{"id":2513,"date":"2018-07-19T15:00:42","date_gmt":"2018-07-19T14:00:42","guid":{"rendered":"https:\/\/www.quantum-bits.org\/?p=2513"},"modified":"2022-08-12T17:15:11","modified_gmt":"2022-08-12T16:15:11","slug":"on-photonic-quantum-computing","status":"publish","type":"post","link":"https:\/\/www.quantum-bits.org\/?p=2513","title":{"rendered":"On photonic quantum computing"},"content":{"rendered":"

The worldwide quest to build practical quantum computers is undergoing a critical period. Fault-tolerant quantum computers will soon provide significant computational speedups for problems like factoring, search, or linear algebra, etc. During the next few years, a number of different quantum devices will become available to the public. <\/p>\n

Over the past decade, a wide variety of physical architectures have been investigated for their suitability for quantum technologies, including (among others) trapped atoms and ions<\/a> quantum computers, topological quantum computers<\/a>, or photonic quantum computers.<\/p>\n

In 2000 by E. Knill, R. Laflamme and G. Milburn<\/a> proposed a protocol (now named KLM<\/strong> scheme) using photons <\/a>as information carriers to implement linear optical quantum computing. This protocol makes it possible to create universal quantum computers<\/a> solely with linear optical tools.<\/p>\n

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Photons<\/strong><\/p>\n

Let’s start first with a general recap on photons, which are elementary<\/a> spin-1 particles. By virtue of their integer spin, they are bosons<\/a> (as opposed to fermions<\/a> with half-integer spin). By the spin-statistics theorem<\/a>, all bosons obey Bose\u2013Einstein statistics<\/a> (whereas all fermions obey Fermi\u2013Dirac statistics<\/a>). As such, they do not obey the Pauli exclusion principle<\/a> restrictions (no two identical fermions  may occupy the same quantum state simultaneously).<\/p>\n

The following image sketches the difference between bosons and fermions:<\/p>\n

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Imagine two apparati, one containing a gas of bosons, while the other one contains a gas of (non interacting) fermions. As the temperature drops near absolute zero<\/a>, the gas of bosons collapses, forming a Bose-Einstein Condensate<\/a>.  Fermions can\u2019t reach this state, since they can\u2019t occupy the same quantum state. The total energy of the Fermi gas<\/a> is then larger than the sum of the single-particle ground state. The energy of the highest occupied quantum state is called the Fermi energy<\/a>.<\/p>\n

At the most elementary level, one can see fermions as the perfect candidate for building blocks of matter, while bosons are candidates for interactions. As such, photons are the carriers of the electromagnetic interaction.<\/p>\n

Photons are indeed the quantum of the electromagnetic field<\/a> which is understood as a gauge field<\/a>, i.e., as a field that results from requiring that a gauge symmetry holds independently at every position in spacetime. For the electromagnetic field, this gauge symmetry is the Abelian<\/a> U(1) symmetry<\/a>, which reflects the ability to vary the phase<\/a> of a complex field without affecting observables<\/a> such as the energy or the Lagrangian<\/a>.<\/p>\n

The quanta of an Abelian gauge field<\/a> must be massless, uncharged bosons, as long as the symmetry is not broken. The photon thus is massless, moves at the speed<\/a> of light<\/a> in vacuum, has zero electric charge<\/a>. <\/p>\n

Each photon carries one quantum of energy, equal to \\hbar\\omega (where \\omega is its angular frequency<\/a>). Photons are emitted in many natural processes. For example:<\/p>\n