Top page (correct Bohr model )

Strange "spin" is NOT a real thing

Quantum computer is very impractical.

*(Fig.1) D-Wave machine based on quantum tunneling is real ?*

In optimization ( salesman ) problems, he needs to visit **every city** and try **all** possibilities to know the **shortest** path. But it takes almost **infinite** time, so impossible in some cases.

It is said that D-Wave machine with 512 qubits can solve this problem using quantum **tunnelling** and annealing, as shown on this site and this site.

Quantum annealing is a method for finding the global **minimum** from many candidate states using tunneling.

This D-Wave computer is different from traditional quantum computer (= **impractical** ), because it does NOT rely on entanglement.

*(Fig.2) D-Wave is NOT faster than classical computer.*

As shown in this news and this news, independent research group found **NO** quantum speed-up and advantage over conventional classical computer in the recent experiments using D-Wave.

D-Wave is the **Only** commercial adiabatic quantum computer, so this result showed that there is **NO** evidence of **quantum** computer in the real world, now.

Though D-Wave system is a private company, the paper about its machine is published in journal Science.

So I decided to write about D-Wave quantum computer.

*(Fig.3) Quantum tunneling in D-Wave computer really uses quantum mechanics ?*

The reason why D-Wave is called "quantum computer" is quantum **tunneling**.

It is said that quantum tunneling cannot be explained by classical mechanics.

We want to know whether D-Wave **really** uses **purely** quantum mechanical phenomena as tunneling.

By the way, what does "**Quantum**" phenomenon really mean ?

On this page, we show that definition of **quantum** barrier can be **replaced** by **classical** (= realistic ) mechanics in the tunneling in D-Wave.

*(Fig.4) What is the origin of Josephson corrent I(t) ?*

As shown on this site and this site (p.4), the electric current through Josephson junction becomes **periodic**.

Approximately, this periodicity is related to **magnetic flux** (= Φ ) through current loop.

*(Fig.5) Integer number of de Broglie wavelength (= magnetic flux quantum ).*

It is known that magnetic flux through superconducting loop tends to be an **integer** times flux quantum ( n × Φ_{0} ). See also this section.

Though quantum mechanics **avoids** clarifying this **origin** of flux quantum, **de Broglie** relation clearly plays an important role, as shown on this site and this site (p.23).

This sinusoidal curve based on **de Broglie** waves is the **origin** of double well **potential** in the quantum tunneling of D-Wave computer.

*(Fig.6) Induced voltage V by Faraday's law.*

According to Faraday's ( Lenz's ) law, the voltage is induced along the circuit, when the magnetic flux (= Φ ) changes with time.

This voltage produces a current whose magnetic field **opposes** the change which produces it.

See also this site.

*(Fig.7) The time rate of change of electric potential = V × I.*

The time rate of change of **electric** (= Coulomb ) energy is given by the voltage V × current I

( The current I is the amount of charges passing per second. )

The important point is that they use **special** Josephson current of Fig.4 in calculating **Coulomb** potential.

As I said, the **origin** of the sinusoidal curve of this current I is **NOT** electric force, but de Broglie relation.

So we have to consider **NOT only** Coulomb energy but also **other** (= de Broglie ) energy to get **correct** total potential (= barrier ? ) energy.

*(Fig.8) They neglect de Broglie effect to get Josephson energy.*

As shown on this site and this site, they rely **ONLY** on **Coulomb** relation to obtain total Josephson energy.

Total energy (= E_{J} ) is given by integrating I V (= current × voltage ) with respect to the time t.

This is clearly inconsistent.

Because the **sinusoidal** curve of the Josephson current I ( depending on the magnetic flux ) is caused by **other** effects than ordinary Coulomb potential

These other effects are clearly due to **de Broglie** wave nature.

*(Fig.9) Ordinary magnetic energy in solenoid*

The current loop has the property of solenoid with **inductance** L.

So as shown on
this site (p.3) and this site, the energy stored in the magnetic field is given by Fig.9.

The magnetic flux (= Φ ) through this loop is equal to "LI" (= inductance × current ).

*(Fig.10) Total energy = Josephson + magnetic energies ?*

Summing the effects of Fig.8 (= Josephson energy ) and Fig.9 (= ordinary magnetic energy ), total energy becomes like Fig.10.

Φ_{X} is the magnetic flux from the **external** source, which is used for manipulating the total flux.

When this Φ_{X} is a **half** of magnetic flux quantum (= 1/2Φ_{0} ),

*(Fig.11) Total energy ?*

The part of **cosine** (= Josephson energy ) causes, what we call, **double-well** potential in the current loop, as shown in Fig.12 and this site (p.9).

*(Fig.12) What is the origin of potential barrier ?*

As shown in Fig.11 and Fig.12, when the phase θ is equal to 0 and 2π ( Φ = 0 and Φ_{0} ), the total potential becomes the **lowest**.

The difference of magnetic flux is generated by clockwise and counterclockwise Josephson current.

So they insist these two **opposite** currents are in **superposition** state ( when Φ_{X} = 1/2Φ_{0} ), and can be used as **qubit** of quantum computer.

*(Fig.12') Counterclockwise current = spin up ? clockwise = spin down ? ← superposition ?*

Of course, many-world superposition is completely **unrealistic**.

These states just show the **same** probability in the directions of electric current I.

So, this phenomenon indicates some **unknown** forces are working, which tries to become an **integer** number of magnetic flux quantum (= n × Φ_{0} ).

*(Fig.13) Faraday law tries to keep the origical magnetic flux.*

Classical Faraday law tries to **keep** the original magnetic flux constant.

So when the magnetic flux **decreases** from the original 1/2Φ_{0}, the induced voltage causes the current, which **increases** the magnetic flux.

This means the potential is **lower** in the original 1/2Φ_{0} in the **ordinary** electromagnetism.

*(Fig.14) Faraday law tries to obstruct the increase in magnetic flux.*

When the magnetic flux **increases** from the original 1/2Φ_{0}, the induced voltage generates the **opposite** current, which **decreases** the magnetic flux.

As a result, the potential energy in the original 1/2Φ_{0} is the **lowest**, if **ONLY** classical electromagnetism is related, so double-well potential is **NOT** related to the ordinary electric force.

*(Fig.15) Double-well potential (= barrier ) is caused by de Broglie effect.*

**D-Wave** quantum computer claims the quantum **tunneling** can go through the **barrier** of double-well potentials in superconducting circuit, as shown on this paper ( Nature ).

But as shown in Fig.8, the calculation of this potential barrier is based **ONLY** on Coulomb relation (= current × V ), though this double-well is caused by **de Broglie** effect.

This is self-**contradiction**.

*(Fig.16) An integer number of de Broglie wavelength is the origin of doube-well.*

As I said in Fig.5 and this section, the Josephson ( superconducting ) current tends to generate an **integer** number of magnetic flux quantum (= Φ_{0} ).

So when the magneic flux increases from the original 1/2Φ_{0}, it tries to **increase more** to generate 1 × Φ_{0}.

Of course, this driving force is **NOT** due to the original Faraday law.

Because the original Faraday law tries to **suppress** the increase of the current.

As a result, at this point, we have to consider **other** potentials than the ordinary Coulomb barrier.

*(Fig.17)*

As shown in Fig.17, if **ONLY** the ordinary electromagnetic relation is related in superconducting circuit, the double-well potential **cannot** form.

Because the magnetic energy is proportional to the square of magnetic flux (= Φ^{2} ).

*(Fig.18) De Broglie effect is the main reason of double-well.*

In Fig.18, when the magnetic flux decreases from the original 1/2Φ_{0}, it tries to **decrease more** to be the state of 0 × Φ_{0} (= **integer** × magnetic flux quantum ).

As I said, this effect **cannot** be explained ONLY by usual electromagnetic force ( potential ).

*(Fig.19) We have to consider other effects than Coulomb potential (= barrier ).*

But they depend **ONLY** on the usual electromagnetic relation (= current I × voltage V ) in **calculating** the sinusoidal curve of Josephson **energy** (= E_{J}cosθ ).

In superconducting qubits, they **claim** the validity of quantum **tunneling**, based on the equation of Fig.19.

But Fig.19 is **NOT** complete, because it does **NOT** contain **other** important effects such as de Broglie relation.

Also in this paper ( Science ), they just **artificially** define the meaning of "quantum" and "classical" in magnetic susceptibility. So true "classical" (= in the **realistic** sense ) has **NOT** been disproved yet.

*(Fig.20) Counterclockwise current = spin up ? clockwise = spin down ? ← qubits ?*

From here, we explain about the original paper (= Nature ) and this paper of D-Wave quantum computer.

For example, when the magnetic flux through the current loop is 1/2Φ_{0}, two different **superpositions** states (= 1 × Φ_{0} and 0 × Φ_{0} ) exist at the same time according to the current theory.

These contains **two** kinds of counterclockwise and clockwise currents, which they named spin-up and spn-down, though they are NOT real spin. These two states are used as qubits.

*(Fig.21) Quantum tunneling or classical "thermal" effects. *

They can **control** two kinds of external magnetic fluxes to change the height of barrier and depth of two-wells.

Annealing (= tunneling ) is performed by gradually **raising** the energy barrier between two states.

In classical **thermal** annealing, when the barrier becomes much larger than **k _{B}T** (= Boltzmann factor ) at some time, its thermal excitation over the barrier

*(Fig.22) Barrier becomes higher with time → When (= t _{freeze} ) tunneling stops ?*

Also in quantum annealing, tunneling between two states will **cease**, at some time (= **t _{freeze}** ), when the barrier becomes

So if the potential (= height ) of the right-well becomes **lower** than the left-well, **before** the time t_{freeze}, the particles flow into the lower right-well state through **tunneling**, and **probability** of the right-well become **higher**, as shown in Fig.21.

But even if the right-well becomes lower **after** the time t_{freeze}, when the barrier becomes **high** enough, this tunneling ( and thermal excitation ) **cannot** happen, in which case both right and left-well probabilities **remain** the same.

*(Fig.23) Estimation of "thermal" (= classical ) line is really correct ?*

If the thermal (= classical ) activationa causes this tunneling, the tunneling-**ceasing** time t_{freeze} must be **earlier**, obeying **Boltzmann** law.

As I said above, the barrier gradually becomes higher with time, so at **lower** temperature, thermal **energy** overcoming this barrier becomes **small**.

So at **earlier** time, tunneling is **blocked** (= t_{freeze} is smaller ), they insist.

The experimental result showed this time t_{freeze} is **slightly** larger than the classically (= thermal ) **predicted** line.

The problem is whether this **thermally** (= classically ) expected line is really correct or **NOT** ?

*(Fig.24) ↓ This result really proved "quantum" tunneling ?*

Boltzmann factor is based on **free** particles, as shown on this page.

On the other hand, the current inside superconductor is generated mainly by strong electromagnetic ( **NOT** free ! ) interaction.

Of course, this estimation of Boltzman factor is very **rough**.

And there is **NO** guarantee that this Boltzmann factor **precisely** acts on the electric current even at **extremely low** temperature ( 20 ~ 60 mK ).

Furthermore, the difference between quantum and classical is ONLY **8 microseconds** in t_{freeze}.

Considering very **rough** estimation of this factor, the **validity** of this thermal lines is very **doubtful**.

*(Fig.25) Coulomb + de Broglie effect need to be considered.*

As I said in Fig.19, though the sinusoidal curve of Josephson current is generated by de Broglie ( NOT electromagnetic ) effect, they **neglect** it and consider ONLY Coulomb relation (= I × V ).

So to know **true** potential curve and barrier, we have to add **other** effects such as **de Broglie** waves.

The value of Josephson energy itself **needs** to be reconsidered.

*(Fig.26) Potential barrier and double-well = Effects other than Coulomb.*

First, if ONLY electromagnetic effects are related, double-well potential curve ( and barrier ) itself **cannot** form, as shown in Fig.26.

As a result, quantum tunneling itself does **NOT** happen.

We have to **clarify** the **true** mechanism of an **integer** number of magnetic flux quantum and Josephson current, to **judge** whether the quantum tunneling is real or not.

*(Fig.27) Entanglemnt among eight qubits in D-Wave ?*

Though it was said D-Wave quantum computer does NOT rely on quantum entanglement, the recent paper claims the entanglement effect is seen also in D-Wave machine.

But they observed ONLY **eight** qubits are entangled, which means "**impractical**".

And each qubit is just linked by coupling circuit, so **ordinaly** electromagnetic interations play a major role in this phenomenon.

Actually, within very short interval ( ~μm ), it is **impossible** to prove faster-than-light (= nonlocal ) entanglement.

*(Fig.28) Quantum computer is very impractical.*

Basically, the coherence (= working ) time of flux qubit is extremely **short** (= about **100 nanoseconds**, as shown in this site and this site (p.17) ).

Within this short time, it is **impossible** to use them as quantum computer and confirm their validity.

Furthermore, the temperature must be almost absolute zero (= 12.5 mK ) to work this machine.

Considering this **uselessness** of quantum computer ( if it really exits ) even after **infinite** academic papers are published, it is about time we **give up** quantum computer ( and entanglement ) itself and **change** basic ideas.

*(Ap.1) Phonon is only a ficititous "quasiparticle".*

The behavior of superconductor suggests that electron pairs are coupling (= **Cooper** pair ) over a range of hundreds of nanometers, **three** orders of magnitude **larger** than the lattice spacing, as shown on this site.

As you know, two negative electrons usually **repel** each other, if Coulomb law is right.

This **unnatural** attractive force between electrons is said to be caused by vague quasiparticle, "**phonon**".

But this phonon is just **virtual** quasiparticle, so scientists **must** clarify what this phonon **really** is, stopping "Shut up and calculate !".

*(Ap.2) Quantized de Broglie wavelength.*

Due to Meissner effect, magnetic field inside superconductor is **cancelled** out by electron's responding motions ( obeying Lorentz force ).

But inside a hole in a superconductor, an **integer** times magnetic flux quantum ( Φ = n × Φ_{0} ) is seen, as shown on this site.

*(Ap.3)*

As shown on this page, the current quantum mechanics tries to explain this phenomenon by quantized **vector potential** "A".
They insist "**2e**" of Ap.3 means "Cooper pair".

As shown in Ap.3, phase Θ includes **de Broglie** relation, so planck constant **h** appears, also in quantum mechanical approach.

But they **never** try to say what the "**quantized** vector potential" really means.

This troublesome attitude clearly **obstructs** the development of science.

*(Ap.4) Lorentz force + de Broglie relation.*

If we suppose each electron is moving obeying Lorentz magnetic force (= F = evB ) and its orbital length is an **integer** number of de Broglie wavelength, we can describe this quantized magnetic flux **naturally**.

Centripetal force is equal to Lorentz magnetic force in Ap.4 left.

Ap.4 right means de Broglie relation holds in the circumference.

*(Ap.5) ← Ap.4*

Solving Ap.4, we get Ap.5.

And the total magnetic flux (= Φ ) is given by the area (= πr^{2} ) of this circular orbit × magnetic flux density (= B ).

So total magnetic flux (= πr^{2}B ) is equal to an **integer** (= n ) number of magnetic flux quantum (= **h/2e** ) as shown in Ap.6.

*(Ap.6) Magnetic flux quantum (= h/2e ) can be gotten from de Broglie relation.*

As shown in Ap.6, the magnetic flux (= Φ ) through a hole is just **quantized** ( Φ = n × Φ_{0} ).

This is an **origin** of magnetic flux quantum **without** invoking Cooper pair.

So we have to think about the force (= potential ) caused by this de Broglie wave ( **inteference** ) to calculate the potential barrier.

2014/6/23 updated. Feel free to link to this site.