Incoming links: LC circuit
Both are harmonic oscillators.
In the LC circuit:
- the current current may be seen as the velocity and containing the kinetic energy
- the charge stored in the capacitor as the potential energy
You can kickstart motion in either of those systems in two ways:
- charge the capacitor, i.e. pull the string, and then let it go, i.e. close the circuit. This is the simpler one to realise. Shown concretely at: Video "LC circuit dampened oscillations on an oscilloscope by Queuerious Guy (2014)"
- give speed to the mass, i.e. make a current pass through the inductor
When Ciro Santilli was studying electronics at the University of São Paulo, the courses, which were heavily inspired from the USA 50's were obsessed by this one! Thinking about it, it is kind of a cool thing though.
That Wikipedia page is the epitome of Wikipedia failure to explain things in a way that is of any interest to any learner. Video 1. "Tutorial on LC resonant circuits by w2aew (2012)" is the opposite.
Tutorial on LC resonant circuits by w2aew (2012)
Source. - youtu.be/hqhV50852jA?t=239 series LC circuit on a breadboard driven by an AC source. Shows behaviour on oscilloscope as source frequency is modified. We clearly see voltage going to zero at resonance. This is why thie circuit can be seen as a filter.
- youtu.be/hqhV50852jA?t=489 shows the parallel LC circuit. We clearly see current reaching a maximum on resonance.
LC circuit dampened oscillations on an oscilloscope by Queuerious Guy (2014)
Source. Finally a video that shows the oscillations without a driving AC source. The dude just move wires around on his breadboard manually, first charging the capacitor and then closing the LC circuit, and is able to see damped oscillations on the oscilloscope.Introduction to LC Oscillators by USAF (1974)
Source. - youtu.be/W31CCN_ZF34?t=740 mentions that LC circuit formation is the root cause for Audio feedback with a quick demo. Not very scientific, but cool.
LC circuit by Eugene Khutoryansky (2016)
Source. Exactly what you would expect from an Eugene Khutoryansky video. The key insight is that the inductor resists to changes in current. So when current is zero, it slows down the current. And when current is high, it tries to keep it going, which recharges the other side of the capacitor.Oscillator made of an LC circuit.
A quantum version of the LC circuit!
TODO are there experiments, or just theoretical?
Superconducting quantum computer need non-linear components Updated 2025-03-25 +Created 1970-01-01
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)".
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:
Input:
- microwave radiation to excite circuit, or do nothing and wait for it to fall to 0 spontaneously
- interaction: TODO
- readout: TODO
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.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 circuitusing the newly created just now Ciro's ASCII art circuit diagram notation. Note that the block on the right is a SQUID device.
+-----+ | | | +-+-+ | | | C X X | | | | +-+-+ | | +-----+ - youtu.be/uPw9nkJAwDY?t=471 mentions that the frequency between states 0 and 1 is chosen to be 6 GHz:This explains why we need to go to much lower temperatures than simply the superconducting temperature of aluminum!
- 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 aboutFrom the definition of the Boltzmann constant, the temperature which has that average energe of particles is of the order of:
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
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
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 The circuit is then analogous to a LC circuit, with the islands being the capacitor. The Josephson junction functions as a non-linear inductor.
X in the diagram as per-Ciro's ASCII art circuit diagram notation:+-------+ +-------+
| | | |
| Q_1() |---X---| Q_2() |
| | | |
+-------+ +-------+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.
The superconducting transmon qubit as a microwave resonator by Daniel Sank (2021)
Source.