Algorithmic cooling for holographic quantum circuits

Quantum computers are capable of efficiently contracting unitary tensor networks, a task that is likely to remain difficult for classical computers. A particularly promising subclass of such networks is holographic; these networks can be contracted on a small quantum computer to aid a simulation of a large quantum system. However, without an ability to selectively reset a subset of qubits, the associated spatial cost can be exorbitant. In this paper, we propose a protocol that can unitarily reset the qubits, thus dramatically reducing the requisite spatial cost to implement the contraction algorithm on general near-term quantum computers. This protocol generates fresh qubits from the used ones, by partially applying the time-reversed quantum circuit over the 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...0>, up to an error exponentially small in the number of gates applied. We also provide a numerical evidence that the protocol works in the presence of noise.