Fast quantum modular exponentiation
نویسندگان
چکیده
concurrent architecture, NTC, neighbor-only, two-qubit gate, concurrent architecture; and Perf, performance relative to VBE algorithm for that architecture, based on CCNOTs for AC and CNOTs for NTC.
منابع مشابه
Fast quantum modular exponentiation architecture for Shor's factoring algorithm
We present a novel and efficient, in terms of circuit depth, design for Shor’s quantum factorization algorithm. The circuit effectively utilizes a diverse set of adders based on the Quantum Fourier transform (QFT) Draper’s adders to build more complex arithmetic blocks: quantum multiplier/accumulators by constants and quantum dividers by constants. These arithmetic blocks are effectively archit...
متن کاملFast and Constant-Time Implementation of Modular Exponentiation
Modular exponentiation is an important operation which requires a vast amount of computations. Therefore, it is crucial to build fast exponentiation schemes. Since Cache and data-dependent branching behavior can alter the runtime of an algorithm significantly, it is also important to build an exponentiation scheme with constant run-time. However, such approaches have traditionally added signifi...
متن کاملHow to Maximize the Potential of FPGA-Based DSPs for Modular Exponentiation
This paper describes a modular exponentiation processing method and circuit architecture that can exhibit the maximum performance of FPGA resources. The modular exponentiation architecture proposed by us comprises three main techniques. The first one is to improve the Montgomery multiplication algorithm in order to maximize the performance of the multiplication unit in an FPGA. The second one i...
متن کاملComparison of Three Modular Reduction Functions
Three modular reduction algorithms for large integers are compared with respect to their performance in portable software: the classical algorithm, Barrett’s algorithm and Montgomery’s algorithm. These algorithms are a time critical step in the implementation of the modular exponentiation operation. For each of these algorithms their application in the modular exponentiation operation is consid...
متن کاملConstant-optimized quantum circuits for modular multiplication and exponentiation
Reversible circuits for modular multiplication Cx%M with x < M arise as components of modular exponentiation in Shor’s quantum number-factoring algorithm. However, existing generic constructions focus on asymptotic gate count and circuit depth rather than actual values, producing fairly large circuits not optimized for specific C and M values. In this work, we develop such optimizations in a bo...
متن کامل