Quantum Computing Systems and Methods for Quantum Computation

A computer program product comprising computer program code recorded on a storage medium and adapted for execution by a quantum computation system to control the quantum computation system to perform a method comprising:

• providing a representation of a physical quantum system as an input to a quantum computation system, the representation of the physical quantum system including at least one operator to perform a function with respect to a quantum state of the physical quantum system;
• generating a plurality of quantum circuits from the representation of the physical quantum system, which quantum circuits are adapted to calculate expectation values for a series of moments of the at least one operator;
• executing the plurality of quantum circuits to calculate expectation values for the series of moments of the at least one operator;
• and
• using cumulant expansion, calculating a Green's Function from the calculated values for the series of moments to determine one or more properties of the physical quantum system.

A quantum computation system comprising:

• a classical digital computing apparatus that is configured to receive an input representation of a physical quantum system, the representation of the physical quantum system including at least one operator to perform a function with respect to a quantum state of the physical quantum system, and is configured to generate a plurality of quantum circuits from the representation of the physical quantum system, which quantum circuits are adapted to calculate expectation values for a series of moments of the at least one operator;
• and
• a quantum computing apparatus, coupled to the classical digital computing apparatus, which quantum computing apparatus is configured to execute the plurality of quantum circuits to calculate expectation values for the series of moments of the at least one operator;
• wherein the quantum computation system is also configured to perform a cumulant expansion based on the calculated expectation values for the series of moments, to calculate a Green's Function to determine one or more properties of the physical quantum system.