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.

• Received 7 January 2021
• Accepted 12 April 2021

DOI:https://doi.org/10.1103/PhysRevA.103.042613