# Demonstration of a compiled version of Shor's quantum factoring algorithm using photonic qubits.

@article{Lu2007DemonstrationOA, title={Demonstration of a compiled version of Shor's quantum factoring algorithm using photonic qubits.}, author={Chaoyang Lu and Dan E. Browne and Tao Yang and Jian-Wei Pan}, journal={Physical review letters}, year={2007}, volume={99 25}, pages={ 250504 } }

We report an experimental demonstration of a complied version of Shor's algorithm using four photonic qubits. We choose the simplest instance of this algorithm, that is, factorization of N=15 in the case that the period r=2 and exploit a simplified linear optical network to coherently implement the quantum circuits of the modular exponential execution and semiclassical quantum Fourier transformation. During this computation, genuine multiparticle entanglement is observed which well supports its…

## 216 Citations

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

- PhysicsScience
- 2009

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.

### 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.

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

- PhysicsOptics express
- 2020

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.

### Remarks on Quantum Modular Exponentiation and Some Experimental Demonstrations of Shor's Algorithm

- PhysicsIACR Cryptol. ePrint Arch.
- 2014

An efficient quantum modular exponentiation method is indispensible for Shor's factoring algorithm. But we find that all descriptions presented by Shor, Nielsen and Chuang, Markov and Saeedi, et al.,…

### Quantum adiabatic algorithm for factorization and its experimental implementation.

- Physics, Computer SciencePhysical review letters
- 2008

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 demonstration of a teleportation-based programmable quantum gate

- Physics
- 2009

We experimentally demonstrate a programmable quantum gate that applies a sign flip operation to data qubit in an arbitrary basis fully specified by the quantum state of a two-qubit program register.…

### Adding control to arbitrary unknown quantum operations

- PhysicsNature communications
- 2011

An architecture-independent technique is developed and demonstrated that simplifies adding control qubits to arbitrary quantum operations—a requirement in many quantum algorithms, simulations and metrology, and is demonstrated in a photonic system.

### Implementation of Quantum Fourier Transform and Its Applications via Quantum-Dot Spins and Microcavity

- Physics
- 2009

A scheme for implementing discrete quantum Fourier transform is proposed via quantum dots embedded in a microcavity, and then some of its applications are investigated, i.e., Deutsch–Jozsa algorithm…

### 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.

### Quantum computing with photons: introduction to the circuit model, the one-way quantum computer, and the fundamental principles of photonic experiments

- Physics, Computer Science
- 2015

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.

## References

SHOWING 1-10 OF 46 REFERENCES

### Resource-efficient linear optical quantum computation.

- PhysicsPhysical review letters
- 2005

This work introduces a scheme for linear optics quantum computation, that makes no use of teleported gates, and requires stable interferometry over only the coherence length of the photons, and demonstrates the universality and usefulness of generic parity measurements.

### Linear optical quantum computing with photonic qubits

- Physics
- 2007

Linear optics with photon counting is a prominent candidate for practical quantum computing. The protocol by Knill, Laflamme, and Milburn [2001, Nature (London) 409, 46] explicitly demonstrates that…

### Quantum Computation and Shor's Factoring Algorithm

- Computer Science
- 1996

The authors give an exposition of Shor's algorithm together with an introduction to quantum computation and complexity theory, and discuss experiments that may contribute to its practical implementation.

### Efficient classical simulation of slightly entangled quantum computations.

- Computer Science, PhysicsPhysical review letters
- 2003

The results imply that a necessary condition for an exponential computational speedup is that the amount of entanglement increases with the size n of the computation, and provide an explicit lower bound on the required growth.

### Optical quantum computation using cluster States.

- PhysicsPhysical review letters
- 2004

An approach to optical quantum computation in which a deterministic entangling quantum gate may be performed using a few hundred coherently interacting optical elements using the abstract cluster-state model of quantum computation.

### Experimental one-way quantum computing

- Physics, Computer ScienceNature
- 2005

The implementation of Grover's search algorithm demonstrates that one-way quantum computation is ideally suited for such tasks.

### A scheme for efficient quantum computation with linear optics

- PhysicsNature
- 2001

It is shown that efficient quantum computation is possible using only beam splitters, phase shifters, single photon sources and photo-detectors and are robust against errors from photon loss and detector inefficiency.

### Experimental application of decoherence-free subspaces in an optical quantum-computing algorithm.

- PhysicsPhysical review letters
- 2003

This work presents the first use of DFSs to improve the performance of a quantum algorithm, an optical implementation of the Deutsch-Jozsa algorithm, made insensitive to a particular class of phase noise by encoding information in the appropriate subspaces.

### High-speed linear optics quantum computing using active feed-forward

- Physics, Computer ScienceNature
- 2007

It is demonstrated that, for a perfect cluster state and no photon loss, the one-way quantum computation scheme would operate with good fidelity and that the feed-forward components function with very high speed and low error for detected photons.

### Semiclassical Fourier transform for quantum computation.

- Physics, Computer SciencePhysical review letters
- 1996

It is shown that the Fourier transform preceding the final measurement in Shor's algorithm for factorization on a quantum computer can be carried out in a semiclassical way by using the ``classical''…