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A Quantum-Logic Gate between Distant Quantum-Network Modules
Severin Daiss, Stefan Langenfeld, Stephan Welte, Emanuele Distante, Philip Thomas, Lukas Hartung, Olivier Morin, Gerhard Rempe
TL;DR
Distributed quantum computing requires logic gates between distant qubits in separate modules. The experiment uses a photon reflected successively from two remote modules, followed by heralding detection and feedback. It realizes a non-local controlled quantum gate and uses it to generate all four Bell states.
Problem
Quantum networks need quantum-logic gates between distant qubits to connect smaller modules into larger computing clusters.
Method
A photon is reflected successively from two remote qubit modules, and heralding detection triggers a feedback rotation on the first qubit.
Results
The implementation realizes a controlled quantum-PHASE gate and experimentally confirms α = β = γ = 0, with |↑z↑z⟩ preserved at (98.6 ± 0.6)%.
Takeaways & Limitations
The demonstrated gate provides a non-local operation between independent modules connected through a 60 m optical link.
Takeaways & Limitations
The gate is limited by atomic coherence, polarization and frequency stability, mode matching, and other experimental imperfections.
Abstract
from arXiv · showhide
The big challenge in quantum computing is to realize scalable multi-qubit systems with cross-talk free addressability and efficient coupling of arbitrarily selected qubits. Quantum networks promise a solution by integrating smaller qubit modules to a larger computing cluster. Such a distributed architecture, however, requires the capability to execute quantum-logic gates between distant qubits. Here we experimentally realize such a gate over a distance of 60m. We employ an ancillary photon that we successively reflect from two remote qubit modules, followed by a heralding photon detection which triggers a final qubit rotation. We use the gate for remote entanglement creation of all four Bell states. Our non-local quantum-logic gate could be extended both to multiple qubits and many modules for a tailor-made multi-qubit computing register.
Experimental Setup
Two independent cavity-atom modules are connected by a stabilized 60 m optical fiber, with Raman control and atom-state detection available at each module.
- Experimental Setup: The setup uses two independent qubit modules connected by a 60 m single-mode optical fiber, with each module containing a strongly coupled 87Rb atom in a single-sided cavity.Fiber squeezers and reference beams compensate birefringence and thermal drifts in the network link.
- Experimental Setup: The cavities are tuned to the atomic transition |↑z⟩↔|e⟩, establishing the coupling condition used by the protocol.Module a and Module b denote the first and second photon interactions, respectively.
- Experimental Setup: Each atom is initialized in |↑z⟩ and manipulated using Raman-beam rotations, including π pulses completed within 8 µs.The rotation axis is controlled through the phase between the Raman beams.
- Experimental Setup: Atom-state detection uses resonant side illumination that scatters photons into the cavity mode for collection and measurement.An acousto-optic path switch routes detection light from Module a to a detection setup.
Definitions
The paper defines separate atomic and polarization bases, then specifies wave-plate and atomic-rotation transformations in those bases.
- Definitions: The protocol uses defined basis states for the atomic qubits and for the photonic polarization.These bases provide the representation for the subsequent cavity reflections and measurements.
- Definitions: A quarter-wave plate is represented by a transformation in the chosen polarization basis.The transformation describes how the relevant polarization states change before and between cavity interactions.
- Definitions: The atomic π and π/2 rotations around the x- and y-axes are represented by transformation matrices.The angle appears as a subscript, while the rotation axis appears as a superscript.
Reflection from the Cavity
Cavity reflection converts the atom-dependent coupling of circular polarizations into a phase-sensitive interaction between the photon and atomic state.
- Reflection from the Cavity: For a coupled atom in |↑z⟩, |R⟩ light is blocked from entering the cavity and is directly reflected without an additional phase shift.This behavior follows from the normal-mode splitting of the coupled atom-cavity system.
- Reflection from the Cavity: For |L⟩ light or a non-coupling atom in |↓z⟩, the photon enters the cavity and acquires a π phase shift upon reflection.The phase shift occurs as the light exits through the incoupling mirror.
- Reflection from the Cavity: Table S1 lists the relevant cavity quantum-electrodynamics parameters for the two modules.The supplied table caption identifies the table as the parameter reference for both modules.
Full Protocol of the Non-Local Quantum Gate
A photon interacts successively with two remote atoms, is measured to herald the operation, and can implement a controlled phase gate whose phases are tested through Bell-state generation and state preservation.
- Full Protocol of the Non-Local Quantum Gate: A single mediating photon is reflected from the first and second modules, creating an atom-atom-photon state before polarization measurement.The first and second spins correspond to the modules encountered in that order by the photon.
- Full Protocol of the Non-Local Quantum Gate: The photon is detected in the |A⟩/|D⟩ basis, and an |A⟩ result triggers a Z-gate feedback rotation on the first atom.The feedback combines a π rotation around y followed by a π rotation around x; a |D⟩ result receives no feedback.
- Full Protocol of the Non-Local Quantum Gate: The resulting operation is a fully controlled quantum-PHASE gate, which is equivalent to a CNOT when combined with two Hadamard gates.The same gate can also be considered in a superposition basis.
- Full Protocol of the Non-Local Quantum Gate: Truth-table populations alone cannot reveal non-zero implementation phases, so additional measurements are required to determine the phases of the unitary.Bell-state production from selected input states supplies these additional constraints.
- Full Protocol of the Non-Local Quantum Gate: The experiment determines α = β = γ = 0 by producing two Bell states and preserving |↑z↑z⟩ with probability (98.6 ± 0.6)%.The preservation measurement used 361 detected photon events and supports the conclusion that the energy eigenstate is an eigenstate under photon reflection.
Reconstructed Density Matrices after the Gate Protocol
The two-qubit output states are characterized by full state tomography after generating all four Bell states. Figure S1 reports the residual imaginary components of the reconstructed density matrices.
- Full tomography analyzes the combined quantum state of the two distant qubits after the gate creates all four Bell states.
- The main text presents the real parts of the reconstructed density matrices for these states.
- Figure S1 shows the small residual imaginary contributions remaining after density-matrix reconstruction.
Simulating the Effects of Errors
The experiment is modeled numerically with QuTiP and input-output theory, using independently estimated transmission, detection, coherence, detuning, and birefringence parameters. The error analysis attributes fidelity reductions to decoherence, polarization and mode mismatch, preparation and measurement, and resonator fluctuations.
- Simulation approach: QuTiP simulations use input-output theory and experimentally estimated transmission, detection, decoherence, detuning, and birefringence parameters.
- Decoherence: Close to 400 µs coherence times limit entanglement fidelity through atomic dephasing, mainly in the first module during feedback pulses.
- Optical imperfections: 2.7% fidelity error is attributed to polarization overlap limitations from drifts, polarization-dependent losses, fiber compensation, and cavity birefringence.
- Control and stability: State preparation and measurement contribute 2.7% error, while resonator frequency fluctuations and drifts contribute 1.9% error for the truth table.
- Mode matching: Imperfect transversal fiber–resonator mode matching produces an additional error, while detector dark counts and cQED parameters contribute sub-percent effects.