Method for measuring an observable on a quantum computing device

A computer implemented method for measuring on a quantum computing device an expectation value of an observable in a given quantum state, the method comprising:

• (a) obtaining an efficient tensor network representation T of the observable in the Pauli basis;
• (b) extracting from the observable a sum of one or more directly measurable operators wherein each directly measurable operator is diagonal in a fixed basis with a single quantum circuit;
• (c) for each directly measurable operator, measuring said qubits in said fixed basis to compute expectation values corresponding to each of said directly measurable operators;
• (d) combining the expectation values of said directly measurable operators to compute an approximation of the expectation value of the observable.

A computer system, comprising:

• (a) a quantum computing device comprising a plurality of qubits and measurement circuitry configured to measure the plurality of qubits;
• (b) one or more processors communicatively coupled to the quantum computing device;
• and
• (c) a memory storing instructions that, when executed by the one or more processors, cause the computer system to:
• i) obtain an efficient tensor network representation T of an observable in a Pauli basis;
• ii) extract from the observable a sum of one or more directly measurable operators, each directly measurable operator being:
• (a) such that after applying a local qubit rotation at each qubit site, said directly measurable operator is diagonal in a Z basis, and
• (b) represented by an efficient tensor network;
• iii) for each directly measurable operator, applying said local qubit rotations on the qubits of the quantum device and measuring said qubits in a computational basis to compute expectation values corresponding to each of said directly measurable operators;
• iv) combining the expectation values of said directly measurable operators to compute an approximation of the expectation value of the observable.