In circuit quantum electrodynamics, measuring the state of a superconducting qubit introduces a loss channel which can enhance spontaneous emission through the Purcell effect, thus decreasing qubit lifetime. This decay can be mitigated by performing the measurement through a Purcell filter which forbids signal propagation at the qubit transition frequency. If the filter is also well-matched at the readout cavity frequency, it will protect the qubit from decoherence channels without sacrificing measurement speed. We propose and analyze design for a mechanical Purcell filter, which we also fabricate and characterize at room temperature. The filter is comprised of an array of nanomechanical resonators in thin-film lithium niobate, connected in a ladder topology, with series and parallel resonances arranged to produce a bandpass response. The modest footprint, steep band edges, and absence of cross-talk in these filters make them a novel and appealing alternative to analogous electromagnetic versions currently used in microwave quantum machines.Quantum information processing calls for systems which are well isolated from their environment, whose states can nonetheless be measured and manipulated with precision. 1 These fundamentally contradictory requirements can be satisfied by cleverly engineering devices and interactions between them. In the circuit QED platform, 2-4 nonlinear superconducting circuits called qubits are used to store and process quantum information. Their internal states need to be read out rapidly and with low rates of error. An appealing approach for this is to couple the qubit circuit to an auxiliary, linear electromagnetic resonator (often called the readout cavity). Resonators have long been used to amplify emission from atoms, for instance, via Purcell enhancement. 5-7 Conversely, qubit emission into the environment can be suppressed by tuning the qubit away from the resonator's frequency by many times the linewidth and interaction energy. The qubit state is then measured "dispersively" by monitoring the resonator frequency for shifts induced by changes in the qubit state 3 (although we note that alternative measurement strategies exist). 8 Dispersive shifts of the cavity can be measured and amplified to demonstrate extremely efficient single-shot measurements of qubits using this scheme. 9,10 Nonetheless, the conflicting requirements of efficient readout and qubit isolation persist in the desired properties of the resonator. Fast, efficient readout requires strong coupling between the resonator and environment. This in turn increases the probability of qubit relaxation through the resonator in a process called Purcell decay. 5,[11][12][13] Purcell filters, often consisting of a second stage electromagnetic resonator, have been used effectively to mitigate this process. [14][15][16][17][18][19] As qubit coherence times continue to improve, the basic limit imposed by Purcell decay will become more important. In principle, progressively higher order electromagnetic filters can be incorporated, ...