Quantum Machine Learning Adam Brown, HEP-AI Quantum Computing - PowerPoint PPT Presentation

Quantum Machine Learning Adam Brown, HEP-AI

Quantum Computing Machine Learning

Quantum Computing Machine Learning

Quantum Computing Machine Learning so hot so so hot

Quantum Computing Machine Learning

Quantum Computing Machine Learning “I would predict that in 10 years there’s nothing but quantum machine learning.” [famous QML researcher in 2015]

Classical Quantum Dataset Dataset Use Classical Classical Machine Computer Learning Use Quantum Computer

The Power of Quantum Computers (in theory)

The Power of Quantum Computers (in theory) easy on classical computer “P"

The Power of Quantum Computers (in theory) easy on classical computer “P" • multiplication

The Power of Quantum Computers (in theory) easy on quantum computer “BQP" easy on classical computer “P" • multiplication

The Power of Quantum Computers (in theory) (i) BQP contains P a quantum computer can (quickly) do everything a classical computer can (quickly) do easy on quantum computer “BQP" easy on classical computer “P" • multiplication

The Power of Quantum Computers (in theory) (i) BQP contains P a quantum computer can (quickly) do everything a classical computer can (quickly) do easy on (ii) P does not contain BQP quantum computer “BQP" a quantum computer can do some things quickly that a classical computer cannot do quickly ENCOURAGING • factoring • quantum simulation easy on classical computer “P" • multiplication

The Power of Quantum Computers (in theory) exponential time on classical computer “EXP” (i) BQP contains P a quantum computer can (quickly) do everything a classical computer can (quickly) do easy on (ii) P does not contain BQP quantum computer “BQP" a quantum computer can do some things quickly that a classical computer cannot do quickly ENCOURAGING • factoring • quantum simulation (iii) EXP contains BQP a classical computer can eventually do easy on everything a quantum computer can do classical computer “P" • multiplication

The Power of Quantum Computers (in theory) exponential time on classical computer “EXP” (i) BQP contains P a quantum computer can (quickly) do • traveling salesman everything a classical computer can (quickly) do • solving GO on NxN board easy on (ii) P does not contain BQP quantum computer “BQP" a quantum computer can do some things quickly that a classical computer cannot do quickly ENCOURAGING • factoring • quantum simulation (iii) EXP contains BQP a classical computer can eventually do easy on everything a quantum computer can do classical computer “P" (iv) BQP does not contain EXP a quantum computer does not give • multiplication generic exponential speed-up

The Power of Quantum Computers (in theory) exponential time on classical computer “EXP” (i) BQP contains P a quantum computer can (quickly) do • traveling salesman everything a classical computer can (quickly) do • solving GO on NxN board easy on (ii) P does not contain BQP quantum computer “BQP" a quantum computer can do some things quickly that a classical computer cannot do quickly ENCOURAGING • factoring • quantum simulation (iii) EXP contains BQP a classical computer can eventually do easy on everything a quantum computer can do classical computer “P" (iv) BQP does not contain EXP a quantum computer does not give • multiplication generic exponential speed-up DISCOURAGING

The Power of Quantum Computers (in theory) exponential time on classical computer “EXP” (i) BQP contains P a quantum computer can (quickly) do • traveling salesman everything a classical computer can (quickly) do • solving GO on NxN board easy on (ii) P does not contain BQP quantum computer “BQP" a quantum computer can do some things quickly that a classical computer cannot do quickly ENCOURAGING • factoring • quantum simulation (iii) EXP contains BQP a classical computer can eventually do easy on everything a quantum computer can do classical computer “P" (iv) BQP does not contain EXP a quantum computer does not give • multiplication generic exponential speed-up “NO FREE LUNCH”

The Power of Quantum Computers (in theory) exponential time on quantum superpower: classical computer “EXP” EXPONENTIATION “HILBERT SPACE IS HUGE” • traveling salesman • solving GO on NxN board to describe state of N qubits easy on N takes 2 real numbers quantum computer “BQP" . . . + α 2 N | 11111111 i α 1 | 00000000 i + . . . ENCOURAGING • factoring • quantum simulation (iii) EXP contains BQP a classical computer can eventually do easy on everything a quantum computer can do classical computer “P" (iv) BQP does not contain EXP a quantum computer does not give • multiplication generic exponential speed-up “NO FREE LUNCH”

The Power of Quantum Computers (in theory) exponential time on quantum superpower: classical computer “EXP” EXPONENTIATION “HILBERT SPACE IS HUGE” • traveling salesman • solving GO on NxN board to describe state of N qubits easy on N takes 2 real numbers quantum computer “BQP" . . . + α 2 N | 11111111 i α 1 | 00000000 i + . . . ENCOURAGING • factoring • quantum simulation easy on classical computer quantum superweakness: “P" LINEARITY cannot directly see wave function • multiplication “NO FREE LUNCH”

Encouraging Fact #1 you are here you want to be here

Encouraging Fact #1 you are here you want to be here ∼ e − height /T thermally fluctuate

Encouraging Fact #1 you are here you want to be here thermally fluctuate ∼ e − height /T quantum tunnel ∼ e −√ height × width / ~

Encouraging Fact #1 you are here you want to be here ∼ e − height /T thermally fluctuate ∼ e −√ height × width / ~ quantum tunnel quantum beats classical for tall, thin barriers

Encouraging Fact #2 H T T H H H H T there are short quantum circuits whose output is hard to classically sample (follows directly from BQP not in P)

Encouraging Fact #2 H T T H H H H T there are short quantum circuits whose output is hard to classically sample (follows directly from BQP not in P) there are functions that can be expressed with a polynomial size quantum neural network that would require an exponentially large classical neural network

Encouraging Fact #3 Harrow, Hassidim, Lloyd algorithm (2008)

Encouraging Fact #3 Harrow, Hassidim, Lloyd algorithm (2008) given N x N matrix H and given vector b “find” the vector x such that H x = b

Encouraging Fact #3 Harrow, Hassidim, Lloyd algorithm (2008) given N x N matrix H and given vector b “find” the vector x such that H x = b c takes O(N ) classically

Encouraging Fact #3 Harrow, Hassidim, Lloyd algorithm (2008) given N x N matrix H and given vector b “find” the vector x such that H x = b c takes O(N ) classically 2 HHL: with quantum takes (log N) !

Encouraging Fact #3 Harrow, Hassidim, Lloyd algorithm (2008) given N x N matrix H and given vector b “find” the vector x such that H x = b c takes O(N ) classically 2 HHL: with quantum takes (log N) ! ( H x - b ) 2 subroutine in classical supervised learning is minimize function ansatz gives H best fit is x datapoints are b

The Power of Quantum Computers (in theory) exponential time on classical computer “EXP” (i) BQP contains P a quantum computer can (quickly) do • traveling salesman everything a classical computer can (quickly) do • solving GO on NxN board easy on (ii) P does not contain BQP quantum computer “BQP" a quantum computer can do some things quickly that a classical computer cannot do quickly ENCOURAGING • factoring • quantum simulation (iii) EXP contains BQP a classical computer can eventually do easy on everything a quantum computer can do classical computer “P" (iv) BQP does not contain EXP a quantum computer does not give • multiplication generic exponential speed-up DISCOURAGING

The Power of Quantum Computers (in practice) exponential time on classical computer “EXP” (i) BQP contains P a quantum computer can (quickly) do • traveling salesman everything a classical computer can (quickly) do • solving GO on NxN board easy on (ii) P does not contain BQP quantum computer “BQP" a quantum computer can do some things quickly that a classical computer cannot do quickly ENCOURAGING • factoring • quantum simulation (iii) EXP contains BQP a classical computer can eventually do easy on everything a quantum computer can do classical computer “P" (iv) BQP does not contain EXP a quantum computer does not give • multiplication generic exponential speed-up DISCOURAGING

The Power of Quantum Computers (in practice) • if “you” ever measure, coherence is destroyed • no cloning principle makes error correction hard -24 -2 • classical = 10 errors per gate, quantum = 10 errors per gate

The Power of Quantum Computers (in practice) • if “you” ever measure, coherence is destroyed • no cloning principle makes error correction hard -24 -2 • classical = 10 errors per gate, quantum = 10 errors per gate CLASSICAL QUANTUM