In this work we provide a derivation of a nonlinear sign gate (NLSG) configuration using microring resonators (mrr), and an examine of the probability of success as a function of its operational parameters. Such NLSG in a mrr extends the work of Knill-Laflamme-Milburn (KLM) version of an optical CNOT gate for quantum computing from a single point solution for the transmission coefficients using three beam splitters, to a manifold of solutions when the three beam splitters are replaced my three mrrs.
In this work we provide a derivation of a nonlinear sign gate (NLSG) configuration using microring resonators (mrr), and an examine of the probability of success as a function of its operational parameters. Such NLSG in a mrr extends the work of Knill-Laflamme-Milburn (KLM) version of an optical CNOT gate for quantum computing from a single point solution for the transmission coefficients using three beam splitters, to a manifold of solutions when the three beam splitters are replaced my three mrrs.
We propose a scalable version of a Knill-Laflamme-Milburn (KLM) controlled-not (cnot) gate based upon integrated waveguide microring resonators (MRR), vs the original KLM approach using beam splitters. The core element of our KLM 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 parameter spaces of the MRRs. This allows for an increased level of flexibility in operation of the NLPSG that allows for the fabrication of dynamically tunable MRR-based devices with high precision and low loss.
The first section of the work investigates light modes as a means of implementing optical qubits and qudits. The modes considered are polarization mode, path mode, transverse spatial mode, frequency mode, temporal bin-mode and temporal mode. Subsequently, mathematical model of linear optical elements like beam splitters (BS) and phase shifters are deduced and their capability of representing any single qubit optical gate is exposed. Finally Knill, Laflamme and Milburn (KLM) method of using linear optical elements to promote nonlinear operations based on nonlinear (nondeterministic) sign-flip gate (NS) is explained, and designs of two qubits conditional sign flip gate (c-z1/16) and CNOT gate, both based on KLM method, are demonstrated. So, universal set of quantum gates based on linear optics is possible.
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.
In this Letter, the problem of finding optimal success probabilities of linear optics quantum gates is linked to the theory of convex optimization. It is shown that by exploiting this link, upper bounds for the success probability of networks realizing single-mode gates can be derived, which hold in generality for postselected networks of arbitrary size, any number of auxiliary modes, and arbitrary photon numbers. As a corollary, the previously formulated conjecture is proven that the optimal success probability of a nonlinear sign shift without feedforward is 1/4, a gate playing the central role in the scheme of Knill-Laflamme-Milburn for quantum computation. The concept of Lagrange duality is shown to be applicable to provide rigorous proofs for such bounds, although the original problem is a difficult nonconvex problem in infinitely many objective variables. The versatility of this approach is demonstrated.
Abstract Knill, Laflamme, and Milburn showed that linear optics techniques could be used to implement a nonlinear sign gate. They also showed that two of their nonlinear sign gates could be combined to implement a controlled-phase gate, which has a number of practical applications. Here we describe an alternative implementation of a controlled-phase gate that only requires the use of a single nonlinear sign gate. This gives a much higher average probability of success when the required ancilla photons are generated using heralding techniques. This implementation of a controlled-phase gate destroys the control qubit, which is acceptable in a number of applications where the control qubit would have been destroyed in any event, such as in a postselection process.
Quantum information science addresses how uniquely quantum mechanical phenomena such as superposition and entanglement can enhance communication, information processing, and precision measurement. Photons are appealing for their low-noise, light-speed transmission and ease of manipulation using conventional optical components. However, the lack of highly efficient optical Kerr nonlinearities at the single photon level was a major obstacle. In a breakthrough, Knill, Laflamme, and Milburn (KLM) showed that such an efficient nonlinearity can be achieved using only linear optical elements, auxiliary photons, and measurement [Knill E, Laflamme R, Milburn GJ (2001) Nature 409:46-52]. KLM proposed a heralded controlled-NOT (CNOT) gate for scalable quantum computation using a photonic quantum circuit to combine two such nonlinear elements. Here we experimentally demonstrate a KLM CNOT gate. We developed a stable architecture to realize the required four-photon network of nested multiple interferometers based on a displaced-Sagnac interferometer and several partially polarizing beamsplitters. This result confirms the first step in the original KLM "recipe" for all-optical quantum computation, and should be useful for on-demand entanglement generation and purification. Optical quantum circuits combining giant optical nonlinearities may find wide applications in quantum information processing, communication, and sensing.