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<p>The Tracy-Singh product of matrices (TS) is an efficient tool, for the construction of gates, which preserves properties such as unitary, primitive and entangling. Moreover, if <i>c</i> and <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4878_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(c'\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>c</mi> <mo>′</mo> </msup> </math></EquationSource> </InlineEquation> are both Yang-Baxter gates, then <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4878_Article_IEq2.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(c \boxtimes c'\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>c</mi> <mo>⊠</mo> <msup> <mi>c</mi> <mo>′</mo> </msup> </mrow> </math></EquationSource> </InlineEquation>, their TS product, is also a Yang-Baxter gate. A natural question arises whether the TS product preserves enhanced YBE pairs and the existing connections between primitive gates and knot invariants. Another question we consider is how to implement the gates <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4878_Article_IEq2.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(c \boxtimes c'\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>c</mi> <mo>⊠</mo> <msup> <mi>c</mi> <mo>′</mo> </msup> </mrow> </math></EquationSource> </InlineEquation>.</p>

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On the Realization of quantum gates coming from the Tracy-Singh product

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月11日

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  • Fabienne Chouraqui

摘要

The Tracy-Singh product of matrices (TS) is an efficient tool, for the construction of gates, which preserves properties such as unitary, primitive and entangling. Moreover, if c and \(c'\) c ′ are both Yang-Baxter gates, then \(c \boxtimes c'\) c ⊠ c ′ , their TS product, is also a Yang-Baxter gate. A natural question arises whether the TS product preserves enhanced YBE pairs and the existing connections between primitive gates and knot invariants. Another question we consider is how to implement the gates \(c \boxtimes c'\) c ⊠ c ′ .