Abstract
The realization of strong photon–photon interactions has presented an enduring challenge across photonics, particularly in quantum computing, where two-photon gates form essential components for scalable quantum information processing (QIP). While linear-optic schemes have enabled probabilistic entangling gates in spatio-polarization encoding, solutions for many other useful degrees of freedom remain missing. In particular, no two-photon gate for the important platform of frequency encoding has been experimentally demonstrated, due in large part to the additional challenges imparted by the mismatched wavelengths of the interacting photons. In this article, we design and implement an entangling gate for frequency-bin qubits, a coincidence-basis controlled-NOT (CNOT), using line-by-line pulse shaping and electro-optic modulation. We extract a quantum unitary fidelity of 0.91 ± 0.01 via a parameter inference approach based on Bayesian machine learning, which enables accurate gate reconstruction from measurements in the two-photon computational basis alone. Our CNOT imparts a single-photon frequency shift controlled by the frequency of another photon—an important capability in itself—and should enable new directions in fiber-compatible QIP.
Highlights
While two-qubit gates succeed only probabilistically in this paradigm, linear-optical quantum computation (LOQC)[2] is in principle scalable with polynomial auxiliary resource requirements and has laid the foundation for many subsequent advances in photonic quantum information processing (QIP).[3,16,17,18,19,20,21,22,23,24,25]. It is this approach which we invoked in proposing spectral LOQC—a universal QIP scheme tailored to frequency-bin qubits which makes use of electro-optic phase modulators (EOMs) and Fourier-transform pulse shapers (PSs).[26]
Using the predicted matrix V as an initial guess for the slice sampler, a procedure which we found important to speed up convergence given the large search space of 28 independent variables, we converge to the Bayesian fidelity estimate F Bayesian mean estimation (BME) 1⁄4 0:91 ± 0:01, where F is defined according to Eq (2)
Moving forward, it will be valuable to implement this gate with input states beyond just the computational basis, useful for implementing photonic QIP algorithms such as the variational quantum eigensolver[38] and Shor factoring.[39]
Summary
As carriers of quantum information, optical photons feature a host of valuable attributes, such as immunity to environmentally induced decoherence, availability of precise tools for state control, and room temperature operation, enabling quantum information processing (QIP)[1] in a variety of encodings such as space/ polarization[2,3,4] and temporal modes.[5,6,7] Frequency-bin encoding —which offers additional advantages in terms of compatibility with state-of-the-art fiber-optic networks—has advanced rapidly in recent years, facilitated by the development of integrated frequency-bin photon sources[8,9,10,11] and quantum gates based on both nonlinear-optical[12,13] and electro-optical[14,15] mixing approaches. Waveshaper 4000A), WSS wavelength selective switch (Finisar 1 × 9 Flexgrid), SNSPD superconducting nanowire single-photon detector (Quantum Opus model Opus One, >80% detection efficiency), ATT variable radio-frequency (RF) attenuator, AMP RF amplifier determined by the product of the singles counts and our timing resolution.[28,29] The nonuniform distribution of accidentals stems from the fact that the singles counts vary significantly across input/output state combinations This is a natural feature of coincidence-basis gates: they are designed to discard cases when one of the qubit spaces is empty or doubly occupied, so that photon detection rates in a specific mode can change without impacting the designed operation. Motivated simplifications[35] and alternatives[36] to QPT are of significant value in quantum information, and so, in our particular case, the key question is a EOM 1 QFP Shaper EOM 2
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