  Achieving near-term quantum advantage will require accurate estimation of
quantum observables despite significant hardware noise. For this purpose, we
propose a novel, scalable error-mitigation method that applies to gate-based
quantum computers. The method generates training data
$\{X_i^{\text{noisy}},X_i^{\text{exact}}\}$ via quantum circuits composed
largely of Clifford gates, which can be efficiently simulated classically,
where $X_i^{\text{noisy}}$ and $X_i^{\text{exact}}$ are noisy and noiseless
observables respectively. Fitting a linear ansatz to this data then allows for
the prediction of noise-free observables for arbitrary circuits. We analyze the
performance of our method versus the number of qubits, circuit depth, and
number of non-Clifford gates. We obtain an order-of-magnitude error reduction
for a ground-state energy problem on 16 qubits in an IBMQ quantum computer and
on a 64-qubit noisy simulator.
