Ultracoherent superconducting cavity-based multiqudit platform with error-resilient control

TL;DR

This work demonstrates an ultrahigh-coherence, two-mode SRF cavity platform that preserves cavity quality while delivering fast, ancilla-error-resilient control via sideband interactions. By weakly coupling a transmon and employing sideband gates, SFP, PF, and VRBS techniques, the authors achieve high-fidelity preparation of large Fock states up to $N=20$ and near-unity two-mode entanglement fidelities after post-selection. The VRBS protocol enables coherent beamsplitter and entangling operations in the single-photon subspace, with coherence-limited fidelities around $99.7$–$99.9\%$, and mid-circuit error detection further enhances performance. Collectively, these results establish a scalable, qudit-capable bosonic platform with strong potential for modular quantum memories, high-dimensional encodings, and quantum simulations, while outlining clear paths for further improvements in coherence and control infrastructure. $3$–$5$ sentence high-level summary: The problem is achieving fast, high-fidelity control in ultrahigh-coherence bosonic cavities without compromising their long lifetimes. The approach combines a two-mode TESLA-based SRF cavity with a weakly coupled transmon, leveraging sideband interactions and real-time feedforward to mitigate ancilla-induced losses. The key contributions are (i) long-lived cavity modes with lifetimes in the tens of milliseconds, (ii) Fock-state preparation up to $N=20$ with fidelities exceeding $95\%$, (iii) a virtual Raman beamsplitter enabling high-fidelity two-mode entanglement, and (iv) a scalable pathway toward high-dimensional qudit encodings and modular quantum memories. The practical impact is a robust platform for bosonic quantum computing and simulations with potential extensions to larger multimode networks and distributed quantum processing.

Abstract

Superconducting radio-frequency (SRF) cavities offer a promising platform for quantum computing due to their long coherence times, yet integrating nonlinear elements like transmons for control often introduces additional loss. We report a multimode quantum system based on a 2-cell elliptical shaped SRF cavity, comprising two cavity modes weakly coupled to an ancillary transmon circuit, designed to preserve coherence while enabling efficient control of the cavity modes. We mitigate the detrimental effects of the transmon decoherence through careful design optimization that reduces transmon-cavity couplings and participation in the dielectric substrate and lossy interfaces, to achieve single-photon lifetimes of 20.6 ms and 15.6 ms for the two modes, and a pure dephasing time exceeding 40 ms. This marks an order-of-magnitude improvement over prior 3D multimode memories. Leveraging sideband interactions and novel error-resilient protocols, including measurement-based correction and post-selection, we achieve high-fidelity control over quantum states. This enables the preparation of Fock states up to $N = 20$ with fidelities exceeding 95%, the highest reported to date to the authors' knowledge, as well as two-mode entanglement with an estimated coherence-limited fidelities of 99.9% after post-selection. These results establish our platform as a robust foundation for quantum information processing, allowing for future extensions to high-dimensional qudit encodings.

Figures (16)

• Figure 1: Device architecture and coherence properties.(a) Schematic of the double-cell elliptical SRF cavity with four ports for RF control. Three ports are used in this experiment. The chip (blue) contains an ancilla transmon, a Purcell filter, and a stripline resonator for measuring the transmon. (b) Picture of the niobium cavity (top panel) with mounting brackets made of oxygen-free copper. Bottom panel shows the electric field distribution of the two fundamental modes dubbed 'Alice' and 'Bob'. (c) Coherence times of the single photon states obtained using T$_1$ and Ramsey experiments. (d) Relaxation times of Alice mode's Fock levels up to $|20\rangle$ with a fit to $1/(n \gamma_1)$, where $n$ is the Fock state photon number and $\gamma_1=1/T_1^{(1)}$ is the decay rate of $|1\rangle$. The inset shows that the theoretical decay rate of Fock $|n\rangle$ is equal to $n\gamma_1$ for a harmonic oscillator.
• Figure 2: Fock state preparation and characterization.(a) Sideband scheme demonstrating the transfer of population starting from $|g0\rangle$ to $|gn\rangle$. Addition of one photon in the bosonic ladder involves application of unconditional $\pi_{ge}$ (light blue arrows) and $\pi_{ef}$ (red arrows) pulses on the transmon followed by a $\pi$ pulse ($\pi_{sb}$) which allows the sideband transition $|f,n\rangle\leftrightarrow |g,n+1\rangle$ (green arrows). (b) Pulse protocol for correcting ancilla errors and cavity single-photon loss. After each $\pi_{sb}$ pulse, the transmon is measured, followed by application of conditional pulses to correct transmon errors, termed as 'sideband feedforward protocol' (SFP). At the end of the sequence, a parity filter (PF) is applied to post-select results with the expected parity. The PF is implemented by applying two opposite $\pi_{ge}/2$ pulses conditioned on $n$ photons with a gap of $\pi/|\chi_e|$ so that the correct state is always mapped to $|g\rangle$. (c) Photon-number-resolved spectroscopy (PNRS) of the $\lvert20\rangle$ state, prepared in the Alice mode, using sideband (SB) only (left), SFP (middle), and both SFP and PF (right). SFP significantly improves the height of the target peak, with remaining infidelity primarily caused by leakage to the off-target state $\lvert19\rangle$. This error is further suppressed by implementing PF and post-selecting on the correct state. (d) Fidelities of different Fock states in the Alice (round markers) and Bob (triangular markers for $|20\rangle$ state only) modes prepared using the three methods. The error-resilient methods clearly improve the state preparation fidelities.
• Figure 3: Virtual Raman-assisted beamsplitter (VRBS) operation.(a) Level diagram showing microwave drives for realizing the VRBS operation between the two modes and relevant stochastic processes that can lead to errors. The green arrows represent detuned $|f0\rangle \leftrightarrow |g1\rangle$ transition for both modes with rates $g_{sb}$. The gray lines show single-photon decay channels giving rise to erasure errors. The red lines represent transmon heating events arising due to sideband drives. (b) Characterization of VRBS interactions. The three panels show beamsplitter rates, cavity decoherence rates, and gate fidelities as a function of the sideband detuning. Blue and red markers denote experimental data and numerical simulation results, respectively. (c) The time-domain VRBS measurement at the optimal detuning. The top panel shows the circuit diagram, while the middle and bottom panels show data before and after discarding shots containing the erasure error. Fidelity numbers are obtained using Eq. \ref{['eq:BS_fidelity']}. (d) Circuit diagram and the three oscillation graphs showing the VRBS-induced swap operations with heating checks. The swap operations $U_\text{SWAP}$ are applied to the initial state, with a swap time determined from the result in (c). The transmon is measured after each swap (top oscillation graph) and a heating check is performed by not discarding the shots only if it is found in $|g\rangle$. The gates $U_{\rm BS}$ and $U_{\rm BS}(\phi)$ are only applied for the initialization and readout of the state $(|10\rangle+|01\rangle)/\sqrt{2}$. The extracted swap fidelity improves when the heating check is performed, for both the $|10\rangle$ and $(|10\rangle+|01\rangle)/\sqrt{2}$ initial states (middle and bottom graph).
• Figure A1: Bare cavity characterization.(a) Ringdown measurements for the Alice mode showing raw data and linear fits. (b) Similar measurements for the Bob mode. (c) Internal quality factors as a function of the mixing chamber plate's temperature for both modes and fitting to the TLS model.
• Figure A2: Sideband pulse calibration. (a) By initializing the state in $\lvert f,n\rangle$ and sweeping the sideband drive frequency, we observe the dip in the transmon $|f\rangle$ state population $P(f)$ that represents the corresponding sideband resonance frequency. (b) Driving the sideband transition at the measured resonance leads to the oscillations of $P(f)$, from which we extract the $\pi$-pulse time. We plot the first five sideband pulses for the Bob mode as an example, utilizing the SFP and PF techniques for enhancing the contrast of the calibration measurements.