Picosecond Schrödinger cat states for ultrafast optical quantum processing

Problem
Universal, fault-tolerant optical quantum computing requires non-Gaussian resource states, specifically Schrödinger cat states and Gottesman–Kitaev–Preskill (GKP) qubits. While these states can be generated via heralded protocols such as generalized photon subtraction (GPS), the supply rate of such resources has been severely limited by two factors: low heralding probabilities and operation restricted to nanosecond-scale temporal modes. Existing demonstrations of complex non-Gaussian states often rely on nanosecond wave packets, where limited source and detector bandwidth, timing jitter, and imperfect mode matching increase effective loss. Consequently, the generation rate of high-quality non-Gaussian states remains insufficient for practical, scalable optical quantum information processing. Furthermore, fault-tolerant architectures (such as cat-code encodings and adaptive breeding for GKP states) require cat states with sufficiently large amplitudes, a regime that has been difficult to access in ultrashort temporal modes.

Methodology
The authors demonstrate multi-photon generalized photon subtraction (GPS) within picosecond optical wave packets to address the temporal-mode bottleneck. The experimental platform utilizes two independently phase-controlled broadband optical parametric amplifiers (OPAs) based on type-0 periodically poled lithium niobate (PPLN) waveguides, pumped by 772.66-nm pulses at a 5-MHz repetition rate with a duration of approximately 10 ps. These OPAs generate squeezed-vacuum states at 1545.32 nm.

The two squeezed modes are interfered on a variable beam splitter. One output arm undergoes spectral filtering and is detected by a high-speed Ti–Au transition-edge sensor (TES) capable of photon-number-resolving detection (PNRD). This detection heralds the generation of a non-Gaussian state in the other arm. The heralding condition is set for the detection of $n$ photons, where $n \ge 2$. The generated state is characterized using pulsed balanced homodyne detection, where the local oscillator (LO) pulses are shaped to match the 10-ps temporal mode of the signal. The system achieves temporal and spatial mode overlaps exceeding 90% and 98%, respectively. Quantum-state tomography is performed on over $10^8$ homodyne samples across 12 quadrature settings, with density matrices reconstructed via maximum-likelihood estimation without loss correction.

Key Contributions

• Temporal Mode Scaling: The work extends GPS from conventional nanosecond-scale wave packets to picosecond temporal modes ($\sim$10 ps), representing a roughly two-order-of-magnitude reduction in temporal width compared to recent integrated GKP demonstrations.
• High-Rate Platform: By integrating broadband squeezing, high-speed TES detection, and picosecond-mode homodyne detection, the authors establish a platform compatible with high-repetition-rate, scalable time-multiplexed photonic architectures.
• Large-Amplitude Generation: The protocol successfully generates multi-photon heralded cat states with effective amplitudes approaching the regime of practical relevance for fault-tolerant bosonic encodings.

Results
The experiment successfully heralded Schrödinger cat states for photon detection events of $n=2, 3,$ and $4$.

• State Characterization: Reconstructed Wigner functions exhibit clear negativity without loss correction. For $n=4$, the Wigner function displays up to four distinct negative regions.
• Fidelity: The experimentally reconstructed states show high fidelity ($F > 0.99$) with numerical simulations based on independently calibrated squeezing and loss parameters.
• Effective Amplitude: The effective cat-state amplitude ($\alpha_{\text{eff}}$), extracted directly from uncorrected quadrature marginals, reaches $\alpha_{\text{eff}} = 1.69$ for the $n=4$ case. When correcting only for the 80% homodyne efficiency, the amplitude is $\alpha_{\text{in}} = 1.88$.
• Comparison to Requirements: The achieved amplitude of $\alpha_{\text{eff}} = 1.69$ lies within approximately 5% of the theoretical requirement ($\alpha \approx 1.77$) for generating a five-peak lattice suitable for adaptive breeding toward GKP-state generation. It also enters the regime of practical relevance for cat-code architectures, where large amplitudes suppress bit-flip errors exponentially.

Significance
The paper claims to establish the missing experimental capability for high-rate non-Gaussian state generation. By operating in picosecond temporal modes, the platform addresses the repetition-rate bottleneck that has constrained the supply of non-Gaussian resources. The results demonstrate that multi-photon GPS can produce states with large effective amplitudes and clear Wigner negativity in ultrashort temporal modes, providing a necessary foundation for adaptive breeding protocols and time-multiplexed optical quantum information processing. The authors note that while the current repetition rate is limited by the TES timing jitter and homodyne receiver bandwidth, the conceptual framework supports future scaling toward hundreds of megahertz or gigahertz regimes with improved detectors and amplification techniques.