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Measurement-induced long-distance
entanglement of superconducting qubits
using optomechanical transducers
Ondřej Černotík ...
Cernotík (Hannover): Entanglement of superconducting qubitsˇ
Superconducting systems are among the
best candidates for qua...
Cernotík (Hannover): Entanglement of superconducting qubitsˇ
Entanglement between two qubits can be
generated by measureme...
Cernotík (Hannover): Entanglement of superconducting qubitsˇ
Mechanical oscillators can mediate
coupling between microwave...
Cernotík (Hannover): Entanglement of superconducting qubitsˇ
Mechanical oscillators can mediate
coupling between microwave...
Cernotík (Hannover): Entanglement of superconducting qubitsˇ
Optomechanical transducer acts as a
force sensor.
6
F = ~ /(
...
Cernotík (Hannover): Entanglement of superconducting qubitsˇ
The thermal mechanical bath affects the
qubit.
7
mech = S2
f ...
Cernotík (Hannover): Entanglement of superconducting qubitsˇ
The system can be modelled using a
conditional master equatio...
Cernotík (Hannover): Entanglement of superconducting qubitsˇ
The transducer is Gaussian and can be
adiabatically eliminate...
Cernotík (Hannover): Entanglement of superconducting qubitsˇ
We obtain an effective equation for the
qubits.
10
d⇢q =
2X
j...
Cernotík (Hannover): Entanglement of superconducting qubitsˇ
Optical losses introduce additional
dephasing.
11
d⇢q =
2X
j=...
Cernotík (Hannover): Entanglement of superconducting qubitsˇ
A transmon qubit can capacitively couple
to a nanobeam oscill...
Cernotík (Hannover): Entanglement of superconducting qubitsˇ
The mechanical oscillator can also be
formed by a membrane.
1...
Cernotík (Hannover): Entanglement of superconducting qubitsˇ
Mechanical oscillators can mediate
interaction between light ...
Cernotík (Hannover): Entanglement of superconducting qubitsˇ
More complex schemes can be designed.
15
• Using a microwave ...
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Measurement-induced long-distance entanglement of superconducting qubits using optomechanical transducers Slide 1 Measurement-induced long-distance entanglement of superconducting qubits using optomechanical transducers Slide 2 Measurement-induced long-distance entanglement of superconducting qubits using optomechanical transducers Slide 3 Measurement-induced long-distance entanglement of superconducting qubits using optomechanical transducers Slide 4 Measurement-induced long-distance entanglement of superconducting qubits using optomechanical transducers Slide 5 Measurement-induced long-distance entanglement of superconducting qubits using optomechanical transducers Slide 6 Measurement-induced long-distance entanglement of superconducting qubits using optomechanical transducers Slide 7 Measurement-induced long-distance entanglement of superconducting qubits using optomechanical transducers Slide 8 Measurement-induced long-distance entanglement of superconducting qubits using optomechanical transducers Slide 9 Measurement-induced long-distance entanglement of superconducting qubits using optomechanical transducers Slide 10 Measurement-induced long-distance entanglement of superconducting qubits using optomechanical transducers Slide 11 Measurement-induced long-distance entanglement of superconducting qubits using optomechanical transducers Slide 12 Measurement-induced long-distance entanglement of superconducting qubits using optomechanical transducers Slide 13 Measurement-induced long-distance entanglement of superconducting qubits using optomechanical transducers Slide 14 Measurement-induced long-distance entanglement of superconducting qubits using optomechanical transducers Slide 15
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Measurement-induced long-distance entanglement of superconducting qubits using optomechanical transducers

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Although superconducting systems provide a promising platform for quantum computing, their networking poses a challenge as they cannot be interfaced to light---the medium used to send quantum signals through channels at room temperature. We show that mechanical oscillators can mediated such coupling and light can be used to measure the joint state of two distant qubits. The measurement provides information on the total spin of the two qubits such that entangled qubit states can be postselected. Entanglement generation is possible without ground-state cooling of the mechanical oscillators for systems with optomechanical cooperativity moderately larger than unity; in addition, our setup tolerates a substantial transmission loss. The approach is scalable to generation of multipartite entanglement and represents a crucial step towards quantum networks with superconducting circuits.

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Measurement-induced long-distance entanglement of superconducting qubits using optomechanical transducers

  1. 1. Measurement-induced long-distance entanglement of superconducting qubits using optomechanical transducers Ondřej Černotík and Klemens Hammerer Leibniz Universität Hannover, Germany GRS Ventura, 5 March 2016 arXiv:1512.00768
  2. 2. Cernotík (Hannover): Entanglement of superconducting qubitsˇ Superconducting systems are among the best candidates for quantum computers. 2 • Controlling microwave fields with qubits Hofheinz et al., Nature 454, 310 (2008); Nature 459, 546 (2009) • Feedback control of qubits Ristè et al., PRL 109, 240502 (2012); Vijay et al., Nature 490, 77 (2012); de Lange et al., PRL 112, 080501 (2014) • Quantum error correction Córcoles et al., Nature Commun. 6, 6979 (2015), Kelly et al., Nature 519, 66 (2015), Ristè et al., Nature Commun. 6, 6983 (2015) • Entanglement generation Ristè et al., Nature 502, 350 (2013); Roch et al., PRL 112, 170501 (2014); Saira et al., PRL 112, 070502 (2014) Schoelkopf
  3. 3. Cernotík (Hannover): Entanglement of superconducting qubitsˇ Entanglement between two qubits can be generated by measurement and postselection. 3 C. Hutchison et al., Canadian J. Phys. 87, 225 (2009) N. Roch et al., PRL 112, 170501 (2014) Hint = za† aDispersive coupling |11i |00i |01i + |10i
  4. 4. Cernotík (Hannover): Entanglement of superconducting qubitsˇ Mechanical oscillators can mediate coupling between microwaves and light. 4 T. Bagci et al., Nature 507, 81 (2014)R. Andrews et al., Nature Phys. 10, 321 (2014) Z. Yin et al., PRA 91, 012333 (2015)
  5. 5. Cernotík (Hannover): Entanglement of superconducting qubitsˇ Mechanical oscillators can mediate coupling between microwaves and light. 5 K. Xia et al., Sci. Rep. 4, 5571 (2014) K. Stannigel et al., PRL 105, 220501 (2010)
  6. 6. Cernotík (Hannover): Entanglement of superconducting qubitsˇ Optomechanical transducer acts as a force sensor. 6 F = ~ /( p 2xzpf ) S2 F (!) = x2 zpf /[8g2 2 m(!)]Sensitivity: ! ⌧ !m ⌧meas = S2 F (!) F2 = !2 m 16 2g2 ⌧ T1,2Measurement time: H = z(b + b† ) + !mb† b + g(a + a† )(b + b† )
  7. 7. Cernotík (Hannover): Entanglement of superconducting qubitsˇ The thermal mechanical bath affects the qubit. 7 mech = S2 f (!) = 2 2 !2 m ¯nDephasing rate: ⌧meas < 1 mech ! C = 4g2  ¯n > 1 2
  8. 8. Cernotík (Hannover): Entanglement of superconducting qubitsˇ The system can be modelled using a conditional master equation. 8 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)
  9. 9. Cernotík (Hannover): Entanglement of superconducting qubitsˇ The transducer is Gaussian and can be adiabatically eliminated. 9 OC et al., PRA 92, 012124 (2015)ˇ 2 qubits Mechanics, light
  10. 10. Cernotík (Hannover): Entanglement of superconducting qubitsˇ We obtain an effective equation for the qubits. 10 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)
  11. 11. Cernotík (Hannover): Entanglement of superconducting qubitsˇ Optical losses introduce additional dephasing. 11 d⇢q = 2X j=1 ✓ 1 T1 D[ j ] + 1 T2 D[ j z] ◆ ⇢qdt + [(1 ⌧) meas + mech]D[ 1 z]⇢qdt + ⌧ mechD[ 2 z]⇢qdt + ⌧ measD[ 1 z + 2 z]⇢qdt + p ⌧⌘ measH[ 1 z + 2 z]⇢qdW
  12. 12. Cernotík (Hannover): Entanglement of superconducting qubitsˇ A transmon qubit can capacitively couple to a nanobeam oscillator. 12 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 ⌘ Psucc Psucc
  13. 13. Cernotík (Hannover): Entanglement of superconducting qubitsˇ The mechanical oscillator can also be formed by a membrane. 13 R. Andrews et al., Nature Phys. 10, 312 (2014) T. Bagci et al., Nature 507, 81 (2014) J. Pirkkalainen et al., Nature 494, 211 (2013)
  14. 14. Cernotík (Hannover): Entanglement of superconducting qubitsˇ Mechanical oscillators can mediate interaction between light and SC qubits. 14 • Strong optomechanical cooperativity, • Sufficient qubit lifetime OC & K. Hammerer, arXiv:1512.00768ˇ - C = 4g2  ¯n > 1 2
  15. 15. Cernotík (Hannover): Entanglement of superconducting qubitsˇ More complex schemes can be designed. 15 • Using a microwave cavity • Two-mode optomechanical driving • Measurement-based feedback • More experimental implementations OC & K. Hammerer, arXiv:1512.00768ˇ -

Although superconducting systems provide a promising platform for quantum computing, their networking poses a challenge as they cannot be interfaced to light---the medium used to send quantum signals through channels at room temperature. We show that mechanical oscillators can mediated such coupling and light can be used to measure the joint state of two distant qubits. The measurement provides information on the total spin of the two qubits such that entangled qubit states can be postselected. Entanglement generation is possible without ground-state cooling of the mechanical oscillators for systems with optomechanical cooperativity moderately larger than unity; in addition, our setup tolerates a substantial transmission loss. The approach is scalable to generation of multipartite entanglement and represents a crucial step towards quantum networks with superconducting circuits.

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