Source-linked AI summary
Robust concurrent remote entanglement between two superconducting qubits
A. Narla, S. Shankar, M. Hatridge, Z. Leghtas, K. M. Sliwa, E. Zalys-Geller, S. O. Mundhada, W. Pfaff, L. Frunzio, R. J. Schoelkopf, M. H. Devoret
TL;DR
Remote entanglement with superconducting qubits needs loss-robust flying-photon protocols, but detecting low-energy microwave single photons is difficult. This work implements a transmon-based microwave photon detector and uses it in a concurrent remote-entanglement protocol, generating pairs with fidelity 0.57 ± 0.01 at 200 Hz. The experiment demonstrates tools for loss-tolerant entanglement and supports modular superconducting-qubit architectures.
Problem
Single-photon remote-entanglement protocols are robust to losses, but efficient single-photon detection is challenging for low-energy microwave quanta.
Method
The experiment uses a transmon-based microwave photon detector with qubit-photon entangling operations and two-click conditioning to generate remote entanglement.
Results
0.57 ± 0.01 fidelity and 200 Hz generation rate were achieved for remote entangled pairs.
Takeaways & Limitations
The experiment demonstrates flying microwave single-photon sources and detectors, photon interference, and loss-tolerant entanglement between distant superconducting qubits.
Abstract
from arXiv · showhide
Entangling two remote quantum systems which never interact directly is an essential primitive in quantum information science and forms the basis for the modular architecture of quantum computing. When protocols to generate these remote entangled pairs rely on using traveling single photon states as carriers of quantum information, they can be made robust to photon losses, unlike schemes that rely on continuous variable states. However, efficiently detecting single photons is challenging in the domain of superconducting quantum circuits because of the low energy of microwave quanta. Here, we report the realization of a robust form of concurrent remote entanglement based on a novel microwave photon detector implemented in the superconducting circuit quantum electrodynamics (cQED) platform of quantum information. Remote entangled pairs with a fidelity of $0.57\pm0.01$ are generated at $200$ Hz. Our experiment opens the way for the implementation of the modular architecture of quantum computation with superconducting qubits.
I. INTRODUCTION
Microwave photons are difficult to reveal and manipulate because their energies are 4 to 5 orders of magnitude lower than optical photons. Single-photon remote-entanglement protocols are robust to losses and support distant-qubit links for modular quantum computing.
- Microwave photon energies are 4 to 5 orders of magnitude lower than optical photons, complicating their detection and manipulation.
- Continuous-variable coherent-state protocols are practical at microwave frequencies but are sensitive to losses in the flying-state paths.
- Single-photon protocols are robust to losses because successful photon detection is linked to producing a pure entangled state.
- Concurrent remote entanglement is vital for modular superconducting quantum computing because it connects distant stationary qubits without direct module connections.
II. OVERVIEW OF EXPERIMENT AND PROTOCOL
The experiment entangles two remote transmon qubits by converting their states into flying single microwave photons, interfering the photons, and heralding on two consecutive detector clicks. Dual conditioning removes the unwanted component while making losses reduce success probability rather than entanglement fidelity.
- Alice and Bob are separate 3D transmon-cavity systems whose output ports feed a 180° hybrid, with one output connected to a transmon-based photon detector.
- Each qubit is entangled with a flying photon through a CNOT-like operation, producing joint stationary-and-photonic states before interference.
- The hybrid erases photon which-path information by mapping the two flying odd Bell states into a single-photon detector branch.
- Detector clicks ideally select the odd Bell state, but losses and failure to distinguish |1⟩ from |2⟩ introduce an undesired |ee⟩ component.
- A second entangling-and-detection round maps the unwanted component away, and two consecutive clicks herald the |O+⟩ state.
- Losses reduce the protocol’s success probability but not the fidelity of the generated entangled state under dual conditioning.
III. DESCRIPTION OF THE QUBIT-PHOTON ENTANGLEMENT PROCESS
The qubit-photon entangling operation maps a qubit superposition onto a correlated qubit-cavity state, after which the photon leaks out as a traveling state. Nearly matched cavity frequencies and bandwidths make photons from Alice and Bob indistinguishable.
- The CNOT-like operation maps α|g0⟩+β|e0⟩ onto α|g0⟩+β|e1⟩, correlating the qubit with an intracavity photon.
- A π-pulse and two sideband tones implement the mapping through the transmon’s second excited state and the |f0⟩↔|e1⟩ transition.
- The photon leaks from the cavity into a traveling state while remaining entangled with its qubit.
- Nearly identical cavity frequencies and bandwidths produce indistinguishable photon waveforms, without requiring identical qubits.
IV. DESCRIPTION OF MICROWAVE SINGLE PHOTON DETECTION
The experiment uses a transmon-cavity system as a microwave single-photon detector by selectively mapping an intracavity photon onto the detector qubit. The detector’s efficiency, dark-count rate, and reset time are sufficient for remote entanglement, which is verified through tomography and control measurements.
- The detector selectively π-pulses its transmon conditioned on one intracavity photon, converting photon presence into a measurable qubit excitation.
- Matching cavity linewidths maximizes detector efficiency, while a selective π-pulse determines detection based on photon arrival.
- The CNOT-like operation is identified by a maximized click probability at a 254 ns sideband-pulse duration.
- The detector has efficiency η ≈ 0.5, dark-count probability Pd < 0.01, and a 450 ns re-arm time.
- Conditioned on two clicks, tomography shows remote-entanglement signatures, including negative ⟨ZZ⟩ and sinusoidal Pauli components.
V. EXPERIMENTAL RESULTS
The experiment demonstrates remote entanglement between superconducting qubits through flying microwave photons, conditioned on photon detections. Joint tomography confirms an odd Bell state with corrected fidelity 0.57 ± 0.01, while entanglement generation proceeds at about 200 Hz.
- Qubit–photon entanglement: The CNOT-like operation maps a qubit superposition onto an entangled qubit–photon state by converting α|g0⟩ + β|e0⟩ into α|g0⟩ + β|e1⟩.The operation maps both the relative weights and phase of the qubit superposition onto the traveling photon state.
- Remote entanglement protocol: θ = π/2 maximizes remote entanglement, while θ = 0 and θ = π produce separable states with the expected odd-parity signature.The extremal Pauli components and negative ⟨ZZ⟩ identify the entangled and separable preparation regimes.
- Remote entanglement protocol: φoff = 3π/10, and the measured Pauli components follow the expected sinusoidal dependence for the generated Bell state.The tomography shows constant negative ⟨ZZ⟩ and sinusoidal behavior in the other displayed components.
- Entanglement characterization: 0.57 ± 0.01 corrected fidelity is obtained for the odd Bell state, with raw fidelity 0.53 ± 0.01 and concurrence 0.1 ± 0.01 exceeding the entanglement threshold.The theoretical model includes qubit decoherence, detector imperfections, and tomography infidelity.
- Generation rate: 200 Hz is the measured entanglement generation rate, based on a 21 µs repetition time and 0.4% overall success probability.The success probability combines 57% state-initialization post-selection with 8% and 9% detector-click probabilities in the two rounds.
VI. OUTLOOK AND CONCLUSIONS
The outlook combines hardware and software upgrades with the demonstrated microwave-photon toolkit to improve remote-entanglement generation. The authors conclude that these capabilities support modular quantum information processing with superconducting circuits.
- VI. OUTLOOK AND CONCLUSIONS: A second detector could increase success probability by a factor of 4, while mode matching could increase detection efficiency by at least 50% and multiply generation rate by at least 2.The proposed improvements target both detector configuration and temporal mode matching of photons and detection pulses.
- VI. OUTLOOK AND CONCLUSIONS: Around 10 kHz is the projected generation rate after combined upgrades, exceeding approximately 100 Hz decoherence rates demonstrated in 3D cQED-based quantum memories.The authors connect these upgrades to storing generated states, reusing qubits, and remote entanglement distillation.
- VI. OUTLOOK AND CONCLUSIONS: The experiment demonstrates flying microwave single-photon sources and detectors, indistinguishable traveling photons, two-photon interference, and loss-tolerant remote entanglement.These tools are presented as enabling new prospects for distributing quantum information with microwave flying photons.
A. Sample Fabrication and Parameters
The experiment combines three superconducting qubit–cavity modules with filtered cryogenic wiring, shared amplification, and calibrated readout. Joint Alice–Bob tomography achieved Fjoint > 90%, while detector readout exceeded 99% fidelity; calibration corrected the measured entanglement fidelity to 57%.
- Device fabrication: Three transmon qubits were fabricated on sapphire and housed in separate indium-plated copper 3D cavities for Alice, Bob, and the detector.The junctions used Al/AlOx/Al fabrication, and the cavities were coupled through coaxial input and output ports.
- Cryogenic environment: The cavities were operated in a dilution refrigerator below 50 mK with magnetic shielding, filtered input and output lines, and cryogenic amplification.Home-made Eccosorb filters, commercial low-pass filters, attenuators, isolators, and a 3 K HEMT amplifier conditioned the signals.
- Frequency matching: Alice and Bob cavity frequencies were matched, and the detector cavity was tuned to the photon frequency so the emitted photons were indistinguishable and could enter the detector.Aluminum screws were used to fine-tune the cavity frequencies.
- Readout chain: A single JPC provided nearly quantum-limited phase-preserving amplification for high-fidelity single-shot readout of all three qubit–cavity systems.The JPC operated with 20 dB gain and an 8 MHz bandwidth centered at 7.6314 GHz.
- Readout performance: Alice and Bob were jointly read out with 2 µs pulses, yielding Fjoint > 90%, while detector readout used 700 ns pulses with Fdet > 99%.The joint signal encoded the two qubit states along orthogonal axes and included their correlation.
B. Detector Characterization
The detector distinguishes single-photon inputs through state-dependent click probabilities and supports photons arriving from either module. Detection is maximized by timing the selective pulse to the detector-cavity photon population.
- The detector shows an increased response near ω0 ge −χ when the input is |1⟩, because the detector is excited by an incoming photon.
- Similar responses for Alice and Bob inputs demonstrate detection from both systems and comparable losses along the two paths.
- Pclick is maximized when the selective detection pulse peaks while the detector cavity contains the maximum photon population.
- The experimental timing point identified by the delay scan was used in the remote entanglement experiments.
C. Detector Optimization
Detector optimization balances dark counts, click probability, selectivity, and protocol duration. Threshold post-selection reduces dark-count contamination, while pulse broadening introduces competing costs.
- Dark counts mix the desired Bell state with unwanted states and reduce measured fidelity.
- The dark-count-to-click ratio Pd/Pclick is the relevant figure of merit for reducing infidelity caused by dark counts.
- Increasing the detection-pulse width improves selectivity but increases protocol duration and decoherence-related infidelity.
- The detector simulations found maximum efficiency near σ ∼κ, so increasing σ further raises Pd/Pclick.
- A stricter readout threshold reduced Pd/Pclick from 0.1 to 0.05 in the second detection round.
APPENDIX E. DETAILED EXPERIMENTAL PROTOCOL
The protocol initializes three qubits, performs two photon-mediated detection rounds, and conditions final tomography on two detector clicks. Post-selected initialization enables rapid repetition.
- 57% initialization success was obtained by cooling all three qubits and post-selecting trials with successful ground-state preparation.
- The experiment repeated every Trep = 21 µs, faster than any qubit’s relaxation time.
- Each protocol round applies a CNOT-like operation followed by photon detection, with an unconditional reset between rounds.
- Joint Alice–Bob tomography is conditioned on measuring two detector clicks in consecutive rounds.
B. Control Experiments
Control experiments without flying photons test whether the observed correlations arise from photon-mediated operations. They find no two-qubit entanglement under these controls, while modeling identifies decoherence as a substantial imperfection.
- B. Control Experiments: The control experiments interleaved with Fig. 3 measurements were designed to rule out systematic error.
- B. Control Experiments: Without generated photons, the protocol produces no two-qubit entanglement, as indicated by ⟨ZZ⟩ = 0.
- B. Control Experiments: The no-photon control lacks the correlation patterns observed with photon-mediated entanglement, including the expected odd-Bell-state oscillations.
- A. Qubit Decoherence: The imperfection model represents two qubits, photon-number branches, and two detectors with a 36 × 36 density matrix.
- A. Qubit Decoherence: Independent phase damping was modeled with T2E,A = 10 µs and T2E,B = 16 µs, producing FT2Bell ∼= 0.8.
B. Dark Counts
The analysis models how detector dark counts and finite efficiency contaminate the remotely generated Bell state, then estimates the resulting fidelity from measured click probabilities. A second protocol round improves fidelity by removing the |ee⟩ component and stabilizing the Bell-state phase.
- Detector imperfections: The detector model treats |0⟩, |1⟩, and |2⟩ as inputs and produces either a click or no-click outcome.The model uses generalized measurement operators and projects the input density matrix onto one of two output density matrices.
- Fidelity estimate: Fdet ≅ 0.9 was obtained from Pd,1 = 0.006, Pd,2 = 0.005, Preal,1 = 0.21, and Preal,2 = 0.26.The estimate models the final two-qubit state after two protocol rounds and successful photon detection.
- State model: The state after the first round is modeled as ρclick3 = N |O+⟩⟨O+| + (1 − N) |ee⟩⟨ee| before additional dark-count contamination is included.Without losses or dark counts, the detector's inability to distinguish |1⟩ from |2⟩ determines the normalization constant N.
- Detector imperfections: Dark counts mix the heralded Bell state with |gg⟩ and |O−⟩, lowering the generated entanglement fidelity.The first-round click state is further contaminated beyond the ideal mixture with |O+⟩ and |ee⟩.
- Protocol design: The two-round protocol increases fidelity by removing weight in |ee⟩ and stabilizes the Bell-state phase against experimental drifts.The phase protection includes the Ry(π) pulse on Alice and Bob, despite the longer protocol time.
D. Error Analysis
The fidelity uncertainty is dominated by statistical error from the finite number of tomography outcomes used to reconstruct the density matrix in the Pauli basis.
- Statistical uncertainty: Around 2 × 10^5 successful shots per Pauli component limited the error to around 1%.The resulting uncertainty in the quoted fidelity was propagated by varying each Pauli component within its respective error.