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We report a proof-of-concept demonstration of a quantum order-finding algorithm for factoring the integer 21. Our demonstration involves the use of a compiled version of the quantum phase estimation routine, and builds upon a previous demonstration by Martin-L{o}pez et al. in Nature Photonics 6, 773 (2012). We go beyond this work by using a configuration of approximate Toffoli gates with residual phase shifts, which preserves the functional correctness and allows us to achieve a complete factoring of N=21. We implemented the algorithm on IBM quantum processors using only 5 qubits and successfully verified the presence of entanglement between the control and work register qubits, which is a necessary condition for the algorithms speedup in general. The techniques we employ may be useful in carrying out Shors algorithm for larger integers, or other algorithms in systems with a limited number of noisy qubits.
We study the results of a compiled version of Shors factoring algorithm on the ibmqx5 superconducting chip, for the particular case of $N=15$, $21$ and $35$. The semi-classical quantum Fourier transform is used to implement the algorithm with only a
The quantum multicomputer consists of a large number of small nodes and a qubus interconnect for creating entangled state between the nodes. The primary metric chosen is the performance of such a system on Shors algorithm for factoring large numbers:
We determine the cost of performing Shors algorithm for integer factorization on a ternary quantum computer, using two natural models of universal fault-tolerant computing: (i) a model based on magic state distillation that assumes the availability
Shors powerful quantum algorithm for factoring represents a major challenge in quantum computation and its full realization will have a large impact on modern cryptography. Here we implement a compiled version of Shors algorithm in a photonic system
The number of steps any classical computer requires in order to find the prime factors of an $l$-digit integer $N$ increases exponentially with $l$, at least using algorithms known at present. Factoring large integers is therefore conjectured to be i