Automatic synthesis of quantum circuits for point addition on ordinary binary elliptic curves

作者：Budhathoki Parshuram^*; Steinwandt Rainer

来源：Quantum Information Processing, 2015, 14(1): 201-216.

DOI：10.1007/s11128-014-0851-6

• Quantum circuit
• Shor's algorithm
• Discrete logarithm problem

When designing quantum circuits for Shor's algorithm to solve the discrete logarithm problem, implementing the group arithmetic is a cost-critical task. We introduce a software tool for the automatic generation of addition circuits for ordinary binary elliptic curves, a prominent platform group for digital signatures. The resulting circuits reduce the number of T-gates by a factor 13/5 compared to the best previous construction, without increasing the number of qubits or T-depth. The software also optimizes the (CNOT) depth for F-2-linear operations by means of suitable graph colorings.

• 出版日期2015-1