The Quantum Supremacy Experiment John Martinis, Google & UCSB New tests of QM: Does QM work for 10 15 Hilbert space? Does digitized error model also work? Demonstrate exponential computing power: Check 50 qubit quantum computer with largest classical supercomputer
Quantum Data 0!+ 1!
Quantum Data ( 0!+ 1! ) 2 = 00!+ 01!+ 10!+ 11!
Really Big Data ( 0!+ 1! ) 300 more states than atoms in universe
Encoding of quantum bits H atom: quantum circuit: 0) 100!m 1) orbitals 6 GHz microwave oscillator Easier control for large size
Building a Real Quantum Computer! For one device, qubits have Coherence Coupling Measurement Low errors! Good control each qubit! Room for control circuitry! Reprogrammable! Flexible architecture! Scalable competing requirements general purpose What s so hard? Systems vs. Control: Can t copy quantum information Hard to separate into sub-functions Quantum Systems Engineering
Quantum vs. Classical-Supercomputer Challenge
Quantum Supremacy Proposal by Google Theory Group*! Simple qubit test, results checked by supercomputer (>42-50, can t check anymore)! Demonstrates exponential processing power but does not compute anything useful (yet)! A sensitive and complex test: results fail with one qubit error! Good test of scalable quantum computation Proves complex quantum processing Error metrology Fundamental test of error digitization for 10 15 state space Forward compatible to error correction *S. Boixo et. al., arxiv:1608:08752
Algorithm for Supremacy Test: Qubit Speckle 1) Run 1 sequence, chosen randomly from gateset d (time) Clifford Non-Clifford n qubits initialize "! = 0! measure k X, Z, H, X 1/2! Z 1/4 CZ 2) Run quantum computer, measure k (0 to 2 n -1; ex. 5 = {0!0101}) repeat sampling 100,000 times 3) Random guess: any outcome k has probability p cl = 1/2 n 4) Calculate "!, p(k)= #k "! 2 not uniform; store in lookup table (fully entangled with complexity 2 n : 1-D, d>n; 2-D, d>n 1/2 ) 1 s days 200 drives 5) Correlation: cross entropy S = # ln p(k)/p cl! 6) Compare to theory S qu 0.42 quantum S cl -0.58 classical 7) Try another sequence
9 How Does it Work? Im{$} 4 3 2 p1/2 7 6 5 4 3 2 1 1 0 Re{$} 0-1 -2 1/2n -3-4 -4 probability p(k)/pcl! Gaussian distribution Re{$} & Im{$} gives Porter-Thomas (exponential) distribution 8-3 -2-1 0 1 2 3 4 0 2000 4000 index6000 k 2n 8000 10000
How Does it Work?! Gaussian distribution Re{$} & Im{$} gives Porter-Thomas (exponential) distribution! With one error anywhere distribution is flat (classical like) probability of no error probability p(k)/p cl e -p S tot P 0 S qu + (1-P 0 ) S cl 0 index k [p(k)-ordered] 2 n P 0 = (1!! 1 ) nd (1!! 2 ) nd (1!! m ) n " exp[!nd(! 1 +! 2 )+ n! m ] # exp[!n e ] Include all 1, 2, measure errors % Need total error N e < 3 ~
Exponential Decay of Quantum Information info. dist. S tot - S cl 1 0.8 0.6 0.4 0.2 need N e < 3 ~ 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 number of errors N e nd % 2
Errors Destroy Quantum Computation S tot P 0 S qu + (1-P 0 ) S cl Probability of no error: P 0 = exp[ -N g % g ] Average number of errors: N g % g = 49 x 7 x 0.005005 = 1.7 Need: scaling with low errors
Roadmap Metric for Scaling and Errors Shows system performance Worst (2-qubit) error 10-1 10-2 10-3 demonstrations supremacy / analog quantum error correction logical gates difficult direction quantum computer 10-4 Number qubits 1 10 100 10 4 10 6 10 8
Roadmap Metric for Scaling and Errors Much to invent, especially scaling Worst (2-qubit) error 10-1 10-2 10-3 quantum computer 10-4 1 10 100 10 4 10 6 10 8 Number qubits
Initial Scalable Device Operation fidelities: (in same device) 1 qubit: 99.9% 2 qubit: 99.5% measure: 99% Key to building a QC: High fidelity gates in a scalable architecture
9 Xmons: hifi gates fast readout surface code compa6ble
CNOTs measure read decay state flip Control Waveforms for 9 qubits Cycle though error measurement 8 times measure data 1 2 3 4 5 6 7 8 Q 0 Q 1 Q 2 Q 3 Q 4 Q 5 Q 6 Q 7 Q 8
9 Qubit Data: Bit-Flip Error Correction Works! & = 3.2 > 1, so better memory for higher order fault tolerant behavior!
Digitized Adiabatic Quantum Computing!"#$%&'()*%"#*+%"+%+,)-% C,)-%,:;(349D%E"-A;9>%-;-8+*;&'"+F#%,-./"4%3&."./ " 01% +)-234%&'()*% 5607% 8%9)#:;<"=4%#>%#?1% 07@% G32;:)*$9%F94H%ID0%'+% 8%)A34% BB5% 8%=):*'"3%,$"+4% 5B6% >10 3 gates
1J%G::"K>%.;9,"F(34%<)*$%!::;:%.;::4#F;-% Bump bonding to separate functions Qubit: coherent materials Wiring: control signals For error correction with surface code!architecture to achieve fault-tolerance!2d nearest neighbor coupling
Revised 200k lines of code code review, automate tests Scaling of Hardware (in test) 100 chan/crate, Gs/s DAC 0.5 m dilution refrigerator 4000 superconducting bump bonds (qubits work) 1000 coax wires
Improving Coherence AND Scalability Surface Loss Google qubit Q Pitch Al Si C. Wang et al. Appl. Phys. Lett. 107, 162601 (2015)
Self-Driving Qubits Qubits to Calibrate Calibration DAG (36 nodes) PhD scientist 1.! Choose cal 2.! Run cal 3.! Analyze data a 4.! Update Robot 1.! Choose cal 2.! Run cal 3.! Analyze data 4.! Update Next qubit cal d serially cal d parallel Automation formalism makes calibration scalable
Summary of Quantum Supremacy Experiment! Working to demonstrate exponential state-space! Tests gate error model! Can develop short algorithms that are useful? Cloud service for academic & government users
1000-2000 qubits Potential vs. coordinates (abstract)
Market: Solve optimization problems (spin glass) Conjecture: Build QC without much coherence Technology: Use standard Josephson fabrication Machine has superb engineering Physicists: No exponential computing power What does Nature have to say? Belief Propagation (exact) For random couplings Simulated Quantum Annealing First Results: No faster than classical code median execution times D-Wave Matthias Troyer (ETH) and collaborators Simulated Annealing generic optimized parallelized GPU
Carefully chosen problem, based on working knowledge Solved efficiently with tree-search (Selby) With conventional solvers, see big prefactor speedup Tailored problem: weak-strong clusters 10 7
Google Annealer 2.0 Now know operating principles of annealer Redesign to make more powerful 1) Coherence: low loss dielectrics, improve flux noise Longer range tunneling Beyond incoherent tunneling & QMC 2) Connectivity: beyond ~ nearest neighbors, 6 to 40 Classical solvers then ineffective 3) Control: Fast control, with xmon electronics Interface with classical annealers, get best of both We retain using flux qubit, since double well gives stable classical solution to optimization problem. Different approach than Dwave
Google Fluxmon: Coplanar waveguide + DC SQUID (like xmon, but shorted end for inductor) Conventional 3- junction flux qubit readout resonator Fluxmon 100 $m %! Length: ~ 2000 um %! Distributed geometrical inductance: ~ 700 ph