Linear optical quantum computing
In optical systems for quantum information processing, the unit of light in a given mode—or photon—is used to represent a qubit.
Superpositions of quantum states can be easily represented, encrypted, transmitted and detected using photons.
Each linear optical element equivalently applies a unitary transformation on a finite number of qubits.
Quantum computing with continuous variables is also possible under the linear optics scheme.
) can be realized by only using mirrors, beam splitters and phase shifters[9] (this is also a starting point of boson sampling and of computational complexity analysis for LOQC).
If using a non-deterministic scheme, this fact also implies that LOQC could be resource-inefficient in terms of the number of optical elements and time steps needed to implement a certain quantum gate or circuit, which is a major drawback of LOQC.
Operations via linear optical elements (beam splitters, mirrors and phase shifters, in this case) preserve the photon statistics of input light.
[3] Due to this reason, people usually use single photon source case to analyze the effect of linear optical elements and operators.
One way to solve this problem is to bring nonlinear devices into the quantum network.
For instance, the Kerr effect can be applied into LOQC to make a single-photon controlled-NOT and other operations.
[10][11] It was believed that adding nonlinearity to the linear optical network was sufficient to realize efficient quantum computation.
In 2000, Knill, Laflamme and Milburn proved that it is possible to create universal quantum computers solely with linear optical tools.
[2] Their work has become known as the "KLM scheme" or "KLM protocol", which 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.
[3] At its root, the KLM scheme induces an effective interaction between photons by making projective measurements with photodetectors, which falls into the category of non-deterministic quantum computation.
It is based on a non-linear sign shift between two qubits that uses two ancilla photons and post-selection.
Meanwhile, the KLM scheme is based on the fact that proper quantum coding can reduce the resources for obtaining accurately encoded qubits efficiently with respect to the accuracy achieved, and can make LOQC fault-tolerant for photon loss, detector inefficiency and phase decoherence.
The more limited boson sampling model was suggested and analyzed by Aaronson and Arkhipov in 2010.
On 3 December 2020, a team led by Chinese Physicist Pan Jianwei (潘建伟) and Lu Chaoyang (陆朝阳) from University of Science and Technology of China in Hefei, Anhui Province submitted their results to Science in which they solved a problem that is virtually unassailable by any classical computer; thereby proving Quantum supremacy of their photon-based quantum computer called Jiu Zhang Quantum Computer (九章量子计算机).
Jiu Zhang was named in honor of China's oldest surviving mathematical text (Jiǔ zhāng suàn shù) The Nine Chapters on the Mathematical Art [18] DiVincenzo's criteria for quantum computation and QIP[19][20] give that a universal system for QIP should satisfy at least the following requirements: As a result of using photons and linear optical circuits, in general LOQC systems can easily satisfy conditions 3, 6 and 7.
[3] The following sections mainly focus on the implementations of quantum information preparation, readout, manipulation, scalability and error corrections, in order to discuss the advantages and disadvantages of LOQC as a candidate for QIP A qubit is one of the fundamental QIP units.
For example, a set of modes could be different polarization of light which can be picked out with linear optical elements, various frequencies, or a combination of the two cases above.
By using a conditional single-photon source, the output state is guaranteed, although this may require several attempts (depending on the success rate).
In general, an arbitrary quantum state can be generated for QIP with a proper set of photon sources.
Ignoring error correction and other issues, the basic principle in implementations of elementary quantum gates using only mirrors, beam splitters and phase shifters is that by using these linear optical elements, one can construct any arbitrary 1-qubit unitary operation; in other words, those linear optical elements support a complete set of operators on any single qubit.
[21]) of beam splitters and phase shifters in an optical experimental table is challenging and unrealistic.
On the other hand, it seems that the scalability issues in boson sampling are more manageable than those in the KLM protocol.
[16] In the KLM protocol, there are non-deterministic quantum gates, which are essential for the model to be universal.
Another, earlier model which relies on the representation of several qubits by a single photon is based on the work of C. Adami and N. J.
The figures below are examples of making an equivalent Hadamard-gate and CNOT-gate using beam splitters (illustrated as rectangles connecting two sets of crossing lines with parameters
In the optical realization of the CNOT gate, the polarization and location are the control and target qubit, respectively.
