The Quantum Supremacy Experiment

Transcription

1 The Quantum Supremacy Experiment John Martinis, Google & UCSB New tests of QM: Does QM work for Hilbert space? Does digitized error model also work? Demonstrate exponential computing power: Check 50 qubit quantum computer with largest classical supercomputer

2 Quantum Data 0!+ 1!

3 Quantum Data ( 0!+ 1! ) 2 = 00!+ 01!+ 10!+ 11!

4 Really Big Data ( 0!+ 1! ) 300 more states than atoms in universe

5 Encoding of quantum bits H atom: quantum circuit: 0) 100!m 1) orbitals 6 GHz microwave oscillator Easier control for large size

6 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

7 Quantum vs. Classical-Supercomputer Challenge

8 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 state space Forward compatible to error correction *S. Boixo et. al., arxiv:1608:08752

9 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 classical 7) Try another sequence

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11 9 How Does it Work? Im{$} p1/ Re{$} /2n probability p(k)/pcl! Gaussian distribution Re{$} & Im{$} gives Porter-Thomas (exponential) distribution index6000 k 2n

12 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 ~

13 Exponential Decay of Quantum Information info. dist. S tot - S cl need N e < 3 ~ number of errors N e nd % 2

14 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 = 1.7 Need: scaling with low errors

15 Roadmap Metric for Scaling and Errors Shows system performance Worst (2-qubit) error demonstrations supremacy / analog quantum error correction logical gates difficult direction quantum computer 10-4 Number qubits

16 Roadmap Metric for Scaling and Errors Much to invent, especially scaling Worst (2-qubit) error quantum computer Number qubits

17 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

18 9 Xmons: hifi gates fast readout surface code compa6ble

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21 CNOTs measure read decay state flip Control Waveforms for 9 qubits Cycle though error measurement 8 times measure data Q 0 Q 1 Q 2 Q 3 Q 4 Q 5 Q 6 Q 7 Q 8

22 9 Qubit Data: Bit-Flip Error Correction Works! & = 3.2 > 1, so better memory for higher order fault tolerant behavior!

23 Digitized Adiabatic Quantum Computing!"#$%&'()*%"#*+%"+%+,)-% C,)-%,:;(349D%E"-A;9>%-;-8+*;&'"+F#%,-./"4%3&."./ " 01% +)-234%&'()*% 5607% 8%9)#:;<"=4%#>%#?1% G32;:)*$9%F94H%ID0%'+% 8%)A34% BB5% 8%=):*'"3%,$"+4% 5B6% >10 3 gates

24 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

25 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

26 Improving Coherence AND Scalability Surface Loss Google qubit Q Pitch Al Si C. Wang et al. Appl. Phys. Lett. 107, (2015)

27 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

28 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

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30 qubits Potential vs. coordinates (abstract)

31 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

32 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

33 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

34 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