Quantum computers are capable of efficiently contracting unitary tensor networks, a task that is likely to remain difficult for classical computers. For instance, networks based on matrix product states or the multiscale entanglement renormalization ansatz can be contracted on a small quantum computer to aid the simulation of a large quantum system. However, without the ability to selectively reset qubits, the associated spatial cost can be exorbitant. In this paper, we propose a protocol that can unitarily reset qubits when the circuit has a common convolutional form, thus dramatically reducing the spatial cost for implementing the contraction algorithm on general near-term quantum computers. This protocol generates fresh qubits from used ones by partially applying the time-reversed quantum circuit over qubits that are no longer in use. In the absence of noise, we prove that the state of a subset of these qubits becomes $|0\cdots 0\rangle$, up to an error exponentially small in the number of gates applied. We also provide numerical evidence that the protocol works in the presence of noise and formulate a condition under which the noise-resilience follows rigorously.

中文翻译：

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在近期量子计算机中回收量子位

量子计算机能够有效地收缩单一张量网络，而对于传统计算机而言，这项任务可能仍然很困难。例如，可以在小型量子计算机上收缩基于矩阵乘积状态或多尺度纠缠重归一化ansatz的网络，以辅助大型量子系统的仿真。但是，由于无法选择性地重置量子位，因此相关的空间成本可能过高。在本文中，我们提出了一种协议，当电路具有常见的卷积形式时，该协议可以统一重置量子位，从而显着降低在一般的近期量子计算机上实现压缩算法的空间成本。该协议通过在不再使用的量子位上部分应用时间反向量子电路，从使用过的量子位中生成新的量子位。$|0\cdots 0〉$，直到所应用的浇口数量的误差成倍地减小。我们还提供了数值证据，表明该协议可在存在噪声的情况下工作，并制定了严格遵循抗噪声能力的条件。