Mitigating Depolarizing Noise on Quantum Computers with Noise-Estimation Circuits

A significant problem for current quantum computers is noise. While there are many distinct noise channels, the depolarizing noise model often appropriately describes average noise for large circuits involving many qubits and gates. We present a method to mitigate the depolarizing noise by first estimating its rate with a noise-estimation circuit and then correcting the output of the target circuit using the estimated rate. The method is experimentally validated on a simulation of the Heisenberg model. We find that our approach in combination with readout-error correction, randomized compiling, and zero-noise extrapolation produces close to exact results even for circuits containing hundreds of CNOT gates. We also show analytically that zero-noise extrapolation is improved when it is applied to the output of our method.

Figure 1

Randomized compiling. Each CNOT gate is dressed with the $P$, $Q$, $R$, and $S$ gates.

Figure 2

Quantum circuit for the simulation of the XX chain. (a) Preparation of the initial domain-wall state and basis transformation to a convenient basis. The dotted gates were replaced by random rotations in the estimation circuit. (b) One step of the time evolution. Multiple steps are obtained by repeating this subcircuit. The dotted gates were removed in the estimation circuit. (c) Basis transformation and measurement of the last qubit. The dotted gates were replaced by the inverses of the random rotations from the initialization step in the estimation circuit.

Figure 3

Comparison of the original and mitigated results for the time evolution of the local magnetization in the XX chain. The original results were obtained using the original circuits without any mitigation. There are 14 CNOT gates per time step and the longest original circuit contains 210 CNOT gates. Target results use readout-error correction, randomized compiling, and zero-noise extrapolation. Mitigated results use readout-error correction, randomized compiling, mitigation with estimation circuits, and zero-noise extrapolation. Data for extrapolation were obtained with circuits where each CNOT gate was replaced by one, three, or five CNOT gates. Each circuit was executed with 448 random instances. Error bars represent the standard error of processed data. Exact solution takes the Trotter–Suzuki decomposition into account.