Abstract
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.
Highlights
In the current era of noisy intermediate scale quantum computers [1], quantum architectures are limited by connectivity, gate fidelity, and various other sources of errors that limit both circuit depth and width
A number of problems exist that are solvable in polynomial time by universal quantum computers but conjectured to be impossible for classical computers to solve without a superpolynomial slowdown, so a quantum computer’s universality implies its quantum supremacy [8,10]
This work is an attempt to be minimalistic about the resources and assumptions underlying both implementations and models of universal quantum computation and quantum supremacy
Summary
In the current era of noisy intermediate scale quantum computers [1], quantum architectures are limited by connectivity, gate fidelity, and various other sources of errors that limit both circuit depth and width. Various models of quantum computation have been developed that are designed to be relatively easy to implement on existing hardware The strength of these models is confirmed by demonstrating their ability to achieve universality [2,3,4,5,6] or quantum supremacy [7,8,9,10,11,12,13,14,15,16,17]. Universality is a stronger attribute, as it implies the ability to reproduce the quantum supremacy results of other models In this spirit, here we propose a model of quantum computation that is computationally universal even when restricted to a one-dimensional (1D) chain of qubits with only nearestneighbor interactions and a limited degree of control.
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