Experimental implementation of efficient linear optics quantum computation

Gerard J Milburn, Timothy C. Ralph, Alexei Gilchrist +3 more

Geoff J. Pryde, Jeremy L. O’Brien, T. B. Bell +4 more

We consider realizing the efficient linear optical quantum computing scheme of Knill, Laflamme and Milburn [Nature 409, 46 (2001)]. A number of the issues in implementing a coincidence-basis version of a CNOT gate are addressed experimentally, including source brightness and mode quality.

Gerard J Milburn, Timothy C. Ralph, Andrew G. White

One of the earliest proposals for implementing quantum computation was based on encoding each qubit in two optical modes, each containing exactly one photon. However, it is extremely difficult to unitarily couple two optical modes containing few photons. In 2001, Knill, Laflamme, and Milburn (KLM) found a way to circumvent this restriction and implement efficient quantum computation using only passive linear optics, photodetectors, and single photon sources. This efficient linear optical quantum computing (LOQC) is distinct from other linear optical schemes that are not efficiently scalable. The technological requirements for even the simplest gates in the KLM proposal initially seemed out of reach. However, Ralph, White, Munro and Milburn soon showed that, in principle, demonstrations of key gates and techniques could be achieved with current technology. The objective of the research undertaken in this project was to produce, in three years, a prototype two-qubit gate for photons using the KLM linear optics quantum computation approach, and to develop a blue-print for a multiple qubit device that might be implemented over a longer time scale. A non-deterministic two-qubit gate was demonstrated that operates with high fidelity. A number of key tasks were demonstrated using this gate, and several theoretical investigations of short, medium, and longer term issues for the LOQC approach were successfully completed.

Nobuyuki Matsuda

Yosep Kim, Kang-Hee Hong, Joonsuk Huh +1 more

Linear optical computing (LOC) with thermal light has recently gained attention because the problem is connected to the permanent of a Hermitian positive semidefinite matrix (HPSM), which is of importance in the computational complexity theory. Despite the several theoretical analyses on the computational structure of an HPSM in connection to LOC, the experimental demonstration and the computational complexity analysis via the linear optical system have not been performed yet. We present, herein, experimental LOC for estimating the permanent of an HPSM. From the linear optical experiments and theoretical analysis, we find that the LOC efficiency for a multiplicative error is dependent on the value of the permanent and that the lower bound of the computation time scales exponentially. Furthermore, our results are generalized and applied to LOC of permanents of unitary matrices, which can be implemented with a multiport quantum interferometer involving single photons at the input ports. We find that LOC with single photons, for the permanent estimation, is on average less efficient than the most efficient classical algorithm known to date, even in ideal conditions.

Christoph Adami, Nicolas J. Cerf