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Undergraduate computational physics projects on quantum computing

### Abstract

Computational projects on quantum computing suitable for students in a junior-level quantum mechanics course are described. In these projects students write their own programs to simulate quantum computers. Knowledge is assumed of introductory quantum mechanics through the properties of spin 1/2. Initial, more easily programmed projects treat the basics of quantum computation, quantum gates, and Grover's quantum search algorithm. These are followed by more advanced projects to increase the number of qubits and implement Shor's quantum factoring algorithm. The projects can be run on a typical laptop or desktop computer, using most programming languages. Supplementing resources available elsewhere, the projects are presented here in a self-contained format especially suitable for a short computational module for physics students.

© 2015 American Association of Physics Teachers

Received 30 December 2014
Accepted 22 May 2015

Article outline:

I. INTRODUCTION
A. Classroom experience
B. Quantum computing paradigm
C. Straightforward and more challenging projects
D. Computer projects, programming hints, and exercises
E. Sources for further information
II. THE *N*-QUBIT REGISTER
III. THE QUANTUM GATE ARRAY COMPUTER
IV. MEASUREMENTS OF THE *N*-QUBIT REGISTER
*A. Programming project 1: Simulate measurement of the*
*N*-qubit register
V. QUANTUM GATES
A. The Hadamard gate
B. The phase shift gate
C. Applying a gate to the *N*-qubit register
D. Programming project 2: First full quantum computations
VI. GROVER'S QUANTUM SEARCH ALGORITHM
A. Grover's algorithm:Details
B. Programming project 3: Implement Grover's quantum search
VII. GATES OPERATING ON MORE THAN ONE QUBIT
A. Programming project 4: Computations using CNOT gates
VIII. INCREASING THE NUMBER OF QUBITS
A. Matrices for gates with an arbitrary number of qubits
B. Programming project 5: Handle an arbitrary number of qubits
C. Using sparse matrices
D. Programming project 6: Use sparse matrices to increase *N*
IX. SHOR'S QUANTUM FACTORING ALGORITHM
A. Shor's algorithm step by step
B. The quantum part of Shor's algorithm: Period-finding
C. Shor's algorithm with seven qubits
D. Programming project 7: Implement Shor's algorithm with seven qubits
E. How the quantum part of Shor's algorithm works
F. Implementing Shor's algorithm for arbitrary *N*
G. Programming project 8: Implement Shor's algorithm with N > 7
H. Using continued fractions to guess the period
X. POSTSCRIPT: IS QUANTUM COMPUTATION TRULY POWERFUL?

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2015-08-01

2016-10-22

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