### On two subgroups of U(n), useful for quantum computing

(2015) Journal of Physics : Conference Series. 597.- abstract
- As two basic building blocks for any quantum circuit, we consider the 1-qubit PHASOR circuit Phi(theta) and the 1-qubit NEGATOR circuit N(theta). Both are roots of the IDENTITY circuit. Indeed: both (NO) and N(0) equal the 2 x 2 unit matrix. Additionally, the NEGATOR is a root of the classical NOT gate. Quantum circuits (acting on w qubits) consisting of controlled PHASORs are represented by matrices from ZU(2(w)); quantum circuits consisting of controlled NEGATORs are represented by matrices from XU(2(w)). Here, ZU(n) and XU(n) are subgroups of the unitary group U(n): the group XU(n) consists of all n x n unitary matrices with all 2n line sums (i.e. all n row sums and all n column sums) equal to 1 and the group ZU(n) consists of all n x n unitary diagonal matrices with first entry equal to 1. Any U(n) matrix can be decomposed into four parts: U = exp(i alpha) Z(1)XZ(2), where both Z(1) and Z(2) are ZU(n) matrices and X is an XU(n) matrix. We give an algorithm to find the decomposition. For n = 2(w) it leads to a four-block synthesis of an arbitrary quantum computer.

Please use this url to cite or link to this publication:
http://hdl.handle.net/1854/LU-5937344

- author
- Alexis De Vos UGent and Stijn De Baerdemacker UGent
- organization
- year
- 2015
- type
- conference (proceedingsPaper)
- publication status
- published
- subject
- keyword
- unitary group, MATRICES, subgroup, quantum computing, reversible computing, COMPUTATION
- in
- Journal of Physics : Conference Series
- volume
- 597
- issue title
- XXXth International colloquium on group theoretical methods in physics (ICGTMP)
- article number
- 012030
- pages
- 10 pages
- publisher
- IOP
- place of publication
- Bristol, UK
- conference name
- 30th International colloquium on Group Theoretical Methods in Physics (ICGTMP)
- conference location
- Ghent, Belgium
- conference start
- 2014-07-14
- conference end
- 2014-07-18
- Web of Science type
- Proceedings Paper
- Web of Science id
- 000354929400030
- ISSN
- 1742-6588
- DOI
- 10.1088/1742-6596/597/1/012030
- language
- English
- UGent publication?
- yes
- classification
- P1
- copyright statement
*I have retained and own the full copyright for this publication*- id
- 5937344
- handle
- http://hdl.handle.net/1854/LU-5937344
- date created
- 2015-04-20 08:24:22
- date last changed
- 2018-01-29 12:12:26

@inproceedings{5937344, abstract = {As two basic building blocks for any quantum circuit, we consider the 1-qubit PHASOR circuit Phi(theta) and the 1-qubit NEGATOR circuit N(theta). Both are roots of the IDENTITY circuit. Indeed: both (NO) and N(0) equal the 2 x 2 unit matrix. Additionally, the NEGATOR is a root of the classical NOT gate. Quantum circuits (acting on w qubits) consisting of controlled PHASORs are represented by matrices from ZU(2(w)); quantum circuits consisting of controlled NEGATORs are represented by matrices from XU(2(w)). Here, ZU(n) and XU(n) are subgroups of the unitary group U(n): the group XU(n) consists of all n x n unitary matrices with all 2n line sums (i.e. all n row sums and all n column sums) equal to 1 and the group ZU(n) consists of all n x n unitary diagonal matrices with first entry equal to 1. Any U(n) matrix can be decomposed into four parts: U = exp(i alpha) Z(1)XZ(2), where both Z(1) and Z(2) are ZU(n) matrices and X is an XU(n) matrix. We give an algorithm to find the decomposition. For n = 2(w) it leads to a four-block synthesis of an arbitrary quantum computer.}, articleno = {012030}, author = {De Vos, Alexis and De Baerdemacker, Stijn}, booktitle = {Journal of Physics : Conference Series}, issn = {1742-6588}, keyword = {unitary group,MATRICES,subgroup,quantum computing,reversible computing,COMPUTATION}, language = {eng}, location = {Ghent, Belgium}, pages = {10}, publisher = {IOP}, title = {On two subgroups of U(n), useful for quantum computing}, url = {http://dx.doi.org/10.1088/1742-6596/597/1/012030}, volume = {597}, year = {2015}, }

- Chicago
- De Vos, Alexis, and Stijn De Baerdemacker. 2015. “On Two Subgroups of U(n), Useful for Quantum Computing.” In
*Journal of Physics : Conference Series*. Vol. 597. Bristol, UK: IOP. - APA
- De Vos, Alexis, & De Baerdemacker, S. (2015). On two subgroups of U(n), useful for quantum computing.
*Journal of Physics : Conference Series*(Vol. 597). Presented at the 30th International colloquium on Group Theoretical Methods in Physics (ICGTMP), Bristol, UK: IOP. - Vancouver
- 1.De Vos A, De Baerdemacker S. On two subgroups of U(n), useful for quantum computing. Journal of Physics : Conference Series. Bristol, UK: IOP; 2015.
- MLA
- De Vos, Alexis, and Stijn De Baerdemacker. “On Two Subgroups of U(n), Useful for Quantum Computing.”
*Journal of Physics : Conference Series*. Vol. 597. Bristol, UK: IOP, 2015. Print.