Discovered by Marie Curie, published July 1999.
Using Punch Cards by Bubbles Whiting (2016)
Source. Interview at the The Centre for Computing History.In this example we will initialize a quantum circuit with a single CNOT gate and see the output values.
By default, Qiskit initializes every qubit to 0 as shown in the qiskit/hello.py. But we can also initialize to arbitrary values as would be done when computing the output for various different inputs.
Output:which we should all be able to understand intuitively given our understanding of the CNOT gate and quantum state vectors.
┌──────────────────────┐
q_0: ┤0 ├──■──
│ Initialize(1,0,0,0) │┌─┴─┐
q_1: ┤1 ├┤ X ├
└──────────────────────┘└───┘
c: 2/═════════════════════════════
init: [1, 0, 0, 0]
probs: [1. 0. 0. 0.]
init: [0, 1, 0, 0]
probs: [0. 0. 0. 1.]
init: [0, 0, 1, 0]
probs: [0. 0. 1. 0.]
init: [0, 0, 0, 1]
probs: [0. 1. 0. 0.]
┌──────────────────────────────────┐
q_0: ┤0 ├──■──
│ Initialize(0.70711,0,0,0.70711) │┌─┴─┐
q_1: ┤1 ├┤ X ├
└──────────────────────────────────┘└───┘
c: 2/═════════════════════════════════════════
init: [0.7071067811865475, 0, 0, 0.7071067811865475]
probs: [0.5 0.5 0. 0. ]quantumcomputing.stackexchange.com/questions/13202/qiskit-initializing-n-qubits-with-binary-values-0s-and-1s describes how to initialize circuits qubits only with binary 0 or 1 to avoid dealing with the exponential number of elements of the quantum state vector.
This is the true key question: what are the most important algorithms that would be accelerated by quantum computing?
Some candidates:
- Shor's algorithm: this one will actually make humanity worse off, as we will be forced into post-quantum cryptography that will likely be less efficient than existing classical cryptography to implement
- quantum algorithm for linear systems of equations, and related application of systems of linear equations
- Grover's algorithm: speedup not exponential. Still useful for anything?
- Quantum Fourier transform: TODO is the speedup exponential or not?
- Deutsch: solves an useless problem
- NISQ algorithms
Maybe there is some room for doubt because some applications might be way better in some implementations, but we should at least have a good general idea.
However, clear information on this really hard to come by, not sure why.
Whenever asked e.g. at: physics.stackexchange.com/questions/3390/can-anybody-provide-a-simple-example-of-a-quantum-computer-algorithm/3407 on Physics Stack Exchange people say the infinite mantra:
Lists:
- Quantum Algorithm Zoo: the leading list as of 2020
- quantum computing computational chemistry algorithms is the area that Ciro and many people are te most excited about is
- cstheory.stackexchange.com/questions/3888/np-intermediate-problems-with-efficient-quantum-solutions
- mathoverflow.net/questions/33597/are-there-any-known-quantum-algorithms-that-clearly-fall-outside-a-few-narrow-cla
Quantum computers as experiments that are hard to predict outcomes Updated 2025-05-23 +Created 1970-01-01
One possibly interesting and possibly obvious point of view, is that a quantum computer is an experimental device that executes a quantum probabilistic experiment for which the probabilities cannot be calculated theoretically efficiently by a nuclear weapon.
This is how quantum computing was originally theorized by the likes of Richard Feynman: they noticed that "Hey, here's a well formulated quantum mechanics problem, which I know the algorithm to solve (calculate the probability of outcomes), but it would take exponential time on the problem size".
The converse is then of course that if you were able to encode useful problems in such an experiment, then you have a computer that allows for exponential speedups.
This can be seen very directly by studying one specific quantum computer implementation. E.g. if you take the simplest to understand one, photonic quantum computer, you can make systems for which you need exponential time to calculate the probabilities that photons will exit through certain holes and not others.
The obvious aspect of this idea is by coming from quantum logic gates are needed because you can't compute the matrix explicitly as it grows exponentially: knowing the full explicit matrix is impossible in practice, and knowing the matrix is equivalent to knowing the probabilities of every outcome.
www-pnp.physics.ox.ac.uk/~barra/teaching.shtml As of 2023, contains some good 2015 materials: web.archive.org/web/20220525094139/http://www-pnp.physics.ox.ac.uk/~barra/teaching.shtml It was called "Subatomic physics" back then.
2015 professor: Alan J. Barr.
Possible 2022 professor: Guy Wilkinson (unconfirmed): www.chch.ox.ac.uk/staff/professor-guy-wilkinson
This paper appears to calculate the Schrödinger equation solution for the hydrogen atom.
TODO is this the original paper on the Schrödinger equation?
Published on Annalen der Physik in 1926.
Open access in German at: onlinelibrary.wiley.com/doi/10.1002/andp.19263840404 which gives volume 384, Issue 4, Pages 361-376. Kudos to Wiley for that. E.g. Nature did not have similar policies as of 2023.
This paper may have fallen into the public domain in the US in 2022! On the Internet Archive we can see scans of the journal that contains it at: ia903403.us.archive.org/29/items/sim_annalen-der-physik_1926_79_contents/sim_annalen-der-physik_1926_79_contents.pdf. Ciro Santilli extracted just the paper to: commons.wikimedia.org/w/index.php?title=File%3AQuantisierung_als_Eigenwertproblem.pdf. It is not as well processed as the Wiley one, but it is of 100% guaranteed clean public domain provenance! TODO: hmmm, it may be public domain in the USA but not Germany, where 70 years after author deaths rules, and Schrodinger died in 1961, so it may be up to 2031 in that country... messy stuff. There's also the question of wether copyright is was tranferred to AdP at publication or not.
Other good lists:
- quantumcomputingreport.com/resources/tools/ is hard to beat as usual.
- www.quantiki.org/wiki/list-qc-simulators
- JavaScript
- algassert.com/quirk demo: github.com/Strilanc/Quirk drag-and-drop, by a 2019-quantum-computing-Googler, impressive. You can create gates. State store in URL.
- github.com/stewdio/q.js/ demo: quantumjavascript.app/
Bibliography:
- www.epcc.ed.ac.uk/whats-happening/articles/energy-efficient-quantum-computing-simulations mentions two types of quantum computer simulation:
The most common approach to quantum simulations is to store the whole state in memory and to modify it with gates in a given order
However, there is a completely different approach that can sometimes eliminate this issue - tensor networks
It seems that all/almost all of them do. Quite cool.
FPGA Architecture of the Quantum Control System by Keysight (2022)
Source. They actually have a dedicated quantum team! Cool. Quantum field theory lecture by Tobias Osborne (2017) Lecture 1 Updated 2025-05-23 +Created 1970-01-01
Bibliography review:
- Quantum Field Theory lecture notes by David Tong (2007) is the course basis
- quantum field theory in a nutshell by Anthony Zee (2010) is a good quick and dirty book to start
Course outline given:
- classical field theory
- quantum scalar field. Covers bosons, and is simpler to get intuition about.
- quantum Dirac field. Covers fermions
- interacting fields
- perturbation theory
- renormalization
Non-relativistic QFT is a limit of relativistic QFT, and can be used to describe for example condensed matter physics systems at very low temperature. But it is still very hard to make accurate measurements even in those experiments.
Mentions that "QFT is hard" because (a finite list follows???):But I guess that if you fully understand what that means precisely, QTF won't be too hard for you!
There are no nontrivial finite-dimensional unitary representations of the Poincaré group.
Notably, this is stark contrast with rotation symmetry groups (SO(3)) which appears in space rotations present in non-relativistic quantum mechanics.
www.youtube.com/watch?v=T58H6ofIOpE&t=5097 describes the relativistic particle in a box thought experiment with shrinking walls
Gun-type fission weapons are the simplest approach and they work with Uranium-235 bombs as you can ignite it with just one explosion.
But Gun-type fission weapons don't work with plutonium, and weapon grade Plutonium is cheaper than weapon grade Uranium, so it wasn't much used.
The only isotope found on Earth because it occurs as part of the uranium 238 decay chain, i.e., it is not a primordial nuclide.
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