We show a significant reduction of the number of quantum operations and the improvement of the circuit depth for the realization of the Toffoli gate by using qudits. This is done by establishing a general relation between the dimensionality of qudits and their topology of connections for a scalable multi-qudit processor, where higher qudit levels are used for substituting ancillas. The suggested model is of importance for the realization of quantum algorithms and as a method of quantum error correction codes for single-qubit operations.Introduction.-Remarkable progress in realizing controllable quantum systems of an intermediate scale [1][2][3][4][5] makes it realistic to study properties of strongly correlated quantum matter [6-9] and to implement various quantum algorithms [10][11][12][13][14]. However, existing quantum computing systems lack either coherence or controllable interactions between qubits, and this limits their capabilities. A serious obstacle in realizing quantum algorithms is a large number of two-qubit gates, which requires programmable inter-qubit interactions and can cause decoherence. The situation becomes even more challenging in the case of mulit-qubit gates, such as an N -qubit Toffoli gate, which is a basic building block for quantum algorithms like Shor's algorithm [15] and for quantum error corrections schemes [16][17][18]. Its implementation requires 12N − 23 two-qubit gates with N − 2 ancilla qubits or O(N 2 ) gates without them [19], which is of high cost for near-term noisy intermediate-scale quantum devices. Therefore, the reduction of the number of operations that are required for the realization of multi-qubit gates remains a crucial problem.One of possible ways to reduce the number of required operations is to use additional degrees of freedom of quantum systems. This idea has stimulated an extended activity [20,21] in theoretical [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] and experimental studies [39][40][41][42][43][44][45][46] of quantum computing models with qudits, which are d-dimensional (d > 2) quantum systems. In particular, qudits can be used for substituting ancillas [30,[37][38][39], which allows the reduction of the required number of interactions between information carriers for the realization of multi-qubit gates. In experiments with photonic quantum circuits [39], for a system of an Ndimensional qudit connected with N − 1 qubits, the Nqubit Toffoli gate was realized with 2N − 3 qubit-qudit gates. However, it is hard to expect scalability for such

A precise security analysis of practical quantum key distribution (QKD) systems is an important step for improving their performance. Here we consider a class of quantum soft filtering operations, which generalizes the unambiguous state discrimination (USD) technique. These operations can be applied as a basis for a security analysis of the original coherent one-way (COW) QKD protocol since their application interpolates between beam-splitting (BS) and USD attacks. We demonstrate that a zero-error attack based on quantum soft filtering operations gives a larger amount of the information for Eve at a given level of losses. We calculate the Eve information as a function of the channel length. The efficiency of the proposed attack highly depends on the level of the monitoring under the maintenance of the statistics of control (decoy) states, and best-case results are achieved in the case of the absence of maintenance of control state statistics. Our results form additional requirements for the analysis of practical QKD systems based on the COW QKD protocol and its variants by providing an upper bound on the security.

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