Scalable controlled-not gate for linear optical quantum computing using microring resonators

Abstract

We propose a scalable version of a KLM CNOT gate based upon integrated waveguide microring resonators (MRR), vs the original KLM-approach using beam splitters (BS). The core element of our CNOT gate is a nonlinear phase-shift gate (NLPSG) using three MRRs, which we examine in detail. We find an expanded parameter space for the NLPSG over that of the conventional version. Whereas in all prior proposals for bulk optical realizations of the NLPSG the optimal operating point is precisely a single zero dimensional manifold within the parameter space of the device, we find conditions for effective transmission amplitudes which define a set of one dimensional manifolds in the parameters spaces of the MRRs. This allows for an unprecedented level flexibility in operation of the NLPSG that and allows for the fabrication of tunable MRR-based devices with high precision and low loss. In 2001, Knill, Laflamme and Milburn (KLM) proposed an efficient scheme for linear optical quantum computing [1]. The KLM proposal is based upon a probabilistic, two-qubit, Controlled NOT (CNOT) gate along with local unitary operations on individual qubits. Some years later, Okamoto, et. al., demonstrated experimentally a realization the KLM CNOT gate in bulk optics [2]. The KLM CNOT gate, shown schematically in Fig. (1), is itself composed of two Non-Linear Phase Shift Gates (NLPSG), the essential two-qubit element of the CNOT gate. Each NLPSG is a probabilistic device involving three optical modes, that, in the bulk optical realization encounter strategically placed and optimally reflective beam splitters that appropriately route the free space evolution of photonic states through the system. The KLM CNOT gate performs a two qubit operation, namely, a flip of the target qubit (t) conditioned on the value of the control qubit (c), as CNOT c t c t i j i i j    .

A direct interferometric test of the nonlinear phase shift gate

“…It has been shown [3,10] that this action is successful with a maximum probability of 1/4 , and that the result of the projective measurement faithfully indicates the success of the transformation. Consequently, the optimal probability of success for the KLM or MRR CNOT gate is 1/16 [1,4], which employs two NLPSG. This NLPSG-based CNOT gate effectively performs a HOM [4,6] interference on the two-photon branch |2 1 of mode-1, in order to affect the CNOT operation on the remaining branch of mode-1,…”

“…Consequently, the optimal probability of success for the KLM or MRR CNOT gate is 1/16 [1,4], which employs two NLPSG. This NLPSG-based CNOT gate effectively performs a HOM [4,6] interference on the two-photon branch |2 1 of mode-1, in order to affect the CNOT operation on the remaining branch of mode-1,…”

“…where T is transpose, defining the corresponding unitary matrix of coefficients S kj that act as transition coefficients for a photon initially in mode j to be routed to output mode k. Henceforth, we will drop the in, out subscript labels. The action of U on the input state |ψ (in 2) is then given by [4] |ψ…”

“…The original realization of the KLM CNOT was in a bulk optical setting, and, therefore, was not scalable as would be required for the deployment of the gate as part of a practical computing system. So, nearly a decade after that, the present authors proposed a scalable version of the KLM CNOT based upon an integrated silicon nano-photonic architecture composed of directionally coupled Micro-Ring Resonators (MRRs) [4,5]. Currently, we are in the early stages of an experiment to realize the MRR-KLM-CNOT.…”

Computing Effective Hamiltonians of Coupled Electromagnetic Systems

“…Coupled electromagnetic systems are ubiquitous in real life, for example, the coupled photonics microring resonator filters, 1 coupled Parity-Time Non-Hermitian electromagnetic system, 2,3 as well as the finite and infinite coupled Microring Resonators (MRRs) array. 4 For example, in the past decades, MRRs have been considered as one of the strong candidates for building blocks of the optical components and devices such as the high-performance filter such as add-drop filters 5 and wavelength division multiplexers, 6 , 7 optical delay lines, 8 Parity-Time (PT) symmetric devices, 9 nonlinear light-wave and materials interaction such as four wave mixing, 10 single-photon/photon-pair source, 11 , 12 frequency comb generation, 13 optical quantum computing, 14 as well as high-quality sensors. 15 All of these call for efficient computation of the effective Hamiltonian matrix of the coupled electromagnetic system so that the optimal system can be designed for better performance, which is the focus of this paper.…”