Circuit connectivity boosts by quantum-classical-quantum interfaces

High-connectivity circuits are a major roadblock for current quantum hardware. We propose hybrid classical-quantum algorithm to simulate such without swap-gate ladders. As the main technical tool, we introduce quantum-classical-quantum interfaces. These replace an experimentally problematic gate (e.g., long-range one) with single-qubit random measurements followed by state preparations sampled according classical quasiprobability simulation of noiseless gate. Each interface introduces multiplicative statistical overhead which, remarkably, is independent on-chip qubit distance. Hence, applying interfaces longest-range gates in target circuit, significant reductions circuit depth and infidelity can be attained. numerically show efficacy our method Bell-state two increasingly distant qubits variational ground-state solver transverse-field Ising model on ring. Our findings provide versatile toolbox error-mitigation boosts tailored noisy, intermediate-scale computation.