A high-efficiency elementary network of interchangeable superconducting qubit devices
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Michael Mollenhauer, Abdullah Irfan, Xi Cao, Supriya Mandal, Wolfgang Pfaff
What if scaling a quantum computer looked less like fabricating one enormous chip—and more like plugging together replaceable modules? This paper shows a detachable cable moving quantum information with roughly one-percent loss in under one hundred nanoseconds.
Modular architectures are a promising approach to scale quantum devices to the point of fault tolerance and utility [1–3]. Modularity is particularly appealing for superconducting qubits, as monolithically manufactured devices are limited in both system size and quality [4–6]. Constructing complex quantum systems as networks of interchangeable modules can overcome this challenge through ‘Lego-like’ assembly, reconfiguration, and expansion, in a spirit similar to modern classical computers. First prototypical superconducting quantum device networks have been demonstrated [7–18]. Interfaces that simultaneously permit interchangeability and high-fidelity operations remain a crucial challenge, however. Here, we demonstrate a high-efficiency interconnect based on a detachable cable between superconducting qubit devices. We overcome the inevitable loss in a detachable connection through a fast pump scheme, enabling inter-module SWAP efficiencies at the 99%-level in less than 100 ns. We use this scheme to generate high-fidelity entanglement and operate a distributed logical dual-rail qubit. At the observed ∼1% error rate, operations through the interconnect are at the threshold for fault-tolerance. These results introduce a modular architecture for scaling quantum processors with reconfigurable and expandable networks.
Transcript
What if scaling a quantum computer looked less like fabricating one enormous chip—and more like plugging together replaceable modules? This paper shows a detachable cable moving quantum information with roughly one-percent loss in under one hundred nanoseconds. Modular architectures are a promising approach to scale quantum devices to the point of fault tolerance and utility, and modularity is particularly appealing for superconducting qubits because monolithically manufactured devices are limited in both system size and quality.
Networks of interchangeable modules can provide ‘Lego-like’ assembly, reconfiguration, and expansion, but interfaces that simultaneously permit interchangeability and high-fidelity operations remain a crucial challenge. The demonstrated solution is a high-efficiency interconnect based on a detachable cable between superconducting qubit devices, using a fast pump scheme to overcome the inevitable loss in a detachable connection.
That scheme enables inter-module SWAP efficiencies at the 99%-level in less than 100 nanoseconds, and it is used to generate high-fidelity entanglement and operate a distributed logical dual-rail qubit. At the observed roughly one-percent error rate, operations through the interconnect are at the threshold for fault-tolerance.
At the core of a modular device architecture lies the interchangeability of subsystems, an approach recognized as a key scaling strategy for quantum processors. Seamless addition and removal of components enables system upgrades with pre-tested, higher-fidelity qubit modules.
Expansion of system size and computational power can be achieved simply by plugging in additional modules. Because manufactured devices have finite yield and fluctuating parameters, it is difficult to realize monolithic quantum systems containing large numbers of high-quality qubits, especially in superconducting qubits.
Modular quantum computing architectures can therefore be key for overcoming a central challenge in realizing large-scale quantum processors. Achieving modular scaling hinges critically on efficient interchangeable interconnects, but previous work accepted compromises because combining low loss and interchangeability is difficult.
Examples include sparse weak links, measurement-based protocols with non-deterministic entanglement, and low-loss wafer- or wire-bonding that sacrifices plug-and-play interchangeability. A fully modular architecture requires inter-module links on par with intra-module gates, with deterministic operations at the one-percent error level between interchangeable modules.
Experiments to date had losses exceeding fifteen percent, well in excess of requirements for scaling. The architecture uses an interconnect between separately packaged transmon qubits that combines a reliably pluggable coaxial-cable link with fast and high-fidelity Raman transitions.
Using this architecture, the experiment demonstrates inter-module SWAP gates with roughly one-percent loss in under one hundred nanoseconds. The interconnect rivals the performance shown with superconducting bonds between qubit circuits and cables. The speed and efficiency of the pump scheme enable high-fidelity inter-module entanglement and operation of a distributed dual-rail qubit.
The interconnect requires no circuit elements beyond the intrinsic nonlinearity of the qubits, making it applicable for different types of qubits beyond the transmon. A quantum interconnect scheme should combine low loss with flexibility in assembly and connectivity, which makes cable-based connections highly attractive.
Superconducting coaxial cables can serve as low-loss transmission line resonators, allowing their use as an off-chip version of a quantum bus. A detachable connection between qubit and cable implies a capacitive coupling scheme.
The connector mechanism yields quality factors for a demountable bus made of aluminum cable of up to five hundred thousand. The connector is mounted to a sub-cutoff waveguide containing a fixed-frequency transmon. Figure one lays out the complete modular-link concept.
Panel a shows separate qubit modules connected by a detachable cable, while panel b shows the superconducting coaxial cable serving as a high-Q bus between separately packaged chips. Panel c illustrates Raman sideband transitions that transfer excitations through the bus, and panel d simulates swap inefficiency versus swap time for different bus quality factors and drive rates, highlighting the design tradeoff between bus loss, detuning, and gate speed.
The physical link must be combined with a compatible, high-fidelity gate scheme. Capacitive coupling reduces the attainable cable quality factor compared with galvanically bonded cable connections and precludes fast tunable couplers based on flux-tuning.
The gate therefore uses a Raman-type process created by parametrically driving sideband transitions between the qubits and bus mode. Fixed-frequency transmon qubits allow these transitions to be driven natively. A low-frequency driving scheme enables fast sideband rates without introducing excess decoherence, so gate speeds can strongly exceed interconnect loss rates.
The interconnect is assessed through the efficiency of a SWAP gate between distant qubits, because high-fidelity SWAPs are sufficient for executing inter-module circuits in a network of multi-qubit modules. Bus loss causes inefficiency that can be counteracted by detuning, but detuning slows the gate and introduces inefficiency from finite qubit coherence.
The strategy is to make the sideband rate as high as possible and prioritize speed to avoid inefficiency from qubit decoherence. The predictions indicate that high bus quality factor and fast sidebands can produce excitation swaps with sub-percent loss in around one hundred nanoseconds.
The Raman process uses sideband transitions that convert qubit excitations into bus photons, and these transitions can be tuned individually for each module. A mode of the bus resonator is coupled to both qubits in the dispersive regime, allowing the sidebands to be driven by applying a pump tone to the transmon.
The process can be understood as degenerate four-wave mixing, for which the paper predicts faster sidebands than in the more commonly employed non-degenerate case. The sidebands are first calibrated for both qubits individually by preparing each qubit in the excited state and recording its change in state as a function of pump frequency and power.
When the pump is tuned to resonance and Stark shifts are compensated, rapid oscillations between the e-zero and g-one states are induced, with oscillation frequency set by pump power. For sideband rates of five megahertz, the experiment observes sideband Rabi oscillations.
The decay of these oscillations is explained by the undriven loss rates of qubit and cable alone, indicating that the strong pump does not cause excess decoherence. Figure two calibrates fast sideband exchange between each qubit and the detachable high-Q bus.
Panels a and b map the resonances, while c and d show oscillations between the qubit excitation and bus photon at sideband rates of five and ten megahertz. Panel e reveals extra decay at the ten-megahertz rate beyond undriven decoherence, and panel f measures the bus photon lifetime as six point two microseconds—key benchmarks for predicting SWAP-gate performance.
With the individual sidebands tuned, both pumps are turned on simultaneously to realize a Raman transition between the qubits. For zero detuning, the measured sideband rates and bus quality factor predict a fast, high-efficiency SWAP. Using an in-situ bus quality factor of two times ten to the fifth, the predicted swap inefficiency is zero point nine seven percent for sideband rates of five megahertz, including bus loss and qubit decoherence.
The experiment observes high-visibility oscillations in agreement with the dynamics predicted by the total Hamiltonian and established decoherence rates. Fitting the dynamics yields a loss per swap of one point zero plus or minus zero point one percent, in quantitative agreement with the model.
Figure three benchmarks Raman-mediated swaps between modules. Panels a and b show coherent population exchange during a continuous pump and through discrete SWAP gates, while panels c and d track accumulated error over repeated gates for two drive settings. Panel e then verifies phase coherence through the transversal correlation ⟨XXϕ⟩, with simulations including independently measured decoherence and, separately, state-preparation and measurement errors; without those SPAM errors, the computed Bell-state fidelity is zero point nine seven four.
With sidebands tuned to ten megahertz, the gate time drops to seventy nanoseconds, while the loss rate remains the same because of drive-induced excess errors. An inefficiency of about one percent in a sub-one-hundred-nanosecond SWAP gate is the central benchmark, demonstrating a high-efficiency inter-device link.
The Raman transition must preserve phase coherence as well as transfer population, and the experiment tests this through transversal correlations after generating entanglement. Fast sidebands and the high-Q bus enable inter-module entanglement in a simple, stroboscopic fashion.
The sequence prepares qubit one in the excited state, swaps half the population into the bus, and then swaps the full bus population to qubit two, corresponding to a square-root iSWAP entangling gate. The measured correlator is in quantitative agreement with a simulation that includes only the undriven loss of all modes, predicting a Bell-state fidelity of ninety-seven point four percent.
Because the bus is populated for a significant time, this approach has more loss than the SWAP, although detuned Raman transitions could suppress that loss. For a Raman transition with detuning much greater than the sideband rates, the bus is populated only virtually and bus loss is suppressed.
The coherent evolution then occurs in the two-dimensional subspace spanned by e-g and g-e, while the radio-frequency-driven sidebands realize arbitrary rotations of this effective two-level system. This is a distributed dual-rail qubit, a logical encoding relevant to hardware-efficient quantum error correction with superconducting circuits.
Accessing this detuned regime requires sidebands that are fast compared with loss rates. The low-loss interconnect and fast sideband transitions together provide a path toward loss-resilient entanglement and distributed logical qubits.
Figure four shows how detuned Raman driving creates a distributed dual-rail qubit using the states “e g” and “g e,” while keeping the bus only virtually populated to suppress bus loss. The measured oscillations in panel c demonstrate coherent exchange between the two physical qubits, and panel d applies logical operations including a phase flip and half rotations.
The logical relaxation is practically absent, while dephasing remains limited by the individual qubits’ coherence. The network is controlled in the dual-rail subspace consisting of logical zero, e-g, and logical one, g-e, by applying detuned sideband drives with detuning divided by sideband rate approximately equal to five.
The measured time-dependent populations form the characteristic chevron pattern and agree quantitatively with numerical predictions. The observed oscillations remain much faster than effective loss rates, and the swap period stays on the sub-microsecond scale despite strong detuning.
At the half-swap time, the two physical qubits are in a maximally entangled Bell state. From the simulated time dynamics, the Bell-state fidelity is estimated at zero point nine eight plus or minus zero point zero one. In the detuned regime, bus loss is suppressed compared with the resonant regime, while fidelity is limited by on-site decoherence.
The experiment demonstrates a prototypical quantum network of interchangeable superconducting quantum devices. A high-Q detachable quantum bus connection combined with low-frequency parametric pumping realizes a high-efficiency interconnect at the one-percent error level with operations on the order of one hundred nanoseconds.
The drive scheme also enables high-fidelity entanglement and operation of a distributed logical qubit. Although the experiment uses a fairly short cable, no detrimental effects are expected as long as the sideband rate is small compared with the cable free spectral range, placing the length limit at the one-meter scale.
The interconnect can be reattached with reproducible performance, and fast sidebands can be achieved reliably even though system parameters fluctuate strongly between assembly cycles. Figure nine tests repeatability across thirteen bus-mounting cycles, involving five different qubit samples and packages; iteration eight was only thermally cycled rather than reassembled.
Panel a reports relaxation, Ramsey, and echo decay times, while panel b reports the qubit–bus dispersive shift and bus lifetime. This matters because the authors’ main experiment used iterations one and six, and clean sideband oscillations with an omega over two pi of at least five megahertz were obtained in eleven of the thirteen iterations.
The present design has an appreciable impact on qubit coherence. A more mature design that preserves state-of-the-art coherence times would enable inter-module gate infidelities approaching ten to the power of minus three. At that level, operating on inter-module logical qubits would be on equal footing with intra-module operations, removing the need to treat interconnects as weak links.
The central result is a reproducible, detachable superconducting interconnect that combines fast Raman transitions with a high-Q cable, enabling roughly one-percent-error swaps, entanglement, and a distributed dual-rail qubit.
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