# Experimental demonstration of a compiled version of Shor's algorithm with quantum entanglement.

@article{Lanyon2007ExperimentalDO, title={Experimental demonstration of a compiled version of Shor's algorithm with quantum entanglement.}, author={Ben P. Lanyon and Till Weinhold and Nathan K Langford and Marco Barbieri and Daniel F. V. James and Alexei Gilchrist and A. G. White}, journal={Physical review letters}, year={2007}, volume={99 25}, pages={ 250505 } }

Shor's powerful quantum algorithm for factoring represents a major challenge in quantum computation. Here, we implement a compiled version in a photonic system. For the first time, we demonstrate the core processes, coherent control, and resultant entangled states required in a full-scale implementation. These are necessary steps on the path towards scalable quantum computing. Our results highlight that the algorithm performance is not the same as that of the underlying quantum circuit and…

## 237 Citations

### Proof-of-principle demonstration of compiled Shor's algorithm using a quantum dot single-photon source.

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A fully compiled version of Shor's algorithm for factoring 15 has been accomplished with a significantly reduced resource requirement that employs the four-photon cluster state that opens new applications for cluster state beyond one-way quantum computing.

### Shor’s Quantum Factoring Algorithm on a Photonic Chip

- PhysicsScience
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The demonstration of a compiled version of Shor’s quantum factoring algorithm on an integrated waveguide silica-on-silicon chip that guides four single-photon qubits through the computation to factor 15 is reported.

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- Physics, Computer SciencePhysical review letters
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An adiabatic quantum algorithm capable of factorizing numbers, using fewer qubits than Shor's algorithm, is proposed, implemented in a NMR quantum information processor and experimentally factorize the number 21.

### Experimental realisation of Shor's quantum factoring algorithm using qubit recycling

- Physics, Computer Science2013 Conference on Lasers & Electro-Optics Europe & International Quantum Electronics Conference CLEO EUROPE/IQEC
- 2013

This work demonstrates a scalable version of Shor's quantum factoring algorithm in which then qubit control register is replaced by a single qubit that is recycled n times: the total number of qubits is one third of that required in the standard protocol.

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- PhysicsQuantum Inf. Process.
- 2019

This paper tries to find what are the different entanglement SLOCC classes that can be generated by these two algorithms, Grover's and Shor’s algorithms, in the case of pure four-qubit systems.

### Demonstration of Shor's factoring algorithm for N [Formula: see text] 21 on IBM quantum processors.

- Computer ScienceScientific reports
- 2021

This work implemented the quantum order-finding algorithm for factoring the integer 21 using only five qubits and successfully verified the presence of entanglement between the control and work register qubits, which is a necessary condition for the algorithm's speedup in general.

### A compiled version of Shor’s quantum factoring algorithm on a waveguide chip

- Physics
- 2009

We report the realization of a compiled version of Shor’s quantum factoring algorithm on an integrated waveguide chip. This demonstration serves as an illustration to the importance of using…

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This tutorial reviews the fundamental tools of photonic quantum information processing and the quantum circuit model as well as measurement-based models of quantum computing are introduced and it is shown how they can be implemented experimentally using photonic qubits.

### Optimising Matrix Product State Simulations of Shor's Algorithm

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A matrix product state simulation of a 60-qubit instance of Shor's algorithm that would otherwise be infeasible to complete without an optimised entanglement mapping is performed.

### Pretending to factor large numbers on a quantum computer

- Computer Science
- 2013

This work demonstrates how to factor products of large prime numbers using a compiled version of Shor’s quantum factoring algorithm, which can factor all products of p,q such that p, q are unequal primes greater than two, runs in constant time, and requires only two coherent qubits.

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