Generation of time-frequency grid state with integrated biphoton frequency combs
Nicolas Fabre, G. Maltese, Félicien Appas, Simone Felicetti, Andreas Ketterer, Arne Keller, T. Coudreau, F. Baboux, Maria I. Amanti, S. Ducci, P. Milman
Encoding quantum information in continuous variables is intrinsically faulty. Nevertheless, redundant qubits can be used for error correction, as proposed in [1]. We show how to experimentally implement this encoding using time-frequency continuous de- grees of freedom of photon pairs produced by spontaneous parametric down conversion. We illustrate our results using an integrated AlGaAs photon-pair source. We show how sin- gle qubit gates can be implemented and finally propose a theoretical scheme for correcting errors in a circuit-like and in a measurement-based architecture.
Encoding quantum information in continuous variables is intrinsically faulty. Nevertheless, redundant qubits can be used for error correction, as proposed in [1]. We show how to experimentally implement this encoding using time-frequency continuous de- grees of freedom of photon pairs produced by spontaneous parametric down conversion. We illustrate our results using an integrated AlGaAs photon-pair source. We show how sin- gle qubit gates can be implemented and finally propose a theoretical scheme for correcting errors in a circuit-like and in a measurement-based architecture.
Encoding quantum information in continuous variables is intrinsically faulty. Nevertheless, redundant qubits can be used for error correction, as proposed by Gottesman et al. [Phys. Rev. A 64 012310 (2001)]. We show how to experimentally implement this encoding using time-frequency continuous degrees of freedom of photon pairs produced by spontaneous parametric down conversion. We illustrate our results using an integrated AlGaAs photon-pair source. We show how single-qubit gates can be implemented and finally propose a theoretical scheme for correcting errors in circuit-like and measurement-based architectures.
We realize a hardware-native time--frequency Gottesman--Kitaev--Preskill (GKP) logical qubit encoded in the continuous phase space of single photons, establishing a propagating photonic implementation of bosonic grid encoding. Finite-energy grid states are generated deterministically using coherently driven entangled nonlinear biphoton sources that produce single-photon frequency-comb supermodes. An optical-frequency-comb reference anchors the time--frequency phase space and enforces commuting displacement stabilizers directly at the hardware level, continuously defining the logical subspace. Timing jitter, spectral drift, and phase noise map naturally onto Gaussian displacement errors within this lattice, yielding intrinsic correctability inside a stabilizer cell. Logical operations correspond to experimentally accessible phase and delay controls, enabling deterministic state preparation and manipulation. Building on the modal time--frequency GKP framework, we identify a concrete pathway toward active syndrome extraction and deterministic displacement recovery using ancillary grid states and interferometric time--frequency measurements. These primitives establish a hardware-compatible route for integrating the time--frequency GKP logical layer into erasure-aware and fusion-based fault-tolerant photonic architectures.
Encoding quantum information in continuous variables is intrinsically faulty. Nevertheless, redundant qubits can be used for error correction, as proposed by Gottesman, Kitaev and Preskill in Phys. Rev. A \textbf{64} 012310, (2001). We show how to experimentally implement this encoding using time-frequency continuous degrees of freedom of photon pairs produced by spontaneous parametric down conversion. We experimentally illustrate our results using an integrated AlGaAs photon pairs source. We show how single qubit gates can be implemented and finally propose a theoretical scheme for correcting errors in a circuit-like and in a measurement-based architecture.
The on-chip generation of optical quantum states will enable accessible advances for quantum technologies. We demonstrate that integrated quantum frequency combs (based on high-Q microring resonators made from a CMOS-compatible, high refractive-index doped-glass platform) can enable the generation of pure heralded single photons, cross-polarized photon pairs, as well as bi- and multi-photon entangled qubit states over a broad frequency comb covering the S, C, L telecommunications band, with photon frequencies corresponding to standard telecommunication channels spaced by 200 GHz. Exploiting a self-locked, intra-cavity excitation configuration, a highly-stable source of multiplexed heralded single photons is demonstrated, operating continuously for several weeks with less than 5% fluctuations. The photon bandwidth of 110 MHz is compatible with quantum memories, and high photon purity was confirmed through single-photon auto-correlation measurements. In turn, by simultaneously exciting two orthogonal polarization mode resonances, we demonstrate the first realization of type-II spontaneous FWM (in analogy to type-II spontaneous parametric down-conversion), allowing the direct generation of orthogonally-polarized photon pairs on a chip. By using a double-pulse excitation, we demonstrate the generation of time-bin entangled photon pairs. We measure qubit entanglement with visibilities above 90%, enabling the implementation of quantum information processing protocols. Finally, the excitation field and the generated photons are intrinsically bandwidth-matched due to the resonant characteristics of the ring cavity, enabling the multiplication of Bell states and the generation of a four-photon time-bin entangled state. We confirm the generation of this four-photon entangled state through four-photon quantum interference.
Entanglement and encoding in discrete frequency bins – essentially a quantum analogue of wavelength-division multiplexing – represents a relatively new degree of freedom for quantum information with photons. In this talk I discuss biphoton frequency combs, generated either by spontaneous four-wave mixing (SFWM) from on-chip microring resonators or by spectral filtering of spontaneous parametric down conversion (SPDC) in second order nonlinear crystals. Potential advantages include generation of high dimensional units of quantum information (qudits), which can carry multiple qubits per photon, robust transmission over fiber, frequency parallelism and routing, and compatibility with on-chip implementations, as well as hyperentanglement with other photonic degrees, e.g., time-frequency hyperentanglement. Since the initial experiments less than two years ago, frequency bin quantum photonics has been advancing rapidly [1-8]. In this talk I will discuss a method using pulse shapers and phase modulators in order to mix different frequencies and perform two photon interference experiments for characterization of the frequency-bin entanglement. Similar components (pulse shapers and phase modulators) may be used to manipulate the frequency-encoded quantum states; this will be described in another talk by our collaborators at Oak Ridge National Labs. I will also discuss the use of time bins and frequency bins as independent degrees of freedom in a quantum encoding fashion to realize what we believe to be the first deterministic two qudit gates. Finally, I comment briefly on potential applications and on prospects for realization of integrated frequency bin quantum photonics.
Abstract Quantum error correction (QEC) aims to protect logical qubits from noises by using the redundancy of a large Hilbert space, which allows errors to be detected and corrected in real time 1 . In most QEC codes 2–8 , a logical qubit is encoded in some discrete variables, for example photon numbers, so that the encoded quantum information can be unambiguously extracted after processing. Over the past decade, repetitive QEC has been demonstrated with various discrete-variable-encoded scenarios 9–17 . However, extending the lifetimes of thus-encoded logical qubits beyond the best available physical qubit still remains elusive, which represents a break-even point for judging the practical usefulness of QEC. Here we demonstrate a QEC procedure in a circuit quantum electrodynamics architecture 18 , where the logical qubit is binomially encoded in photon-number states of a microwave cavity 8 , dispersively coupled to an auxiliary superconducting qubit. By applying a pulse featuring a tailored frequency comb to the auxiliary qubit, we can repetitively extract the error syndrome with high fidelity and perform error correction with feedback control accordingly, thereby exceeding the break-even point by about 16% lifetime enhancement. Our work illustrates the potential of hardware-efficient discrete-variable encodings for fault-tolerant quantum computation 19 .