Constructing Quantum Circuits for Simple Periodic Functions

Periodic functions are of special importance in quantum computing, particularly in applications of Shor's algorithm. We explore methods of creating circuits for periodic functions to better understand their properties. We introduce a method for constructing the circuit for a simple monoperiodic function, that is one-to-one within a single period, of a given period $p$ . We conjecture that to create a simple periodic function of period $p$ , where $p$ is an $n$ -bit number, one needs at most $n$ Toffoli gates.Periodic functions are of special importance in quantum computing, particularly in applications of Shor's algorithm. We explore methods of creating circuits for periodic functions to better understand their properties. We introduce a method for constructing the circuit for a simple monoperiodic function, that is one-to-one within a single period, of a given period $p$. We conjecture that to create a simple periodic function of period $p$, where $p$ is an $n$-bit number, one needs at most $n$ Toffoli gates.

Quantum Information and ComputationJul 1, 20140 citations

Synthesizing Quantum Circuits for Simple Periodic Functions

Omar Gamel, Daniel F. V. James

Periodic functions are of special importance in quantum computing, particularly in applications of Shor's algorithm. We explore methods of creating circuits for periodic functions to better understand their properties. We introduce a method for constructing the circuit for a simple monoperiodic function, that is one-to-one within a single period, of a given period p. We conjecture that to create a simples periodic function of period p, where p is an n-bit number, one needs at most n Toffoli gates.Periodic functions are of special importance in quantum computing, particularly in applications of Shor's algorithm. We explore methods of creating circuits for periodic functions to better understand their properties. We introduce a method for constructing the circuit for a simple monoperiodic function, that is one-to-one within a single period, of a given period p. We conjecture that to create a simples periodic function of period p, where p is an n-bit number, one needs at most n Toffoli gates.

arXiv:1305.3642May 15, 20132 citations

Basic circuits for quantum computation

Gunajit Kalita

Advances in computersAug 5, 20250 citations

Synthesis of Quantum Circuits

Philipp Niemann, Robert Wille

SpringerBriefs in physicsJan 1, 20170 citations

A universal quantum circuit design for periodical functions

Junxu Li, Sabre Kais

We propose a universal quantum circuit design that can estimate any arbitrary one-dimensional periodic functions based on the corresponding Fourier expansion. The quantum circuit contains N -qubits to store the information on the different N -Fourier components and M + 2 auxiliary qubits with M = ⌈log 2 N ⌉ for control operations. The desired output will be measured in the last qubit q N with a time complexity of the computation of , which leads to polynomial speedup under certain circumstances. We illustrate the approach by constructing the quantum circuit for the square wave function with accurate results obtained by direct simulations using the IBM-QASM simulator. The approach is general and can be applied to any arbitrary periodic function.We propose a universal quantum circuit design that can estimate any arbitrary one-dimensional periodic functions based on the corresponding Fourier expansion. The quantum circuit contains N -qubits to store the information on the different N -Fourier components and M + 2 auxiliary qubits with M = ⌈log 2 N ⌉ for control operations. The desired output will be measured in the last qubit q N with a time complexity of the computation of , which leads to polynomial speedup under certain circumstances. We illustrate the approach by constructing the quantum circuit for the square wave function with accurate results obtained by direct simulations using the IBM-QASM simulator. The approach is general and can be applied to any arbitrary periodic function.

arXiv:2106.02678New Journal of PhysicsOct 1, 20217 citations

p

. We conjecture that to create a simple periodic function of period

p

, where

p

is an

n

-bit number, one needs at most

n

Toffoli gates.