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Quantum computers hold the promise of executing tasks beyond the capability of classical computers. Noise competes with coherent evolution and destroys long-range correlations, making it an outstanding challenge to fully leverage the computation power of near-term quantum processors. We report Random Circuit Sampling (RCS) experiments where we identify distinct phases driven by the interplay between quantum dynamics and noise. Using cross-entropy benchmarking, we observe phase boundaries which can define the computational complexity of noisy quantum evolution. We conclude by presenting an RCS experiment with 70 qubits at 24 cycles. We estimate the computational cost against improved classical methods and demonstrate that our experiment is beyond the capabilities of existing classical supercomputers.

Variational quantum eigensolvers offer a small-scale testbed to demonstrate the performance of error mitigation techniques with low experimental overhead. We present successful error mitigation by applying the recently proposed symmetry verification technique to the experimental estimation of the ground-state energy and ground state of the hydrogen molecule. A finely adjustable exchange interaction between two qubits in a circuit QED processor efficiently prepares variational ansatz states in the single-excitation subspace respecting the parity symmetry of the qubit-mapped Hamiltonian. Symmetry verification improves the energy and state estimates by mitigating the effects of qubit relaxation and residual qubit excitation, which violate the symmetry. A full-density-matrix simulation matching the experiment dissects the contribution of these mechanisms from other calibrated error sources. Enforcing positivity of the measured density matrix via scalable convex optimization correlates the energy and state estimate improvements when using symmetry verification, with interesting implications for determining system properties beyond the ground-state energy., 7 pages, 4 figures + 6 pages, 4 figures in supplemental material

Quantum error correction of a surface code or repetition code requires the pairwise matching of error events in a space-time graph of qubit measurements, such that the total weight of the matching is minimized. The input weights follow from a physical model of the error processes that affect the qubits. This approach becomes problematic if the system has sources of error that change over time. Here we show how the weights can be determined from the measured data in the absence of an error model. The resulting adaptive decoder performs well in a time-dependent environment, provided that the characteristic time scale $\tau_{\mathrm{env}}$ of the variations is greater than $\delta t/\bar{p}$, with $\delta t$ the duration of one error-correction cycle and $\bar{p}$ the typical error probability per qubit in one cycle., Comment: 5 pages, 4 figures