Photonic quantum computing uses photons, particles of light, as the basic carriers of quantum information. Photons can encode qubits in properties like polarization or path (dual-rail encoding), and they interact weakly with their environment, giving long coherence times [1]. Both discrete-variable (single-photon) and continuous-variable (squeezed-state) approaches have been explored pre-2021 [2].

Encoding and Photonic Qubits

In discrete-variable schemes, qubits are often dual-rail encoded: a single photon occupies one of two optical modes, representing |0⟩ and |1⟩ [3]. Polarization encoding is another common method, using horizontal and vertical polarization states. Continuous-variable photonic QC uses squeezed states and homodyne detection to encode information in field quadratures.

Linear Optical Quantum Computing (LOQC)

Knill, Laflamme, and Milburn (KLM) showed in 2000 that universal quantum computation is possible with only linear optical elements, single-photon sources, detectors, and feed-forward control [4]. The KLM protocol uses ancilla photons and post-selection to implement probabilistic gates, with error correction and teleportation boosting success probabilities [1]. Earlier work outlined similar ideas using beam splitters and phase shifters to induce effective nonlinearity [5].

Boson Sampling and Quantum Advantage

Aaronson and Arkhipov proposed boson sampling in 2011 as a specialized photonic experiment that is hard to simulate classically [6]. Boson sampling circuits send n photons through a linear interferometer and sample output distributions, relying on the computational hardness of calculating matrix permanents [7]. Early photonic supremacy experiments, like Jiuzhang, built on these principles (see Post 7) to benchmark photonic processors.

Measurement‑Based Photonic Quantum Computing

Cluster states, large entangled photonic graphs, enable quantum computation via single-qubit measurements and feed-forward operations, known as measurement-based QC [8]. Optical cluster states can be generated probabilistically via fusion gates, stitching smaller entangled states into scalable resource states [8].

Integrated Photonic Platforms

Integrating photonic circuits on-chip using waveguides, modulators, and interferometers offers stability and scalability [9]. Platforms in silicon, silicon nitride, and lithium niobate have demonstrated on-chip sources, routers, and detectors for quantum applications [10]. Continuous-variable integrated platforms also enable compact squeezed-light generation and homodyne measurement.

Experimental Progress and Commercial Efforts

By 2021, multi-photon experiments had reached ~20-photon interference in table-top setups, and integrated chips hosted interference of >8 modes. Companies like Xanadu developed cloud-accessible photonic processors (e.g., Borealis, X8) aimed at Gaussian boson sampling and variational algorithms [11].

Outlook

Photonic QC’s low decoherence and room-temperature operation are attractive, but challenges include probabilistic gates, photon-loss, and scalable on-chip photon generation. Advances in deterministic sources, multiplexing, and error-corrected cluster states are key areas to watch as the field moves beyond NISQ-era demonstrations.

References

[1] Kok, P., et al. (2007). Linear optical quantum computing with photonic qubits. Reviews of Modern Physics, 79(1), 135-174.

[2] Wang, J., et al. (2024). Photonic quantum computing: A review. arXiv:2404.03367.

[3] O’Brien, J. L., et al. (2009). Photonic quantum technologies. Nature Photonics, 3(12), 687-695.

[4] Knill, E., Laflamme, R., & Milburn, G. J. (2001). A scheme for efficient quantum computation with linear optics. Nature, 409(6816), 46-52.

[5] Reck, M., et al. (1994). Experimental realization of any discrete unitary operator. Physical Review Letters, 73(1), 58-61.

[6] Aaronson, S., & Arkhipov, A. (2013). The computational complexity of linear optics. Theory of Computing, 9(4), 143-252.

[7] Hamilton, C. S., et al. (2017). Gaussian boson sampling. Physical Review Letters, 119(17), 170501.

[8] Raussendorf, R., & Briegel, H. J. (2001). A one-way quantum computer. Physical Review Letters, 86(22), 5188-5191.

[9] Wang, J., et al. (2019). Integrated photonic quantum technologies. Nature Photonics, 13(4), 248-257.

[10] Flamini, F., et al. (2018). Photonic integrated quantum technologies. Nature Physics, 14(5), 507-510.

[11] Madsen, L. S., et al. (2022). Quantum computational advantage with a programmable photonic processor. Nature, 606(7912), 75-81.