Title goes here Building a superconducting quantum computer with the surface code Matteo Mariantoni Fall INTRIQ meeting, November 5 th & 6 th 2013

the DQM lab team Thomas G. McConkey Doctoral Student John R. Rinehart Doctoral Student Carolyn “Cary” T. Earnest Doctoral Student Corey Rae H. McRae Doctoral Student Jérémy Béjanin Master’s Student Yousef Rohanizadegan Research Assistant Matteo Mariantoni Principal Investigator Daryoush Shiri Postdoctoral Fellow Collaborators: 1)Prof. Michael J. Hartmann Heriot Watt University 2)Prof. Frederick W. Strauch Williams College 3)Prof. Adrian Lupaşcu IQC 4)Prof. Christopher M. Wilson IQC 5)Prof. Zbig R. Wasilewski WIN 6)Dr. Austin G. Fowler UC Santa Barbara 7)Prof. David G. Cory IQC 8)Prof. Guo-Xing Miao IQC 9)Prof. Roger G. Melko UW 10)Sadegh Raeisi IQC 11)Yuval R. Sanders IQC

lab virtual walkthrough the lab is being setup in these very days; it will be up and running by February 2014 photo credit BlueFors Cryogenics Oy DR

lab real walkthrough the lab is being setup in these very days; it will be up and running by February 2014

nano/micro meterspace milli kelvintemperature giga hertz frequency time on the edge nano/micro meterspace photo credit – M. Mariantoni and E. Lucero University of California Santa Barbara

on the edge milli kelvintemperature photo credit – BlueFors Cryogenics Oy

giga hertz frequency time on the edge photo credit – M. Mariantoni and E. Lucero

LC resonator superconducting quantum circuits

LC resonator superconducting quantum circuits ~ 7 GHz

dielectric material transmission-line resonator superconducting quantum circuits

coplanar waveguide resonator superconducting quantum circuits T 1 ~ 5  s T 2 ~ 2T 1 M. Mariantoni et al., Nature Phys. 7, 287 (2011)

Josephson junction → nonlinearity qubit superconducting quantum circuits

~ 7 GHz ~ 6.8 GHz  an ~ 200 MHz superconducting quantum circuits qubit

superconducting quantum circuits qubit capacitor C inductor L junction T 1 ~ 500 ns T 2 ~ 150 ns M. Mariantoni et al., Nature Phys. 7, 287 (2011)

resonator + qubit superconducting quantum circuits resonator + qubit + control capacitor C inductor L junction X,Y ( ,  /2); Z g(C b ) ~ 100 MHz  10 ns M. Mariantoni et al., Nature Phys. 7, 287 (2011) A. Blais, R.-S. Huang, A. Wallraff, S.M. Girvin, and R.J. Schoelkopf, Phys. Rev. A 69, (2004); A. Wallraff et al., Nature (London) 431, 162 (2004)

one-qubit pulses and one-qubit quantum errors P.W. Shor, Phys. Rev. A 52, 2493 (1995)

Q1Q1 Q2Q2 M1M1 M2M2 B Z2Z2 Z1Z1 create, write, re-create, zero, read entanglement

i M. Mariantoni et al., Science 334, 61 (2011)

the CZ-  gate qubit qutrit

phase qubit qutrit the CZ-  gate

qutrit-resonator interaction the CZ-  gate

qutrit-resonator interaction the CZ-  gate

qutrit-resonator interaction the CZ-  gate

resonant semi-resonant qutrit-resonator interaction the CZ-  gate

resonant semi-resonant two-qubit CZ-  gate the CZ-  gate

resonant semi-resonant control target THEORY: F. W. Strauch et al., Phys. Rev. Lett. 91, (2003) G. Haack,…, M.M.,... et al., Phys. Rev. B 82, (2010) EXPERIMENT: L. DiCarlo et al., Nature (London) 460, (2009) T. Yamamoto,…, M.M.,... et al., Phys. Rev. B 82, (2010) two-qubit CZ-  gate the CZ-  gate

resonant semi-resonant CZ-  gate truth table control target the CZ-  gate

resonant semi-resonant two-qubit CZ-  gate the CZ-  gate

resonant semi-resonant two-qubit CZ-  gate the CZ-  gate M. Mariantoni et al., Science 334, 61 (2011)

resonant semi-resonant M. Mariantoni et al., Science 334, 61 (2011) two-qubit CZ-  gate the CZ-  gate

 -meter: Generalized Ramsey (a) the CZ-  gate

i.compensate dynamic phase ii.varying z cmp  Ramsey fringe  -meter: Generalized Ramsey (a) the CZ-  gate

 -meter: Generalized Ramsey (b) the CZ-  gate

 -meter: Generalized Ramsey (a-b) the CZ-  gate

 -meter: Generalized Ramsey (a-b) the CZ-  gate

 = 0.01  =  /2  =   -meter: Generalized Ramsey (a-b) the CZ-  gate

process tomography the CZ-  gate fidelity ~70% fidelity ~60% qubit T 1 ~500 ns, T 2 ~150 ns

superconducting surface code A.G. Fowler, M. Mariantoni, J.M. Martinis, and A.N. Cleland, Phys. Rev. A 86, (2012) ~ 50 pages of details

2D lattice with nearest neighbor interactions A.G. Fowler, M. Mariantoni, J.M. Martinis, and A.N. Cleland, Phys. Rev. A 86, (2012) ~ 50 pages of details

data and syndrome qubit syndrome → measured data surface code

face and vertex A.Yu. Kitaev, Annals of Physics 303, 2 (2003) surface code

Z-stabilizer stabilizers

Z-stabilizer  zeroing gate stabilizers

Z-stabilizer  projects stabilizers

X-stabilizer  projects stabilizers

one qubit  qubit state destroyed

stabilizers

quiescent state +1 stabilizers

+1 quiescent state stabilizers

quiescent state time quantum error detection

time  bit-flip error quantum error detection

 bit-flip error  phase-flip error time protected memory +1 1)any error 2)boundaries 3)measurement errors  “minimum weight matching” → polynomial +1 quantum error detection

error chains and logical qubits error on first qubit

error chains and logical qubits error on first qubit

error chains and logical qubits error on second qubit

error chains and logical qubits error on second qubit

error chains and logical qubits error on third qubit

error chains and logical qubits error on third qubit

error chains and logical qubits error on fourth qubit

+1 quiescent state error chains and logical qubits

error chains and logical qubits error on last qubit

error chains and logical qubits error on third qubit

error chains and logical qubits back to original quiescent state

fault tolerance – surface codes physical → logical qubit = error rate A.G. Fowler et al., Phys. Rev. A 86, (2012)

fault tolerance – surface codes physical qubits → logical qubit = error rate )nearest neighbor interactions 2)CNOT physical gates fast ~ 100 ns with F ≥ 99 % 3)readout fast ~ 100 ns with F ≥ 90 % 4)interface with classical electronics 5)overhead proof-of-concept → 3/5 physical qubits quantum memory → 10  10 = 10 2 physical qubits Shor → 10 3 to 10 4 physical qubits 

A. Megrant et al., App. Phys. Lett. 100, (2012) fault tolerance – surface codes 1) CNOT physical gates R. Barends et al., Phys. Rev. Lett. 111, (2013) Xmon Xmon lifetime T 1 ~ 50  s T gate ~ 50 ns = 0.05  s → F  exp(- T gate / T 1 ) = exp(  s / 50  s) ~ 99.9 % R. Barends et al., App. Phys. Lett. 99, (2011)

fault tolerance – surface codes physical qubits → logical qubit = error rate )nearest neighbor interactions 2)CNOT physical gates fast ~ 100 ns with F ≥ 99 % 3)readout fast ~ 100 ns with F ≥ 90 % 4)interface with classical electronics 5)overhead proof-of-concept → 3/5 physical qubits quantum memory → 10  10 = 10 2 physical qubits Shor → 10 3 to 10 4 physical qubits  

fault tolerance – surface codes 2) readout R. Vijay et al., Nature (London) 490, 77 (2012) readout time  r ~ 100 ns F > 90 %

fault tolerance – surface codes physical qubits → logical qubit = error rate )nearest neighbor interactions 2)CNOT physical gates fast ~ 100 ns with F ≥ 99 % 3)readout fast ~ 100 ns with F ≥ 90 % 4)interface with classical electronics 5)overhead proof-of-concept → 3/5 physical qubits quantum memory → 10  10 = 10 2 physical qubits Shor → 10 3 to 10 4 physical qubits    

surface code proof-of-concept → 3/5 physical qubits → 3-4 years quantum memory → 10 2 physical qubits → 8-9 years Shor to factor a 2000 bit number in 24 h with 1 nuclear power plant → 300  10 6 physical qubits oon the best classical super-cluster: many times the age of the universe and virtually infinite power perspective

resonator-qubit 2D lattice A,|g ⟩ unit cell B B Z R R R … … … … Q,|  ⟩

A,|g ⟩ B … … … …  higher isolation → OFF coupling B Q,|  ⟩ resonator-qubit 2D lattice

B B Q,|  ⟩ A,|g ⟩ R R R … … …  higher isolation → OFF coupling  encoding → multiple measurement resonator-qubit 2D lattice

Z … … …  higher isolation → OFF coupling  encoding → multiple measurement  zero Q,|  ⟩ leakage to third state resonator-qubit 2D lattice

see also D.P. DiVincenzo, Phys. Scr., T 137, (2009) A,|g ⟩ B B Z R R R … … …  higher isolation → OFF coupling  encoding → multiple measurement  zero and/or store Q,|  ⟩ resonator-qubit 2D lattice