Quantum circuit engineering for correcting coherent noise

Crosstalk and several forms of coherent noise are invisible when a qubit or a gate is calibrated or benchmarked in isolation. These are unlocked during the execution of a full quantum circuit applying entangling gates to several qubits simultaneously. Unitary crosstalk noise, such as an unwanted Z-Z coupling, limits the state fidelity during the execution of cross-resonance controlled-not (cnot) gates in superconductor quantum computers. This work presents (1) a method of tracing coherent errors by exploiting their sensitivity to the arrangement of cnot gates in the circuit and (2) a correction scheme that modifies the original circuit by inserting carefully the chosen compensating gates (single- or two-qubit) to possibly undo coherent errors. On two vastly different types of IBMQ processors offering quantum volume 8 to 32, our experimental results show up to 25% reduction in the infidelity of $[[7,1,3]]$ code $|+\ensuremath{\rangle}$ state (Clifford circuits) and five- to 15-qubit $W$ states (non-Clifford circuits). Our experimental circuits aggressively deploy forced commutation of cnot gates to obtain low-noise state-preparation circuits. An encoded state initialized with fewer errors marks an important step towards successful demonstration of fault-tolerant quantum computers.