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

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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.

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 DPG Spring meeting, 3 March 2016 arXiv:1512.00768
  2. 2. Cernotík (LUH): Entanglement of superconducting qubits, arXiv:1512.00768ˇ 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 (LUH): Entanglement of superconducting qubits, arXiv:1512.00768ˇ 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 (LUH): Entanglement of superconducting qubits, arXiv:1512.00768ˇ 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 (LUH): Entanglement of superconducting qubits, arXiv:1512.00768ˇ Optomechanical transducer acts as a force sensor. 5 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† )
  6. 6. Cernotík (LUH): Entanglement of superconducting qubits, arXiv:1512.00768ˇ The thermal mechanical bath affects the qubit. 6 mech = S2 f (!) = 2 2 !2 m ¯nDephasing rate: ⌧meas < 1 mech ! C = 4g2  ¯n > 1 2
  7. 7. Cernotík (LUH): Entanglement of superconducting qubits, arXiv:1512.00768ˇ The system can be modelled using a conditional master equation. 7 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)
  8. 8. Cernotík (LUH): Entanglement of superconducting qubits, arXiv:1512.00768ˇ We can obtain an effective equation for the qubits. 8 meas = 16 2 g2 !2 m , mech = 2 !2 m (2¯n + 1) OC et al., PRA 92, 012124 (2015)ˇ d⇢q = Lq⇢qdt + 2X j=1 mechD[ j z]⇢qdt + measD[ 1 z + 2 z]⇢qdt + p measH[ 1 z + 2 z]⇢qdW
  9. 9. Cernotík (LUH): Entanglement of superconducting qubits, arXiv:1512.00768ˇ Optical losses introduce additional dephasing. 9 (1 ⌧) measD[ 1 z]⇢q p ⌘ measH[ 1 z + 2 z]⇢q
  10. 10. Cernotík (LUH): Entanglement of superconducting qubits, arXiv:1512.00768ˇ A transmon qubit can capacitively couple to a nanobeam oscillator. 10 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
  11. 11. Cernotík (LUH): Entanglement of superconducting qubits, arXiv:1512.00768ˇ The mechanical oscillator can also be formed by a membrane. 11 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)
  12. 12. Cernotík (LUH): Entanglement of superconducting qubits, arXiv:1512.00768ˇ Mechanical oscillators can mediate interaction between light and SC qubits. 12 • Strong optomechanical cooperativity, • Sufficient qubit lifetime OC & K. Hammerer, arXiv:1512.00768ˇ - C = 4g2  ¯n > 1 2

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