Bit software; qubit hardware

Posted on March 4, 2022 by rpflee

Quantum information is the information of the state of a quantum system.

— Wikipedia on Quantum information

$\displaystyle{\begin{aligned} |a|^2 + |b|^2 &= 1 \\ \end{aligned}}$

For a system with the superposition state

$\displaystyle{\begin{aligned} | \psi \rangle &= a~| \psi_L \rangle + b~| \psi_R \rangle \\ \end{aligned}}$ ,

quantum information is the information of the superposition coefficients $\displaystyle{a}$ and $\displaystyle{b}$ .

— Me@2022-03-03 07:11:10 PM

A quantum state is not a state. Instead, it is a property of a physical system. It is a statistical property of a variable of an experimental setup.

— Me@2022-02-20 06:44:32 AM

— Me@2022-03-03 07:53:09 PM

Quantum information does not exist in physical spacetime. Instead, it exists in the experiment-setup designer’s time. In this sense, it exists in meta-physical time.

It is not information that exists in a physical system. Instead, it is the information about the physical system.

— Me@2022-02-20 11:27:31 PM

Quantum computers are implemented by using qubits, encoding information in the system property (aka quantum state) itself. A qubit is stored in the property of the system, not just arrangements of particles of the system as in a classical media.

Classical information is stored in microscopic setups, such as the arrangements of microscopic particles, of a system.

Quantum information is stored in macroscopic setups, such as the magnetic field direction for maintaining an electron spin’s superposition state, of a system.

— Me@2022-02-20 11:30:37 PM

— Me@2022-03-03 10:29:53 PM

quantum information ~ a system property

conservation of quantum information ~ a property of those system properties

— Me@2022-02-20 8:13 AM

You can locate a piece of classical information in a physical system/information media.

You cannot locate a piece of quantum information in a physical system, because quantum information is stored in the statistical properties of that physical system, which includes objects and experimental processes.

You have to do a large number of identical experiments in order to extract those statistical patterns.

For example, for a fair dice, the numbers on its faces, its weight, etc. are classical information. However, the probability value of getting (such as) 2, which is $\displaystyle{\frac{1}{6}}$ , is quantum information; it does not exist in physical spacetime.

— Me@2022-02-20 11:46:40 PM

“State” and “property” have identical meanings except that:

State is physical. It exists in physical time. In other words, a system's state changes with time.
Property is mathematical. It is timeless. In other words, a system's property does not change. (If you insist on changing a system's property, that system will become, actually, another system.)

For example, “having two wheels” is a bicycle’s property; but the speed is a state, not a property of that bicycle.

— Me@2022-02-20 06:44:32 AM

.

state ~ the easiest-to-change property of a system

— Me@2022-02-21 08:52:34 PM

Classical information is stored in the states of a system (information media).

Quantum information is stored in the properties of a system.

— Me@2022-02-21 08:52:34 PM

A qubit might for instance physically be a photon in a linear optical quantum computer, an ion in a trapped ion quantum computer, or it might be a large collection of atoms as in a superconducting quantum computer. Regardless of the physical implementation, the limits and features of qubits implied by quantum information theory hold as all these systems are mathematically described by the same apparatus of density matrices over the complex numbers.

— Wikipedia on Quantum information

Note that while a bit is a software object, a qubit is a physical object.

— Me@2022-02-23 05:19:02 PM

Constructicons, 2

Posted on March 3, 2022 by rpflee

For a combiner transformer, whose mind (of the component robots) is it?

~ Whose mind is a group of people, such as a company?

Not a fixed one, depending on what the consensus of that group (at that time) is, who the speaker (at that time) is, etc.

In reverse, one person is also a multi-mind.

— Me@2016-06-16 09:07:46 PM

天地創造

Posted on March 3, 2022 by rpflee

心海 4 | 心韻

始於

俊男美女千篇一律

成於

心靈戀情一篇千律

— Me@2022-03-03 01:09:58 PM

Turbo Pascal for Windows

Posted on March 2, 2022 by rpflee

A day in year 1995, somehow, I needed to take a ferry to Hong Kong Island. Before that, I went to the Star Computer Centre in Tsim Sha Tsui. I found a box of Turbo Pascal for Windows. More likely, I went there when I came back from Hong Kong Island.

WinWorld screenshot

More more likely, I went there and saw the box before going to Hong Kong Island; and then went there again to buy it when I was back.

I needed that for doing my programming homework. It cost me 299 HKD.

Throughout that school year, I did almost every exercise in my programming textbook, at the cost of my Additional Mathematics and Biology time. However, for my programming projects, I still needed to test them under Microsoft Pascal, because it was what my school computers ran.

Even during moving house in 2019, I was still not willing to throw this box away.

— Me@2022-03-02 05:20:54 PM

The particle-trajectory model

Posted on March 2, 2022 by rpflee

The 4 bugs, 1.13

The common quantum mechanics “paradoxes” are induced by 4 main misunderstandings.

…

4.1 Each particle always has a definite identity. Wrong.

identical particles

~ some particles are identical, except having different positions

~ some particle trajectories are indistinguishable

.

trajectory indistinguishability

~ particle identity is an approximate concept

— Me@2022-02-11 12:47:14 AM

physical definition

~ define microscopic events in terms of observable physical phenomena such as the change of readings of the measuring device

~ define unobservable events in terms of observable events

— Me@2022-01-31 08:33:01 AM

4.2 Each particle always has a trajectory. Wrong.

“Which trajectory has a particle travelled along” is a hindsight story.

“The electron at location x_1 at time t_1 and the electron at location x_2 at a later time t_2 are actually the same particle” is also a hindsight story.

These kinds of post hoc stories do not exist when some definitions of trajectories are missing in the overall definition of the experiment setup. In such a case, we can only use a superposition state to describe the state of the physical system.

Since such a situation has never happened in a classical (or macroscopic) system, it gives a probability distribution that has never existed before.

…

— Me@2022-01-31 08:33:01 AM

a trajectory story

~ a hindsight story

~ a post hoc story

reality

~ experimental data

~ observable events

story

~ an optional description of an unobservable event

Even though the nature of a trajectory story is a hindsight story or a post hoc story, it must be based on observable events, compatible with experiment results.

— Me@2022-03-01 07:33:31 PM

— Me@2022-03-02 10:30:41 AM

The double slit experiment (and any other experiments that have quantum effects) puts the particle-trajectory model into a stress test and breaks it. The experiment exposes the bug of the particle-trajectory model. For example, the superposition case (aka the no-detector case) cannot be explained by this model.

Another example, even if the two slits on double-slit-plate are all closed, some particles, although not many, will still “go through” the plate.

— Me@2022-02-27 09:17:23 AM

— Me@2022-03-01 11:09:24 PM

quantum effect

~ an effect that cannot use the particle-trajectory model

~ an effect that does not have a trajectory story

— Me@2022-03-02 12:23:54 PM

The 4 bugs, 1.12

Posted on March 1, 2022 by rpflee

EPR paradox, 11.11

3.2 (2.3) In some cases, the wave function of a physical variable of the system is in a superposition state at the beginning of the experiment. And then when measuring the variable during the experiment, that wave function collapses. Wrong.

A wave function (for a particular variable) is an intrinsic property of a physical system.

“Physical system” means the experimental-setup design, which includes not just objects and devices, but also operations.

…

…

The common misunderstanding comes from representing $\displaystyle{| \psi \rangle }$ as a sum of $\displaystyle{| \psi_L \rangle }$ and $\displaystyle{| \psi_R \rangle}$ . But this is not a physical superposition, but a mathematical superposition only.

This mathematical superposition has 3 meanings (applications):

…

3.

…

Only the longcut version can avoid such meaningless questions.

If you insist on answering those questions:

How to collapse a wave function?

Replace system $\displaystyle{A}$ with system $\displaystyle{B}$ .

It is not that the wave function $\displaystyle{\psi}$ evolves into $\displaystyle{\phi}$ . Instead, they are just two different wave functions for two different systems.

How long does it take? How long is the decoherence time?

The time needed for the system replacement.

How to uncollapse a wave function?

Replace system $\displaystyle{B}$ with system $\displaystyle{A}$ .

— Me@2022-02-27 12:41:31 AM

.

The wave function “collapse” is actually a wave function replacement. It “happens” not during the experiment time, but during the meta-time, where the designer has replaced the experiment-setup design (that without activated device) with another one (that with activated device).

That’s how to resolve the paradoxes, such as EPR.

Anything you are going to measure is always classical, in the sense that it is the experiment designer that decides which variable is classical, by adding the measuring devices and measuring actions to the experiment design.

It is not that the wave collapses during the experiment when you turn on the detector to measure.

The detector and the planned action of activating it have already formed a “physical definition” that makes your experiment design to have a system being in a mixed state, instead of a superposition state, since the beginning of the experiment.

Put it more accurately, since a wave function is a mathematical function, not a physical field, it does not exist in physical spacetime.

In a sense, instead of existing at the time level of the experiment and the observer, a wave function exists at the meta-time level, the time level of the experiment-setup designer.

So it is meaningless to say “the experimental setup is in a superposition state (or not) in the beginning of the experiment”. Instead, we should say:

The detector and the planned action of activating it have already formed a “physical definition” that makes your experiment design to have a system being in a mixed state, instead of a superposition state~~, since the beginning of the experiment~~.

— Me@2022-02-14 10:35:27 AM

— Me@2022-02-21 07:17:28 PM

— Me@2022-02-22 07:01:40 PM

Craftsmanship, 2

Posted on March 1, 2022 by rpflee

Shipping, 4

Real Artists Ship.

— Steve Jobs

真正的創造神，會有成果和產品，付運和上市。

— Me@2022-03-01 04:25:27 PM

數學教育 7.2

Posted on March 1, 2022 by rpflee

這段改編自 2010 年 4 月 24 日的對話。

（安：另外，他提的另一個，有關學習數學的要點是，即使假設你在大學中，學到的數學，在日常生活中沒有用，單單是為獲取，那些嶄新的元素概念本身，就已經能夠令你有超能力；令你有一些，常人沒有的思考工具、比喻語言。）

…

又例如，之前我把向量幾何中的「完備集合」概念，應用到學習知識上，引申成「知識完備集合」。

任何一門學問，雖然在起初時，看似有無盡的細節要駕馭，但是，努力收集零碎資料，到一個程度後，你會發現，細節雖然多，原理卻只有幾個，萬變不離其中。

那就有如，雖然在三度空間中，有無數點，而每一點也可以用，一支向量箭尖去代表；但是，要表達所有點的任何之一，你並毋須在事先，就收集無數支向量箭；因為，在三度空間中，你只要收集齊，三支互相獨立的原始元素向量 $\displaystyle{\{ \mathbf i, \mathbf j, \mathbf k \}}$ ，那些任何一點，就可以透過它們的線性組合去代表。