Ciro Santilli @cirosantilli 37

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Snowden (film) by

Ciro Santilli 37  Updated 2025-06-02  +Created 1970-01-01

Aptitude test scene from the Snowden 2016 film

FISA Court Order The Guardian discussion scene from the Snowden 2016 film

How is this Possible? scene from the Snowden 2016 film

Fresh Brains for You scene from the Snowden 2016 film

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Ciro Santilli 37  Updated 2025-06-02  +Created 1970-01-01

numpy.org/doc/1.24/reference/routines.fft.html

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Pauli-X gate by

Ciro Santilli 37  Updated 2025-06-02  +Created 1970-01-01

The quantum NOT gate swaps the state of

∣ 0 ⟩

and

∣ 1 ⟩

, i.e. it maps:

x ∣ 0 ⟩ + y ∣ y ⟩ \to y ∣ 0 ⟩ + x ∣ y ⟩

As a result, this gate also inverts the probability of measuring 0 or 1, e.g.

if the old probability of 0 was 0, then it becomes 1
if the old probability of 0 was 0.2, then it becomes 0.8

[0110]

Quantum NOT gate matrix

.

Figure 1.
Quantum NOT gate symbol
. Source.

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Phase shift gate by

Ciro Santilli 37  Updated 2025-06-02  +Created 1970-01-01

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Mathematics course of the University of Oxford by

Ciro Santilli 37  Updated 2025-06-02  +Created 1970-01-01

www.ox.ac.uk/admissions/undergraduate/courses/course-listing/mathematics

List of handbooks open as of 2022 at: www.maths.ox.ac.uk/members/students/undergraduate-courses/teaching-and-learning/handbooks-synopses Kudos, e.g. unlike the physics course of the University of Oxford which paywalled them. 2022 one: www.maths.ox.ac.uk/system/files/attachments/UG%20Handbook%202022.pdf

The Oxford mathematics Moodle has detailed course listings, and most PDFs are not paywalled.

E.g. the 2024 course:

Year 1: everything seems mandatory:
- Michaelmas Term
  - Introduction to University Mathematics
  - Introduction to Complex Numbers
  - Linear Algebra I
  - Analysis I
  - Introductory Calculus
  - Probability
  - Geometry
- Hilary Term
  - Linear Algebra II
  - Groups and Group Actions
  - Analysis II
  - Dynamics
  - Fourier Series and Partial Differential Equations
  - Multivariable Calculus
- Trinity Term
  - Groups and Group Actions
  - Analysis III
  - Statistics and Data Analysis
  - Constructive Mathematics
Year 2:
- Mandatory big courses:
- long options:
  - Rings and Modules
  - Integration
  - Topology
  - Differential Equations 2
  - Numerical Analysis
  - Probability
  - Statistics
  - Fluids and Waves
  - Quantum Theory
- short options
  - Number Theory
  - Group Theory
  - Projective Geometry
  - Integral Transforms
  - Calculus of Variations
  - Graph Theory
  - Mathematical Modelling in Biology
Year 3: pick any 8 courses. Does not say which courses exist in PDF but we can get them from courses.maths.ox.ac.uk/course/index.php?categoryid=814 of the Oxford mathematics Moodle:
- Michaelmas
  - B1.1 Logic (2024-25)
  - B2.1 Introduction to Representation Theory (2024-25)
  - B3.2 Geometry of Surfaces (2024-25)
  - B3.5 Topology and Groups (2024-25)
  - B4.1 Functional Analysis I (2024-25)
  - B5.2 Applied Partial Differential Equations (2024-25)
  - B5.3 Viscous Flow (2024-25)
  - B5.5 Further Mathematical Biology (2024-25)
  - B6.1 Numerical Solution of Partial Differential Equations (2024-25)
  - B6.3 Integer Programming (2024-25)
  - B7.1 Classical Mechanics (2024-25)
  - B8.1 Probability, Measure and Martingales (2024-25)
  - B8.4 Information Theory (2024-25)
  - B8.5 Graph Theory (2024-25)
  - BO1.1 History of Mathematics (2024-25)
  - BOE Other Mathematical Extended Essay (2024-25)
  - BSP Structured Projects (2024-25)
- Hilary
  - B1.2 Set Theory (2024-25)
  - B2.2 Commutative Algebra (2024-25)
  - B2.3 Lie Algebras (2024-25)
  - B3.1 Galois Theory (2024-25)
  - B3.3 Algebraic Curves (2024-25)
  - B3.4 Algebraic Number Theory (2024-25)
  - B4.3 Distribution Theory (2024-25)
  - B4.2 Functional Analysis II (2024-25)
  - B5.1 Stochastic Modelling of Biological Processes (2024-25)
  - B5.4 Waves and Compressible Flow (2024-25)
  - B5.6 Nonlinear Dynamics, Bifurcations and Chaos (2024-25)
  - B6.2 Optimisation for Data Science (2024-25)
  - B7.2 Electromagnetism (2024-25)
  - B7.3 Further Quantum Theory (2024-25)
  - B8.2 Continuous Martingales and Stochastic Calculus (2024-25)
  - B8.3 Mathematical Models of Financial Derivatives (2024-25)
  - B8.6 High Dimensional Probability (2024-25)
  - SB3.1 Applied Probability (2024-25)
  - BO1.1 History of Mathematics (2024-25)
  - BOE Other Mathematical Extended Essay (2024-25)
  - BSP Structured Projects (2024-25)
Year 4: pick any 8 courses (up to 10 if you're crazy). Does not say which courses exist in PDF but we can get them from courses.maths.ox.ac.uk/course/index.php?categoryid=814 of the Oxford mathematics Moodle:
- Michaelmas
  - C1.1 Model Theory (2024-25)
  - C1.4 Axiomatic Set Theory (2024-25)
  - C2.2 Homological Algebra (2024-25)
  - C2.4 Infinite Groups (2024-25)
  - C2.7 Category Theory (2024-25)
  - C3.1 Algebraic Topology (2024-25)
  - C3.3 Differentiable Manifolds (2024-25)
  - C3.4 Algebraic Geometry (2024-25)
  - C3.7 Elliptic Curves (2024-25)
  - C3.8 Analytic Number Theory (2024-25)
  - C4.1 Further Functional Analysis (2024-25)
  - C4.3 Functional Analytic Methods for PDEs (2024-25)
  - C5.2 Elasticity and Plasticity (2024-25)
  - C5.5 Perturbation Methods (2024-25)
  - C5.7 Topics in Fluid Mechanics (2024-25)
  - C5.11 Mathematical Geoscience (2024-25)
  - C5.12 Mathematical Physiology (2024-25)
  - C6.1 Numerical Linear Algebra (2024-25)
  - C6.5 Theories of Deep Learning (2024-25)
  - C7.1 Theoretical Physics (C6) (2024-25)
  - C7.5 General Relativity I (2024-25)
  - C8.1 Stochastic Differential Equations (2024-25)
  - C8.3 Combinatorics (2024-25)
  - CCD Dissertations on a Mathematical Topic (2024-25)
  - COD Dissertations on the History of Mathematics (2024-25)
- Hilary
  - C1.2 Gödel's Incompleteness Theorems (2024-25)
  - C1.3 Analytic Topology (2024-25)
  - C2.3 Representation Theory of Semisimple Lie Algebras (2024-25)
  - C2.5 Non-Commutative Rings (2024-25)
  - C2.6 Introduction to Schemes (2024-25)
  - C3.2 Geometric Group Theory (2024-25)
  - C3.5 Lie Groups (2024-25)
  - C3.6 Modular Forms (2024-25)
  - C3.9 Computational Algebraic Topology (2024-25)
  - C3.10 Additive Combinatorics (2024-25)
  - C3.11 Riemannian Geometry (2024-25)
  - C3.12 Low-Dimensional Topology and Knot Theory (2024-25)
  - C4.6 Fixed Point Methods for Nonlinear PDEs (2024-25)
  - C4.9 Optimal Transport & Partial Differential Equations (2024-25)
  - C5.1 Solid Mechanics (2024-25)
  - C5.4 Networks (2024-25)
  - C5.6 Applied Complex Variables (2024-25)
  - C6.2 Continuous Optimisation (2024-25)
  - C6.4 Finite Element Method for PDEs (2024-25)
  - C7.1 Theoretical Physics (C6) (2024-25)
  - C7.4 Introduction to Quantum Information (2024-25)
  - C7.6 General Relativity II (2024-25)
  - C7.7 Random Matrix Theory (2024-25)
  - C8.2 Stochastic Analysis and PDEs (2024-25)
  - C8.4 Probabilistic Combinatorics (2024-25)
  - C8.7 Optimal Control (2024-25)
  - CCD Dissertations on a Mathematical Topic (2024-25)
  - COD Dissertations on the History of Mathematics (2024-25)

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Multi-qubit gate by

Ciro Santilli 37  Updated 2025-06-02  +Created 1970-01-01

The most common way to construct multi-qubit gates is to use single-qubit gates as part of a controlled quantum gate.

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Ciro Santilli 37  Updated 2025-06-02  +Created 1970-01-01

wormwideweb.org/

Browse freely moving whole-brain calcium imaging datasets

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Single-qubit gate by

Ciro Santilli 37  Updated 2025-06-02  +Created 1970-01-01

The first two that you should study are:

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Geography of Europe by

Ciro Santilli 37  Updated 2025-06-02  +Created 1970-01-01

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Ciro Santilli 37  Updated 2025-06-02  +Created 1970-01-01

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Controlled quantum gate by

Ciro Santilli 37  Updated 2025-06-02  +Created 1970-01-01

Controlled quantum gates are gates that have two types of input qubits:

control qubits
operand qubits (terminology made up by Ciro Santilli just now)

These gates can be understood as doing a certain unitary operation only if the control qubits are enabled or disabled.

The first example to look at is the CNOT gate.

Figure 1.
Generic controlled quantum gate symbol
. Source.
The black dot means "control qubit", and "U" means an arbitrary Unitary operation.
When the operand has a conventional symbol, e.g. the Figure "Quantum NOT gate symbol" for the quantum NOT gate to form the CNOT gate, that symbol is used in the operand instead.

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Evening raga by

Ciro Santilli 37  Updated 2025-06-02  +Created 1970-01-01

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Ciro Santilli 37  Updated 2025-06-02  +Created 1970-01-01

Raag Puriya Dhanashri performed on the Sitar by Shahid Parvez

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Ungulate subclade by

Ciro Santilli 37  Updated 2025-06-02  +Created 1970-01-01

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Cow by

Ciro Santilli 37  Updated 2025-06-02  +Created 1970-01-01

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Information Engineering group of the University of Oxford by

Ciro Santilli 37  Updated 2025-06-02  +Created 1970-01-01

www.robots.ox.ac.uk

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Hadamard gate by

Ciro Santilli 37  Updated 2025-06-02  +Created 1970-01-01

The Hadamard gate takes

∣ 0 ⟩

or

∣ 1 ⟩

(quantum states with probability 1.0 of measuring either 0 or 1), and produces states that have equal probability of 0 or 1.

H = \frac{1}{2} [11 1 - 1]

Hadamard gate matrix

.

Figure 1.
Hadamard gate symbol
. Source.

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Empty circle control qubit notation by

Ciro Santilli 37  Updated 2025-06-02  +Created 1970-01-01

Some authors use the convention of:

filled black circle: conventional controlled quantum gate, i.e. operate if control qubit is active
empty (White) circle: operate if control qubit is inactive

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python/numpy/fft_cheat.py by

Ciro Santilli 37  Updated 2025-06-02  +Created 1970-01-01

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Alps by

Ciro Santilli 37  Updated 2025-06-02  +Created 1970-01-01

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