Quantum Theory Made Easy 0 1 Classical p0p0 p1p1 probabilities Quantum a0a0 a1a1 0 1 amplitudes p 0 +p 1 =1|a 0 | 2 +|a 1 | 2 =1 bit qubit p i is a real.

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Quantum Theory Made Easy 0 1 Classical p0p0 p1p1 probabilities Quantum a0a0 a1a1 0 1 amplitudes p 0 +p 1 =1|a 0 | 2 +|a 1 | 2 =1 bit qubit p i is a real numbera i is a complex number Prob(i)=p i Prob(i)=|a i | 2

Quantum Theory Made Easy Classical Evolution 00 01 10 11 00 01 10 11 Quantum Evolution stochastic matrix 00 01 10 11 00 01 10 11 transition probabilitiestransition amplitudes unitary matrix

Interference 0 1 0 1 measure 0 50% 1 measure 0 50% 1 100% 0% 100% 0% qubit input

Interfering Pathways 100% H 50% 50% C 50% H 10% 90% 20% 80% 15% H 85% C 1.0 H 0.707 0.707 C 0.707 H 0.707 -0.707 0.707 0.0 H 1.0 C Always addition!Subtraction! Classical Quantum

Superposition Qubits a0a0 a1a1 0 1 amplitudes a i is a complex number 1 √2√2 ( |  + |  ) Schrödinger’s Cat

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