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FOPRA Experiment 39: Universal Gate Sets for Quantum Computation

Course 0000005388 in SS 2021

General Data

Course Type practical training
Semester Weekly Hours 1 SWS
Organisational Unit TUPHT30
Lecturers Robert König
Simone Warzel
Michael Marc Wolf
Assistants:
Silvia Schulz
Dates

Further Information

Courses are together with exams the building blocks for modules. Please keep in mind that information on the contents, learning outcomes and, especially examination conditions are given on the module level only – see section "Assignment to Modules" above.

additional remarks In the standard (circuit) model of quantum computation, a typical computation proceeds by application of an n-qubit unitary U to a certain initial state and subsequent measurement of each qubit in the computational basis. The hardware of a universal quantum computer should therefore provide the capability of applying an arbitrary unitary U. In practice, however, control of quantum systems is severely limited by the specifics of the system under consideration and/or experimental limitations. For example, control pulses (realizing unitary evolutions) may only be applied along a certain subset of directions with a restricted range of frequencies and/or durations. Is such hardware su cient to reach the desired goal of performing universal quantum computation? If so, how many operations are required to realize a given unitary U? In this project, you will be given a (ficticious) device that implements a single-qubit unitary specified by a discrete set of control parameter values. Your task is to use (several copies of) this device to (approximately) realize an arbitrary n-qubit unitary U. In other words, you will generate an instruction set (a quantum circuit) for executing the corresponding quantum computation using the given hardware. A key notion of interest here is that of a universal gate set, a finite family of (typically single- and two-qubit) unitaries (called gates) such that any unitary U can be approximately written as a product of a certain number L of gates. Given such a universal gate set, we may ask about the relationship between the length L of the gate sequence (ultimately corresponding to the runtime of your computation) and the quality of approximation. In addition, we want to efficiently (by classical computation) find a suitable sequence. The so-called Solovay-Kitaev theorem provides answers to this problem and is the main topic of this project. The project will involve a collection of mathematical exercises. You will also gain experience programming in python by developing and implementing a compilation procedure as described above.
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