## 1 Introduction  
The idea of building a computer based on the manipulation of quantum systems dates back to the early 1980s, when [PERSON], among others, proposed in his pioneering work [1] to build a computer based on the principles of quantum mechanics, to simulate nature. In 1984, [PERSON] and [PERSON] proposed the first quantum key distribution (QKD) algorithm [2] based on the principles of quantum mechanics for the amplification and distribution of secure cryptographic keys. In 1992, [PERSON] together with [PERSON] proposed the dense coding protocol that in quantum communication allows the transfer of a number of classical bits of information, using a smaller number of qubits [3]. In 1993, the protocol of quantum teleportation was proposed, to overcome the distance limitations in transferring a quantum state [4]. In the following decades, many quantum algorithms able to outperform the corresponding classical ones were developed, such as [PERSON]'s quantum-search algorithm [5] and [PERSON]'s factoring algorithm [6]. At the end of the last century, [PERSON] established the analogy to [PERSON]'s theorems, and the beginning of the new millennium saw the formal definition by [PERSON] of the physical requirements for the practical implementation of a universal quantum computer [7]: (i) ability to initialize the state of the qubits; (ii) ability to implement a universal quantum gate; (iii) coherence time larger than the gate operation time; (iv) qubit measurement capability; (v) scalability. Since then, several technologies have been proposed for practical usage based, e.g., on superconducting [8], trapped ions [9], photonic [10] and silicon technologies [11]. Several realizations of qubits and implementations of quantum gates have been conceived. The simplest, but universal, prototype of this kind of circuit is the two-qubit controlled-NOT-(CNOT) gate. It operates by flipping the state of a target qubit in the computational basis \(|0\rangle_{T}\), \(|1\rangle_{T}\) only if the control qubit is in the state \(|1\rangle_{C}\) (see Box 1). The challenge, which is currently being addressed, remains the establishment of a scalable and convenient platform for practical implementation of quantum technologies. Such quantum technologies include protocols and devices able to perform computations that are much more time-efficient than their classical counterparts. In recent years, IBM [12] and Google [13] have realized prototypes of commercial quantum computers. They use superconducting qubits by means of the superposition of supercurrents in Josephson junctions, which require very low temperatures to operate. Also, superconducting opto-electronic circuits integrated with photonic components have been explored for fast, energy-efficient computation [14], photon detection [15; 16], and transduction between microwaves and optical photons [17; 18]. However, these new quantum technologies should be simply integrable into the systems and infrastructures that have been developed for digital and telecom information technologies. This requirement has oriented researchers towards the development of integrated photonics chips in silicon [11; 19; 20; 21]. Due to their potential integration into and compatibility with the complementary metal-oxide-semiconductor-(CMOS) fabrication process at the heart of the digital era, silicon-based-integrated-photonics architectures are promising candidates for integrated-quantum-photonics devices, which do not require an ultra-cryogenic environment. In this view, integrated quantum photonics provides aversatile platform for on-chip generation, processing, and detection of quantum states of light [6; 7]. The aim is the development and implementation of a complete silicon-photonics integrated circuit for quantum computation. However, the lack of photon-photon interaction without a non-linear matter mediator makes such a proposal challenging.