Quantum Computing Examples

Quantum computing examples with QISKit.

Examples

Deutsch's Algorithm

Problem. For given an oracle function f : {0, 1} -> {0, 1}, determine f is balanced or constant.

Deutsch-Jozsa Algorithm

Problem. For given an oracle function f : {0, 1}^n -> {0, 1}, determine f is balanced or constant.

Scheme for n=2:

Bernstein-Vazirani Algorithm

Problem. For given an oracle function f : {0, 1}^n -> {0, 1}, f(x) = a x, determine a.

Scheme for n=3:

Simon's Algorithm

Problem. For given an oracle function f : {0, 1}^n -> {0, 1}^n which has period a: ∃!a != 0: ∀x f(x) = f(y) => y = x ⊕ a. Determine a.

Scheme for n=2:

Quantum Fourier Transform (QFT)

Scheme for n=3:

Superdense Coding

Task. Transmit two bits of classical information between Alice and Bob using only one qubit.

Quantum Teleportation

Task. Alice would like to send Bob a qubit that is in some unknown state.

Quantum Phase Estimation

Problem. Given an unitary operator U, estimate θ in U|ψ>=exp(2πiθ)|ψ>.

Grover's Algorithm

Problem. For given an oracle function f : {0, 1}^n -> {0, 1}^n, ∃! ω : f(ω) = a, find ω.

Scheme for n=3:

Shor's Algorithm

Problem. Shor's algorithm is a quantum computer algorithm for integer factorization. Informally, it solves the following problem: Given an integer N, find its prime factors.

Scheme for find the period r for f(x) = 2^x mod 15:

Swap Test

Task. For given two unknown quantum states, determine how much them differs.

References

• Jonahtan Hui, Quantum Computing Series, Medium

• Qiskit, Medium

• Qiskit, GitHub

• An Introduction to Quantum Computing, Kaye, ‎Laflamme, Mosca

• Learn Quantum Computation using Qiskit