Controlled quantum gates are gates that have two types of input qubits:These gates can be understood as doing a certain unitary operation only if the control qubits are enabled or disabled.
- control qubits
- operand qubits (terminology made up by Ciro Santilli just now)
Generic controlled quantum gate symbol
. Source. 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.
The most common way to construct multi-qubit gates is to use single-qubit gates as part of a controlled quantum gate.
The quantum NOT gate swaps the state of and , i.e. it maps: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
The Hadamard gate takes or (quantum states with probability 1.0 of measuring either 0 or 1), and produces states that have equal probability of 0 or 1.
The first two that you should study are:
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
- Trinity Term
- Groups and Group Actions
- Analysis III
- Statistics and Data Analysis
- Constructive Mathematics
- Michaelmas Term
- 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)
- Michaelmas
- 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)
- Michaelmas
There are unlisted articles, also show them or only show them.