The Quantum Supremacy Experiment
John Martinis, Google & UCSB
New tests of QM:
Does QM work for 1015 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
What’s so hard?
Systems vs. Control:
Can’t copy quantum information
Hard to separate into sub-functions
Quantum Systems Engineering
competing
requirements
general
purpose
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 1015 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
Clifford
measure k
initialize |"! = |0!
n qubits
d (time)
Non-Clifford
X, Z, H, X1/2!
Z1/4
CZ
2) Run quantum computer, measure k (0 to 2n-1; ex. 5 = {0!0101})
repeat sampling 100,000 times
1s
3) Random guess: any outcome k has probability pcl = 1/2n
4) Calculate |"!, p(k)= |#k|"!|2 not uniform; store in lookup table
(fully entangled with complexity 2n: 1-D, d>n; 2-D, d>n1/2)
5) Correlation: cross entropy
S = # ln p(k)/pcl !
6) Compare to theory
Squ 0.42
Scl -0.58
7) Try another sequence
days
200 drives
quantum
classical
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
•! With one error anywhere
distribution is flat (classical like)
probability of no error
Stot P0 Squ + (1-P0) Scl
P0 = (1! !1 )nd (1! ! 2 )nd (1! ! m )n
e-p
•! Gaussian distribution Re{$} & Im{$}
gives Porter-Thomas (exponential)
distribution
probability p(k)/pcl
How Does it Work?
0
index k’ [p(k)-ordered]
Include all 1, 2, measure errors %
" exp[!nd(!1 + ! 2 ) + n! m ]
# exp[!N e ]
Need total error Ne <
~3
2n
info. dist. Stot - Scl
Exponential Decay of Quantum Information
1
0.8
0.6
0.4
0.2
need Ne <
~3
0
0
0.5
1
1.5
2
2.5
3
3.5
number of errors Ne nd %2
4
4.5
5
Errors Destroy Quantum Computation
Stot P0 Squ + (1-P0) Scl
Probability of no error:
P0 = exp[ -Ng %g ]
Average number of errors:
Ng %g = 49 x 7 x 0.005 = 1.7
Need: scaling with low errors
Roadmap Metric for Scaling and Errors
Worst (2-qubit) error
Shows system performance
10-1
demonstrations
difficult
direction
10-2
supremacy /
analog quantum
quantum
computer
10-3
error
correction
10-41
10
100
logical gates
104
Number qubits
106
108
Roadmap Metric for Scaling and Errors
Worst (2-qubit) error
Much to invent, especially scaling
10-1
10-2
quantum
computer
10-3
10-41
10
100
104
Number qubits
106
108
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
9Xmons:
• hifigates
• fastreadout
• surfacecodecompa6ble
1
Q0
Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Cycle though error measurement 8 times
2
3
4
5
6
7
8
measure data
read decay
state flip
CNOTs
measure
Control Waveforms for 9 qubits
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&."
G32;:)*$9%F94H%ID0%'+%
./"
01%
+)-234%&'()*%
5607%
8%9)#:;<"=4%#>%#?1%
07@%
8%)A34%
BB5%
8%=):*'"3%,$"+4%
5B6%
tes
a
g
>10
3
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
Scaling of Hardware (in test)
Revised 200k lines of code
code review, automate tests
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
qubit Q
Pitch
Google
Al
C. Wang et al. Appl. Phys. Lett. 107, 162601 (2015)
Si
Self-Driving Qubits
Qubits to Calibrate
PhD scientist
1.!
2.!
3.!
4.!
Choose cal
Run cal
Analyze data
Update
Robot
Calibration DAG (36 nodes)
1.!
2.!
3.!
4.!
Choose cal
Run cal
Analyze data
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
Potential vs. coordinates (abstract)
1000-2000
qubits
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)
First Results:
No faster than
classical code
median execution times
For random couplings
Simulated
Quantum Annealing
Simulated Annealing
generic
optimized
parallelized
GPU
D-Wave
Matthias Troyer (ETH)
and collaborators
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
107
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)
readout
resonator
Conventional 3junction flux qubit
Fluxmon
100 $m
%! Length: ~ 2000 um
%! Distributed geometrical inductance: ~ 700 pH