Apparatus And Method For Optimizing, Monitoring And Controlling A Real Physical System

A method for using an apparatus for at least one of optimizing, monitoring and controlling a real physical system, wherein the apparatus includes a hybrid computing arrangement including one or more classical computers coupled to one or more quantum computers, wherein the one or more quantum computers are configured to execute one or more quantum circuits that are configured using the one or more classical computers, wherein the method includes:

• (i) obtaining data that are representative of operation of the real physical system;
• (ii) using the data to generate one or more Hamiltonians to define at least one quantum circuit that is executable on the one or more quantum computers, wherein observables (M) obtained from executing the at least one quantum circuit are representative of Gibbs states (namely, statistical distributions) and wherein generation of the observables (M) includes using a combination of thermal pure quantum (TPQ) states and classical shadow tomography;
• (iii) training a computational machine based on the observables (M) representative of the Gibbs states;
• (iv) generating a mathematical model representative of the real physical system including the computational machine;
• and
• (v) applying the mathematical model to data obtained from the real physical system for generating at least one of:
• (a) a monitoring output that is representative of an operating state or operating condition of the real physical system;
• (b) one or more inputs to an optimization function applied to the mathematical model to generate values of parameters to use to operate the real physical system in a more optimized manner;
• and
• (c) one or more inputs to a control function applied to the mathematical model to generate values of parameters to use to control operation of the real physical system.

A quantum mechanical apparatus comprising:

• one or more classical computers coupled to a real physical system;
• and
• one or more quantum computers in data communication with the one or more classical computers;
• wherein the one or more quantum computers comprise a plurality of qubits configured to perform a quantum circuit that includes:
• (a) a first Clifford circuit configured to randomize a thermal pure quantum state |ϕ of the plurality of qubits,
• (b) a quantum signal processing circuit configured to approximate an imaginary time evolution of |ϕ according to one or more Hamiltonians representative of the real physical system, and
• (c) a second Clifford circuit configured to perform a randomized measurement of |ϕ to thereby compute one or more observables representative of Gibbs states;
• wherein the one or more classical computers are configured to control the real physical system on the basis of the computed one or more observables.