Top page (quantum mechanics is false. ← 6/30/2024 )
Quantum supremacy is Not faster.
Quantum information, cryptography are useless
D-Wave is a fake useless quantum computer. ← 6/15/2024
(Fig.1) D-Wave annealing machines can Not solve even travelling salesman problem (= optimization ) faster than the ordinary classical computers
The current basic science has stopped progressing due to unrealistic quantum mechanics, so researchers, academia, corporations and the media came to exaggerate and hype (fictional) scientific achievements, pretending that the current dead-end science may be progressing for the purpose of getting taxpayers' money.
Typical examples of these hyped fictional scientific targets are the so-called (parallel-world) quantum computers and quantum information, which are useless forever, contrary to an incredible amount of the hyped news.
Quantum annealing (= adiabatic ) machines such as D-Wave and Harvard-MIT-quantum simulators for optimization problem (= finding the lowest energy encoded as the right solutions, this p.2-4 ) are Not real quantum computers.
There is No convincing evidence that these annealing machines or quantum simulators for optimization were actually faster than the ordinary classical computers.
D-Wave annealing machines or quantum simulators just set the right (optimal) solution as the lowest energy state (= global energy minimum, this p.4 ), and let the system gradually evolve into the lowest (= ground state ) energy ( this 3rd-paragraph, this p.2 ) with No meaningful calculations and No error-correction ( this p.16, this 10th-paragraph ).
This p.2 2nd-paragraph says
"While the question of whether QA (= quantum annealing ) can
provide a quantum speed-up over classical approaches is still subject of a scientific debate... "
"to the best of our knowledge, there is No industrial application where QA (= quantum annealing ) unquestionably outperforms classical heuristic algorithms."
So all annealing machines or quantum simulators are useless in any application for optimization of traffic, transportation, scheduling, exotic materials, traveling salesman problem (= finding the shortest paths ), and factorizing.
Quantum annealing machines such as D-Wave are often wrongly mentioned as being good at solving the travelling salesman problem = quickly finding the shortest route connecting all cities, which shortest routes or right solutions must be encoded as the lowest energy state of the system in advance.
But actually, the ordinary classical computers can solve the optimization problems such as traveling salesman much faster and more accurately than D-Wave annealing machines which are useless without the help of powerful classical computers as "(deceptive) hybrid, which no longer means quantum computer ( this p.1-left, this p.3 2nd-paragraph )".
This paper's 1st and last paragraphs say
"It is found the quantum annealer can only handle a problem size of 8 or less nodes (= just less than 8 traveled cities, completely useless ) and its performance is subpar compared to the classical solver both in terms of time and accuracy."
"..our experiments with D-Wave QPU did Not demonstrate any quantum advantage."
This 5th-last paragraph says
"It is still Not clear how to prove quantum advantage in this kind of quantum computation (= ex. traveling salesman problem ). In fact, it hasn't been proved yet that quantum annealing gives an advantage over classical optimization algorithms. One of the reasons is because error correction protocols have not been developed for these devices, so the advantage as the number of qubits increases is not clear."
The media-hype like "D-Wave annealing machines solved problems of simulating some exotic magnetism or materials (← vague phrase, actually Not real materials ) three million times faster than classical computers ?" is also hiding the inconvenient fact that unfair comparison with the artificially-chosen worst (fake) classical methods causes such an illusory quantum speed-up.
D-Wave quantum annealing machines (= Not real quantum computers ) try to compare their dubious quantum performance (= actually Not faster than the ordinary classical computers ) with the very slow useless classical algorithms called "simulated annealing (= SA )" and "path-integral quantum Monte Carlo (= QMC ) or simulated quantum annealing (= SQA)", and falsely claim D-Wave outperformed the conventional classical computers ( this 2~3th paragraphs, this 4~15 paragraphs ).
But there are much faster classical algorithms such as " Selby's algorithm" that outperformed the D-Wave annealing machines ( this 3rd-paragraph, this 6th-paragraph, this 3th-paragraph, this 2nd-paragraph ).
This or this 6th-last paragraph says
"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 p.6-left of this Google's original paper admits No quantum speed-up of the dubious D-Wave quantum annealing,
"Based on the results presented here, one cannot claim
a quantum speedup for D-Wave 2X, as this would require
that the quantum processor in question outperforms the
best known classical algorithm. This is not the case for
the weak-strong cluster networks. This is because a variety of heuristic classical algorithms can solve most instances of Chimera structured problems (= optimization problem fit for D-Wave ) much faster than
SA (= simulated annealing = slow classical ), QMC (= quantum Molte-Carlo = slow classical ), and the D-Wave 2X. For instance, the Hamzede Freitas-Selby algorithm (= faster classical method than D-Wave quantum machines ).."
↑ So they deliberataly chose one of very time-consuming bad classical calculation methods called "simulated annealing (= SA, this p.1 2nd-paragraph, this p.5-Fig.4 )", and falsely claimed their quantum annealers might have outperformed classical computers (= using very time-consuming simulated annealing method which must randomly choose, flip each qubit one by one and repeatedly calculate their energy many, many times to reach the lowest energy ) both in D-Wave ( this abstract ) and Harvard's quantum simulators consisting of unstable atoms ( this p.5-Benchmarking against simulated annealing ).
This 2-3 paragraphs say
"the Google research paper on 100M-fold speedup was reporting a quantum algorithm beating a specific classical algorithm (= very time-consuming simulated annealing and path-integral Monte-Carlo methods were unfairly chosen as "(fake) classical methods", this 8th-paragraph ), not claimed or believed to be the best, on highly tailored problem instances. It's not even fair to say "quantum algorithm" to describe what the D-Wave is doing at this point. It may be entirely classical, or classical down to the 8-qubit clusters.
Furthermore, on every instance tested so far, Selby's (classical) annealing algorithm outperforms the D-wave machine, RUNNING ON A LAPTOP. It almost seems like they strategically included an unfair benchmark so that the news media could take the 100M speedup figure to fuel the hype machine."
This 4~8th paragraphs say
"Contrary to D-Wave’s branding of their product, their computer is Not a quantum computer but a quantum annealer.."
"..The D-Wave machine is a quantum annealer running adiabatic quantum computing algorithms. This is great for optimizing solutions to problems by quickly searching over a space and finding a minimum (or “solution”). The latest announcement from Google states that the D-Wave machine is more than 108 times faster than simulated annealing running on a single core. However, (classical) Selby’s algorithm still performs better than the D-Wave quantum computer, so there’s a long way to go for D-Wave."
"..quantum annealing will never be able to run Shor’s algorithm, which breaks common forms of modern cryptography used to protect our bank information, logins, and all web communication."
↑ So "D-Wave annealing machines solved problems faster than classical computers" turned out to be a lie. They just deliberately and unfairly chose the extremely time-consuming methods (= simulated annealing or Monte-Calro, this p.6 ) only for classical computers. There are much faster and simpler classical algorithms (= ex. Selby, ) outperforming D-Wave for optimization problems ( this 6th paragraph, this 7th-paragraph, this p.32(or p.18)-3-4th-paragraphs ).
The latest D-Wave research paper published in journal Nature 2023 also falsely claims "advantage over classical systems" by deliberately comparing their D-Wave with the slowest classical methods such as simulated annealing (= SA ) and simulated quantum annealing (= SQA ) based on path-integral Monte-Carlo, instead of truly faster classical Selby's algorithm ( this p.1-right ). ← Because D-Wave quantum annealers are intrinsically Not faster than classical computers.
↑ Actually this latest research in Nature did Not show D-Wave machines were useful, as this 3rd, 9th paragraphs say
"there are two caveats: errors start to cause the hardware to deviate from ideal performance, and it's Not clear how well this performance edge translates to practical calculations... But again, we lack the theoretical understanding of whether it's possible to get these solutions in some other way that's faster or more efficient.
" ← still useless and No evidence of quantum speed-up despite very long-time researches ( this p.1-last ).
The 6th paragraph of this latest news clearly says
"Current quantum computers cannot outperform classical computers"
It's time for us to give up hopeless quantum computers.
(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 quantum bits or qubits called "flux qubits" which distinguish their 0 and 1 bit states by different electric currents flowing through the (classical) superconducting circuit consisting of capacitors, inductors, and Josephson juction, which current can be freely controlled by the applied external magnetic field ( this p.27-32 ).
Due to the electron's de Broglie wave property (= one circumference of the circuit is an integer times de Broglie wavelength ), the electric current or magnetic field generated in each flux qubit or superconducting circuit tends to be quantized like 0, 1, 2.. (← 0 and 1 quantized currents are chosen as qubit's binary states ), and some potential barrier is created between the qubit's two 0 and 1 states, which is called "double-well potential".
In D-Wave machines, the so-called quantum tunneling and ordinary thermal fluctuation are said to enable the qubit's state to change between 0 and 1 states by magically surpassing the higher potential barrier.
But the difference between these quantum tunnel and (classical) thermal fluctuation is very ambiguous ( this p.18-lower, this p.4-Fig.1, ← actually there is No boundary between classical and quantum, quantum tunnel can be considered to be one of classical thermal fluctuations through very thin barriers ), and even this mysterious quantum tunnel rate can be freely changed by classically manipulating the external magnetic field (= magnetic flux = Φ ) and the potential barrier's height ( this p.6, this p.2, this p.31 ).
This p.1-left says
"The (flux) qubits are initialized in potential with a
low barrier (i.e. large tunneling) between the two wells (= two different current qubit states 0 and 1 ) and no net
persistent current. Toward the end of the anneal, the potential
barrier is raised to reduce the tunneling between the wells, giving
qubits a net persistent current (= no tunnel between two qubit's states 0 ↔ 1 ). A measurement of the persistent
current direction is made to determine the final qubit state."
D-Wave annealing machine's qubits are often associated with the (fictitious) electron spins, which are Not actual spinning, hence. D-Wave's magnetic flux qubits have nothing to do with fictitious quantum mechanical materials such as (anti-)ferromagnet where electron spins are supposed to align and interact with each other by (fictitious) exchange energies lacking real (exchange) forces.
Because this D-Wave annealing machines use the freely-adjustable ordinary classical magnetic field, coils and coupling circuits to manipulate the interaction strength between two qubits ( this p.16 ).
And the quantum tunnel is used also in the ordinary classical computers.
So D-Wave machine has nothing to do with quantum computers, hence, it cannot prove the (illusory) quantum computer's supremacy or advantage at all.
They insist D-Wave annealing machine may utilize (fictitious) quantum superposition, a dead-alive cat state or parallel worlds like other still-unrealized gate-model quantum computers, but this is untrue.
This 12th-paragraph says
"The trouble is, it’s possible to build a device that produces a similar result to quantum annealing without any quantum behavior—i.e., without invoking (quantum) superpositions and parallel universes. "
And this p.2-abstract says
" The decoherence time (= quantum superposition continuing time ) of a single flux qubit is
reported to be on the order of nanoseconds, which is much shorter than the time required to
carry out a computation on the timescale of seconds."
↑ The flux qubit used in D-Wave machine is said to be unable to keep the quantum superposition (= its superposition state is said to be broken, which is called "decoherence", only in nanoseconds ) long enough to carry out annealing which needs at least seconds (= quantum annealing needs exponentially much more time for more complicated problems, which cannot prove quantum speed-up ).
So "D-Wave annealing machines or other quantum simulators for optimization might have showed quantum advantage" is completely false in all things such as quantum tunnel and superposition.
(Fig.3) When the thickness of the insulator (such as vacuum ) is less than a nanometer, the (unseen) potential barrier becomes naturally lower, and an electron can naturally pass through it with positive kinetic energy. = this is a realistic mechanism.
The unrealistic quantum mechanics claims that each electron can penetrate even the insulator barrier with higher potential energy by having (unreal) negative kinetic energies, which is impossible.
For example, negative electrons repel each other through Coulomb electric repulsion, and move farther away from each other. ← This is a realistic force mechanism.
But in the quantum tunnel, even when an electron touches the higher potential energy barrier and feels the repulsion from it, the electron must ignore the repulsion and move in the opposite direction from the repulsion (= caused by potential barrier ) to penetrate the potential barrier.
↑ In the realistic world, all particles such as an electron must move in the same direction as forces applied on them.
But in the unrealistic quantum tunneling, even when the electron is pushed back to the left by repulsive force from the potential barrier, the electron must ignore it and move in the opposite direction from the forces, which is impossible.
As seen in the scanning tunneling microscope, the quantum tunnel happens only when the thickness of the insulator such as air and vacuum (= actually contains No real barriers ) is less than several nanometers, in which case, the unseen potential barrier allegedly caused by the vacuum insulator naturally becomes lower, and an electron can naturally penetrate it even without having unreal negative kinetic energy or disobeying the force's direction. ← this is a realistic tunnel mechanism.
(Fig.4) There are too many wrong solutions or local energy minima where the annealing machines are often stuck.
D-Wave quantum annealing machines are said to reach the lowest energy state set as the right solution by penetrating many obstacles or higher potential barriers using the convenient quantum tunneling.
But the chance of quantum tunneling penetrating the higher potential-energy barrier is extremely small, so even if they can utilize (dubious) quantum tunnel (= which cannot be confirmed ), D-Wave annealing machines would Not reach the lowest energy or right solution, trapped in one of many wrong solutions or local energy minima.
For example, the probability amplitude (= exressed as the wavefunction's height ) of an electron penetrating the higher potential barrier decreases exponentially, as shown in the upper figure.
In order to reach or find the lowest energy state or right solution, each electron or qubit in the annealing machines must go through many higher potential-energy barriers ( this p.2 ), which is almost impossible, especially when a lot of qubits are needed to solve the complicated optimization problems such as factoring and traveling selesman problem.
So when D-Wave annealing machine and Harvard's quantum simulators (= still Not practical simulators at all ) try to find solutions encoded as the lowest energy for optimization problems, they are very likey to give the wrong solutions expressed as the local energy minima ( this p.3 ).
For example, even in a research factoring very simple number 15 = 3 × 5 (= by encoding these prime numbers 3 and 5 as the lowest energy state using only three qubits ), they could narrowly obtain this right answer with chance of only 22% ( this p.55, 53 ) in 50 runs.
Basically, as the number of qubits used increases, and interaction strengths between qubits are more complicated, the chance of quantum annealing machines stuck in the wrong solutions or local energy minima increases.
This 5th-paragraph says
"In this study, the researchers showed that D-Wave One - which has the distinction of being the first commercial quantum annealer - can solve some simple protein folding problems by annealing all the way to the ground state. The problems here only contain a small number of amino acids, so they have only a relatively small number of possible configurations, and can still be solved on a classical computer. Also, the quantum technique has low odds of measuring the ground state, with only 13 out of 10,000 measurements yielding the desired solution. The researchers attribute this low percentage in part to the limitations of the machine itself, and in part to thermal noise that disrupted the computation ( This paper's p.6 Discussion )."
Success rates or probabilites of getting the right solutions drastically decrease and approach almost zero, when the numbers of qubits used increase to about 100 qubits ( this p.12-Fig.4(a), this p.4-Figure 2c ).
In this research ( this p.33-34(or p.31-32 ) ), the chance of D-Wave annealing machine successfully getting the lowest ground state energy (= right solution ) is only 0.2 %.
↑ So in order to find or reach the right soluton encoded as the lowest energy state in optimization problem, the quantum annealing machines must already know the right solution, and artificially adjust the initial state or how the system's energy landscape evolves, which means the quantum annealing machines are completely useless for predicting arbitrary unknown values.
(Fig.5) Each qubit (= q1,q2,q3..) can take two states 1 or -1. When the interaction variable J between two qubits is -1 (or +1 ), it expresses (unrealistic) ferromagnet (or anti-ferromagnet), they claim.
Quantum annealing and simulators are often said to be able to 'simulate' (exotic) magnetism or materials such as ferromagnet, antiferromagnet, Ising model, spin glass, but None of these simulations by annealing are useful ( this p.13 ), because these "materials" allegedly simulated by quantum annealers or simulators do Not represent real materials.
For example, as shown in the upper figure, when there are six qubits (= q1,q2,q3,q4,q5,q6), each qubit of which can take two states -1 or 1, these six qubits are said to be able to 'simulate' ferromagnet in the case of the interaction variable J being negative -1, and the state of all six qubits being 1 (= as if all six spins are up like fictitious ferromagnetic model ) gives the lowest energy state (= right solution for expressing ferromagnetic model ).
↑ Each interaction energy = spin-up-qubit (= 1) × -1(= J) × spin-up-qubit (= 1 ) = 1 × -1 × 1 = -1 (= lower stable energy ) in the ferromagnetic case of the negative intearction J = -1.
And when the interaction variable J is positive +1, when the neighboring qubits become the opposite like +1, -1, +1, -1, +1, -1 (= as if spins become up and down alternately like fictitious antiferromagnetic model ), it gives the lowest energy state ( this p.5 ).
But of course, the actual ferromagnet and antiferromagnet have much more complicated structures than these abstract meaningless spin models, hence these very abtract unrealistic spin models allegedly expressed by quantum simulators or quantum annealing optimizers are completely useless for real science.
We don't need to rely on very expensive D-Wave annealing machines to estimate these very simple alignment of ferromagnet (= just all qubits are 1 or spin-up = No computation is needed ! ) and antiferromagnet (= qubits become 1,-1,1,-1.. or spin-up,down,up,down.. alternately = No computation is needed, either ).
In actual complicated optimization problems such as traveling salesman problem or factoring, each qubit must interact complicatedly with all other qubits to approach the right answer or lowest energy state.
But in D-Wave annealing machines, each qubit can connect with only six ~ 15 other qubits, which is one of reasons why the success rate of D-Wave reaching the lowest energy right answer becomes lower and worse, when the number of qubits increases ( this p.5-Fig.2 ).
We show one example of these quantum annealing qubits expressing fictitious spins giving the wrong answer stuck in the wrong local energy minima (= low success probability of D-Wave quantum annealer or QA this p.35-last-paragraph and Fig.23, this p.5 4th-paragraph ).
In the upper figure, there are three types of qubits or spins consisting of three green qubits, three red qubits and three purple qubits.
The interaction J is supposed to be negative -1 giving ferromagnetic state between the same-color qubits or spins (= the directions of two neighboring qubits with the same colors tend to be the same to lower their interaction energy ), and this interaction J is positive +1 giving antiferromagnetic state between the different-color qubits (= the directions of two neighboring qubits with different colors tend to be the opposite to lower their interaction energy ).
The spin or qubit arrangement in the lower-middle in the upper figure is one of wrong solutions or local energy minima (= Not the lowest energy or right qubits' arrangement ).
In this wrong solution, three red qubits (= spin-down or -1 ) and three purple qubits (= spin-up or 1 ) are mutually in the opposite qubit or spin states which lower the total energy due to the antiferromagnetic interaction between different-color qubits.
But the red qubit and one green qubit (= A ) are in the same spin-down qubit state (= -1 ) in the lower-middle figure of the wrong solution, which increases the total energy against the antiferromagnetic interaction (= interaction energy = -1 × 1 × -1 = 1 = higher energy between green and red qubits ).
In this wrong solution or local energy minimum, neither the green qubit-A nor red qubits try to flip their qubit-state or spins any longer, because all of them are in the stable states (= negative energy state ) through the interaction with other green or red, blue qubits (= ex. the green qubit-A's energy becomes negative and stable by summing two negative stable interactions with other two green qubits + one positive unstable interaction with a red qubit ), which is one of wrong solutions or local energy minima.
In order to become the lowest energy state or right solution like the lower-right arrangement in the upper figure, first, three red qubits must flip simultaneously instead of blue qubits from the initial state, which is left to chance.
As seen here, the more qubits and interactions are used, the more likely D-Wave annealing machines are stuck in the wrong solutions or local energy minima.
Actually, the latest papaer ( this p.1-left-2nd-paragraph ) says
", when executed on the current generation of quantum
hardware, quantum optimization algorithms often fall short of
expectations due to the accumulation of errors over many operations demanded by the algorithm and the resulting inability
to run non-shallow circuits. As a result, the output quality
is deteriorated considerably, with algorithms yielding lower
performance than expected. This makes even the
most straightforward classical optimization approaches better
candidates for solving real-world optimization. For instance,
classical greedy algorithms, which iteratively build a solution
by making the locally optimal choice at each stage, are intuitive, easy to implement, and will most likely outperform
a modern noisy quantum computer running adiabatic evolution or the QAOA (= quantum approximate optimization algorithm )"
(Fig.6) Unfair choice of the impractically time-consuming classical methods such as simultaed annealing and path integral Monte-Carlo (= PIMC ) with imaginary time → causing illusory quantum computer's speed-up or advantage
Quantum annealers such as D-Wave and Harvard's quantum simulators can Not deal with the complicated optimization problems such as traveling salesman finding the shortest route or factoring due to giving the wrong solutions or local energy minima.
So they started to say quantum annealers may be able to "simulate" some (exotic) materials faster than ordinary classical computers.
But all the current (useless) quantum annealing may simulate is very simple abstract useless spin model, which has nothing to do with real complicated materials.
The madia-hype such as "quantum computer's million-time speed-up or advantage" is caused by the unfair comparison where they deliberately chose the very time-consuming impractical calculating method such as "simulated annealing" and "path integral Monte Calro or PIMC ( this 8th-paragraph, this abstract, p.3-5-discussion )" as "(fake) leading classical methods."
There are other simpler and more efficient classical calculation methods such as Selby's algorithm which can outperform the D-Wave quantum annealers and quantum simulators.
This 7th paragraph says
"The D-Wave machine is a quantum annealer running adiabatic quantum computing algorithms. This is great for optimizing solutions to problems by quickly searching over a space and finding a minimum (or “solution”). The latest announcement from Google states that the D-Wave machine is more than 108 times faster than (slower classical) simulated annealing running on a single core. However, (faster classical) Selby’s algorithm still performs better than the D-Wave quantum computer ( this 2-3 paragraphs )."
This path integral Monte Calro (= PIMC ) method or quantum Monte Calro (= QMC, this Fig.1B ), which is often chosen as the (fake) leading classical method for unfair comparison with quantum annealing, uses the unreal imaginary time, which means PIMC can Not represent the legitimate leading 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 probabilties (= 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 Calro 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 Calro and simulated annealing unfairly chosen for comparison with the quantum annealing.
On the other hand, in D-Wave annealing machine, all qubits representing (fictitious) spins experience (classical) magnetic force's interactions (= Not fictitious quantum exchange interaction ) among qubits, and naturally flip their states to lower the total energy instead of being forced to perform the very time-consuming calculations of transition probabilities, which means the (fake) quantum speed-up is Not the result of the actual quantum computer's speed-up but by the unfair choice of the impractically time-consuming bad classical methods.
Actually, there are more efficient, speedier classical methods such as Selby's algorithm which is known to simulate faster than the D-Wave annealing machines (= these inconvenient facts are often deliberately ignored by the media, though ).
(Fig.7) Setting the right prime numbers (= 5 and 3 ) as the lowest-energy qubit state for factoring 15 = 5 × 3 using (impractical) quantum annealing.
To break the current encryption system (= RSA ), we have to factor any arbitrary large numbers far more quickly than the ordinary classical (super)computers.
The still-useless quantum computers are said to exploit the (unrealistic) quantum superposition or parallel worlds to execute multiple different calculations simultaneously using Shor's algorithm for factoring, which dreamlike simultaneous calculations for factoring is impossible forever due to unrealistic quantum parallel worlds whose existence has Not been observed.
Fake quantum computers = quantum annealing machines try to factor some particular numbers (= Not arbitrary unknown numbers ) using small numbers of qubits as one of optimization problems finding the right prime numbers (= ex. 5 and 3 of 15 = 5 × 3 ) encoded as the lowest energy qubit state, even without relying on (fictional) quantum superposition, parallel worlds or Shor's algorithm.
But quantum annealers have been proved to be Not faster than ordinary classical computers in solving optimization problems ( this 7th-paragraph ), and they are often stuck in one of many wrong solutions or local energy minima instead of smoothly reaching the right solutions encoded as the lowest energy state.
So to increase the chance of reaching the lowest energy qubit state or the right answer by the quantum annealers, physicists have to deliberately choose numbers which can be easily factored even by using a very small number of qubits decreasing the chance of being stuck in wrong solutions.
The recent news that Chinese researchers might crack RSA cryptosystem is untrue and it is one of many quantum computer's hypes, because they also relied on the not-faster annealing optimization methods (= instead of authentic Shor's algorithm which is impossible to carry out, forever ) using very small number = only 10 qubits combined with classical computers ( this 2-3rd-paragraphs, this p.1-2 ).
As shown in the upper figure, in order to factor 15 = 3 × 5 using quantum annealing machines such as D-Wave, first, they have to artificially reduce the number of qubits expressing prime numbers as binary numbers for avoiding being stuck in wrong solutions or local energy minima ( this p.51-55 ).
↑ So the quantum annealing can factor only some particular numbers (= Not arbitrary numbers ) whose prime numbers can be expressed using a very small number of qubits, which cannot crack actual RSA encryption.
Here, we use q2 qubit for expressing the decimal number of"3", which is "011 (= 0 q2 1 where the q2 qubit takes 1. ← other 0 and 1 numbers are artificially chosen and fixed for reducing the number of used qubits )" in the binary number.
And the decimal number of "5" is expressed as "101 (= q1 q0 1 where q1-qubit = 1, q0-qubit = 0 )" in the binary form.
↑ Each of these three qubits q0,q1,q3 randomly takes 0 or 1 state in the initial state.
To encode these right solutions of "3" and "5" as the lowest energy state, the total energy H needs to be expressed as the quadratic energy equation of H = (15-a×b)2 where this total energy H becomes the lowest when the integers a and b just become "3" and "5."
These integers a and b need to be expressed using the binary qubit numbers like a =1 + 2q2 (= when the qubit q2 = 1, this becomes "3" ).
They randomly set the initial qubit state where all these qubits q0,q1,q2 can randomly take 0 or 1 state, and manage to let all these three qubits gradually change into the lowest-energy qubit state where q2=1, q1=1, q0=0 using quantum annealing machines, after setting (magnetic) interaction strength (= for example, in the term of 16q0q1 in the upper figure, the coefficient 16 means the interaction strength between qubits q0 and q1 ).
But even in this factorization of the very small number = 15 = 3 × 5 using a few qubits, the chance of quantum annealing machines such as D-Wave obtaining the right prime numbers (= 3 and 5 in this case ) is very small = success rate is only less than 0.4 or 40% ( this p.7-Figure.1(a) ).
And the chance of factoring larger numbers is much smaller and miserable, D-Wave did Not show data of (bad) success rates of factoring larger numbers such as 143=11×13 encoded as only four qubits ( this p.7-8 ).
This p.15-3rd-paragraph says
"Integer factorization has been implemented on the D-Wave 2000Q by a similar strategy.
Quantified experimental results are only provided for factoring 15 and 21. As the authors note, there
is No evidence that quantum annealing will find factors with significant likelihood in polynomial (or
even sub-exponential) time." ← No quantum speed-up.
The problem is the current quantum annealing machines connecting two qubits through adjustable magnetic field cannot handle interactions among more than two qubits like 128q0q1q2 term in the upper figure.
So they need to add new qubit = q3 = q1q2 and the new penalty (= constraint ) equation which is set to give the wrong higher energy when the qubit q3 is wrongly not equal to q1q2.
(Fig.8) Initial qubits = q0=q1=q2=0, then q2=1 → q0=1 giving the wrong local energy minimum = (15-9)2
We show one example of wrong energy solution or local energy minimum in the quantum annealing factorization of 15 = 5 × 3.
The initial qubit state is supposed to be q0=q1=q2=q3=0 which gives prime integers 1 × 1, hence the total energy H becomes (15-1)2 = 196, which total energy is much higher than the right solution or the lowest total energy H = (15-15)2=0.
And then, the qubit q2 is flipped to 1 (= one prime number changes from 1 to 3 ), which lowers the total energy H to (15-3)2 = 144.
Next, the qubit0 is flipped to 1 (= both two prime numbers become 3 ), which further lowers the total energy H to (15-3×3)2 = 36, which is one of wrong solutions or local energy minima.
Because even if we flip the qubit-1 into 1 after that, this heightens the total enegy H to (15-21)2+100(= penalty term due to q3 Not equal to q1 × q2 ) = 136.
And instead, even if we flip the qubit q3, it also heightens the total energy H to (15-9)2+100 = 136.
Hence, quantum annealing is often stuck in this wrong solution of local energy minimum H = (15-9)2, which cannot reach the right lowest-energy solution of H = (15-15)2 = 0
2023/1/12 updated. Feel free to link to this site.
