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Faculty of Mathematics and Physics
Department of Algebra
Quantum Information
Universal set of gates
Universal set of gates
Section outline
◄
Reversible computation
►
Shor's algorithm
Select activity Universal set of gates
Universal set of gates
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Select activity Lecture notes implicitly invite the following task...
Lecture notes implicitly invite the following tasks:
Verify the function of the circuit ABC for the one-qubit controlled operator
Verify the equivalence of two distinct ways of multiplication by e^{i\alpha}
Verify the function of two-controlled operator
Verify the equivalence of the two-controlled gate and the one-controlled gate with the CNOT
Verify the ``control by zero'' with help of two X-gates
Try all square roots of negation
(You can also try other functions applied to an operator. For instance, what e^{i A}, where A is a normal operator looks like?)
Verify the function of the two-level operator U and its equivalence with the uncontrolled operator M
Make sure you understand the transformation of the complicated two-level operator to the simple one
Make sure you understand the ``unitary Gaussian elimination''.
Select activity Discussion
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Reversible computation
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Main course page
Mach-Zehnder interferometer
Basics of Complex Linear Algebra
Postulates of Quantum Mechanics
Introduction into tensor products
Deutsch-Jozsa algorithm
Reversible computation
Shor's algorithm
Discrete Fourier transform and its quantum decomposition
Complex projective line representations
Unitary operators as rotations
Extended Euler's formula and the AXBXC decomposition
Quantum Key Sharing principle
Tutorial 2023 examples
Tutorial 2022 examples
Tasks for credit
►
Shor's algorithm