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Quantum Computing Examples

DOI

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's Algorithm

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:

Deutsch-Jozsa Algorithm

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:

Bernstein-Vazirani Algorithm

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:

Simon's Algorithm

Quantum Fourier Transform (QFT)

Scheme for n=3:

Quantum Fourier Transform

Superdense Coding

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

Superdense Coding

Quantum Teleportation

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

Quantum Teleportation

Quantum Phase Estimation

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

Quantum Phase Estimation

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:

Grover's Algorithm

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:

Shor's Algorithm

Swap Test

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

Swap test

References