Frequency-Bin Photonic Qubit

Figure

Description

A frequency-bin photonic qubit uses two discrete optical frequency modes of a single photon,

$|\psi ⟩=\alpha |{\omega }_0⟩+\beta e^{i\varphi }|{\omega }_1⟩.$

Electro-optic phase modulators coherently mix bins, while Fourier-transform pulse shapers apply bin-dependent phases. The same hardware naturally extends from qubits to high-dimensional qudits. Frequency modes share one spatial path and polarization, making them stable in fibre and compatible with dense wavelength multiplexing.

Hamiltonian and Control

An electro-optic modulator driven at the bin spacing creates a synthetic frequency-lattice coupling,

$H_{\mathrm{EOM}}=\hslash {\sum }_m{J}_m{e}^{i{\varphi }_m}{a}_{m+1}^{†}{a}_m+h.c.,$

while a pulse shaper applies $U_{\mathrm{PS}}={\sum }_m{e}^{i{\theta }_m}|m⟩⟨m|$. Alternating these operations synthesizes arbitrary $SU(2)$ rotations on a selected pair of bins and more general unitaries on frequency-bin qudits.

Motivation

• Use telecom-compatible spectral multiplexing without multiplying spatial paths.
• Perform reconfigurable transformations using mature electro-optic and pulse-shaping technology.
• Scale naturally to qudits and parallel frequency channels.

Experimental Status

Lu et al. demonstrated fully arbitrary control of frequency-bin qubits in 2020. A quantum frequency processor implemented all fundamental rotations, tested 41 states across the Bloch sphere, and achieved near-unity mode-transformation fidelity with state verification by Bayesian tomography.

Key Metrics

Metric	Value	Notes	Fidelity reference
Control coverage	Arbitrary $SU(2)$	41 tested Bloch-sphere states	Lu et al. 2020
Mode-transformation fidelity	Near unity	Fundamental rotations in a quantum frequency processor	Lu et al. 2020
Native extension	Qudit	More than two discrete bins	Lu et al. 2020

Scaling Considerations

• Modulator bandwidth, pulse-shaper resolution, and insertion loss bound the usable number of bins.
• Spectral leakage and phase calibration grow with processor dimension.
• Entangling operations still depend on interference, measurement, nonlinear optics, or resource-state architectures.

References

• H.-H. Lu et al., “Fully Arbitrary Control of Frequency-Bin Qubits,” Phys. Rev. Lett. 125, 120503 (2020).

Linked Papers

• lu-2020-frequency-bin-control

Evergreen context

• erasure-error-vs-pauli-error — optical loss remains the dominant fault channel even when control occurs in frequency space.
• quantum-hardware — the encoding is inseparable from the bandwidth, loss, and calibration limits of electro-optic hardware.

Related Entries

• time-bin-photonic-qubit — temporal rather than spectral mode encoding.
• polarization-photonic-qubit — polarization encoding in the same spatial path.
• dual-rail-photonic-qubit — spatial-mode encoding.