2016/10/23 by T Loke, T. Loke, J. B. Wang +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #Cartesian product #Class (philosophy) #Complexity and Algorithms in Graphs #DNA and Biological Computing #Operator (biology) #Product (mathematics) #Quantum #Quantum Computing Algorithms and Architecture #Quantum algorithm #Quantum network #Quantum walk #quant-ph
paper · pdf · doi:10.1088/1751-8121/aa53a9
arxiv created 2016/10/23 · openalex created_date 2016/11/04 · openalex publication_date 2017/01/06 · arxiv updated 2017/02/01 · openalex updated_date 2026/08/06
Abstract In this paper, we investigate the simulation of continuous-time quantum walks on specific classes of graphs, for which it is possible to fast-forward the time-evolution operator to achieve constant-time simulation complexity and to perform the simulation exactly, i.e. <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mi>ϵ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mstyle> </mml:math> , while maintaining <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mrow> <mml:mi mathvariant="normal">p</mml:mi> <mml:mi mathvariant="normal">o</mml:mi> <mml:mi mathvariant="normal">l</mml:mi> <mml:mi mathvariant="normal">y</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mi mathvariant="normal">l</mml:mi> <mml:mi mathvariant="normal">o</mml:mi> <mml:mi mathvariant="normal">g</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:mstyle> </mml:math> efficiency. In particular, we discuss two classes of composite graphs, commuting graphs and Cartesian product of graphs, that contain classes of graphs which can be simulated in this fashion. This allows us to identify new families of graphs that we can efficiently simulate in a quantum circuit framework, providing practical and explicit means to explore quantum-walk based algorithms in laboratories.