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Entangling distant superconducting qubits using nanomechanical transducers

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Optical fields are ideal for transmission of quantum information due to low losses and high repetition rates. Microwave fields, on the other hand, can be used to manipulate superconducting systems that belong among the most promising candidates for quantum computing architecture. A device enabling conversion between electromagnetic fields of such distinct frequencies would thus represent a basic building block of future quantum computer networks. Nanomechanical oscillators represent an extremely suitable platform for this task as they can couple to both optical and microwave fields. The electromechanical interaction is achieved through capacitance of an LC circuit, where the change of voltage couples to the position of a mechanical membrane forming one plate of the capacitor, while coupling to the visible light is due to radiation pressure from light reflected off the membrane.
Here we study how such nanomechanical transducers can be employed to generate entanglement between two superconducting qubits placed on two separate chips. Our protocol is based on continuous Bell measurement of the outgoing light fields and applying feedback on the qubits. With such a setup, it is, in principle, possible to generate entanglement between qubits deterministically in the steady state.

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Entangling distant superconducting qubits using nanomechanical transducers

  1. 1. Entangling distant superconductingEntangling distant superconducting qubits using nanomechanicalqubits using nanomechanical transducerstransducers Ondřej Černotík, Denis Vasilyev, and Klemens HammererOndřej Černotík, Denis Vasilyev, and Klemens Hammerer Institute for Theoretical Physics, Institute for Gravitational Physics (Albert EinsteinInstitute for Theoretical Physics, Institute for Gravitational Physics (Albert Einstein Institute), Leibniz University HannoverInstitute), Leibniz University Hannover DPG Spring Meeting Heidelberg, 26 March 2015DPG Spring Meeting Heidelberg, 26 March 2015
  2. 2. DPG Spring Meeting HeidelbergDPG Spring Meeting Heidelberg 26.3.201526.3.2015 Černotík, Vasilyev, and Hammerer (Leibniz University Hannover)Černotík, Vasilyev, and Hammerer (Leibniz University Hannover) Entangling distant superconducting qubits using nanomechanical transducersEntangling distant superconducting qubits using nanomechanical transducers22 There are several possible implementations forThere are several possible implementations for quantum computers:quantum computers: ● superconducting qubits,superconducting qubits, ● trapped ions,trapped ions, ● optical lattices,optical lattices, …… Quantum networks require optical signals forQuantum networks require optical signals for successful long-distance transmission.successful long-distance transmission.
  3. 3. DPG Spring Meeting HeidelbergDPG Spring Meeting Heidelberg 26.3.201526.3.2015 Černotík, Vasilyev, and Hammerer (Leibniz University Hannover)Černotík, Vasilyev, and Hammerer (Leibniz University Hannover) Entangling distant superconducting qubits using nanomechanical transducersEntangling distant superconducting qubits using nanomechanical transducers33 Mechanical oscillators can be used to interfaceMechanical oscillators can be used to interface microwave and optical felds.microwave and optical felds. Bagci,Bagci, et al.et al.,, Nature 507, 81 (2014)Nature 507, 81 (2014) Andrews,Andrews, et al.et al.,, Nat. Phys. 10, 321Nat. Phys. 10, 321 (2014)(2014)
  4. 4. DPG Spring Meeting HeidelbergDPG Spring Meeting Heidelberg 26.3.201526.3.2015 Černotík, Vasilyev, and Hammerer (Leibniz University Hannover)Černotík, Vasilyev, and Hammerer (Leibniz University Hannover) Entangling distant superconducting qubits using nanomechanical transducersEntangling distant superconducting qubits using nanomechanical transducers44 We use measurement and feedback to generateWe use measurement and feedback to generate entanglement deterministically.entanglement deterministically. Other approaches:Other approaches: Abdi,Abdi, et al.et al., Ann. Phys. 527, 139, Ann. Phys. 527, 139 (2015)(2015) Yin,Yin, et al.et al., PRA 91, 012333 (2015), PRA 91, 012333 (2015)
  5. 5. DPG Spring Meeting HeidelbergDPG Spring Meeting Heidelberg 26.3.201526.3.2015 Černotík, Vasilyev, and Hammerer (Leibniz University Hannover)Černotík, Vasilyev, and Hammerer (Leibniz University Hannover) Entangling distant superconducting qubits using nanomechanical transducersEntangling distant superconducting qubits using nanomechanical transducers55 We can use parity-like measurementWe can use parity-like measurement obtained from QND interactionobtained from QND interaction …… Hutchison,Hutchison, et al.et al.,, Can. J. Phys. 87, 225Can. J. Phys. 87, 225 (2009)(2009) Riste,Riste, et al.et al., Nature 502, 350 (2013), Nature 502, 350 (2013) Roch,Roch, et al.et al., PRL 112, 170501 (2014), PRL 112, 170501 (2014)
  6. 6. DPG Spring Meeting HeidelbergDPG Spring Meeting Heidelberg 26.3.201526.3.2015 Černotík, Vasilyev, and Hammerer (Leibniz University Hannover)Černotík, Vasilyev, and Hammerer (Leibniz University Hannover) Entangling distant superconducting qubits using nanomechanical transducersEntangling distant superconducting qubits using nanomechanical transducers66 We can use parity-like measurementWe can use parity-like measurement obtained from QND interactionobtained from QND interaction …… Hutchison,Hutchison, et al.et al.,, Can. J. Phys. 87, 225Can. J. Phys. 87, 225 (2009)(2009) Riste,Riste, et al.et al., Nature 502, 350 (2013), Nature 502, 350 (2013) Roch,Roch, et al.et al., PRL 112, 170501 (2014), PRL 112, 170501 (2014)
  7. 7. DPG Spring Meeting HeidelbergDPG Spring Meeting Heidelberg 26.3.201526.3.2015 Černotík, Vasilyev, and Hammerer (Leibniz University Hannover)Černotík, Vasilyev, and Hammerer (Leibniz University Hannover) Entangling distant superconducting qubits using nanomechanical transducersEntangling distant superconducting qubits using nanomechanical transducers77 …… or using entanglement swapping with theor using entanglement swapping with the entangling interactionentangling interaction Hofer,Hofer, et al.et al.,, PRL 111, 170404PRL 111, 170404 (2013)(2013)
  8. 8. DPG Spring Meeting HeidelbergDPG Spring Meeting Heidelberg 26.3.201526.3.2015 Černotík, Vasilyev, and Hammerer (Leibniz University Hannover)Černotík, Vasilyev, and Hammerer (Leibniz University Hannover) Entangling distant superconducting qubits using nanomechanical transducersEntangling distant superconducting qubits using nanomechanical transducers88 …… or using entanglement swapping with theor using entanglement swapping with the entangling interactionentangling interaction Hofer,Hofer, et al.et al.,, PRL 111, 170404PRL 111, 170404 (2013)(2013)
  9. 9. DPG Spring Meeting HeidelbergDPG Spring Meeting Heidelberg 26.3.201526.3.2015 Černotík, Vasilyev, and Hammerer (Leibniz University Hannover)Černotík, Vasilyev, and Hammerer (Leibniz University Hannover) Entangling distant superconducting qubits using nanomechanical transducersEntangling distant superconducting qubits using nanomechanical transducers99 We adiabatically eliminate the conditional GaussianWe adiabatically eliminate the conditional Gaussian dynamics of the transducer.dynamics of the transducer. OČ, DV, KH, arXiv:1503.07484OČ, DV, KH, arXiv:1503.07484
  10. 10. DPG Spring Meeting HeidelbergDPG Spring Meeting Heidelberg 26.3.201526.3.2015 Černotík, Vasilyev, and Hammerer (Leibniz University Hannover)Černotík, Vasilyev, and Hammerer (Leibniz University Hannover) Entangling distant superconducting qubits using nanomechanical transducersEntangling distant superconducting qubits using nanomechanical transducers1010 We adiabatically eliminate the conditional GaussianWe adiabatically eliminate the conditional Gaussian dynamics of the transducer.dynamics of the transducer. OČ, DV, KH, arXiv:1503.07484OČ, DV, KH, arXiv:1503.07484
  11. 11. DPG Spring Meeting HeidelbergDPG Spring Meeting Heidelberg 26.3.201526.3.2015 Černotík, Vasilyev, and Hammerer (Leibniz University Hannover)Černotík, Vasilyev, and Hammerer (Leibniz University Hannover) Entangling distant superconducting qubits using nanomechanical transducersEntangling distant superconducting qubits using nanomechanical transducers1111 We use an LC circuit coupled to a qubit and a mechanicalWe use an LC circuit coupled to a qubit and a mechanical oscillator.oscillator.
  12. 12. DPG Spring Meeting HeidelbergDPG Spring Meeting Heidelberg 26.3.201526.3.2015 Černotík, Vasilyev, and Hammerer (Leibniz University Hannover)Černotík, Vasilyev, and Hammerer (Leibniz University Hannover) Entangling distant superconducting qubits using nanomechanical transducersEntangling distant superconducting qubits using nanomechanical transducers1212 Long-distance entanglement of superconductingLong-distance entanglement of superconducting qubits seems possible in the near future.qubits seems possible in the near future. Nanomechanical oscillators can help with this task.Nanomechanical oscillators can help with this task.

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