ 4th-last paragraphs (3/31/2025) say
"there are No obvious commercial applications (of D-Wave),... there are large number of powerful classical optimization algorithms that can solve these problems directly,"

"notes that media coverage suggesting the results could have practical applications is misleading.... for commercially relevant problems I think this is still far away."

↑ Quantun annealing or D-Wave is still useless (forever despite very long time fruitless researches and hypes ) with No evidence of quantum supremacy nor practical use.

D-Wave's fake quantum supremacy is due to deliberately avoiding comparison with good classical computer's methods (= classical Selby, Gurobi, good tensor network.. outperformed D-Wave )

The 1st and 2nd-last paragraphs of this (or this, 3/12/2025 ) say
"D-Wave’s fresh claim that it has achieved “quantum advantage” has sparked criticism of the company—and of the scientific process itself"
"Claims of beating 'all classical methods' are very hard to justify scientifically"

↑ Actually, all these (dubious, fake) quantum supremacy claims of quantum annealing or D-Wave is due to unfair comparisons with deliberately-chosen bad classical computer's methods.

This-p.44-X. monte carlo dynamics (or this-p.47-X ) in this latest Science on (fake) D-Wave supremacy in 2025 mentions D-Wave compared the quantum annealing with (only bad) classical computer methods such as simulated quantum annealing (= SQA ) and Monte Carlo (= MC ), which classical computer methods were allegedly faster than classical tensor-network.

But actually there are various better, faster classical computer's methods such as Selby, Gurobi, even good classical tensor network ) that could outperform the quantum annealing or D-Wave ( this-15~21th-paragraphs,   this-p.6-left-C,  this-p.1-abstract ).

The fact that D-Wave's (fake) quantum computer or quantum annealing (= QA ) is more useless, error-prone, slower than classical computers is why D-Wave applied only (deceptive) hybrid computers called CQM (= just classical computers ) to practical purpose, which also cannot match today's good classical computer's methods ( this-p.28-1st-paragraph,  this-p.10-2nd-last-paragraph, p.12-conclusion ).

(Fig.C)  D-Wave gave up using their error-prone useless quantum ( annealing ) computers, and instead, started to use classical computers as 'hybrid'.

Unlike D-Wave bold claim, quantum computers or annealers can never be useful.

The recent D-Wave claim ( after the useless Willow thing ) that their ( fake ) quantum computers (= annealers ) might benefit business operation is completely untrue.

D-Wave quantum annealing machines are useless, too error-prone to be practical (= often giving wrong local energy minima ), so No quantum advantage ( this p.1-right-last-paragraph ), deadend ( this-2nd-paragraph ).

↑ If D-Wave annealing machines for the alleged faster scheduling were really useful, many ordinary companies should have already used them, which did Not happen ( this-lower should you invest.. in D-Wave ? ) despite the decades of research, except for research or hype purpose collecting investment money by controlling the media.

This p.10-2nd-last-paragraph (in 2024) says
"we can conclude that quantum annealers are too small and too prone to errors, and hence, for more accurate solutions to larger problems, we opt for hybrid quantum-classical solvers (= needing more practical classical computers )"

NTT, Mastercard use 'hybrid classical' computers, Not quantum computers that are useless.

For example, NTT-Docomo uses D-Wave's hybrid' computer (= called CQM solver ) allegedly combining the ordinary classical computer and D-Wave's error-prone machine ( this p.1-left-last ). But this hybrid computer is just a classical computer, and No quantum computer's advantage ( this p.1-abstract-last, p.7-2nd-last-paragraph,  this 7~9th-paragraphs ).

This p.27-7. says
"The purely quantum D-Wave Advantage6.1 QPU solver (= quantum annealer ) was only able to obtain optimal solutions for the five-node case due to scale limitations (= useless )"

Mastercard is also one of D-Wave's small number of customers, and using this misleading 'hybrid' machines (= just classical computers, this 2nd-paragraph ) with No quantum computer's advantage.

This-10th-paragraph~ says
"A purely quantum system is Not desirable because quantum computers are Not better than classical computers for every task,"

Even these (misleading) hybrid computers (= which are just classical computers ) could Not outperform the conventional classical computer's methods (= which is just a competition between different classical computer's methods, irrelevant to quantum computer's advantage ).

D-Wave started to rely on classical computers as (deceptive) 'hybrid', which cannot outperform conventional classical computers after all.

This p.12-conclusions-1st-paragraph (in 2024 ) says
"While we have Not yet demonstrated a quantum advantage ( not only in the error-prone quantum annealing but also in hybrid computers )"

This recent research's p.1-abstract-last (10/2/2024) says
"While D-Wave (= hybrid machines ) can solve such problems, its performance has Not yet matched that of its classical counterparts"

This research's p.28-1st-paragraph (12/17/2024) says
"While the CQM hybrid solver (= D-Wave hybrid machine used in NTT ) does Not outperform classical solvers in general,"

Actually, NTT can use only classical computers to do the same operation, when the expensive D-Wave quantum annealers are unavailable (= so the expensive bulky quantum annealing machines are unnecessary from the beginning,  this p.4-lower ).

D-Wave quantum (annealing) computer is far worse than a classical computer, so D-Wave hides whether their hybrid computer really uses the quantum computer, or just uses a classical computer.

This p.1-abstract and p.15-last (12/10/2024) say
"the Hybrid (= classical + quantum ) solver and SA (= classical simulated annealing method ) algorithm consistently achieve the global optimum, outperforming the QPU (= D-Wave quantum annealing )"  ← D-Wave quantum annealing machine is worse than a classical computer.

"For larger instances where global optima are unknown, we observe that the SBM (= using classical computer, this 2nd-paragraph,  this 2nd-paragraph ).. deliver competitive solution quality, while the Hybrid solver.. performed noticeably worse"  ← D-Wave hybrid machine is also worse.

"it is frustrating that the Hybrid solver operates as a black-box cloud solution, leaving us without insight into its internal workings"  ← D-Wave still hides whether their hybrid machine really uses their (useless) quantum annealing or uses only a practical classical computer.

Actually, D-Wave itself admits they are overhyping their performance ( this-last-forward-looking statement ).

The 4th paragraph of this overhyped news (3/31/2025) says Ford showed some speed-up of the hybrid quantum annealing (= "hybrid" means just "classical computer") in car industry.

But other group's latest research (3/31/2025) says No quantum annealing advantage.

This paper's abstract and p.1-right-2nd-paragraph (3/31/2025) says D-Wave's hybrid quantum annealer called CQM often gave wrong (infeasible) results that must be corrected by other classical computers' heuristic methods (= p.4-Fig.3 ).

This p.7-right-2nd-paragraph says
"we benchmarked against Google’s OR-Tools optimization suite, a robust classical solver, on the same six problems... Still, the performance between the two (= Google's classical method, and D-Wave hybrid HQTS, p.4-right ) is similar on average (= No quantum annealing advantage )."

Overhyped fake quantum speed-up of quantum annealing or D-Wave is due to comparison with bad classical methods.  Good classical computer's methods outperform quantum annealing, so No quantum advantage.

(Fig.1')  Good classical computer's methods (= Selby ) outperformed quantum annealing or D-Wave.

D-Wave or quantum annealing machines were inferior to the faster classical computer's methods such as Selby.

It is known that these quantum annealing machines are slower and more error-prone than ordinary classical computers using best classical calculation methods such as (classical) Selby's algorithm ( this 6th-paragraph,  this 2nd-paragraph,  this p.6-left-c ).

This 3rd-pagagraph says
"on every instance tested so far, Selby's (classical) annealing algorithm outperforms the D-wave machine,... they strategically included an unfair benchmark so that the news media could take the 100M speedup figure to fuel the hype machine"

This 15th, 19th paragraphs say
"So besides (classical) simulated annealing, there are two more classical algorithms that are actors in this story. One of them is quantum Monte Carlo, which is actually a classical optimization method (= simulated annealing and Monte Carlo are bad slower classical computer's methods )"

"What the Google paper finds is that Selby's algorithm, which runs on a classical computer, totally outperforms the D-Wave machine on all the instances they tested"

↑ The faster classical computer's method called Selby outperformed D-Wave annealing machines.

This 2nd-last-paragraph says
"The VW research team also notes that their primary goal is.. not to prove supremacy over every existing classical clustering algorithm."  ← Because quantum annealing is slower than the good classical computer's method.

↑ So all the overhyped ( fake ) quantum advantage claims in quantum annealing (= QA ) optimization problems is due to unfair comparison with slower bad classical methods such as simulated annealing (= SA ) and Monte Carlo (= MC ), as shown in this p.1-right-1st-paragraph,  this p.5-left benchmark against simulated annealing,  this p.47-X (= all of which did Not compare quantum annealing with faster classical methods such as Selby ).

Classical computer's best faster algorithm such as Selby can easily outperformed quantum annealing machines (= classical Selby gave more accurate results than the error-prone D-Wave (= DW ), this p.16-Table.2, p.15-lower ).

In some tasks, even against slow classical simulated annealing, quantum annealing could not show quantum advantage ( this p.1-abstract-lower ).

The fact that quantum annealing machines or D-Wave are still Not used for practical purpose shows No hope of quantum advantage.

As a result, contrary to many (unfounded) hypes, (fake) quantum computers or quantum annealing are slower and showing No quantum advantage over ordinary classical computers ( this p.1-last ).

Actually, despite extremely longtime research and hypes, still Nobody and No companies use these overhyped D-Wave annealing machines for practical optimization problems (= Only a tiny number of companies use D-Wave only for fruitless researches or spreading hypes to get investment money or research funds ).

This p.2-4th-paragraph (9/9/2024) says
"the current implementations of quantum annealing in optimisation are limited in size and Not yet upscaled to real-world situations"  ← Quantum annealers or D-Wave are still useless.

This 8th-paragraph (5/23/2023) says
"but to date, No quantum computer has outperformed a classical supercomputer in practical tasks"

Also in one of optimization problems called travelling salesman problem finding shortest route, quantum annealing machines showed No advantage over classical computers ( this p.1-abstract,  this abstract ).

This 5th-last-paragraph says
"In fact, it hasn't been proved yet that quantum annealing gives an advantage over classical optimization algorithms"

(Fig.2) Classical electric current difference induced by applied magnetic field generates D-Wave's flux qubit-0 and 1 states.

D-Wave annealing machines use the direction of classical electric current flowing through the superconducting circuit as their ( flux ) qubit state 0 or 1.  No quantum mechanics is used.

Electron's current tends to be quantized due to the (classical) electron's ( an integer times ) de Broglie wavelength in D-Wave's superconducting flux qubit or circuit that can be manipulated by external magnetic field ( this p.6-7 ).

↑ By adjusting applied magnetic field (= flux ) in qubits (= classical superconducting circuits ) and couplers connecting qubits, D-Wave can optimize the final lowest-energy stable solution.

Quantum tunneling is a realistic classical phenomena (= electric current over only very short distance ) irrelevant to unrealistic quantum mechanical negative kinetic energy

The best faster classical computer's methods easily outperform quantum annealing machines or D-Wave, so No quantum advantage.

(Fig.3)  One of bad time-consuming classical methods called path integral Monte-Carlo (= PIMC ) ↓

Quantum annealing outperformed only bad slow impractical methods with No quantum advantage.

The (fake) quantum advantage of quantum annealing or D-Wave is caused by comparison with the artificially-chosen bad slow classical computer's methods such as simulated annealing and Monte-Carlo.

One of those bad classical methods is path integral Monte Calro (= PIMC ) method or quantum Monte Carlo (= QMC, this Fig.1B ) using the unreal imaginary time, which means PIMC can Not represent the realistic classical calculation method at all.

In this unrealistic very time-consuming classical method called path integral Monte Carlo, they first divide the process of annealing into many fictitious imaginary time periods (= σ1, σ2, σ2 .. σm,  this p.2 ).

And then, they randomly chose an arbitrary qubit representing "spin direction" included in random imaginary times one by one, calculated the total energy (=H ) before and after the qubit (or spin ) flip ( 0 ↔ 1,  this p.2 ), and decided whether this chosen qubit is flipped or not based on the calculated imaginary-time probabilities (= function of total energy,  this p.30-40 ), until the system may reach the lowest energy state ( this p.20,  this p.8,  this p.9,  this p.9 ).

↑ This impractical Monte Carlo classical method takes extremely much time, because it must randomly calculate each qubit's energy or flipping probability one by one without knowing the real forces by which all qubits naturally decide whether they flip or not simultaneously to lower the total energy.

Whether quantum or classical, all things and particles in the nature are gradually evolving into the lowest energy state by interacting and exerting real forces on each other simultaneously, which real classical process in the nature is completely different from these impractical extremely time-consuming artificial classical methods such as path integral Monte Carlo and simulated annealing unfairly chosen for comparison with the quantum annealing.

Quantum annealers cannot factor large numbers, because they are often trapped in wrong solutions or local energy minima.

(Fig.4) Setting the right prime numbers (= 5 and 3 ) as the lowest-energy qubit state for factoring 15 = 5 × 3 using (impractical) quantum annealing.

Quantum annealing machines for optimization problems are said to be able to factor numbers.

They encode solutions of factorization into the lowest energy state (= expressed as binary qubit states ) in D-Wave annealing machines.

The problem is quantum annealing or D-Wave often give wrong answers stuck in one of local energy minima instead of the lowest energy state (= right answers,  this p.3 ).

Even in factoring the simplest 15 = 3 × 5, D-Wave annealing machines are known to often give wrong answers ( this p.55,  this p.7-Figure 1,  this p.34 ).

So it is impossible to use the error-prone quantum annealing or D-Wave for practical factoring or some calculations.  Only hypes remain.

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