  Quantum error mitigation plays a crucial role in the current
noisy-intermediate-scale-quantum (NISQ) era. As we advance towards achieving a
practical quantum advantage in the near term, error mitigation emerges as an
indispensable component. One notable prior work, Jigsaw, demonstrates that
measurement crosstalk errors can be effectively mitigated by measuring subsets
of qubits. Jigsaw operates by running multiple copies of the original circuit,
each time measuring only a subset of qubits. The localized distributions
yielded from measurement subsetting suffer from less crosstalk and are then
used to update the global distribution, thereby achieving improved output
fidelity. Inspired by the idea of measurement subsetting, we propose QuTracer,
a framework designed to mitigate both gate and measurement errors in subsets of
qubits by tracing the states of qubit subsets throughout the computational
process. In order to achieve this goal, we introduce a technique, qubit
subsetting Pauli checks (QSPC), which utilizes circuit cutting and Pauli Check
Sandwiching (PCS) to trace the qubit subsets distribution to mitigate errors.
The QuTracer framework can be applied to various algorithms including, but not
limited to, VQE, QAOA, quantum arithmetic circuits, QPE, and Hamiltonian
simulations. In our experiments, we perform both noisy simulations and real
device experiments to demonstrate that QuTracer is scalable and significantly
outperforms the state-of-the-art approaches.
