Abstract: For respective positive integer value n, performing an outer and inner procedures, for states sufficiently representing coherent-error in a quantum system. Inner procedure creates copies state entangling n-qudits using randomized compiling, and obtains measurements of n-qudits in a basis corresponding to f-states. An outcome bit string forms for the state from measurement. The outer procedure and the forming string repeats, obtaining outcome bit strings for each state. Error-rate is determined for each state using the outcome bit strings for the respective value n. The outer procedure through determining error-rate repeats for different n drawn from positive-integers, determines error-rate for each state for respective values n. For state-S, error-rate fits for each respective value-n of the state to a corresponding quadratic function, the error-rate as dependent variable and n as independent variable.

Abstract: Systems and methods for estimating a property of an error in a circuit implemented on an n-qubit quantum system are provided, where the circuit comprises a gate set that comprises a first subset () and a second subset () of elementary gates. The first subset comprises a third subset () of elementary gates each of which consists of an n-fold tensor product of a plurality of single qubit gates. A first procedure is executed that comprises preparing the system in a state ? and then applying D1=T1 to the system. The procedure further comprises, for each respective clock cycle t in clock cycles t?{2, . . . , m+1}, (a) applying H to the system, where H is an elementary gate in the second subset, and then (b) applying a gate Dt=TtGHTt?1†H† to the system, where Dt is an element of the first subset. The procedure further comprises performing a measurement readout R.

Abstract: Computer systems and methods for constructing a model of the noise afflicting a quantum computer comprising a plurality of qubits are provided. A graph G that describes a conditional independence structure of the noise is obtained. The graph G includes a node for each qubit in the plurality of qubits. The noise afflicting the quantum computer is logically reduced to Pauli noise. The graph G is broken into a plurality of sets. Each respective set Cj in the plurality of sets (i) corresponds a respective qubit j in the plurality of qubits and (ii) comprises a representation of the respective qubit j and the parent qubits ?+j in the graph G. For each respective set Cj in the plurality of sets, a corresponding local conditional probability distribution Pr(ej|e?+j) is characterized in which ej?j is a Pauli error on the jth qubit.