An Exact Quantum Algorithm for the 2-Junta Problem
This paper proposes a novel quantum learning algorithm based on Bernstein and Vazirani’s quantum circuit to find the dependent variables of the 2-junta problem. Typically, for a given Boolean function f : {0, 1} n → {0, 1} that depends on only 2 out of n variables, the dependent variables are obta...
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| Veröffentlicht in: | International journal of theoretical physics 2021, Vol.60 (1), p.80-91 |
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| container_title | International journal of theoretical physics |
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| creator | Chen, Chien-Yuan |
| description | This paper proposes a novel quantum learning algorithm based on Bernstein and Vazirani’s quantum circuit to find the dependent variables of the 2-junta problem. Typically, for a given Boolean function
f
: {0, 1}
n
→ {0, 1} that depends on only 2 out of
n
variables, the dependent variables are obtained by evaluating the function 4
n
times in the worst-case. However, the proposed quantum algorithm only requires
O
(
log
2
n
) function operations in the worst-case. Moreover, the algorithm requires an average of 5.3 function operations at the most when
n
≥ 8. |
| doi_str_mv | 10.1007/s10773-020-04662-3 |
| format | Article |
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f
: {0, 1}
n
→ {0, 1} that depends on only 2 out of
n
variables, the dependent variables are obtained by evaluating the function 4
n
times in the worst-case. However, the proposed quantum algorithm only requires
O
(
log
2
n
) function operations in the worst-case. Moreover, the algorithm requires an average of 5.3 function operations at the most when
n
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f
: {0, 1}
n
→ {0, 1} that depends on only 2 out of
n
variables, the dependent variables are obtained by evaluating the function 4
n
times in the worst-case. However, the proposed quantum algorithm only requires
O
(
log
2
n
) function operations in the worst-case. Moreover, the algorithm requires an average of 5.3 function operations at the most when
n
≥ 8.</description><subject>Algorithms</subject><subject>Boolean algebra</subject><subject>Boolean functions</subject><subject>Circuits</subject><subject>Dependent variables</subject><subject>Elementary Particles</subject><subject>Machine learning</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Physics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Field Theory</subject><subject>Quantum Physics</subject><subject>Theoretical</subject><issn>0020-7748</issn><issn>1572-9575</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kMtKAzEUhoMoWKsv4CrgOnpymWRmWUq1SkEFXYdMLr3QmalJBvTtnTqCO8_mLM73_wc-hK4p3FIAdZcoKMUJMCAgpGSEn6AJLRQjVaGKUzSB40kpUZ6ji5R2AFCBKCeIzVq8-DQ249fetLlv8Gy_7uI2bxocuojzxmNGnvo2G_wSu3rvm0t0Fsw--avfPUXv94u3-ZKsnh8e57MVsZxWmTgurffccSNLWYGS4FwpbM0UtcHX3rLgwDspRM2dDUzVUJZCMuDBeMsrPkU3Y-8hdh-9T1nvuj62w0vNhKqGkUoOFBspG7uUog_6ELeNiV-agj660aMbPQjQP240H0J8DKUBbtc-_lX_k_oGZRRlpg</recordid><startdate>2021</startdate><enddate>2021</enddate><creator>Chen, Chien-Yuan</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-4162-9695</orcidid></search><sort><creationdate>2021</creationdate><title>An Exact Quantum Algorithm for the 2-Junta Problem</title><author>Chen, Chien-Yuan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-d36cee3d3a68690760dd84cb271cfebec2fd0ed644b3dcf27b08846203faec393</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Algorithms</topic><topic>Boolean algebra</topic><topic>Boolean functions</topic><topic>Circuits</topic><topic>Dependent variables</topic><topic>Elementary Particles</topic><topic>Machine learning</topic><topic>Mathematical analysis</topic><topic>Mathematical and Computational Physics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Field Theory</topic><topic>Quantum Physics</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chen, Chien-Yuan</creatorcontrib><collection>CrossRef</collection><jtitle>International journal of theoretical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chen, Chien-Yuan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An Exact Quantum Algorithm for the 2-Junta Problem</atitle><jtitle>International journal of theoretical physics</jtitle><stitle>Int J Theor Phys</stitle><date>2021</date><risdate>2021</risdate><volume>60</volume><issue>1</issue><spage>80</spage><epage>91</epage><pages>80-91</pages><issn>0020-7748</issn><eissn>1572-9575</eissn><abstract>This paper proposes a novel quantum learning algorithm based on Bernstein and Vazirani’s quantum circuit to find the dependent variables of the 2-junta problem. Typically, for a given Boolean function
f
: {0, 1}
n
→ {0, 1} that depends on only 2 out of
n
variables, the dependent variables are obtained by evaluating the function 4
n
times in the worst-case. However, the proposed quantum algorithm only requires
O
(
log
2
n
) function operations in the worst-case. Moreover, the algorithm requires an average of 5.3 function operations at the most when
n
≥ 8.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10773-020-04662-3</doi><tpages>12</tpages><orcidid>https://orcid.org/0000-0002-4162-9695</orcidid></addata></record> |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Algorithms Boolean algebra Boolean functions Circuits Dependent variables Elementary Particles Machine learning Mathematical analysis Mathematical and Computational Physics Physics Physics and Astronomy Quantum Field Theory Quantum Physics Theoretical |
| title | An Exact Quantum Algorithm for the 2-Junta Problem |
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