• Corpus ID: 198147332

Quantum Computing: Lecture Notes

  title={Quantum Computing: Lecture Notes},
  author={Ronald de Wolf},
This is a set of lecture notes suitable for a Master's course on quantum computation and information from the perspective of theoretical computer science. The first version was written in 2011, with many extensions and improvements in subsequent years. The first 10 chapters cover the circuit model and the main quantum algorithms (Deutsch-Jozsa, Simon, Shor, Hidden Subgroup Problem, Grover, quantum walks, Hamiltonian simulation and HHL). They are followed by 2 chapters about complexity, 4… 

Quantum Computing: Implementing Hitting Time for Coined Quantum Walks on Regular Graphs

A quantum circuit for the MNRS algorithm, which finds a marked node in a graph with a quantum walk, is designed and used to find a hitting time for the marked nodes in the walk, and it is shown that the execution on a noise-free simulator results in hitting times that agree with the theoretical expectations.

Demonstration of Shor's factoring algorithm for N [Formula: see text] 21 on IBM quantum processors.

This work implemented the quantum order-finding algorithm for factoring the integer 21 using only five qubits and successfully verified the presence of entanglement between the control and work register qubits, which is a necessary condition for the algorithm's speedup in general.

Sublinear quantum algorithms for estimating von Neumann entropy

The problem of obtaining estimates to within a multiplicative factor γ > 1 of the Shannon entropy of probability distributions and the von Neumann entropy of mixed quantum states is studied, and it is proved that no polynomial query algorithm can multiply the entropy of distributions with arbitrarily low entropy.

Thermodynamic optimization of quantum algorithms: on-the-go erasure of qubit registers

There is a trade-off: if the authors have enough partial information about a problem to build efficient on-the-go erasure, they can use it to instead simplify the algorithm, so that fewer qubits are needed to run the computation in the first place.

Quantum protocols for few-qubit devices

This thesis focuses on near-term experiments that feature a small number of qubits that lose the stored information after a short amount of time, and proposes various theoretical protocols that can get the best out of such highly limited computers.

Sample complexity of hidden subgroup problem


  • Computer Science
  • 2018
This thesis attempts to answer whether there exists a stabilizer testing algorithm that is perfectly complete and independent of the number of qubits given less than 6 copies of the state, and investigates whether there is a protocol that is more efficient than the one that just repeats the 6-copy algorithm many times.

Quantum Analysis of AES Lowering Limit of Quantum Attack Complexity

This work presents the least Toffoli depth and full depth implementations of AES, thereby improving from Zou et al.

Quantum Natural Language Generation on Near-Term Devices

This paper designs a hybrid quantum-classical algorithm for sentence generation based on the well-known simulated annealing technique for combinatorial optimisation, and uses this algorithm to demonstrate successful sentence generation on both simulated and real quantum hardware.

Quantum Analysis of AES

This work presents the least Toffoli depth and full depth implementations of AES, thereby improving from Zou et al.



Classical computing, quantum computing, and Shor's factoring algorithm

This is an expository talk written for the Bourbaki Seminar on the structure of the classical deterministic computations and relates Kolmogorov's complexity to the spectral properties of computable function.

Quantum vs. classical communication and computation

A simple and general simulation technique is presented that transforms any black-box quantum algorithm to a quantum communication protocol for a related problem, in a way that fully exploits the quantum parallelism, to obtain new positive and negative results.

Quantum complexity theory

This paper gives the first formal evidence that quantum Turing machines violate the modern (complexity theoretic) formulation of the Church--Turing thesis, and proves that bits of precision suffice to support a step computation.

Quantum computation and quantum information

  • T. Paul
  • Physics
    Mathematical Structures in Computer Science
  • 2007
This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing. The first two papers deal

On the power of quantum computation

  • Daniel R. Simon
  • Computer Science
    Proceedings 35th Annual Symposium on Foundations of Computer Science
  • 1994
This work presents here a problem of distinguishing between two fairly natural classes of function, which can provably be solved exponentially faster in the quantum model than in the classical probabilistic one, when the function is given as an oracle drawn equiprobably from the uniform distribution on either class.

Quantum lower bounds by polynomials

This work examines the number T of queries that a quantum network requires to compute several Boolean functions on {0,1}/sup N/ in the black-box model and gives asymptotically tight characterizations of T for all symmetric f in the exact, zero-error, and bounded-error settings.

Quantum computation of Fourier transforms over symmetric groups

A quantum polynomial time algorithm for the Fourier transform for the symmetric groups Sn is given, adapting results obtained by Clausen and Diaconis–Rockmore to the quantum setting.

Quantum Circuit Complexity

  • A. Yao
  • Computer Science
  • 1993
It is shown that any function computable in polynomial time by a quantum Turing machine has aPolynomial-size quantum circuit, and this result enables us to construct a universal quantum computer which can simulate a broader class of quantum machines than that considered by E. Bernstein and U. Vazirani (1993), thus answering an open question raised by them.

Quantum speed-up of Markov chain based algorithms

  • M. Szegedy
  • Computer Science
    45th Annual IEEE Symposium on Foundations of Computer Science
  • 2004
It is shown that under certain conditions, the quantum version of the Markov chain gives rise to a quadratic speed-up, and that the quantum escape time, just like its classical version, depends on the spectral properties of the transition matrix with the marked rows and columns deleted.

Optimal Hamiltonian Simulation by Quantum Signal Processing.

It is argued that physical intuition can lead to optimal simulation methods by showing that a focus on simple single-qubit rotations elegantly furnishes an optimal algorithm for Hamiltonian simulation, a universal problem that encapsulates all the power of quantum computation.