# Efficient networks for quantum factoring.

@article{Beckman1996EfficientNF, title={Efficient networks for quantum factoring.}, author={Beckman and Chari and Devabhaktuni and Preskill}, journal={Physical review. A, Atomic, molecular, and optical physics}, year={1996}, volume={54 2}, pages={ 1034-1063 } }

We consider how to optimize memory use and computation time in operating a quantum computer. In particular, we estimate the number of memory quantum bits (qubits) and the number of operations required to perform factorization, using the algorithm suggested by Shor [in Proceedings of the 35th Annual Symposium on Foundations of Computer Science, edited by S. Goldwasser (IEEE Computer Society, Los Alamitos, CA, 1994), p. 124]. A K-bit number can be factored in time of order K3 using a machine…

## 48 Citations

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In the context of modular exponentiation, this work offers several constant-factor improvements, as well as an improvement by a constant additive term that is significant for few-qubit circuits arising in ongoing laboratory experiments with Shor's algorithm.

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

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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.

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### Factorization and malleability of RSA modules, and counting points on elliptic curves modulo N

- Mathematics, Computer ScienceMathematics
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It is shown that factoring is equivalent, in deterministic polynomial time, to counting points on a pair of twisted Elliptic curves modulo N, to construct a particular N′ that helps the factorization of N.

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### High Performance Quantum Modular Multipliers

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We present a novel set of reversible modular multipliers applicable to quantum computing, derived from three classical techniques: 1) traditional integer division, 2) Montgomery residue arithmetic,…

### Toward the first quantum simulation with quantum speedup

- Computer ScienceProceedings of the National Academy of Sciences
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It is argued that simulating the time evolution of spin systems is a classically hard problem of practical interest that is among the easiest to address with early quantum devices, and develops optimized implementations and performs detailed resource analyses for several leading quantum algorithms for this problem.