# Faster Quantum Number Factoring via Circuit Synthesis

@article{Markov2013FasterQN, title={Faster Quantum Number Factoring via Circuit Synthesis}, author={Igor L. Markov and Mehdi Saeedi}, journal={ArXiv}, year={2013}, volume={abs/1301.3210} }

A major obstacle to implementing Shor's quantum number-factoring algorithm is the large size of modular-exponentiation circuits. We reduce this bottleneck by customizing reversible circuits for modular multiplication to individual runs of Shor's algorithm. Our circuit-synthesis procedure exploits spectral properties of multiplication operators and constructs optimized circuits from the traces of the execution of an appropriate GCD algorithm. Empirically, gate counts are reduced by 4-5 times…

## 27 Citations

### Constant-optimized quantum circuits for modular multiplication and exponentiation

- Computer Science, MathematicsQuantum Inf. Comput.
- 2012

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.

### Low-quantum cost circuit constructions for adder and symmetric Boolean functions

- Computer Science2016 IEEE International Symposium on Circuits and Systems (ISCAS)
- 2016

This paper revisits the adder construction of Vedral, Barenco and Eckert to show that improvement of gate count and QC is achievable by exploiting a construction based only on Peres gates and reports improved constructions of symmetric Boolean functions by following an approach recently proposed in the context of Boolean function complexity analysis.

### 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.,…

### Lowering the T-depth of Quantum Circuits via Logic Network Optimization

- Computer ScienceACM Transactions on Quantum Computing
- 2022

A dynamic programming based logic synthesis algorithm to reduce the multiplicative depth of logic networks that makes use of cut enumeration, tree balancing, and exclusive sum-of-products (ESOP) representations.

### Simplified Factoring Algorithms for Validating Small-Scale Quantum Information Processing Technologies

- Computer Science
- 2013

This work proposes a different verification scheme based on compiled versions of Shor's factoring algorithm that may be extended to large circuits in the future and demonstrates that an additional layer of compilation can be added using classical operations, that will reduce the number of qubits and gates needed in a given compiled circuit.

### Factoring with Qutrits: Shor's Algorithm on Ternary and Metaplectic Quantum Architectures

- Computer ScienceArXiv
- 2016

The cost of performing Shor's algorithm for integer factorization on a ternary quantum computer is determined using two natural models of universal fault-tolerant computing: a model based on magic state distillation and a modelbased on a metaplectic topological quantum computer.

### Lowering the T-depth of Quantum Circuits By Reducing the Multiplicative Depth Of Logic Networks

- Computer ScienceArXiv
- 2020

A dynamic programming based logic synthesis algorithm to reduce the multiplicative depth in logic networks that makes use of cut enumeration, tree balancing, and exclusive sum-of-products (ESOP) representations.

### Reversible logic synthesis by quantum rotation gates

- Computer ScienceQuantum Inf. Comput.
- 2013

A rotation-based synthesis framework for reversible logic that constructs intermediate quantum states that may be in superposition and combines techniques from reversible Boolean logic and quantum computation is proposed.

### Low Quantum Cost Construction for Adder and Symmetric Boolean Function

- Computer Science
- 2017

This paper revisits the adder construction of Vedral, Barenco and Eckert to show that improvement of gate count and QC is achievable by exploiting a construction based only on Peres gates, and reports improved constructions of symmetric Boolean functions by following an approach recently proposed in the context of Boolean function complexity analysis.

### Boolean satisfiability in quantum compilation

- Computer Science, PhysicsPhilosophical Transactions of the Royal Society A
- 2019

The flow of quantum compilation is described and algorithms based on Boolean satisfiability are proposed, which are a good match to tackle such computationally complex problems.

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