Lecture and tutorial classes
Characterization and verification of quantum simulations
(Summer term 2019)
Quantum simulations and quantum computing are among the most exciting applications of quantum mechanics.
More generally,
in the quantum technology research field one aims to develop new devices using quantum superposition and entanglement.
In a popular wording, these anticipated developments will lead to the second quantum revolution.
A main milestone is the use of quantum capabilities to solve a (computational) problem that cannot practically be solved otherwise.
Theoretical proposals include integer factoring (Shor's algorithm),
speedups for optimization and machine learning algorithms,
the simulation of complex quantum systems,
and certain sampling experiments specifically tailored to that milestone.
But if one cannot obtain the output of a quantum simulation or computation by conventional means how can one make sure that the outcome is correct?
The output of integer factorization can efficiently be checked but, for instance, for the estimation of energies in quantum manybody systems, or outcomes of dynamical simulations, the situation is much less clear.
Hence, for the development of trusted quantum technologies special characterization and verification techniques are urgently required.
This course gives an introduction to the research field,
to the problems of characterization, validation, and verification,
and first ways to solve them.
More specifically, quantum state tomography, quantum states certification, quantum process tomography, and randomized benchmarking will be covered.
In particular, the course provides an overview of the latest developments in this still young and very active research field.
The approaches of the course are mainly of conceptual and mathematical nature.
Content
Fidelity estimation and certification of quantum state preparations
Randomized benchmarking for quantum dynamics
Quantum state and process tomography (based on compressed sensing)
Exercises and other files will be uploaded here.
Lecture notes can be found here.
Formal things
Lecture and tutorial class
Monday 8:30am, room 25.32.03.51 (lecture)
Tuesday 10:30am, room 25.32.02.51 (tutorial class)
The course consists of
2 hours lecture (L) by Martin Kliesch (teaching@mkliesch.eu) and
2 hours tutorial (T) class (Übung) by Raphael Brieger (raphael.brieger@hhu.de)
There will be student presentations in the last part of the course (if the number of students admits it).
Assignments will be uploaded every two weeks.
The solutions to the assignment sheets need to be handed in.
At least 70% of the sheets need to be finished as a prerequisite for the exam.
There will be no corrections but the solutions will be discussed in the tutorial classes.
Collaboration policy: Collaborations are only allowed, if they are disclosed on the exercise submissions.
Preliminary schedule
April
01  L  Motivation, course outline, formalities  Exercise 1 handed out 
02  T  Introduction, POVMs, SVD  
08  L  QST, informational completeness  
09  L  Informational completeness 2  
15  L  Linear inversion, frame theory  Due date for Ex. 1, Ex. 2 handed out 
16  T  Student questions & discussion  
22   Public holiday (Easter Monday)  
23  L  kdesigns  
29  L  Symmetric measurements  Due date for Ex. 2, Ex. 3 handed out 
30  T  Discussion of Ex. 2  

May
06  L  Symmetric measurements  
07  T   
13  L  Certification  Due date for Ex. 3, Ex. 4 handed out 
14  T  Tail bounds, direct fidelity estimation  
20  L  Direct fidelity estimation  
21  T  Student questions & discussion  
27  L  Direct fidelity estimation  Due date for Ex. 4, Ex. 5 handed out 
28  T  Discussion Ex. 4  

June
03  L  Quantum state certification  
04  L  Quantum state certification  
10   Public Holiday (Whit Monday)  
11  T  Discussion Ex. 5  Due date for Ex. 5, Ex. 6 posted on June 12 
17  L  Q. state tomography II  
18  L  Q. state tomography II  
24  L  Quantum processes  Due date for Ex. 6, Ex. 7 handed out 
25  T  Discussion Ex. 6  

July
01  L  Randomized benchmarking (RB)  
02  L  Interleaved RB and process tomography  
08  L  Projected least squares estimation  Due date for Ex. 7 
09  T  Discussion Ex. 7  

