page_title: KLM protocol
section_title: Implementation of nondeterministic conditional sign flip gate
hierarchical_section_title: KLM protocol / Elements of the KLM scheme / Implementation of nondeterministic conditional sign flip gate
caption_attribution_description: English: Linear optics implementation of NS gate.
context_page_description: The KLM scheme or KLM protocol is an implementation of linear optical quantum computing, developed in 2000 by Knill, Laflamme and Milburn. This protocol makes it possible to create universal quantum computers solely with linear optical tools. The KLM protocol uses linear optical elements, single photon sources and photon detectors as resources to construct a quantum computation scheme involving only ancilla resources, quantum teleportations and error corrections.
context_section_description: An important element of the KLM scheme is the conditional sign flip or nonlinear sign flip gate (NS-gate) as shown in the figure below on the right. It gives a nonlinear phase shift on one mode conditioned on two ancilla modes.
  In the picture on the right, the labels on the left of the bottom box indicate the modes. The output is accepted only if there is one photon in mode 2 and zero photons in mode 3 detected, where the ancilla modes 2 and 3 are prepared as the  state. The subscript  is the phase shift of the output, and is determined by the parameters of inner optical elements chosen. For  case, the following parameters are used: , , , , , , and . For the  case, the parameters can be chosen as , , , , , , and . Similarly, by changing the parameters of beam splitters and phase shifters, or by combining multiple NS gates, one can create various quantum gates. By sharing two ancilla modes, Knill invented the following controlled-Z gate (see the figure on the right) with success rate of 2/27.
  The advantage of using NS gates is that the output can be guaranteed conditionally processed with some success rate which can be improved to nearly 1. Using the configuration as shown in the figure above on the right, the success rate of an  NS gate is . To further improve successful rate and solve the scalability problem, one needs to use gate teleportation, described next.
caption: Linear optics implementation of NS-gate. The elements framed in the box with dashed border is the linear optics implementation with three beam splitters and one phase shifter (see text for parameters). Modes 2 and 3 are ancilla modes.
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