Expectation value assessment system and method

A method executed by a system, wherein

• the system includes:
• a quantum computing unit including a manipulation unit that manipulates a quantum state, a state maintaining unit that maintains the quantum state, and a measurement unit that observes the quantum state;
• and
• a classical computing unit that performs post-processing based on output from the quantum computing unit,
• the method comprises:
• obtaining, by the manipulation unit, a first operator that produces a superposition state of a plurality of random variables;
• performing, by the manipulation unit, iteration of a first operation and a second operation on an initial quantum state using the state maintaining unit to produce a final quantum state, the first operation producing a second state by performing a computation that inverts a first state with respect to a state obtained by applying a Hermitian conjugate of the first operator to a quantum state where a last bit of a bit string is 0, the second operation performing a computation that inverts the second state with respect to the first state, thereby producing a new first state;
• measuring, by the measurement unit, the bit string in the final quantum state;
• recording, by the measurement unit and in the classical computing unit, a number of hits that is a number of times a quantum state where all bits of the bit string are 0 is observed;
• and
• calculating, by the classical computing unit, an expectation value of the random variables by maximum likelihood estimation according to the number of hits.

A non-transitory computer-readable storage medium storing instructions, wherein

• the instructions are executed by a system,
• the system includes:
• a quantum computing unit including a manipulation unit that manipulates a quantum state, a state maintaining unit that maintains the quantum state, and a measurement unit that observes the quantum state;
• and
• a classical computing unit that performs post-processing based on output from the quantum computing unit, and
• when executed by the system, the instructions perform a method, the method comprising:
• obtaining, by the manipulation unit, a first operator that produces a superposition state of a plurality of random variables;
• performing, by the manipulation unit, iteration of a first operation and a second operation on an initial quantum state using the state maintaining unit to produce a final quantum state, the first operation producing a second state by performing a computation that inverts a first state with respect to a state obtained by applying a Hermitian conjugate of the first operator to a quantum state where a last bit of a bit string is 0, the second operation performing a computation that inverts the second state with respect to the first state, thereby producing a new first state;
• measuring, by the measurement unit, the bit string in the final quantum state;
• recording, by the measurement unit and in the classical computing unit, a number of hits that is a number of times a quantum state where all bits of the bit string are 0 is observed;
• and
• calculating, by the classical computing unit, an expectation value of the random variables by maximum likelihood estimation according to the number of hits.