Eniac 1950: 30 tons, 150 KW, 1 KB, 100 KHz

  qc today comparable to early days of classical computers in the 1950's

  predates me; mom

  developing programs by hand before Eniac,et.al. was built,
  vs. now using computers (information processing) to create and
  simulate next generation

Phone 2018: 5 oz., 1 W, 4 GB, 2 GHz

QC 2018: tons, KW, 20 Qubit (2**20 = 1 Mb), 1 MHz

  daughter

QC 2050: ???

  100 years after Eniac

  Dwave current, multivariable function minimization, simulated annealing

Ion Trap Quantum Device

  Two energy bands, represent 0/1, blue is applied laser, red is fluorescence

  Before measurement (c) is in superposition of both states

One Qubit

  Math, model of reality, complex amplitudes, magnitude squared = probability.

  doesn't make sense on macroscopic scale, agrees with experiments/measurements

  Operations are unitary matrices, preserve norm, reversible (conjugate transpose)

Single Qubit Operations

  2x2 complex matrices

  compare with classical bit: can't do much other than NOT (X gate)

  Hadamard transformation:  0 -> superposition of 0 and 1

  Parallelism

Two Qubits

  3 qubits -> 8 amplitudes, 4 qubits -> 16 amplitudes, etc.

  keeps doubling: 32 qubits -> 2**32 ~= 4 billion amplitudes

  Simulation limit: ~50 qubits with some tricks for certain problems

  Break 2000-bit RSA key: 4000 qubits

  DWave: ~2000 qubits but only adiabatic, multivariable function
   minimization, like simulated annealing, not general purpose

  independent qubits vs. entangled

  general normalization constraint