The Klein-Gordon equation can be written in terms of the d'Alembert operator as:so we can expand the d'Alembert operator in Einstein notation to:
Just like as for classic gates, we would like to be able to select quantum computer physical implementations that can represent one or a few gates that can be used to create any quantum circuit.
Unfortunately, in the case of quantum circuits this is obviously impossible, since the space of N x N unitary matrices is infinite and continuous.
Therefore, when we say that certain gates form a "set of universal quantum gates", we actually mean that "any unitary matrix can be approximated to arbitrary precision with enough of these gates".
Or if you like fancy Mathy words, you can say that the subgroup of the unitary group generated by our basic gate set is a dense subset of the unitary group.
The first two that you should study are:
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.
They are the finite projective special linear groups.
This was the first infinite family of simple groups discovered after the simple cyclic groups and alternating groups. The first case discovered was by Galois. You should understand that one first.
Mathematics and Statistics course of the University of Oxford Updated 2025-03-28 +Created 1970-01-01
Public landing page: www.ox.ac.uk/admissions/undergraduate/courses/course-listing/mathematics-and-statistics
Mathematics and Statistics at Oxford University by University of Oxford (2017)
Source. How Microwaves Work by National MagLab (2017)
Source. A bit meh. Does not mention the word cavity magnetron!How a Microwave Oven Works by EngineerGuy
. Source. Cool demonstration of the standing waves in the cavity with cheese!As you would expect, not much secret here, we just dumped a 1 liter glass bottle with a rope attached around the neck in a few different locations of the river, and pulled it out with the rope.
And, in the name of science, we even wore gloves to not contaminate the samples!
Measuring the river water sample temperature with a mercury thermometer
. Source. 
Because Ciro's a software engineer, and he's done enough staring in computers for a lifetime already, and he believes in the power of Git, he didn't pay much attention to this part ;-)
According to the eLife paper, the code appears to have been uploaded to: github.com/d-j-k/puntseq. TODO at least mention the key algorithms used more precisely.
Ciro can however see that it does present interesting problems!
Because it was necessary to wait for 2 days to get our data, the workshop first reused sample data from previous collections done earlier in the year to illustrate the software.
First there is some signal processing/machine learning required to do the base calling, which is not trivial in the Oxford Nanopore, since neighbouring bases can affect the signal of each other. This is mostly handled by Oxford Nanopore itself, or by hardcore programmers in the field however.
After the base calling was done, the data was analyzed using computer programs that match the sequenced 16S sequences to a database of known sequenced species.
This is of course not just a simple direct string matching problem, since like any in experiment, the DNA reads have some errors, so the program has to find the best match even though it is not exact.
The PuntSeq team would later upload the data to well known open databases so that it will be preserved forever! When ready, a link to the data would be uploaded to: www.puntseq.co.uk/data
This was Ciro Santilli's main study/work music for several years around 2020. Tabla rules.
Just like a classic programmer does not need to understand the intricacies of how transistors are implemented and CMOS semiconductors, the quantum programmer does not understand physical intricacies of the underlying physical implementation.
The main difference to keep in mind is that quantum computers cannot save and observe intermediate quantum state, so programming a quantum computer is basically like programming a combinatorial-like circuit with gates that operate on (qu)bits:
For this reason programming a quantum computer is much like programming a classical combinatorial circuit as you would do with SPICE, verilog-or-vhdl, in which you are basically describing a graph of gates that goes from the input to the output
For this reason, we can use the words "program" and "circuit" interchangeably to refer to a quantum program
Also remember that and there is no no clocks in combinatorial circuits because there are no registers to drive; and so there is no analogue of clock in the quantum system either,
Another consequence of this is that programming quantum computers does not look like programming the more "common" procedural programming languages such as C or Python, since those fundamentally rely on processor register / memory state all the time.
Quantum programmers can however use classic languages to help describe their quantum programs more easily, for example this is what happens in Qiskit, where you write a Python program that makes Qiskit library calls that describe the quantum program.
Quantum logic gates are needed for physical implementation Updated 2025-03-28 +Created 1970-01-01
One direct practical reason is that we need to map the matrix to real quantum hardware somehow, and all quantum hardware designs so far and likely in the future are gate-based: you manipulate a small number of qubits at a time (2) and add more and more of such operations.
While there are "quantum compilers" to increase the portability of quantum programs, it is to be expected that programs manually crafted for a specific hardware will be more efficient just like in classic computers.
TODO: is there any clear reason why computers can't beat humans in approximating any unitary matrix with a gate set?
This is analogous to what classic circuit programmers will do, by using smaller logic gates to create complex circuits, rather than directly creating one huge truth table.
The most commonly considered quantum gates take 1, 2, or 3 qubits as input.
The gates themselves are just unitary matrices that operate on the input qubits and produce the same number of output qubits.
For example, the matrix for the CNOT gate, which takes 2 qubits as input is:
1 0 0 0
0 1 0 0
0 0 0 1
0 0 1 0The final question is then: if I have a 2 qubit gate but an input with more qubits, say 3 qubits, then what does the 2 qubit gate (4x4 matrix) do for the final big 3 qubit matrix (8x8)? In order words, how do we scale quantum gates up to match the total number of qubits?
The intuitive answer is simple: we "just" extend the small matrix with a larger identity matrix so that the sum of the probabilities third bit is unaffected.
More precisely, we likely have to extend the matrix in a way such that the partial measurement of the original small gate qubits leaves all other qubits unaffected.
For example, if the circuit were made up of a CNOT gate operating on the first and second qubits as in:
0 ----+----- 0
|
1 ---CNOT--- 1
2 ---------- 2then we would just extend the 2x2 CNOT gate to:
TODO lazy to properly learn right now. Apparently you have to use the Kronecker product by the identity matrix. Also, zX-calculus appears to provide a powerful alternative method in some/all cases.
Multiple addresses translate to a single physical address Updated 2025-03-28 +Created 1970-01-01
The same linear address can translate to different physical addresses for different processes, depending only on the value inside
cr3.Both linear addresses
00002 000 from process 1 and 00004 000 from process 2 point to the same physical address 00003 000. This is completely allowed by the hardware, and it is up to the operating system to handle such cases.This often in normal operation because of Copy-on-write (COW), which be explained elsewhere.
Such mappings are sometime called "aliases".
Happening multiple times a day on Ubuntu 22.04 for Chromium, even though I turn computer on and off daily, unbearable:
- askubuntu.com/questions/1412575/pending-update-of-snap-store
- askubuntu.com/questions/1412140/pending-update-of-firefox-snap-close-the-app-to-avoid-disruptions
- forum.snapcraft.io/t/how-to-disable-snapd-update-notifications-permanently/31117 Settings > Notifications > Snapd User Session Agent
- www.reddit.com/r/Ubuntu/comments/v1s919/disable_pending_update_of_snap_message_kiosk/
- forum.snapcraft.io/t/refresh-app-awareness-call-for-testing/29123
gfx_v11_0_priv_reg_irq: register access in command stream Updated 2025-03-28 +Created 1970-01-01
Had this happen on P14s on Ubuntu 23.10 while causally using Chromium. The screen went blank for a few seconds, but it apparently managed to reboot itself, and things started working again, except that and most windows were killed:It appears to be a bug in the AMDGPU open source driver.
[drm:gfx_v11_0_priv_reg_irq [amdgpu]] *ERROR* Illegal register access in command stream
[drm:amdgpu_job_timedout [amdgpu]] *ERROR* ring gfx_0.0.0 timeout, signaled seq=5774109, emitted seq=5774111
[drm:amdgpu_job_timedout [amdgpu]] *ERROR* Process information: process chrome pid 14023 thread chrome:cs0 pid 14087
amdgpu 0000:64:00.0: amdgpu: GPU reset begin!
[drm:mes_v11_0_submit_pkt_and_poll_completion.constprop.0 [amdgpu]] *ERROR* MES failed to response msg=3
[drm:amdgpu_mes_unmap_legacy_queue [amdgpu]] *ERROR* failed to unmap legacy queue
[drm:mes_v11_0_submit_pkt_and_poll_completion.constprop.0 [amdgpu]] *ERROR* MES failed to response msg=3
[drm:amdgpu_mes_unmap_legacy_queue [amdgpu]] *ERROR* failed to unmap legacy queue
[drm:mes_v11_0_submit_pkt_and_poll_completion.constprop.0 [amdgpu]] *ERROR* MES failed to response msg=3
[drm:amdgpu_mes_unmap_legacy_queue [amdgpu]] *ERROR* failed to unmap legacy queue
[drm:mes_v11_0_submit_pkt_and_poll_completion.constprop.0 [amdgpu]] *ERROR* MES failed to response msg=3
[drm:amdgpu_mes_unmap_legacy_queue [amdgpu]] *ERROR* failed to unmap legacy queue
[drm:mes_v11_0_submit_pkt_and_poll_completion.constprop.0 [amdgpu]] *ERROR* MES failed to response msg=3
[drm:amdgpu_mes_unmap_legacy_queue [amdgpu]] *ERROR* failed to unmap legacy queue
[drm:mes_v11_0_submit_pkt_and_poll_completion.constprop.0 [amdgpu]] *ERROR* MES failed to response msg=3
[drm:amdgpu_mes_unmap_legacy_queue [amdgpu]] *ERROR* failed to unmap legacy queue
[drm:mes_v11_0_submit_pkt_and_poll_completion.constprop.0 [amdgpu]] *ERROR* MES failed to response msg=3
[drm:amdgpu_mes_unmap_legacy_queue [amdgpu]] *ERROR* failed to unmap legacy queue
[drm:mes_v11_0_submit_pkt_and_poll_completion.constprop.0 [amdgpu]] *ERROR* MES failed to response msg=3
[drm:amdgpu_mes_unmap_legacy_queue [amdgpu]] *ERROR* failed to unmap legacy queue
[drm:mes_v11_0_submit_pkt_and_poll_completion.constprop.0 [amdgpu]] *ERROR* MES failed to response msg=3
[drm:amdgpu_mes_unmap_legacy_queue [amdgpu]] *ERROR* failed to unmap legacy queue
[drm:gfx_v11_0_cp_gfx_enable.isra.0 [amdgpu]] *ERROR* failed to halt cp gfx
Dec 27 15:03:38 ciro-p14s kernel: amdgpu 0000:64:00.0: amdgpu: MODE2 reset
Dec 27 15:03:38 ciro-p14s kernel: amdgpu 0000:64:00.0: amdgpu: GPU reset succeeded, trying to resume
Dec 27 15:03:38 ciro-p14s kernel: [drm] PCIE GART of 512M enabled (table at 0x0000008000900Related reports:
I think this was on Wayland. Possibly relatd but on X Window System, crashed the UI, showed message "oh no! Something has gone wrong."
2024-01-13_21-55-07@ciro@ciro-p14s$ cat /var/log/apport.log
ERROR: apport (pid 975172) 2024-01-13 21:41:02,087: host pid 3528 crashed in a separate mount namespace, ignoring
INFO: apport (pid 975227) 2024-01-13 21:41:02,398: called for pid 2728, signal 5, core limit 0, dump mode 1
INFO: apport (pid 975227) 2024-01-13 21:41:02,401: executable: /usr/bin/gnome-shell (command line "/usr/bin/gnome-shell")
INFO: apport (pid 975227) 2024-01-13 21:41:12,667: wrote report /var/crash/_usr_bin_gnome-shell.1000.crashFFFFF 000 points to its own physical address FFFFF 000. This kind of translation is called an "identity mapping", and can be very convenient for OS-level debugging. Unlisted articles are being shown, click here to show only listed articles.