Realization of a Knill-Laflamme-Milburn controlled-NOT photonic quantum circuit combining effective optical nonlinearities

The KLM NS gate. (A) If the NS gate succeeds it is heralded; indicated conceptually by the light globe. (B) The original KLM NS gate is heralded by detection of a photon at the upper detector and no photon at the lower detector. Gray indicates the surface of the BS from which a sign change occurs upon reflection. (C) A simplified KLM NS gate for which the heralding signal is detection of one photon.

PNAS – Realization of a Knill-Laflamme-Milburn controlled-NOT photonic quantum circuit combining effective optical nonlinearities

An international research group led by scientists from the University of Bristol, UK, and the Universities of Osaka and Hokkaido, Japan, has demonstrated a fundamental building block for quantum computing that could soon be employed in a range of quantum technologies. The optical circuit enables a new approach to quantum technologies. The researchers have demonstrated a quantum logic gate acting on four particles of light – photons. The researchers believe their device could provide important routes to new quantum technologies, including secure communication, precision measurement, and ultimately a quantum computer—a powerful type of computer that uses quantum bits (qubits) rather than the conventional bits used in today’s computers.

“Each time we add a photon, the complexity of the problem we are able to investigate increases exponentially, so if a one-photon quantum circuit has 10 outcomes, a two-photon system can give 100 outcomes and a three-photon system 1000 solutions and so on.”

The Centre for Quantum Photonics now plans to use their chip-based approach to increase the complexity of their experiment not only by adding more photons but also by using larger circuits.

Quantum information science addresses how uniquely quantum mechanical phenomena such as superposition and entanglement can enhance communication, information processing, and precision measurement. Photons are appealing for their low-noise, light-speed transmission and ease of manipulation using conventional optical components. However, the lack of highly efficient optical Kerr nonlinearities at the single photon level was a major obstacle. In a breakthrough, Knill, Laflamme, and Milburn (KLM) showed that such an efficient nonlinearity can be achieved using only linear optical elements, auxiliary photons, and measurement. KLM proposed a heralded controlled-NOT (CNOT) gate for scalable quantum computation using a photonic quantum circuit to combine two such nonlinear elements. Here we experimentally demonstrate a KLM CNOT gate. We developed a stable architecture to realize the required four-photon network of nested multiple interferometers based on a displaced-Sagnac interferometer and several partially polarizing beamsplitters. This result confirms the first step in the original KLM “recipe” for all-optical quantum computation, and should be useful for on-demand entanglement generation and purification. Optical quantum circuits combining giant optical nonlinearities may find wide applications in quantum information processing, communication, and sensing.

The KLM CNOT gate. (A) The gate is constructed of two NS gates; the output is accepted only if the correct heralding signal is observed for each NS gate. Gray indicates the surface of the BS from which a sign change occurs upon reflection. (B) The KLM CNOT gate with simplified NS gate. (C) The same circuit as (B) but using polarization encoding and PPBSs. (D) The stable optical quantum circuit used here to implement the KLM CNOT gate using PPBSs and a displaced-Sagnac architecture. The target MZ, formed by BS11 and BS12 in Fig. 2B, can be conveniently incorporated into the state preparation and measurement, corresponding to a change of basis, as described in the caption to Fig. 3. The blue line indicates optical paths for vertically polarized components, and the red line indicates optical paths for horizontally polarized components.

The data presented confirm the realization of the CNOT gate proposed by KLM, which is an optical circuit combining a pair of efficient nonlinear elements induced by measurement. This result confirms the first step in the KLM recipe for all-optical quantum computation and illustrates how efficient nonlinearities induced by measurement can be utilized for quantum information science; such measurement-induced optical nonlinearities could also be an alternative to nonlinear media used for quantum nondemolition detectors or photonic pulse shaping. By emulating fundamental nonlinear processes, such measurement-induced optical nonlinearities can also improve our understanding of the quantum dynamics in nonlinear media. Conversely, future technical progress may permit the replacement of these effective optical nonlinearities in the network by approaches based on nonlinearities in material systems such as atoms, solid state devices, hybrid systems, or optical fiber Kerr nonlinearities. In this context, our demonstration provides an experimental test for quantum networks based on nonlinear optical elements and may serve as a reference point for comparisons with future networks using other optical nonlinearities. In particular, the present results may be useful as a starting point for a more general analysis of quantum error propagation in nonlinear optical networks. Our device will be useful for conventional and cluster state approaches to quantum computing, as well as quantum communication, and optical quantum metrology. This circuit could be implemented using an integrated waveguide architecture, in which case a dual-rail encoding could conveniently be used.

In the present tests of the performance of CNOT gate operation, we used threshold detectors to monitor the output state. For applications in which the output state cannot be monitored, high-efficiency number-resolving photon detectors could be used at DA1 and DA2 to generate the heralding signals. We also used spontaneous parametric fluorescence as single photon sources. Note that alternative approaches that do not follow the KLM recipe as closely can be useful for scalable linear optics quantum information processing. For all these approaches, further progress in on-demand single photon sources and practical photon resolving detectors will be crucial to ensure reliable operation

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