Quantum Machine Learning Adam Brown, HEP-AI Quantum Computing Machine Learning Quantum MachineComputing Learning Quantum Computing Machine Learning so hot so so hot Quantum MachineComputing Learning Quantum MachineComputing 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 quantum computer (ii) P does not contain BQP “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 quantum computer (ii) P does not contain BQP “BQP" a quantum computer can do some things quickly that a classical computer cannot do quickly ENCOURAGING • factoring • quantum simulation (iii) EXP contains BQP easy on a classical computer can eventually do classical computer everything a quantum computer can do “P" • multiplication The Power of Quantum Computers (in theory) exponential time on classical computer “EXP” (i) BQP contains P • traveling salesman a quantum computer can (quickly) do • solving GO on NxN board everything a classical computer can (quickly) do easy on quantum computer (ii) P does not contain BQP “BQP" a quantum computer can do some things quickly that a classical computer cannot do quickly ENCOURAGING • factoring • quantum simulation (iii) EXP contains BQP easy on a classical computer can eventually do classical computer everything a quantum computer can do “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 • traveling salesman a quantum computer can (quickly) do • solving GO on NxN board everything a classical computer can (quickly) do easy on quantum computer (ii) P does not contain BQP “BQP" a quantum computer can do some things quickly that a classical computer cannot do quickly ENCOURAGING • factoring • quantum simulation (iii) EXP contains BQP easy on a classical computer can eventually do classical computer everything a quantum computer can do “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 • traveling salesman a quantum computer can (quickly) do • solving GO on NxN board everything a classical computer can (quickly) do easy on quantum computer (ii) P does not contain BQP “BQP" a quantum computer can do some things quickly that a classical computer cannot do quickly ENCOURAGING • factoring • quantum simulation (iii) EXP contains BQP easy on a classical computer can eventually do classical computer everything a quantum computer can do “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 classical computer quantum superpower: “EXP” EXPONENTIATION • traveling salesman “HILBERT SPACE IS HUGE” • solving GO on NxN board to describe state of N qubits easy on N quantum computer takes 2 real numbers “BQP" ↵ 00000000 + ...+ ↵ N 11111111 1| i 2 | i ENCOURAGING • factoring • quantum simulation (iii) EXP contains BQP easy on a classical computer can eventually do classical computer everything a quantum computer can do “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 classical computer quantum superpower: “EXP” EXPONENTIATION • traveling salesman “HILBERT SPACE IS HUGE” • solving GO on NxN board to describe state of N qubits easy on N quantum computer takes 2 real numbers “BQP" ↵ 00000000 + ...+ ↵ N 11111111 1| i 2 | i ENCOURAGING • factoring • quantum simulation easy on classical computer “P" quantum superweakness: LINEARITY • multiplication cannot directly see wave function “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 height/T thermally fluctuate e− ⇠ Encouraging Fact #1 you are here you want to be here height/T thermally fluctuate e− ⇠ pheight width/ quantum tunnel e− ⇥ ~ ⇠ Encouraging Fact #1 you are here you want to be here height/T thermally fluctuate e− ⇠ pheight width/ quantum tunnel e− ⇥ ~ ⇠ 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 HHL: with quantum takes (log N)2 ! 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 HHL: with quantum takes (log N)2 ! 2 subroutine in classical supervised learning is minimize ( H x - b ) 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 • traveling salesman a quantum computer can (quickly) do • solving GO on NxN board everything a classical computer can (quickly) do easy on quantum computer (ii) P does not contain BQP “BQP" a quantum computer can do some things quickly that a classical computer cannot do quickly ENCOURAGING • factoring • quantum simulation (iii) EXP contains BQP easy on a classical computer can eventually do classical computer everything a quantum computer can do “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 • traveling salesman a quantum computer can (quickly) do • solving GO on NxN board everything a classical computer can (quickly) do easy on quantum computer (ii) P does not contain BQP “BQP" a quantum computer can do some things quickly that a classical computer cannot do quickly ENCOURAGING • factoring • quantum simulation (iii) EXP contains BQP easy on a classical computer can eventually do classical computer everything a quantum computer can do “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 • classical = 10 -24 errors per gate, quantum = 10 -2 errors per gate The Power of Quantum Computers (in practice) • if “you” ever measure, coherence is destroyed • no cloning principle makes error correction hard • classical = 10 -24 errors per gate, quantum = 10 -2 errors per gate CLASSICAL QUANTUM The Power of Quantum Computers (in practice) • if “you” ever measure, coherence is destroyed • no cloning principle makes error correction hard • classical = 10 -24 errors per gate, quantum = 10 -2 errors per gate CLASSICAL QUANTUM 15 = 3 x 5 The Power of Quantum Computers (in practice) • if “you” ever measure, coherence is destroyed • no cloning principle makes error correction hard • classical = 10 -24 errors per gate, quantum = 10 -2 errors per gate CLASSICAL QUANTUM 15 = 3 x 5 143 = 11 x 13 The Power of Quantum Computers (in practice) • if “you” ever measure, coherence is destroyed • no cloning principle makes error correction hard • classical = 10 -24 errors per gate, quantum = 10 -2 errors per gate CLASSICAL QUANTUM 15 = 3 x 5 143 = 11 x 13 “quantum supremacy” 2018?? The Power of Quantum Computers (in practice) “quantum supremacy” 2018?? H T T H H H H T input random state into ~50 qubit random quantum