Ciro Santilli @cirosantilli 34

 Incoming links: SQUID device

Applications of Josephson Junctions  Updated 2024-12-15  +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

Ciro's ASCII art circuit diagram notation  Updated 2024-12-15  +Created 1970-01-01

This notation is designed to be relatively easy to write. This is achieved by not drawing ultra complex ASCII art boxes of every component. It would be slightly more readable if we did that, but prioritizing the writer here.

Two wires are only joined if + is given. E.g. the following two wires are not joined:

  |
--|--
  |

but the following are:

  |
--+--
  |

Simple symmetric components:

-, + and |: wire
AC: AC source. Parameters:
- Hz: frequency
- V: peak voltage
e.g.:
```
AC_1Hz_2V
```
If only one side is given, the other is assumed to be at a ground G.
C: capacitor
G: ground. Often used together with DC, e.g.:
```
DC_10---R_10---G
```
means applying a voltage of 10 V across a 10 Ohm resistor, which would lead to a current of 1 A
L: inductor
MICROPHONE. As a multi-letter symmetric component, you can connect the two wires anywhere, e.g.
```
---MICROPHONE---
```
or:
```
|
MICROPHONE
    |
```
SPEAKER
R: resistor
SQUID: SQUID device
X: Josephson junction

Asymmetric components have multiple letters indicating different ports. The capital letter indicates the device, and lower case letters the ports. The wires then go into the ports:

D: diode
- a: anode (where electrons can come in from)
- c: cathode
Sample usage in a circuit:
```
--aDc--
```
Can also be used vertically like aany other circuit:
```
|
a
D
c
|
```
We can also change the port order, the device is still the same due to capital D:
```
--cDa--

 |
Dac--

 |
Dca--

   |
--caD
```
DC DC source. Ports:
- p: positive
- n: negative
E.g. a 10 V source with a 10 Ohm resistor would be:
```
+---pDC_10_n---+
|              |
+----R_10------+
```
If only one side is given, the other is assumed to be at a the ground G. We can also omit p and m in that case and assume that p is the one used, e.g. the above would be equivalent to:
```
DC_10---R_10---G
```
If the voltage is not given, it is assumed to be a potentiometer.
T: transistor. The ports are sgTd:
- s: source
- g: gate
- d: gate
Sample usage in a circuit:
```
---+
   |
--sgTd--
```
All the following are also equivalent:
```
   |
   g
--sTd--

    |
--Tsgd--
   |
```
I: electric current source. Ports:
- s: electron source
- d: electron destination
V: Voltmeter. Ports:
- p: positive
- n: negative
If we don't need to specify explicit positive and negative sides, we can just use:
```
---V---
```
without any ports. This is notably often the case for AC circuits.
Optionaly, we can also add the sides as in:

Numbers characterizing components are put just next to each component with an underscore. When there is only one parameter, standard units are assumed, e.g.:

+-----+
|     |
C_1p  R_2k
|     |
+-----+

means:

a capacitor with 1 pico Faraday
a resistor with 2 k Ohms

Micro is denoted as u.

Wires can just freely come in and out of specs of a component, they are then just connected to the component, e.g.:

DC_10---R_10---G

means applying a voltage of 10 V across a 10 Ohm resistor, which would lead to a current of 1 A

If a component has more than two parameters, units are used to distinguish them when possible, e.g.:

AC_1kV_2MHz

means an AC source with:

1 kV voltage
1 MHz frequency

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It is OK to treat things as black boxes  Updated 2024-12-15  +Created 1970-01-01

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Nature is a black box, right?

You don't need to understand the from first principles derivation of every single phenomena.

And most important of all: you should not start learning phenomena by reading the from first principles derivation.

Instead, you should see what happens in experiments, and how matches some known formula (which hopefully has been derived from first principles).

Only open the boxes (understand from first principles derivation) if the need is felt!

E.g.:

you don't need to understand everything about why SQUID devices have their specific I-V curve curve. You have to first of all learn what the I-V curve would be in an experiment!
you don't need to understand the fine details of how cavity magnetrons work. What you need to understand first is what kind of microwave you get from what kind of input (DC current), and how that compares to other sources of microwaves
lasers: same

Physics is all about predicting the future. If you can predict the future with an end result, that's already predicting the future, and valid.

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Magnetometer  Updated 2024-12-15  +Created 1970-01-01

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Implementations:

Hall effect based, i.e. a Hall effect sensor
SQUID device

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SQUID device  Updated 2024-12-15  +Created 1970-01-01

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Can be used as a very precise magnetometer.

There are high temperature yttrium barium copper oxide ones that work on liquid nitrogen.

Video 1.

Superconducting Quantum Interference Device by Felipe Contipelli (2019)

Source. Good intuiotionistic video. Some points deserved a bit more detail.

Video 2.

Mishmash of SQUID interviews and talks by Bartek Glowaki

. Source.

The videos come from: www.ascg.msm.cam.ac.uk/lectures/. Vintage.

Mentions that the SQUID device is analogous to a double-slit experiment.

One of the segments is by John Clarke.

Video 3.

Superconducting Quantum Interference Devices by UNSW Physics (2020)

Source.

An experimental lab video for COVID-19 lockdown. Thanks, COVID-19. Presented by a cute and awkward Adam Stewart.

Uses a SQUID device and control system made by STAR Cryoelectronics. We can see Mr. SQUID EB-03 written on the probe and control box, that is their educational product.

As mentioned on the Mr. SQUID specs, it is a high-temperature superconductor, so liquid nitrogen is used.

He then measures the I-V curve on an Agilent Technologies oscilloscope.

Unfortunately, the video doesn't explain very well what is happening behind the scenes, e.g. with a circuit diagram. That is the curse of university laboratory videos: some of them assume that students will have material from other internal sources.

youtu.be/ql2Yo5LgU8M?t=211 shows the classic voltage oscillations, presumably on a magnetic field sweep, and then he puts a magnet next to the device from outside the Dewar
youtu.be/ql2Yo5LgU8M?t=253 demonstrates the formation of Shapiro steps. Inserts a Rohde & Schwarz signal generator into the Dewar to vary the flux. The result is not amazing, but they are visible somewhat.

Video 4.

The Ubiquitous SQUID by John Clarke (2018)

Source.

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Superconducting quantum computer need non-linear components  Updated 2024-12-15  +Created 1970-01-01

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Non-linearity is needed otherwise the input energy would just make the state go to higher and higher energy levels, e.g. from 1 to 2. But we only want to use levels 0 and 1.

The way this is modelled in by starting from a pure LC circuit, which is an harmonic oscillator, see also quantum LC circuit, and then replacing the linear inductor with a SQUID device, e.g. mentioned at: youtu.be/eZJjQGu85Ps?t=1655 Video "Superconducting Qubits I Part 1 by Zlatko Minev (2020)".

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Superconducting quantum computing  Updated 2024-12-15  +Created 1970-01-01

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Based on the Josephson effect. Yet another application of that phenomenal phenomena!

Philosophically, superconducting qubits are good because superconductivity is macroscopic.

It is fun to see that the representation of information in the QC basically uses an LC circuit, which is a very classical resonator circuit.

As mentioned at en.wikipedia.org/wiki/Superconducting_quantum_computing#Qubit_archetypes there are actually a few different types of superconducting qubits:

flux
charge
phase

and hybridizations of those such as:

transmon

Input:

microwave radiation to excite circuit, or do nothing and wait for it to fall to 0 spontaneously
interaction: TODO
readout: TODO

Video 1.

Quantum Computing with Superconducting Qubits by Alexandre Blais (2012)

Source.

Video 2.

Quantum Transport, Lecture 16: Superconducting qubits by Sergey Frolov (2013)

Source. youtu.be/Kz6mhh1A_mU?t=1171 describes several possible realizations: charge, flux, charge/flux and phase.

Video 3.

Building a quantum computer with superconducting qubits by Daniel Sank (2019)

Source. Daniel wears a "Google SB" t-shirt, which either means shabi in Chinese, or Santa Barbara. Google Quantum AI is based in Santa Barbara, with links to UCSB.

youtu.be/uPw9nkJAwDY?t=293 superconducting qubits are good because superconductivity is macroscopic. Explains how in non superconducting metal, each electron moves separatelly, and can hit atoms and leak vibration/photos, which lead to observation and quantum error
youtu.be/uPw9nkJAwDY?t=429 made of aluminium
youtu.be/uPw9nkJAwDY?t=432 shows the circuit diagram, and notes that the thing is basically a LC circuit
```
+-----+
|     |
|   +-+-+
|   |   |
C   X   X
|   |   |
|   +-+-+
|     |
+-----+
```
using the newly created just now Ciro's ASCII art circuit diagram notation. Note that the block on the right is a SQUID device.
youtu.be/uPw9nkJAwDY?t=471 mentions that the frequency between states 0 and 1 is chosen to be 6 GHz:
- higher frequencies would be harder/more expensive to generate
- lower frequencies would mean less energy according to the Planck relation. And less energy means that thermal energy would matter more, and introduce more noise.
  6 GHz is about $6^{9} \times h = 6 \times 1 0^{9} \times 6.62 \times 1 0^{- 34} \approx 4 \times 1 0^{- 24} J$
  From the definition of the Boltzmann constant, the temperature which has that average energe of particles is of the order of:
  $T = E / k_{b} = 4 \times 1 0^{- 24} / 1.38 \times 1 0^{- 23} \approx 0.3 K$
  (1)
This explains why we need to go to much lower temperatures than simply the superconducting temperature of aluminum!

Video 4.

A Brief History of Superconducting quantum computing by Steven Girvin (2021)

Source.

youtu.be/xjlGL4Mvq7A?t=138 superconducting quantum computer need non-linear components (too brief if you don't know what he means in advance)
youtu.be/xjlGL4Mvq7A?t=169 quantum computing is hard because we want long coherence but fast control

Video 5.

Superconducting Qubits I Part 1 by Zlatko Minev (2020)

Source.

The Q&A in the middle of talking is a bit annoying.

youtu.be/eZJjQGu85Ps?t=2443 the first actually useful part, shows a transmon diagram with some useful formulas on it

Video 6.

Superconducting Qubits I Part 2 by Zlatko Minev (2020)

Source.

Video 7.

How to Turn Superconductors Into A Quantum Computer by Lukas's Lab (2023)

Source. This video is just the introduction, too basic. But if he goes through with the followups he promisses, then something might actually come out of it.

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Transmon  Updated 2024-12-15  +Created 1970-01-01

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Used e.g. in the Sycamore processor.

The most basic type of transmon is in Ciro's ASCII art circuit diagram notation, an LC circuit e.g. as mentioned at youtu.be/cb_f9KpYipk?t=180 from Video "The transmon qubit by Leo Di Carlo (2018)":

+----------+
| Island 1 |
+----------+
   |   |
   X   C
   |   |
+----------+
| Island 2 |
+----------+

youtu.be/eZJjQGu85Ps?t=2443 from Video "Superconducting Qubits I Part 1 by Zlatko Minev (2020)" describes a (possibly simplified) physical model of it, as two superconducting metal islands linked up by a Josephson junction marked as X in the diagram as per-Ciro's ASCII art circuit diagram notation:

+-------+       +-------+
|       |       |       |
| Q_1() |---X---| Q_2() |
|       |       |       |
+-------+       +-------+

The circuit is then analogous to a LC circuit, with the islands being the capacitor. The Josephson junction functions as a non-linear inductor.

Others define it with a SQUID device instead: youtu.be/cb_f9KpYipk?t=328 from Video "The transmon qubit by Leo Di Carlo (2018)". He mentions that this allows tuning the inductive element without creating a new device.

Video 1.

The superconducting transmon qubit as a microwave resonator by Daniel Sank (2021)

Source.

Video 2.

Calibration of Transmon Superconducting Qubits by Stefan Titus (2021)

Source. Possibly this Keysight which would make sense.

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Yttrium barium copper oxide  Updated 2024-12-15  +Created 1970-01-01

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Upside: superconducting above 92K, which is above the 77K of liquid nitrogen, and therefore much much cheaper to obtain and maintain than liquid helium.

Downside: it is brittle, so how do you make wires out of it? Still, can already be used in certain circuits, e.g. high temperature SQUID devices.

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