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Quantum networks
with superconducting circuits
and optomechanical transducers
Ondřej Černotík
Leibniz Universität Hannover...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ
Superconducting systems are among the
bes...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ
Light is ideal for quantum communication
...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ
There is a large gap between
superconduct...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ
Mechanical oscillators can mediate
coupli...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ 6
Parity measurements
in circuit QED
Opto...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ
Full control of a qubit is possible using...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ
Full control of a qubit is possible using...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ
Dispersive coupling can be used to read
o...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ
Spin measurement can be used to
generate ...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ
Optomechanical interaction arises due to
...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ
⌦
Strong coupling can be achieved using
l...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ
⌦
Strong coupling can be achieved using
l...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ
⌦
Strong coupling can be achieved using
l...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ
Standard quantum limit bounds the
sensiti...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ
Standard quantum limit bounds the
sensiti...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ
Optomechanical transducer acts as a
force...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ
The thermal mechanical bath affects the
q...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ
The system can be modelled using a
condit...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ
The transducer is Gaussian and can be
adi...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ
We obtain an effective equation for the
q...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ
Optical losses introduce additional
depha...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ
A transmon qubit can capacitively couple
...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ
A transmon qubit can capacitively couple
...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ
With high-frequency mechanical
oscillator...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ
Microwave cavity can improve the
lifetime...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ
Both techniques can also be combined in
o...
Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ
Mechanical oscillators can mediate
intera...
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Quantum networks with superconducting circuits and optomechanical transducers Slide 1 Quantum networks with superconducting circuits and optomechanical transducers Slide 2 Quantum networks with superconducting circuits and optomechanical transducers Slide 3 Quantum networks with superconducting circuits and optomechanical transducers Slide 4 Quantum networks with superconducting circuits and optomechanical transducers Slide 5 Quantum networks with superconducting circuits and optomechanical transducers Slide 6 Quantum networks with superconducting circuits and optomechanical transducers Slide 7 Quantum networks with superconducting circuits and optomechanical transducers Slide 8 Quantum networks with superconducting circuits and optomechanical transducers Slide 9 Quantum networks with superconducting circuits and optomechanical transducers Slide 10 Quantum networks with superconducting circuits and optomechanical transducers Slide 11 Quantum networks with superconducting circuits and optomechanical transducers Slide 12 Quantum networks with superconducting circuits and optomechanical transducers Slide 13 Quantum networks with superconducting circuits and optomechanical transducers Slide 14 Quantum networks with superconducting circuits and optomechanical transducers Slide 15 Quantum networks with superconducting circuits and optomechanical transducers Slide 16 Quantum networks with superconducting circuits and optomechanical transducers Slide 17 Quantum networks with superconducting circuits and optomechanical transducers Slide 18 Quantum networks with superconducting circuits and optomechanical transducers Slide 19 Quantum networks with superconducting circuits and optomechanical transducers Slide 20 Quantum networks with superconducting circuits and optomechanical transducers Slide 21 Quantum networks with superconducting circuits and optomechanical transducers Slide 22 Quantum networks with superconducting circuits and optomechanical transducers Slide 23 Quantum networks with superconducting circuits and optomechanical transducers Slide 24 Quantum networks with superconducting circuits and optomechanical transducers Slide 25 Quantum networks with superconducting circuits and optomechanical transducers Slide 26 Quantum networks with superconducting circuits and optomechanical transducers Slide 27 Quantum networks with superconducting circuits and optomechanical transducers Slide 28
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Connecting distant chips in a quantum network is one of biggest challenges for superconducting quantum computers. Superconducting systems operate at microwave frequencies; transmission of microwave signals through room-temperature quantum channels is impossible due to the omnipresent thermal noise. I will show how two well-known experimental techniques—parity measurements on superconducting systems and optomechanical force sensing—can be combined to generate entanglement between two superconducting qubits through a room-temperature environment. An optomechanical transducer acting as a force sensor can be used to determine the state of a superconducting qubit. A joint readout of two qubits and postselection can lead to entanglement between the qubits. From a conceptual perspective, the transducer senses force exerted by a quantum object, entering a new paradigm in force sensing. In a typical scenario, the force sensed by an optomechanical system is classical. I will argue that the coherence between different states of the qubit (which give rise to different values of the force) can be preserved during the measurement, making it an important resource for quantum communication.

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Quantum networks with superconducting circuits and optomechanical transducers

  1. 1. Quantum networks with superconducting circuits and optomechanical transducers Ondřej Černotík Leibniz Universität Hannover IST Austria, 10 November 2016 -
  2. 2. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ Superconducting systems are among the best candidates for quantum computers. 2 • Quantum gates and processors
 L. DiCarlo et al., Nature 460, 240 (2009); ibid. 467, 574 (2010); A. Fedorov et al., Nature 481, 170 (2011) • Quantum teleportation
 L. Steffen et al., Nature 500, 319 (2013) • Quantum simulations
 A. Houck et al., Nature Physics 8, 292 (2012) • Quantum error correction
 A. Córcoles et al., Nature Commun. 6, 6979
 (2015); J. Kelly et al., Nature 519, 66 (2015); 
 D. Ristè et al., Nature Commun. 6, 6983 (2015) R. Schoelkopf, Yale
  3. 3. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ Light is ideal for quantum communication due to low losses and noise. 3 • Quantum key distribution
 F. Grosshans et al., Nature 421, 238 (2003); T. Schmitt-Manderbach et al., PRL 98, 010504 (2007); H. Yin et al., PRL 117, 190501 (2016) • Quantum teleportation
 D. Bouwmeester et al., Nature 390, 575 (1997); A. Furusawa et al., Science 282, 706 (1998); H. Yonezawa et al., Nature 431, 430 (2004); T. Herbst et al., PNAS 112, 14202 (2015) • Loophole-free Bell test
 B. Hensen et al., Nature 526, 682 (2015); M. Giustina 
 et al., PRL 115, 250401 (2015); L. Shalm et al., ibid., 
 250402 (2015) A. Zeilinger
  4. 4. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ There is a large gap between superconducting and optical systems. 4 Superconducting circuits Optical communication 10 GHz 200 THzfrequency 625 0.03thermal occupation (300 K) 0.5 K 10,000 K ground state temperature
  5. 5. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ Mechanical oscillators can mediate coupling between microwaves and light. 5 R. Andrews et al., Nature Phys. 10, 321 (2014) K. Stannigel et al., PRL 105, 220501 (2010)
  6. 6. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ 6 Parity measurements in circuit QED Optomechanical force sensing Long-distance entanglement of superconducting qubits Fext
  7. 7. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ Full control of a qubit is possible using an electromagnetic field. 7 Hint = g(a + + a† ) A. Blais et al., PRA 69, 062920 (2004) Jaynes–Cummings interaction
  8. 8. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ Full control of a qubit is possible using an electromagnetic field. 8 Hint = g2 a† a z A. Blais et al., PRA 69, 062920 (2004) dispersive interaction
  9. 9. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ Dispersive coupling can be used to read out the qubit state. 9 |0i |1i R. Vijay et al., PRL 106, 110502 (2011) K. Murch et al., Nature 502, 211 (2013) Hint = g2 a† a z
  10. 10. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ Spin measurement can be used to generate entanglement of two qubits. 10 C. Hutchison et al., Canadian J. Phys. 87, 225 (2009) N. Roch et al., PRL 112, 170501 (2014) |11i |00i |01i + |10i | 0i = (|0i + |1i)(|0i + |1i)
  11. 11. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ Optomechanical interaction arises due to radiation pressure. 11 a x !,  ⌦, ¯n !(x) ⇡ !(0) + d! dx x Cavity frequency: g0 = d! dx xzpf = ! L xzpfCoupling strength: xzpf = r ~ 2m⌦ x = xzpf (b + b† ), Hamiltonian: H = ~!(x)a† a + ~⌦b† b H = ~!a† a + ~⌦b† b + ~g0a† a(b + b† ) M. Aspelmeyer, et al., RMP 86, 1391 (2014)
  12. 12. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ ⌦ Strong coupling can be achieved using laser driving. 12 Optomechanical coupling is weak g0 = ! xzpf L ⇡ 25 Hz Solution: strong optical drive a ! ↵ + a Interaction Hamiltonian Hint = ~g0↵(a + a† )(b + b† ) M. Aspelmeyer, et al., RMP 86, 1391 (2014) Red-detuned drive: Hint ⇡ ~g(a† b + b† a) Optomechanical cooling !L = ! ⌦
  13. 13. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ ⌦ Strong coupling can be achieved using laser driving. 13 Optomechanical coupling is weak g0 = ! xzpf L ⇡ 25 Hz Solution: strong optical drive a ! ↵ + a ⌦ Interaction Hamiltonian Hint = ~g0↵(a + a† )(b + b† ) M. Aspelmeyer, et al., RMP 86, 1391 (2014) Blue-detuned drive: Hint ⇡ ~g(ab + a† b† ) Two-mode squeezing !L = ! + ⌦
  14. 14. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ ⌦ Strong coupling can be achieved using laser driving. 14 Optomechanical coupling is weak g0 = ! xzpf L ⇡ 25 Hz Solution: strong optical drive a ! ↵ + a Interaction Hamiltonian Hint = ~g0↵(a + a† )(b + b† ) M. Aspelmeyer, et al., RMP 86, 1391 (2014) Resonant drive: Hint ⇡ ~g(a + a† )(b + b† ) Position readout ! = !L
  15. 15. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ Standard quantum limit bounds the sensitivity of displacement measurements. 15 A. Clerk et al., RMP 82, 1155 (2010) M. Aspelmeyer et al., RMP 86, 1391 (2014) ˙x = !mp ˙p = !mx p g(a + a† ) + ⇠ + Fext ˙a =  2 a igx + p ain Fext
  16. 16. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ Standard quantum limit bounds the sensitivity of displacement measurements. 16 A. Clerk et al., RMP 82, 1155 (2010) M. Aspelmeyer et al., RMP 86, 1391 (2014) Fext pout = i(aout a† out) = 4g!m p  (!2 m !2 + i !)( + 2i!) ✓ Fext + ⇠ 2g p   + 2i! xin ◆ +  2i!  + 2i! pin
  17. 17. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ Optomechanical transducer acts as a force sensor. 17 F = ~ /( p 2xzpf ) S2 F (!) = x2 zpf /[8g2 2 m(!)]Sensitivity: ⌧meas = S2 F (!) F2 = !2 m 16 2g2 ⌧ T1,2Measurement time: H = z(b + b† ) + !mb† b + g(a + a† )(b + b† )
  18. 18. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ The thermal mechanical bath affects the qubit. 18 mech = S2 f (!) = 2 2 !2 m ¯nDephasing rate: ⌧meas < 1 mech ! C = 4g2  ¯n > 1 2
  19. 19. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ The system can be modelled using a conditional master equation. 19 D[O]⇢ = O⇢O† 1 2 (O† O⇢ + ⇢O† O) H[O]⇢ = (O hOi)⇢ + ⇢(O† hO† i) H. Wiseman & G. Milburn, Quantum measurement and control (Cambridge) d⇢ = i[H, ⇢]dt + Lq⇢dt + 2X j=1 {(¯n + 1)D[bj] + ¯nD[b† j]}⇢dt + D[a1 a2]⇢dt + p H[i(a1 a2)]⇢dW H = 2X j=1 j z(bj + b† j) + !mb† jbj + g(aj + a† j)(bj + b† j) + i  2 (a1a† 2 a2a† 1)
  20. 20. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ The transducer is Gaussian and can be adiabatically eliminated. 20 OC et al., PRA 92, 012124 (2015)ˇ 2 qubits Mechanics, light
  21. 21. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ We obtain an effective equation for the qubits. 21 d⇢q = 2X j=1  1 T1 D[ j ] + ✓ 1 T2 + mech ◆ D[ j z] ⇢qdt + measD[ 1 z + 2 z]⇢qdt + p measH[ 1 z + 2 z]⇢qdW meas = 16 2 g2 !2 m , mech = 2 !2 m (2¯n + 1)
  22. 22. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ Optical losses introduce additional dephasing. 22 p ⌘ measH[ 1 z + 2 z]⇢q (1 ⌧) measD[ 1 z]⇢q
  23. 23. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ A transmon qubit can capacitively couple to a nanobeam oscillator. 23 G. Anetsberger et al., Nature Phys. 5, 909 (2009) J. Pirkkalainen et al., Nat. Commun. 6, 6981 (2015) = 2⇡ ⇥ 5.8 MHz g = 2⇡ ⇥ 900 kHz  = 2⇡ ⇥ 39MHz !m = 2⇡ ⇥ 8.7 MHz Qm = 5 ⇥ 104 T = 20 mK ¯n = 48 T1,2 = 20 µs C = 10
  24. 24. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ A transmon qubit can capacitively couple to a nanobeam oscillator. 24 = 2⇡ ⇥ 5.8 MHz g = 2⇡ ⇥ 900 kHz  = 2⇡ ⇥ 39MHz !m = 2⇡ ⇥ 8.7 MHz Qm = 5 ⇥ 104 T = 20 mK ¯n = 48 T1,2 = 20 µs C = 10 ⌘ Psucc Psucc OC and K. Hammerer, PRA 94, 012340 (2016)ˇ
  25. 25. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ With high-frequency mechanical oscillators, modulated interaction can be used. 25 H = z(b + b† ) ig(a + a† )(b b† ) meas = 16 2 g2  2 , mech = 2 (2¯n + 1)
  26. 26. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ Microwave cavity can improve the lifetime of the qubit. 26 meas = 256 2 g2 ag2 c 2 a!2 mc , deph = 4 2 a + 256 2 g4 a 3 a!2 m + 16 2 g2 a 2 a!2 m (2¯n + 1) H = z(a + a† ) iga(a a† )(b + b† ) + !mb† b + gc(c + c† )(b + b† ) a b c
  27. 27. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ Both techniques can also be combined in one system. 27 a b c H = z(a + a† ) iga(a a† )(b + b† ) igc(c + c† )(b b† ) meas = 1024 2 g2 ag2 c 2 a 2c , deph = 4 2 a + 64 2 g2 a 2 a (2¯n + 1)
  28. 28. Ondrej Cernotík (Hannover): Quantum networks with SC qubits and OM transducersˇˇ Mechanical oscillators can mediate interaction between light and SC qubits. 28 OC and K. Hammerer, PRA 94, 012340 (2016)ˇ - C = 4g2  ¯n > 1 2 • Strong optomechanical cooperativity, • Sufficient qubit lifetime
  • MohamedHamdy342

    Nov. 27, 2019

Connecting distant chips in a quantum network is one of biggest challenges for superconducting quantum computers. Superconducting systems operate at microwave frequencies; transmission of microwave signals through room-temperature quantum channels is impossible due to the omnipresent thermal noise. I will show how two well-known experimental techniques—parity measurements on superconducting systems and optomechanical force sensing—can be combined to generate entanglement between two superconducting qubits through a room-temperature environment. An optomechanical transducer acting as a force sensor can be used to determine the state of a superconducting qubit. A joint readout of two qubits and postselection can lead to entanglement between the qubits. From a conceptual perspective, the transducer senses force exerted by a quantum object, entering a new paradigm in force sensing. In a typical scenario, the force sensed by an optomechanical system is classical. I will argue that the coherence between different states of the qubit (which give rise to different values of the force) can be preserved during the measurement, making it an important resource for quantum communication.

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