匹配门和空间有界量子计算是等价的
Matchgate and space-bounded quantum computations are equivalent
摘要：
匹配门是一类特别多花的两量子比特最近邻量子门，由一组代数约束定义。它们出现在例如完美匹配的理论图，非相互作用费米子，和一维自旋链。我们表明，电路的匹配门的计算能力是等价的空间有界量子计算与酉门，与空间限制为对数的匹配门电路的宽度。特别是，对于传统的设置多项式大小的（矩阵空间生成的）家庭的匹配门电路，已知是经典的模拟，我们将它们的功率与多项式时间和矩阵空间有界的通用酉量子计算相一致。
英文摘要：
Matchgates are an especially multiflorous class of two-qubit nearest neighbour quantum gates, defined by a set of algebraic constraints. They occur for example in the theory of perfect matchings of graphs, non-interacting fermions, and one-dimensional spin chains. We show that the computational power of circuits of matchgates is equivalent to that of space-bounded quantum computation with unitary gates, with space restricted to being logarithmic in the width of the matchgate circuit. In particular, for the conventional setting of polynomial-sized (logarithmic-space generated) families of matchgate circuits, known to be classically simulatable, we characterise their power as coinciding with polynomial-time and logarithmic-space bounded universal unitary quantum computation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
