A photon-photon quantum gate using a multilevel atomic system

Zhifeng Liu, Zhi‐Cheng Ren, Pei Wan +10 more

Amin Babazadeh, Manuel Erhard, Feiran Wang +4 more

Transformations on quantum states form a basic building block of every quantum information system. From photonic polarization to two-level atoms, complete sets of quantum gates for a variety of qubit systems are well known. For multilevel quantum systems beyond qubits, the situation is more challenging. The orbital angular momentum modes of photons comprise one such high-dimensional system for which generation and measurement techniques are well studied. However, arbitrary transformations for such quantum states are not known. Here we experimentally demonstrate a four-dimensional generalization of the Pauli X gate and all of its integer powers on single photons carrying orbital angular momentum. Together with the well-known Z gate, this forms the first complete set of high-dimensional quantum gates implemented experimentally. The concept of the X gate is based on independent access to quantum states with different parities and can thus be generalized to other photonic degrees of freedom and potentially also to other quantum systems.

Daniel Tiarks, Steffen Schmidt-Eberle, Thomas Stolz +2 more

Timothy C. Ralph, Kevin J. Resch, Alexei Gilchrist

The simplest decomposition of a Toffoli gate acting on 3 qubits requires five 2-qubit gates. If we restrict ourselves to controlled-sign (or controlled-NOT) gates this number climbs to 6. We show that the number of controlled-sign gates required to implement a Toffoli gate can be reduced to just 3 if one of the three quantum systems has a third state that is accessible during the computation---i.e., is actually a qutrit. Such a requirement is not unreasonable or even atypical since we often artificially enforce a qubit structure on multilevel quantums systems (e.g., atoms, photonic polarization plus spatial modes). We explore the implementation of these techniques in optical quantum processing and show that linear optical circuits could operate with much higher probabilities of success.

Bastian Hacker, Stephan Welte, Gerhard Rempe +1 more

S N Andrianov, А. А. Калачев, O. P. Shindyaev

Abstract The possibility of implementing a controlled-NOT gate for frequency-encoded photonic qubits via six-wave mixing in a multilevel atomic system is shown. Starting from the Hamiltonian for six-wave mixing in a cavity, equations of motion for the amplitudes of the photonic states are derived and solved in the framework of input–output formalism. Analysis of these solutions show how to realize two-qubit gates including relevant matching conditions.