intro-quantum-computing

This repo stores some of the code I wrote while reading through a great quantum computing textbook by Thomas Wong. I ran some of it on quantum computers via the IBM Quantum Platform.

Topics Covered + Circuit Implementations

Adders

• Quantum Ripple-Adder

  • link

• Quantum Subtracter

  • link

• QFT Adder

  • Paper: link
  • Quirk: link

Quantum Error Correction

• Bit-Flip Code

  • Rotations about the x-axis (bit flip error)
  • Measure first, classical operations later: link
  • Controlled operations in superposition, then collapse: link

• Phase-Flip Code

  • Rotations about the z-axis (phase flip error -- change in relative phase): link

• Shor Code

  • Shor encoding with bit-flip error correction: link
  • Shor encoding with phase-flip error correction: link

Quantum Teleportation

• Transmitting the state of 1 qubit using 2 classical bits: link

Deutsch's Algorithm

• Finding the parity of two bits with one oracle
  • Quirk: link
  • IBM: link

Deutsch-Jozsa Algorithm

• Finding the parity of a string of bits
  • Quirk: link
  • IBM: link

Bernstein-Vazirani Algorithm

• Finding the value of a bit string s, dotted into an input bit string
  • Quirk: link
  • IBM: link

Grover's Algorithm

• Quantum search / brute force
  • Quirk (4 input qubits with answer w = 1011): link

Quantum Fourier Transform

• Calculate the discrete Fourier transform quantumly!
  • Quirk (6 qubits): link
  • Quirk (IQFT): link

Phase / Eigenvalue Estimation (circuit on cover of textbook)

• Quantum gates are unitary, so their eigenvalues are of the form e^(ix), where x is real and is the phase of the eigenvalue
• Upper part input and output is n-bit eigenvector of matrix U --- eigenstate |v>
• Lower part output is m-bit binary decimal j that gives x = 2pi * j
  • So we estimate the phase --> eigenvalue with m bits of precision
  • Quirk: link

Finding The Period of a Modular Exponentiation

• Find the (nontrivial) value of x such that a^x mod m = a^0 mod m = 1 mod m
  • Quirk: (3^x mod 7) link