Dynamical weight reduction of Pauli measurements

Many routines that one might want to run on a quantum computer can benefit from adaptive circuits, relying on mid-circuit measurements and feed-forward operations. Any such measurement has to be compiled into a sequence of elementary gates involving only a small number of qubits. In this work, we formalize dynamical weight reduction (DWR) schemes in which a high-weight Pauli measurement is decomposed into a sequence of measurements of smaller weight at the cost of adding additional auxiliary qubits. We first present our main method, deforming a ZX diagram that represents the measurement we want to compile. We then construct a general recipe that constructs a DWR on a given connectivity whenever the underlying connectivity graph fulfills certain necessary conditions. Further, we construct a family of DWR schemes using a given number of auxiliary qubits with indications that the schemes we present are optimal in terms of spacetime resource overheads needed for a DWR. We highlight three examples that achieve a constant time or a constant space overhead, respectively. Finally, we discuss different trade-offs of space and time overhead and how they might be chosen differently on different levels of abstraction within a (fault-tolerant) quantum computation. This work showcases the flexibility in compiling a measurement circuit in terms of lower-weight measurements using deformations of ZX diagrams and can find applications in quantum error correction, quantum simulation as well as near-term quantum computing tasks where the quality of a computation highly depends on the physical implementation of a given logical operation.