# Quantum Circuit Identities

@article{Lomont2003QuantumCI, title={Quantum Circuit Identities}, author={Chris Lomont}, journal={arXiv: Quantum Physics}, year={2003} }

There are quantum circuit identities that simplify quantum circuits, reducing the effort needed physically to implement them. This paper constructs all identities made from 3 or fewer operations taken from a common set of one qubit operations, and explains how they may be used to simplify the cost of constructing quantum circuit identities.

## 19 Citations

### Quantum circuit simplification using templates

- Computer ScienceDesign, Automation and Test in Europe
- 2005

This work considers the use of templates to simplify a quantum circuit initially found by other means, and presents and analyzes templates in the general case, and provides particular details for circuits composed of NOT, CNOT and controlled-sqrt-of-NOT gates.

### Optimized Quantum Gate Library for Various Physical Machine Descriptions

- PhysicsIEEE Transactions on Very Large Scale Integration (VLSI) Systems
- 2013

This paper targets quantum logic design with respect to the set of primitive quantum operations that are supported by six different PMDs: quantum dot, superconducting, ion trap, neutral atom, and two photonics systems, and shows that, using one- and two-qubit quantum identity rules, each gate in the library can be efficiently mapped to just theset of primitive operations supported by each of the six PMDs.

### Quantum Circuit Simplification and Level Compaction

- Computer Science, PhysicsIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
- 2008

This paper considers a local optimization technique based on templates to simplify and reduce the depth of nonoptimal quantum circuits and shows how templates can be used to compact the number of levels of a quantum circuit.

### Hybrid simplification rules for boundaries of quantum circuits

- Computer Science
- 2022

We describe rules to simplify quantum circuits at their boundaries, i.e. at state preparation and measurement. There, any strictly incoherent operation may be pushed into a preor post-processing of…

### Block-based quantum-logic synthesis

- Computer ScienceQuantum Inf. Comput.
- 2011

A basic block based on the cosine-sine decomposition method is suggested which contains l qubits and it is shown that the exact value of $l$ affects the number of one-qubit and CNOT gates in the proposed method.

### Reversible and Quantum Circuit Synthesis

- Physics, Computer Science
- 2014

This thesis presents five major tools for the synthesis of reversible and quantum circuits, and proposes FTQLS, a tool that synthesizes and optimizes fault-tolerant quantum circuits by using logic identity rules for various physical machine descriptions.

### Level Compaction in Quantum Circuits

- Computer Science2006 IEEE International Conference on Evolutionary Computation
- 2006

An automated level compactor for quantum circuits is presented and it is shown how the templates can be applied to compact logic levels in quantum circuits, which extends the boundaries of their usefulness.

### An Algorithm For Quantum Circuit Optimization

- Computer Science
- 2012

This project looks at a possible approach to solving the issue of circuit optimization by incorporating classical algorithms as well as touching on another possible application of machine learning.

### Strategies for designing geometric transformations on quantum images

- Computer ScienceTheor. Comput. Sci.
- 2011

### Quanto: Optimizing Quantum Circuits with Automatic Generation of Circuit Identities

- EducationArXiv
- 2021

This research presents a parallel version of the Celada–Seiden cellular automaton that combines the efforts of four generations of scientists to solve the challenge of integrating NoSQL data stores to manage smart phones.

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