Possible new effects in superconductive tunnelling by
Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01
The inaugural that predicted the Josephson effect.
Published on Physics Letters, then a new journal, before they split into Physics Letters A and Physics Letters B. True Genius: The Life and Science of John Bardeen mentions that this choice was made rather than the more prestigious Physical Review Letters because they were not yet so confident about the results.
Controlled quantum gates are gates that have two types of input qubits:These gates can be understood as doing a certain unitary operation only if the control qubits are enabled or disabled.
- control qubits
- operand qubits (terminology made up by Ciro Santilli just now)
The first example to look at is the CNOT gate.
Generic controlled quantum gate symbol
. Source. The black dot means "control qubit", and "U" means an arbitrary Unitary operation.
When the operand has a conventional symbol, e.g. the Figure "Quantum NOT gate symbol" for the quantum NOT gate to form the CNOT gate, that symbol is used in the operand instead.
Empty circle control qubit notation by
Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01
Some authors use the convention of:
- filled black circle: conventional controlled quantum gate, i.e. operate if control qubit is active
- empty (White) circle: operate if control qubit is inactive
The CNOT gate is a controlled quantum gate that operates on two qubits, flipping the second (operand) qubit if the first (control) qubit is set.
This gate is the first example of a controlled quantum gate that you should study.
CNOT gate symbol
. Source. The symbol follow the generic symbol convention for controlled quantum gates shown at Figure "Generic controlled quantum gate symbol", but replacing the generic "U" with the Figure "Quantum NOT gate symbol".To understand why the gate is called a CNOT gate, you should think as follows.
First let's produce a generic quantum state vector where the control qubit is certain to be 0.
On the standard basis:we see that this means that only and should be possible. Therefore, the state must be of the form:where and are two complex numbers such that
If we operate the CNOT gate on that state, we obtain:and so the input is unchanged as desired, because the control qubit is 0.
If however we take only states where the control qubit is for sure 1:
Therefore, in that case, what happened is that the probabilities of and were swapped from and to and respectively, which is exactly what the quantum NOT gate does.
So from this we understand more concretely what "the gate only operates if the first qubit is set to one" means.
Now go and study the Bell state and understand intuitively how this gate is used to produce it.
This gate set alone is not a set of universal quantum gates.
Notably, circuits containing those gates alone can be fully simulated by classical computers according to the Gottesman-Knill theorem, so there's no way they could be universal.
This means that if we add any number of Clifford gates to a quantum circuit, we haven't really increased the complexity of the algorithm, which can be useful as a transformational device.
Set of quantum logic gate composed of the Clifford gates plus the Toffoli gate. It forms a set of universal quantum gates.
A device that exhibits the Josephson effect.
Experimental Evidence for Quantized Flux in Superconducting Cylinders by
Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01
Paywalled at: journals.aps.org/prl/abstract/10.1103/PhysRevLett.7.43
The first published experimental observation of the magnetic flux quantum.
The paper that follows it in the journal is also of interest, "Theoretical Considerations Concerning Quantized Magnetic Flux In Superconducting Cylinders" by N. Byers and C. N. Yang, it starts:So there was some previous confusion about the flux quantum due to the presence of Cooper pairs or not.
In a recent experiment, the magnetic flux through a superconducting ring has been found to be quantized in units of ch/2e. Quantization in twice this unit has been briefly discussed by London' and by Onsager. ' Onsager' has also considered the possibility of quantization in units ch/2e due to pairs of electrons forming quasi-bosons.
Dumping the fitures at: archive.org/details/experimental-evidence-for-quantized-flux-in-superconducting-cylinders One day we can also dump the paper scans when it goes into the public domain in 2056! Public domain scientific paper by year.
(Upper) Trapped flux in cylinder No. 1 as a function of magnetic field in which the cylinder was cooled below the superconducting transition. temperature. The open circles are individual data points. The solid circles represent th, e average value of all data points at a particular value of applied field including all the points plotted and additional data which could not be plotted due to severe overlapping of points. Approximately two hundred data points are represented. The lines are drawn at multiples of hc/2e.(Lower) Net flux in cylinder No. 1 before turning off the applied field in which it was cooled as a function of the applied field. Open and solid circles have the same significance as above. The lower line is the diamagnetic calibration to which all runs have been normalized. The other lines are translated vertically by successive steps of hc/2e.
(Upper) Trapped flux in cylinder No. 2 as a function of magnetic field in which the cylinder was cooled below the superconducting transition temperature. The circles and triangles indicate points for oppositely directed applied fields. Lines are drawn at multiples of hc/2e.(Lower) Net flux in cylinder No. 2 before turning off the applied field as a function of the applied field. The circles and triangles are points for oppositely directed applied fields. The lower line is the diamagnetic calibration to which all runs have The other been normalized. lines are translated vertically by successive steps of hc/2e.
Symmetry breaking in superconductors by
Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01
As mentioned in True Genius: The Life and Science of John Bardeen page 224, the idea of symmetry breaking was a major motivation in Josephson's study of the Josephson effect.
- quantumtech.blog/2023/01/17/quantum-computing-with-neutral-atoms/ OK this one hits it:So we understand that it is truly like the classical computer analog vs digital case.
As Alex Keesling, CEO of QuEra told me, "... whereas in gate-based [digital] quantum computing the focus is on the sequence of the gates, in analog quantum processing it's more about the position of the atoms and where you place them so they can mirror real life problems. We arrange the atoms and define the forces that drive them and then measure the result... so it’s a geometric encoding of the problem itself."
- thequantuminsider.com/2022/06/28/why-analog-neutral-atoms-quantum-computing-is-a-promising-direction-for-early-quantum-advantage on The Quantum Insider useless article mostly by Pasqal
TensorFlow quantum by Masoud Mohseni (2020)
Source. At the timestamp, Masoud gives a thought experiment example of the perhaps simplest to understand analog quantum computer: chained double-slit experiments with carefully calculated distances between slits. Calulating the final propability distribution of that grows exponentially. Applications of Josephson Junctions by
Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01
- the basis for the most promising 2019 quantum computing implementation: superconducting quantum computer
- Josephson voltage standard: the most practical/precise Volt standard, which motivated the definition of the ampere in the 2019 redefinition of the SI base units
- SQUID devices, which are:
- very precise magnetometer
- the basis for superconducting quantum computers
Of course, this only made sense when Apple was more of an underdog to IBM, and Ciro Santilli greatly admires their defiance of the norm.
As of 2020 however, Apple is kind of on the top of the mobile world, and Think different simply makes no sense anymore, notably because it relies on closed source offline software used by millions.
it's Popular Now It Sucks comes to mind.
This is a trap every company that prides itself on it's "alternative culture" sets for itself. If they succeed, they could become the norm.
Take on Apple's Think different logo with Tux instead of the Apple logo
. In 2020, to think different, is to think open knowledge. Work by Ciro Santilli, based on en.wikipedia.org/wiki/File:Tux.svg.1976 Think different. 2011 Think mainstream
. Cropped from wallpapersafari.com/w/RqYUEj. Pinned article: ourbigbook/introduction-to-the-ourbigbook-project
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