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2011-CS9-schulman

# 2011-CS9-schulman - The Sound of a Quantum Computer Leonard...

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The Sound of a Quantum Computer Leonard J. Schulman Caltech CS9, Fall 2011

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Computer Science begins with the question “How hard is a computational problem?” Input-output problems: given input x=(x 1 ... x n ), compute output f(x)=(y 1 ... y n ). Example 1: Multiplication. Easy. (Grade given x=“163,841 350,377” school) compute f(x)=“57,406,118,057” Example 2: Factorization. Hard. (1,000 given x=“57,406,118,057” digits today compute f(x)=“163,841 350,377” infeasible)
Classifying problems by time to solve them Classical poly-time n c 1. Shortest path in a size-n network 2. Checking an n-page proof 3. Linear optimization 4. Multiplying n-digit integers Classical exponential time 2 n 5. Finding an n- page proof of a conjecture 6. Nonlinear optimization 7. Factoring n-digit integers Supposed hardness: basis of RSA cryptosystem

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Types of computers Classical computer Deterministic |000 ...... states ...... |111 Evolves like a clock. Time-reversible time initial state “x” final state “f(x)” Classical computer Randomized |000 ...... states ...... |111 Evolves like a diffusion process (heat). Not time-reversible initial state “x” probability distribution on final states “f(x)” Quantum computer |000 ...... states ...... |111 Evolves like a wave (sound, water). Time-reversible initial state “x” wave-front on final states “f(x)”
Quantum computer |000 ...... states ...... |111 Evolves like a wave (sound, water).

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