As increasingly sophisticated prototypes of quantum computers are being developed, a pressing challenge is to find computational problems that can be solved by an intermediate-scale quantum computer, but are beyond the capabilities of existing classical computers. Previous work in this direction has introduced computational problems that can be solved with certainty by quantum circuits of depth independent of the input size (so-called ‘shallow’ circuits) but cannot be solved with high probability by any shallow classical circuit. Here we show that such a separation in computational power persists even when the shallow quantum circuits are restricted to geometrically local gates in three dimensions and corrupted by noise. We also present a streamlined quantum algorithm that is shown to achieve a quantum advantage in a one-dimensional geometry. The latter may be amenable to experimental implementation with the current generation of quantum computers.

随着越来越复杂的量子计算机原型的开发，迫切的挑战是寻找可以由中型量子计算机解决的计算问题，但这些问题超出了现有经典计算机的能力。在这个方向上的先前工作已经引入了计算问题，这些问题可以通过与输入大小无关的深度量子电路（所谓的“浅”电路）来确定地解决，但是不能通过任何浅经典电路来高概率地解决。在这里，我们表明，即使将浅量子电路限制在三维上的几何局部门并受噪声破坏的情况下，这种计算能力的分离仍然存在。我们还提出了一种简化的量子算法，该算法被证明可以在一维几何结构中实现量子优势。