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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. Les Houches, August 2015 Measurement-induced long- distance entanglement using optomechanical transducers Ondřej Černotík and Klemens Hammerer Leibniz University Hannover
  2. 2. Les Houches, August 2015 Mechanical oscillators can interact with many different systems. 2 Kippenberg Lehnert Treutlein Sillanpää Jayich Polzik
  3. 3. Les Houches, August 2015 We can use an optomechanical system to read out the state of a qubit. 3 H = z(b + b† ) + !b† b + g(a + a† )(b + b† )
  4. 4. Les Houches, August 2015 Performing a joint measurement on two qubits, we can generate entanglement between them. 4 1 z + 2 z | 0i = (|0i + |1i)(|0i + |1i) ! 8 < : |00i |11i |01i + |10i Hutchison et al., Canadian J. Phys. 87, 225 (2009) Ristè et al., Nature 502, 350 (2013) Roch et al., PRL 112, 170501 (2014)
  5. 5. Les Houches, August 2015 Losses and noise can be modelled using a conditional master equation. 5 D[O]⇢ = O⇢O† 1 2 (O† O⇢ + ⇢O† O) H[O]⇢ = (O hOi)⇢ + ⇢(O† hO† i) d⇢ = { D[ j ] + D[ j z]}⇢dt i [ j z(bj + b† j), ⇢]dt i![b† jbj, ⇢]dt + {(¯n + 1)D[bj] + ¯nD[b† j]}⇢dt ig[(aj + a† j)(bj + b† j), ⇢]dt  2 [a† 1a2 a1a† 2, ⇢]dt + D[a1 + a2]⇢dt + p H[i(a1 + a2)]⇢dW
  6. 6. Les Houches, August 2015 The mechanical and optical degrees of freedom can be adiabatically eliminated. 6 PRA 92, 012124 (2015) d⇢q = D[ j ]⇢qdt + D[ j z]⇢qdt + D[ 1 z + 2 z]⇢qdt + p H[ 1 z + 2 z]⇢qdW = 16 2 g2 !2 C = 4g2  ¯n > 1 Measurement rate: Optomechanical cooperativity:
  7. 7. Les Houches, August 2015 We can also include optical losses. 7
  8. 8. Les Houches, August 2015 There is a whole range of possible experimental realisations. 8 Anetsberger et al., Nature Physics 5, 909 (2009) Pirkkalainen et al., Nature Commun. 6, 6981 (2015)
  9. 9. Les Houches, August 2015 There is a whole range of possible experimental realisations. 9 Andrews et al., Nature Physics 10, 312 (2014) Bagci et al., Nature 507, 81 (2014) Pirkkalainen et al., Nature 494, 211 (2013)
  10. 10. Les Houches, August 2015 There is a whole range of possible experimental realisations. 10 Rabl et al., PRB 79, 041302 (2009) Rabl et al., Nature Physics 6, 602 (2010)
  11. 11. Les Houches, August 2015 Mechanical resonators are useful for connecting different quantum systems. 11

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