In *Proceedings 15th international conference on quantum physics and logic, QPL 2018, halifax, canada, 3-7th june 2018.*, volume 287, pages 1–21, 2018. tex.bibsource: dblp computer science bibliography, https://dblp.org tex.biburl: https://dblp.org/rec/bib/journals/corr/abs-1805-06908 tex.crossref: DBLP:journals/corr/abs-1901-09476 tex.timestamp: Wed, 29 May 2019 11:09:08 +0200 Citation Key Alias: amy2019a

Paper doi abstract bibtex

Paper doi abstract bibtex

We introduce a framework for the formal specification and verification of quantum circuits based on the Feynman path integral. Our formalism, built around exponential sums of polynomial functions, provides a structured and natural way of specifying quantum operations, particularly for quantum implementations of classical functions. Verification of circuits over all levels of the Clifford hierarchy with respect to either a specification or reference circuit is enabled by a novel rewrite system for exponential sums with free variables. Our algorithm is further shown to give a polynomial-time decision procedure for checking the equivalence of Clifford group circuits. We evaluate our methods by performing automated verification of optimized Clifford+T circuits with up to 100 qubits and thousands of T gates, as well as the functional verification of quantum algorithms using hundreds of qubits. Our experiments culminate in the automated verification of the Hidden Shift algorithm for a class of Boolean functions in a fraction of the time it has taken recent algorithms to simulate.

@inproceedings{DBLP:journals/corr/abs-1805-06908, title = {Towards large-scale functional verification of universal quantum circuits}, volume = {287}, url = {https://doi.org/10.4204/EPTCS.287.1}, doi = {10/ggb9cz}, abstract = {We introduce a framework for the formal specification and verification of quantum circuits based on the Feynman path integral. Our formalism, built around exponential sums of polynomial functions, provides a structured and natural way of specifying quantum operations, particularly for quantum implementations of classical functions. Verification of circuits over all levels of the Clifford hierarchy with respect to either a specification or reference circuit is enabled by a novel rewrite system for exponential sums with free variables. Our algorithm is further shown to give a polynomial-time decision procedure for checking the equivalence of Clifford group circuits. We evaluate our methods by performing automated verification of optimized Clifford+T circuits with up to 100 qubits and thousands of T gates, as well as the functional verification of quantum algorithms using hundreds of qubits. Our experiments culminate in the automated verification of the Hidden Shift algorithm for a class of Boolean functions in a fraction of the time it has taken recent algorithms to simulate.}, booktitle = {Proceedings 15th international conference on quantum physics and logic, {QPL} 2018, halifax, canada, 3-7th june 2018.}, author = {Amy, Matthew}, year = {2018}, note = {tex.bibsource: dblp computer science bibliography, https://dblp.org tex.biburl: https://dblp.org/rec/bib/journals/corr/abs-1805-06908 tex.crossref: DBLP:journals/corr/abs-1901-09476 tex.timestamp: Wed, 29 May 2019 11:09:08 +0200 Citation Key Alias: amy2019a}, keywords = {Computer Science - Logic in Computer Science, Quantum Physics}, pages = {1--21} }

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