Qubit Idling in MERA with Qubit Reuse

Matthew DeCross et al. introduced the ``greedy heuristic" algorithm, a qubit reuse protocol utilizing mid-circuit measurement to reduce the number of physical qubits required in quantum circuits(DeCross et al., PRX 13, 2023).

This approach is particularly effective in circuits where the number of qubits grows exponentially with circuit depth, such as the multiscale entanglement renormalization ansatz (MERA) used for quantum simulation applications, which is the focus of this work.

While their method successfully reduced the qubit requirement from $\order{N}$ to $\order{\log{N}}$ for an $N$-site system, it did not reduce the associated qubit idling volume, which remains approximately $\order{N \log{N}}$ during state preparation and measurement (SPAM).

The idling volume impacts the run time of the algorithm and coherence of the final result, and the idling during state preparation and measurement (SPAM) can be particularly important as it is a slow operation in some architectures.

In this paper, we propose a ``dynamic grouping" technique that reduces the SPAM idling volume to $\order{N}$, significantly lowering qubit idling.