Systems and methods for compressed sensing measurement of long-range correlated noise

A computer-implemented method for detecting a two-qubit correlated dephasing error, the method comprising:

• accessing a signal of a quantum system, the quantum system includes a plurality of qubits, wherein every qubit of the plurality of qubits has a nonzero rate of dephasing and wherein some qubits have a nonzero rate of correlated dephasing;
• dephasing entangled states of the plurality of qubits based on performing Ramsey spectroscopy using entangled states of random subsets of qubits of the plurality of qubits;
• measuring a linear function of a correlation matrix, where the correlation matrix corresponds to correlated Markovian dephasing between pairs of qubits of the plurality of qubits;
• generating a first vector and a second vector, wherein a plurality of elements of the first vector and of the second vector are randomly chosen;
• and
• estimating a decay rate based on the first vector and the second vector.

A system for detecting a two-qubit correlated dephasing error, the system comprising:

• a processor;
• and
• a memory, including instructions stored thereon, which when executed by the processor, cause the system to:
• access a signal of a quantum system, the signal includes a plurality of qubits, wherein every qubit has a nonzero dephasing rate;
• and
• generate a matrix C in Rn×n, wherein its off-diagonal part is 2s sparse and wherein the matrix C is based on the accessed signal.