Meuli, G., Soeken, M., Campbell, E. et al. (2 more authors) (2019) The role of multiplicative complexity in compiling Low T-count Oracle circuits. In: 2019 IEEE/ACM International Conference on Computer-Aided Design (ICCAD). 2019 IEEE/ACM International Conference on Computer-Aided Design (ICCAD), 04-07 Nov 2019, Westminster, CO, USA. IEEE ISBN 9781728123516
Abstract
We present a constructive method to create quantum circuits that implement oracles |x〉|y〉|0〉 k →|x〉|y⊕f(x)〉|0〉 k for n-variable Boolean functions f with low T-count. In our method f is given as a 2-regular Boolean logic network over the gate basis {∧, ⊕, 1}. Our construction leads to circuits with a T-count that is at most four times the number of AND nodes in the network. In addition, we propose a SAT-based method that allows us to trade qubits for T gates, and explore the space/complexity trade-off of quantum circuits. Our constructive method suggests a new upper bound for the number of T gates and ancilla qubits based on the multiplicative complexity c∧(f) of the oracle function f, which is the minimum number of AND gates that is required to realize f over the gate basis {∧, ⊕, 1}. There exists a quantum circuit computing f with at most 4c∧(f)T gates using k=c∧(f) ancillae. Results known for the multiplicative complexity of Boolean functions can be transferred. We verify our method by comparing it to different state-of-the-art compilers. Finally, we present our synthesis results for Boolean functions used in quantum cryptoanalysis.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. Reproduced in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > Department of Physics and Astronomy (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 12 Feb 2020 15:57 |
Last Modified: | 26 Dec 2020 01:39 |
Status: | Published |
Publisher: | IEEE |
Refereed: | Yes |
Identification Number: | 10.1109/iccad45719.2019.8942093 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:156758 |