Direct interferometric test of the nonlinear phase-shift gate

Abstract

Probabilistic quantum gates permeate nearly all aspects of modern linear optical quantum computing. This is largely due to the measurement induced nonlinearities of which they are capable. The tradeoff between the cost of resources required to boost success probabilities to scalable levels and the realization of effective photon-photon interactions required grows ever more favorable to this paradigm with rapidly evolving advancements in integrated nanophotonics. As quantum circuits generating cluster states become increasingly complex, component analysis is critical. In this paper, we propose and demonstrate the experimental viability of testing a probabilistic gate. Specifically, as an illustrative example of the technique, we propose a direct test of the nonlinear phase-shift gate (NLPSG), an essential component of a Knill-Laflamme-Milburn (KLM) controlled-not (cnot) gate. We develop our analysis for both the case of the original bulk optical KLM NLPSG and the case of the scalable integrated nanophotonic NLPSG based on microring resonators (MRRs) that we have proposed very recently. We consider the interference between the target photon mode of the NLPSG along one arm of a Mach-Zehnder interferometer (MZI) and a mode subject to an adjustable linear phase along the other arm. Analysis of triple-photon coincidences between the two modes at the output of the MZI and the success ancillary mode of the NLPSG provides a signature of the conditionally successful operation of the NLPSG. We examine the triple coincidence results for experimentally realistic cases of click or no-click detection with subunity detection efficiencies. Further, we compare the case for which the MZI input modes are seeded with weak coherent states with that for which the input states are those resulting from colinear spontaneous parametric down conversion (cl-SPDC). In particular, we show that, though more difficult to prepare, cl-SPDC states offer clear advantages for performing the test, especially in the case of relatively low photon detector efficiency. We develop the interferometric analysis in terms of a general four-mode unitary so that comparison and contrast of the signatures of the specific NLPSG implementation (i.e., KLM and MRR) can be carried out easily by substituting in the appropriate unitary matrix elements at the end of the calculation. The analysis is readily extendable to other several-mode low photon number quantum circuits the successful operation of which is heralded by the measurement of ancilla photons, under nonideal detection conditions germane to laboratory experiments.