We consider a model of quantum computation we call "Varying-$Z$" (V$Z$), defined by applying controllable $Z$-diagonal Hamiltonians in the presence of a uniform and constant external $X$-field, and prove that it is universal, even in 1D. Universality is demonstrated by construction of a universal gate set with $O(1)$ depth overhead. We then use this construction to describe a circuit whose output distribution cannot be classically simulated unless the polynomial hierarchy collapses, with the goal of providing a low-resource method of demonstrating quantum supremacy. The V$Z$ model can achieve quantum supremacy in $O(n)$ depth, equivalent to the random circuit sampling models despite a higher degree of homogeneity: it requires no individually addressed $X$-control.
The Cost of Removing Tunability in Quantum Data Re-Uploading
Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；Department of Mathematics, National University of Singapore（新加坡国立大学数学系）
The Power of Power-of-SWAP: Postselected Quantum Computation with the Exchange Interaction
Cavendish Laboratory, Department of Physics, University of Cambridge（剑桥大学卡文迪许实验室物理系）；Department of Computer Science, University of Oxford（牛津大学计算机系）；International Centre for Theory of Quantum Technologies, University of Gdańsk（格但斯克大学量子技术理论国际中心）
Architectural mechanisms of a universal fault-tolerant quantum computer
Harvard University（哈佛大学）；Massachusetts Institute of Technology（麻省理工学院）；Harvard-Smithsonian Center for Astrophysics（哈佛-史密森天体物理中心）；QuEra Computing Inc.（QuEra计算公司）；Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（量子信息与计算机科学联合中心，美国国家标准与技术研究院/马里兰大学）
