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.

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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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.