# US 12,223,393 B2 · Expectation value assessment system and method

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- Number: US 12,223,393 B2
- Document ID: US12223393B2
- Status: Granted
- Kind: B2
- Application number: 17/738,305
- Filed: 2022-05-06
- Published: 2022-11-24
- Granted: 2025-02-11
- Earliest claimed: 2021-05-11
- Assignees: Mizuho Research & Technologies, Ltd.; Mizuho Financial Group, Inc.
- Applicants: Mizuho Research & Technologies, Ltd.; Mizuho Financial Group, Inc.
- Inventors: Shumpei Uno
- Web page: https://patentgrep.com/patent/US12223393B2

## CPC

- G06N 10/60: Quantum algorithms, e.g. based on quantum optimisation, quantum Fourier or Hadamard transforms
- G06N 10/70: Quantum error correction, detection or prevention, e.g. surface codes or magic state distillation
- G06N 10/20: Models of quantum computing, e.g. quantum circuits or universal quantum computers
- G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS

## Abstract

A system obtains an operator that produces a superposition state of a plurality of random variables. The system performs iteration of a first operation and a second operation on an initial quantum state to produce a final quantum state. The first operation produces 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 operator to a quantum state where the last bit of a bit string is 0. The second operation produces a new first state by performing a computation that inverts the second state with respect to the first state. The system measures the bit string in the final quantum state, records the number of times a quantum state where all bits of the bit string are 0 is observed, and calculate an expectation value of the random variables according to the number.

## Claims

### Claim 1

A system comprising:
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, wherein the system is configured to:
by the manipulation unit, obtain a first operator that produces a superposition state of a plurality of random variables,
by the manipulation unit, perform 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,
by the measurement unit, measure the bit string in the final quantum state,
by the measurement unit, record, 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
by the classical computing unit, calculate an expectation value of the random variables by maximum likelihood estimation according to the number of hits.

### Claim 2 (depends on 1)

The system according to claim 1, wherein the manipulation unit is configured to perform the iteration a number of times corresponding to a reciprocal of an accuracy required in measurement of the bit string.

### Claim 3 (depends on 1)

The system according to claim 1, wherein the classical computing unit is configured to perform maximum likelihood estimation of amplitude through classical computing based on the number of hits and assess the expectation value.

### Claim 4

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.

### Claim 5

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.