Quantum logic gates are needed because you can't compute the matrix explicitly as it grows exponentially by 
Ciro Santilli 37 Updated 2025-07-16
Ciro Santilli 37 Updated 2025-07-16One key insight, is that the matrix of a non-trivial quantum circuit is going to be huge, and won't fit into any amount classical memory that can be present in this universe.
This is because the matrix is exponential in the number qubits, and is more than the number of atoms in the universe!
Therefore, off the bat we know that we cannot possibly describe those matrices in an explicit form, but rather must use some kind of shorthand.
But it gets worse.
This is because knowing the matrix, basically means knowing the probability result for all possible outputs for each of the possible inputs.
But if we had those probabilities, our algorithmic problem would already be solved in the first place! We would "just" go over each of those output probabilities (OK, there are of those, which is also an insurmountable problem in itself), and the largest probability would be the answer.
So if we could calculate those probabilities on a classical machine, we would also be able to simulate the quantum computer on the classical machine, and quantum computing would not be able to give exponential speedups, which we know it does.
To see this, consider that for a given input, say and therefore when you multiply it by the unitary matrix of the quantum circuit, what you get is the first column of the unitary matrix of the quantum circuit. And
000 on a 3 qubit machine, the corresponding 8-sized quantum state looks like:000 -> 1000 0000 == (1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)001, gives the second column and so on.As a result, to prove that a quantum algorithm is correct, we need to be a bit smarter than "just calculate the full matrix".
Which is why you should now go and read: Section "Quantum algorithm".
This type of thinking links back to how physical experiments relate to quantum computing: a quantum computer realizes a physical experiment to which we cannot calculate the probabilities of outcomes without exponential time.
So for example in the case of a photonic quantum computer, you are not able to calculate from theory the probability that photons will show up on certain wires or not.
These can be used to break cells apart from tissue, and also break up larger DNA or RNA molecules into smaller ones, suitable for sequencing.
As of 2021, their location is a small business park in Haywards Heath, about 15 minutes north of Brighton[ref]
Funding rounds:
- 2022:
- 67m euro contract with the German government: www.uktech.news/deep-tech/universal-quantum-german-contract-20221102 Both co-founders are German. They then immediatly announced several jobs in Hamburg: apply.workable.com/universalquantum/?lng=en#jobs so presumably linked to the Hamburg University of Technology campus of the German Aerospace Center.
- medium.com/@universalquantum/universal-quantum-wins-67m-contract-to-build-the-fully-scalable-trapped-ion-quantum-computer-16eba31b869e
- 2021: $10M (7.5M GBP) grant from the British Government: www.uktech.news/news/brighton-universal-quantum-wins-grant-20211105This grant is very secretive, very hard to find any other information about it! Most investment trackers are not listing it.The article reads:Interesting!
Universal Quantum will lead a consortium that includes Rolls-Royce, quantum developer Riverlane, and world-class researchers from Imperial College London and The University of Sussex, among others.
A but further down the article gives some more information of partners, from which some of the hardware vendors can be deduced:The consortium includes end-user Rolls-Royce supported by the Science and Technology Facilities Council (STFC) Hartree Centre, quantum software developer Riverlane, supply chain partners Edwards, TMD Technologies (now acquired by Communications & Power Industries (CPI)) and Diamond Microwave
- Edwards is presumably Edwards Vacuum, since we know that trapped ion quantum computers rely heavily on good vacuum systems. Edwards Vacuum is also located quite close to Universal Quantum as of 2022, a few minutes drive.
- TMD Technologies is a microwave technology vendor amongst other things, and we know that microwaves are used e.g. to initialize the spin states of the ions
- Diamond Microwave is another microwave stuff vendor
www.riverlane.com/news/2021/12/riverlane-joins-7-5-million-consortium-to-build-error-corrected-quantum-processor/ gives some more details on the use case provided by Rolls Royce:The work with Rolls Royce will explore how quantum computers can develop practical applications toward the development of more sustainable and efficient jet engines.This starts by applying quantum algorithms to take steps to toward a greater understanding of how liquids and gases flow, a field known as 'fluid dynamics'. Simulating such flows accurately is beyond the computational capacity of even the most powerful classical computers today.This funding was part of a larger quantum push by the UKNQTP: www.ukri.org/news/50-million-in-funding-for-uk-quantum-industrial-projects/ - 2020: $4.5M (3.5M GBP) www.crunchbase.com/organization/universal-quantum. Just out of stealth.
Co-founders:
- Sebastian Weidt. He is German, right? Yes at youtu.be/SwHaJXVYIeI?t=1078 from Video 3. "Fireside Chat with with Sebastian Weidt by Startup Grind Brighton (2022)". The company was founded by two Germans from Essex!
- Winfried Hensinger: if you saw him on the street, you'd think he plays in a punk-rock band. That West Berlin feeling.
Homepage points to foundational paper: www.science.org/doi/10.1126/sciadv.1601540
Universal Quantum emerges out of stealth by University of Sussex (2020)
Source. Explains that a more "traditional" trapped ion quantum computer would user "pairs of lasers", which would require a lot of lasers. Their approach is to try and do it by applying voltages to a microchip instead.- youtu.be/rYe9TXz35B8?t=127 shows some 3D models. It shows how piezoelectric actuators are used to align or misalign some plates, which presumably then determine conductivity
Quantum Computing webinar with Sebastian Weidt by Green Lemon Company (2020)
Source. The sound quality is to bad to stop and listen to, but it presumaby shows the coding office in the background.Fireside Chat with with Sebastian Weidt by Startup Grind Brighton (2022)
Source. Very basic target audience:- youtu.be/SwHaJXVYIeI?t=680 we are not at a point where you can buy victory. There is too much uncertainty involved across different approaches.
- youtu.be/SwHaJXVYIeI?t=949 his background
- youtu.be/SwHaJXVYIeI?t=1277 difference between venture capitalists in different countries
- youtu.be/SwHaJXVYIeI?t=1535 they are 33 people now. They've just setup their office in Haywards Heath, north of Bristol.
Architecture All Access: Quantum Computing by James Clarke (2021)
Source. Jeremy O'Brien told his peers that he had the best tech, and that he should get it all.
Some well connected peers from well known universities did not agree however, and also bid for the money, and won.
Jeremy was defeated. And pissed.
Makes for a reasonable the old man lost his horse.
www.ft.com/content/afc27836-9383-11e9-aea1-2b1d33ac3271 British quantum computing experts leave for Silicon Valley talks a little bit about them leaving, but nothing too juicy. They were called PsiQ previously apparently.More interestingly, the article mentions that this was party advised by early investor Hermann Hauser, who is known to be preoccupied about UK's ability to create companies. Of course, European Tower of Babel.
The departure of some of the UK’s leading experts in a potentially revolutionary new field of technology will raise fresh concerns over the country’s ability to develop industrial champions in the sector.
In Ciro's ASCII art circuit diagram notation, it is a loop with three Josephson junctions:
+----X-----+
| |
| |
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+--X----X--+
Superconducting Qubit by NTT SCL (2015)
Source. Offers an interesting interpretation of superposition in that type of device (TODO precise name, seems to be a flux qubit): current going clockwise or current going counter clockwise at the same time. youtu.be/xjlGL4Mvq7A?t=1348 clarifies that this is just one of the types of qubits, and that it was developed by Hans Mooij et. al., with a proposal in 1999 and experiments in 2000. The other type is dual to this one, and the superposition of the other type is between N and N + 1 copper pairs stored in a box.
Their circuit is a loop with three Josephson junctions, in Ciro's ASCII art circuit diagram notation:
+----X-----+
| |
| |
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+--X----X--+When half the magnetic flux quantum is applied as microwaves, this produces the ground state:where and cancel each other out. And the first excited state is:Then he mentions that:
- to go from 0 to 1, they apply the difference in energy
- if the duration is reduced by half, it creates a superposition of .
How MRI Works Part 1 by thePIRL (2018)
Source. - youtu.be/TQegSF4ZiIQ?t=326 the magnet is normally always on for the entire lifetime of the equipment!
- youtu.be/TQegSF4ZiIQ?t=465 usage of non-ionizing radiation (only radio frequencies) means that it is very safe to use. The only dangerous part is the magnetic field interacting with metallic objects.
Dr Mansfield's MRI MEDICAL MARVEL by BBC
. Source. Broadcast in 1978. Description:Tomorrow's World gave audiences a true world first as Dr Peter Mansfield of the University of Nottingham demonstrated the first full body prototype device for Magnetic resonance imaging (MRI), allowing us to see inside the human body without the use of X-rays.
OpenSuperQ intro by Quantum Flagship (2021)
Source. Pinned article: Introduction to the OurBigBook Project
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