# US 2025/0096801 A1 · Characterizing Noisy Non-Clifford Gates Through Partial Pauli Twirling or Through Alternating Pauli Twirling

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- Number: US 2025/0096801 A1
- Document ID: US20250096801A1
- Status: Published application
- Kind: A1
- Application number: 18/468,473
- Filed: 2023-09-15
- Published: 2025-03-20
- Earliest claimed: 2023-09-15
- Assignees: International Business Machines Corporation
- Applicants: International Business Machines Corporation
- Inventors: David LAYDEN; Bradley K MITCHELL; Andrew EDDINS
- Web page: https://patentgrep.com/patent/US20250096801A1

## CPC

- H03K 17/92: by the use, as active elements, of superconductive devices
- G06N 10/20: Models of quantum computing, e.g. quantum circuits or universal quantum computers
- G06N 10/40: Physical realisations or architectures of quantum processors or components for manipulating qubits, e.g. qubit coupling or qubit control
- G06N 10/70: Quantum error correction, detection or prevention, e.g. surface codes or magic state distillation
- B82Y 10/00: Nanotechnology for information processing, storage or transmission, e.g. quantum computing or single electron logic
- H03K: PULSE TECHNIQUE (measuring pulse characteristics G01R; modulating sinusoidal oscillations with pulses H03C; transmission of digital information H04L; discriminator circuits detecting phase difference between two signals by counting or integrating cycles of oscillation H03D3/04; automatic control, starting, synchronisation or stabilisation of generators of electronic oscillations or pulses where the type of generator is irrelevant or unspecified H03L; coding, decoding or code conversion, in general H03M)
- G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- B82Y: SPECIFIC USES OR APPLICATIONS OF NANOSTRUCTURES; MEASUREMENT OR ANALYSIS OF NANOSTRUCTURES; MANUFACTURE OR TREATMENT OF NANOSTRUCTURES

## Abstract

A system to characterize noise of a quantum gate can comprise a memory that stores, and a processor that executes, computer executable components that perform operations comprising generating a quantum circuit comprising one or more instances of a quantum gate of interest, and that generates the quantum circuit having each instance of the quantum gate of interest being bounded by a pair of Pauli gates, wherein each pair of Pauli gates comprises two of the same bounding Pauli gate, inserting, according to a determined probability, an initial Pauli gate, that is based on an initial quantum state of the quantum circuit, into the quantum circuit prior to the one or more instances, and, based on one or more parameters of a curve, to which an expectation value, resulting from a measurement outcome of execution of the quantum circuit, is fitted, generating an element characterizing the noise.

## Claims

### Claim 1

A system, comprising:
a memory that stores computer executable components; and
a processor that executes the computer executable components stored in the memory, wherein the computer executable components comprise:
a quantum circuit generation component that generates a quantum circuit comprising a series of one or more instances of a quantum gate of interest, wherein the quantum circuit generation component further generates the quantum circuit having each instance of the quantum gate of interest being bounded by a pair of Pauli gates, and wherein each pair of Pauli gates comprises two of the same bounding Pauli gate;
a selection component that randomly selects, separately for each instance of the quantum gate of interest, the bounding Pauli gate to employ for each instance of the quantum gate of interest;
an insertion component that inserts, according to a determined probability, an initial Pauli gate, that is based on an initial quantum state of the quantum circuit, into the quantum circuit prior to the series of one or more instances of the quantum gate of interest; and
a finalization component that, based on one or more parameters of a curve, to which an expectation value, resulting from a measurement outcome of execution of the quantum circuit at a quantum system, is fitted, generates an element characterizing noise of the quantum gate of interest.

### Claim 2 (depends on 1)

The system of claim 1, further comprising:
an execution component that executes the quantum circuit at a quantum processor of the quantum system, resulting in the measurement outcome.

### Claim 3 (depends on 1)

The system of claim 1, wherein the quantum gate of interest is a 2-qubit, non-Clifford quantum gate.

### Claim 4 (depends on 1)

The system of claim 1,
wherein the selection component randomly selects the bounding Pauli gate from a group of Pauli gates that commute with a rotation axis of the quantum gate of interest, and
wherein the insertion component inserts the initial Pauli gate according to a 50% probability.

### Claim 5 (depends on 1)

The system of claim 1, further comprising:
a state preparation component that selects the initial quantum state based on a rotation axis A⊗B of the quantum gate of interest,
wherein the insertion component selects the initial Pauli gate (Pi) from a set of Pauli gates where Pi and Pj∝(A⊗B)Pi both anti-commute with the rotation axis A⊗B, and
wherein A, B∈{X, Y, Z}.

### Claim 6 (depends on 1)

The system of claim 1, further comprising:
a readout twirling component that directs performance of readout twirling of the initial Pauli gate at the quantum system to result in output of the measurement outcome by the quantum system.

### Claim 7 (depends on 1)

The system of claim 1, wherein the finalization component generates the element absent employment of an amplitude parameter of the curve, resulting in the element being non-biased by state preparation and measurement noise related to operation of the quantum gate of interest.

### Claim 8 (depends on 1)

The system of claim 1, further comprising:
a primary iteration component that directs the quantum circuit generation component, selection component, insertion component and finalization component to perform their respective operations for one or more additional quantum circuits having a series of a same number of one or more instances of the quantum gate of interest as the quantum circuit.

### Claim 9 (depends on 8)

The system of claim 8, further comprising:
a curve fitting component that fits the expectation value, and an additional one or more expectation values resulting from the additional quantum circuits, to the curve being a decaying sinusoid curve based on a selected curve-fitting process.

### Claim 10 (depends on 8)

The system of claim 8, further comprising:
a secondary iteration component that directs the quantum circuit generation component, selection component, insertion component, finalization component and primary iteration component to perform their respective operations for one or more further quantum circuits each having a series of a second same number of one or more instances of the quantum gate of interest as the quantum circuit,
wherein the second same number is different than the same number; and
a state preparation component that selects a second initial quantum state, different from the initial quantum state, and, based on a rotation axis A⊗B of the quantum gate of interest,
wherein A, B∈{X, Y, Z}, and
wherein the state preparation component further directs the quantum circuit generation component, selection component, insertion component, finalization component, primary iteration component and secondary iteration component to perform their respective operations relative to the second initial quantum state.

### Claim 11

A computer-implemented method, comprising:
generating, by a system comprising a processor, a quantum circuit comprising a series of one or more instances of a quantum gate of interest, and having each instance of the quantum gate of interest being bounded by a pair of Pauli gates, wherein each pair of Pauli gates comprises two of the same bounding Pauli gate;
randomly selecting, by the system, separately for each instance of the quantum gate of interest, the bounding Pauli gate to employ for each instance of the quantum gate of interest;
inserting, by the system, according to a determined probability, an initial Pauli gate, that is based on an initial quantum state of the quantum circuit, into the quantum circuit prior to the series of one or more instances of the quantum gate of interest; and
based on one or more parameters of a curve, to which an expectation value, resulting from a measurement outcome of execution of the quantum circuit at a quantum system, is fitted, generating, by the system, an element characterizing noise of the quantum gate of interest.

### Claim 12 (depends on 11)

The computer-implemented method of claim 11, further comprising:
executing, by the system, the quantum circuit at a quantum processor of the quantum system; and
directing, by the system, performance of readout twirling of the initial Pauli gate at the quantum system to result in output of the measurement outcome by the quantum system.

### Claim 13 (depends on 11)

The computer-implemented method of claim 11, further comprising:
randomly selecting, by the system, the bounding Pauli gate from a group of Pauli gates that commute with a rotation axis of the quantum gate of interest; and
inserting, by the system, the initial Pauli gate according to a 50% probability.

### Claim 14 (depends on 11)

The computer-implemented method of claim 11, further comprising:
selecting, by the system, the initial quantum state based on a rotation axis A⊗B of the quantum gate of interest; and
selecting, by the system, the initial Pauli gate (Pi) from a set of Pauli gates where Pi and Pj∝(A⊗B)Pi both anti-commute with the rotation axis A⊗B,
wherein A, B∈{X, Y,Z}.

### Claim 15 (depends on 11)

The computer-implemented method of claim 11, further comprising:
generating, by the system, the element absent employment of an amplitude parameter of the curve, resulting in the element being non-biased by state preparation and measurement noise related to operation of the quantum gate of interest.

### Claim 16

A computer program product facilitating a process to characterize a noisy quantum gate, the computer program product comprising a computer readable storage medium having program instructions embodied therewith, the program instructions executable by a processor to cause the processor to:
generate, by the processor, a quantum circuit comprising a series of one or more instances of a quantum gate of interest, and having each instance of the quantum gate of interest being bounded by a pair of Pauli gates, wherein each pair of Pauli gates comprises two of the same bounding Pauli gate;
randomly select, by the processor, separately for each instance of the quantum gate of interest, the bounding Pauli gate to employ for each instance of the quantum gate of interest;
insert, by the processor, according to a determined probability, an initial Pauli gate, that is based on an initial quantum state of the quantum circuit, into the quantum circuit prior to the series of one or more instances of the quantum gate of interest; and
based on one or more parameters of a curve, to which an expectation value, resulting from a measurement outcome of execution of the quantum circuit at a quantum system, is fitted, generate, by the processor, an element characterizing noise of the quantum gate of interest.

### Claim 17 (depends on 16)

The computer program product of claim 16, wherein the program instructions are further executable by the processor to cause the processor to:
execute, by the processor, the quantum circuit at a quantum processor of the quantum system; and
direct, by the processor, performance of readout twirling of the initial Pauli gate at the quantum system to result in output of the measurement outcome by the quantum system.

### Claim 18 (depends on 16)

The computer program product of claim 16, wherein the program instructions are further executable by the processor to cause the processor to:
randomly select, by the processor, the bounding Pauli gate from a group of Pauli gates that commute with a rotation axis of the quantum gate of interest; and
insert, by the processor, the initial Pauli gate according to a 50% probability.

### Claim 19 (depends on 16)

The computer program product of claim 16, wherein the program instructions are further executable by the processor to cause the processor to:
select, by the processor, the initial quantum state based on a rotation axis A⊗B of the quantum gate of interest; and
select, by the processor, the initial Pauli gate (Pi) from a set of Pauli gates where Pi and Pj∝(A⊗B)Pi both anti-commute with the rotation axis A⊗B,
wherein A, B∈{X, Y, Z}.

### Claim 20 (depends on 16)

The computer program product of claim 16, wherein the program instructions are further executable by the processor to cause the processor to:
generate, by the processor, the element absent employment of an amplitude parameter of the curve, resulting in the element being non-biased by state preparation and measurement noise related to operation of the quantum gate of interest.