An Algebraic Approach to Linear-Optical Schemes for Deterministic Quantum Computing
نویسندگان
چکیده
Linear-Optical Passive (LOP) devices and photon counters are sufficient to implement universal quantum computation with single photons, and particular schemes have already been proposed. In this paper we discuss the link between the algebraic structure of LOP transformations and quantum computing. We first show how to decompose the Fock space of N optical modes in finite-dimensional subspaces that are suitable for encoding strings of qubits and invariant under LOP transformations (these subspaces are related to the spaces of irreducible unitary representations of U(N)). Next we show how to design in algorithmic fashion LOP circuits which implement any quantum circuit deterministically. We also present some simple examples, such as the circuits implementing a CNOT gate and a Bell-State Generator/Analyzer.
منابع مشابه
Photon counting schemes and performance of non–deterministic nonlinear gates in linear optics
The performance of nondeterministic nonlinear gates in linear optics relies on the photon counting scheme being employed and the efficiencies of the detectors in such schemes. We assess the performance of the nonlinear sign gate, which is a critical component of linear optical quantum computing, for two standard photon counting methods: the double detector array and the visible light photon cou...
متن کاملRole of negative dielectric and optical quantum dot waveguiding methods in communication
While the application of optical and photonic technologies in the communications, computing, medicine and industrial manufacturing has been growing rapidly, the miniaturization of these technologies has been slow due to the limitation on the diffraction. However, the developments of nanoscale components and guiding methods are continuing with a rapid pace. Since waveguiding is a fundamental iss...
متن کاملNonlinear optics quantum computing with circuit QED.
One approach to quantum information processing is to use photons as quantum bits and rely on linear optical elements for most operations. However, some optical nonlinearity is necessary to enable universal quantum computing. Here, we suggest a circuit-QED approach to nonlinear optics quantum computing in the microwave regime, including a deterministic two-photon phase gate. Our specific example...
متن کاملRole of negative dielectric and optical quantum dot waveguiding methods in communication
While the application of optical and photonic technologies in the communications, computing, medicine and industrial manufacturing has been growing rapidly, the miniaturization of these technologies has been slow due to the limitation on the diffraction. However, the developments of nanoscale components and guiding methods are continuing with a rapid pace. Since waveguiding is a fundamental iss...
متن کاملLinear optics quantum computing – construction of small networks and asymptotic scaling
In the paradigm of linear optics, quantum states of optical field modes are manipulated by means of photon sources, beam splitters, and photodetectors. This restriction of the allowed interactions introduces non-unit success probabilities into every non-trivial computation irrevocably. The resulting probabilistic nature of this architecture opens up questions about scalability of this approach ...
متن کامل