Circuit for Shor's algorithm using 2n+3 qubits

نویسنده

  • Stéphane Beauregard
چکیده

We try to minimize the number of qubits needed to factor a number of n bits using Shor’s algorithm on a quantum computer. The best we could achieve was a circuit with 2n + 3 qubits and O(nlg(n)) quantum gates, but with a depth of O(n). The circuit is computable in polynomial time on a classical computer and is completely general as it does not rely on any properties of the number to be factored.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Factoring with n + 2 clean qubits and n − 1 dirty qubits

We present reversible classical circuits for performing various arithmetic operations aided by dirty ancillae (i.e. extra qubits in an unknown state that must be restored before the circuit ends). We improve the number of clean qubits needed to factor an n-bit number with Shor’s algorithm [12] from 2n + 2 [15, 8] to n + 2, and the total number of qubits needed from 2n+2 to 2n+ 1, without increa...

متن کامل

nt - p h / 06 01 09 7 v 1 1 5 Ja n 20 06 Shor ’ s algorithm with fewer ( pure ) qubits

In this note we consider optimised circuits for implementing Shor's quantum factoring algorithm. First I give a circuit for which non of the about 2n qubits need to be initialised (though we still have to make the usual 2n measurements later on). Then I show how the modular additions in the algorithm can be carried out with a superposition of an arithmetic sequence. This makes parallelisation o...

متن کامل

A logarithmic-depth quantum carry-lookahead adder

We present an efficient addition circuit, borrowing techniques from the classical carry-lookahead arithmetic circuit. Our quantum carrylookahead (qcla) adder accepts two n-bit numbers and adds them in O(log n) depth using O(n) ancillary qubits. We present both in-place and out-of-place versions, as well as versions that add modulo 2n and modulo 2n − 1. Previously, the linear-depth ripple-carry ...

متن کامل

Factoring using $2n+2$ qubits with Toffoli based modular multiplication

We describe an implementation of Shor’s quantum algorithm to factor n-bit integers using only 2n+2 qubits. In contrast to previous space-optimized implementations, ours features a purely Toffoli based modular multiplication circuit. The circuit depth and the overall gate count are in O(n3) and O(n3 logn), respectively. We thus achieve the same space and time costs as Takahashi et al. [1], while...

متن کامل

Efficient factorization with a single pure qubit and logN mixed qubits.

It is commonly assumed that Shor's quantum algorithm for the efficient factorization of a large number N requires a pure initial state. Here we demonstrate that a single pure qubit, together with a collection of log 2N qubits in an arbitrary mixed state, is sufficient to implement Shor's factorization algorithm efficiently.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Quantum Information & Computation

دوره 3  شماره 

صفحات  -

تاریخ انتشار 2003