Method and system for estimating trace operator for a machine learning task

A non-transitory computer readable storage medium is disclosed for storing computer-executable instructions which, when executed, cause a computer to perform a method for estimating a trace operator to be used in a machine learning task, the method comprising:

• obtaining an indication of a pair of points;
• constructing a quantum circuit comprising a single control qubit and a plurality of register qubits using the obtained pair of points, the constructing comprising:
• receiving an encoding pattern and an architecture of quantum circuit,
• encoding the pair of points into the plurality of register qubits,
• initializing the quantum circuit, and
• compiling the quantum circuit for a quantum device;
• evolving the quantum circuit on the quantum device;
• obtaining an indication of at least one measurement on the single control qubit of the corresponding quantum circuit;
• determining an indication of an estimated trace of the unitary operator representing the plurality of register qubits using the obtained indication of at least one measurement on the single control qubit;
• and
• providing the indication of the estimated trace of the unitary operator.

A computer comprising:

• a central processing unit;
• a display device;
• a communication port for operatively connecting the computer with a quantum device;
• a memory unit comprising an application for estimating a trace operator for a machine learning task, the application comprising:
• instructions for obtaining an indication of a pair of points;
• instructions for constructing a quantum circuit comprising a single control qubit and a plurality of register qubits using the obtained pair of points, the constructing comprising:
• receiving an encoding pattern and an architecture of quantum circuit,
• encoding the pair of points into the plurality of register qubits,
• initializing the quantum circuit, and
• compiling the quantum circuit for the quantum device;
• instructions for evolving the quantum circuit on the quantum device;
• instructions for obtaining an indication of at least one measurement on the single control qubit of the corresponding quantum circuit;
• instructions for determining an indication of an estimated trace of the unitary operator representing the plurality of register qubits using the obtained indication of at least one measurement on the single control qubit;
• and
• instructions for providing the indication of the estimated trace of the unitary operator.