Quantum Circuits for S-Box Implementation without Ancilla Qubits
- PDF / 565,198 Bytes
- 9 Pages / 612 x 792 pts (letter) Page_size
- 57 Downloads / 249 Views
MOLECULES, OPTICS
Quantum Circuits for S-Box Implementation without Ancilla Qubits D. V. Denisenko Bauman Moscow State Technical University, Moscow, 105005 Russia e-mail: [email protected] Received January 23, 2019; revised January 27, 2019; accepted January 29, 2019
Abstract—A method is presented for implementing substitutions (S-boxes) in the form of quantum circuits without ancilla qubits. Quantum circuits are presented that implement substitutions in the GOST R 34.122015 block cipher “Magma” on four logical qubits, and the descriptions of quantum circuits implementing AES and GOST R 34.12-2015 “Kuznechik” S-boxes on 8 logical qubits—quantum circuits with minimum number of logical qubits—are given. DOI: 10.1134/S1063776119050108
1. INTRODUCTION The theory of quantum computations has been intensively developed since the end of the last century. To date, a number of formal models of quantum computations have been constructed according to which the quantum nature of objects used for computations theoretically allows one to solve some computational problems efficiently [1–3]. Currently, fundamental research is aimed at the development of quantum simulators and quantum processors: in 2017, a group of physicists announced the development of a programmable 51-qubit quantum simulator [4], and the authors of [5] developed a 53-qubit simulator based on ions and optical traps. IBM successfully tested a prototype 50-qubit quantum processor [6], and, in December 2017, article [7] was published in which the authors presented the project of a scalable silicon-based quantum processor, which represents an array of 24 × 20 = 480 qubits. In January 2018, Intel announced a 49-qubit superconducting quantum chip called “Tangle Lake.” In March 2018, Google announced a 72-qubit quantum processor “Bristlecone.” The company hopes that Bristlecone will demonstrate quantum supremacy [8, 9]. At the end of 2018, a report [10] was published in which the authors summarize the current state in the development of quantum technologies in the field of quantum computing. In particular, they conclude that progress in the gate model of quantum computation can be tracked by the key parameters that determine the performance of a quantum processor: error rate when performing basic operations on one or two qubits, and the depth of interaction of qubits in one hardware module. The report notes that quantum supremacy (solving a problem that is difficult to solve
on a classical computer, regardless of whether this problem has practical utility) has not been demonstrated yet; at the same time, the report presents estimates for the resources of a quantum computer required to solve some problems, including those related to the implementation of cryptographic algorithms in the form of quantum circuits. The present paper is a continuation of [11, 12], where we considered a secret key search problem for block cipher algorithms with the use of Grover’s algorithm. In [11], we presented a quantum circuit with minimum number of logical qubits that implements SD
Data Loading...
