# US 11,451,231 B2 · Robust quantum logical gates

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- Number: US 11,451,231 B2
- Document ID: US11451231B2
- Status: Granted
- Kind: B2
- Application number: 16/959,184
- Filed: 2019-01-05
- Published: 2020-12-31
- Granted: 2022-09-20
- Earliest claimed: 2018-01-05
- Assignees: Yale University
- Applicants: Yale University
- Inventors: Liang Jiang; Steven M. Girvin; Brian Lester; Yvonne Gao; Robert J. Schoelkopf, III
- Web page: https://patentgrep.com/patent/US11451231B2

## CPC

- 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
- H01P 5/18: consisting of two coupled guides, e.g. directional couplers
- H03K 19/195: using superconductive devices
- B82Y 10/00: Nanotechnology for information processing, storage or transmission, e.g. quantum computing or single electron logic
- H10N 60/12: Josephson-effect devices
- G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- H01P: WAVEGUIDES; RESONATORS, LINES, OR OTHER DEVICES OF THE WAVEGUIDE TYPE (operating at optical frequencies G02B)
- 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)
- B82Y: SPECIFIC USES OR APPLICATIONS OF NANOSTRUCTURES; MEASUREMENT OR ANALYSIS OF NANOSTRUCTURES; MANUFACTURE OR TREATMENT OF NANOSTRUCTURES
- H10N: ELECTRIC SOLID-STATE DEVICES NOT OTHERWISE PROVIDED FOR

## Abstract

Techniques for implementing robust quantum logic gates are provided and described. In some aspects, a quantum logic gate between a plurality of cavities comprising a first cavity and a second cavity is implemented by performing a first beam splitter operation between the first cavity and the second cavity using a coupling transmon that is dispersively coupled to both the first cavity and the second cavity, and performing a controlled phase shift operation between the second cavity and an ancilla transmon that is dispersively coupled to the second cavity but not dispersively coupled to the first cavity.

## Claims

### Claim 1

A method for implementing a quantum logic gate between a plurality of cavities comprising a first cavity and a second cavity, the method comprising:
performing a first beam splitter (BS) operation between the first cavity and the second cavity using a coupling transmon that is dispersively coupled to both the first cavity and the second cavity; and
performing a controlled phase shift (CPS) operation between the second cavity and an ancilla transmon that is dispersively coupled to the second cavity but not dispersively coupled to the first cavity.

### Claim 2 (depends on 1)

The method of claim 1, further comprising performing a second BS operation between the first cavity and the second cavity using the coupling transmon, wherein the first BS operation is performed before the CPS operation and the second BS operation is performed after the CPS operation.

### Claim 3 (depends on 2)

The method of claim 2, wherein the quantum logic gate comprises a controlled-SWAP (c-SWAP) operation.

### Claim 4 (depends on 3)

The method of claim 3, wherein the quantum logic gate comprises an exponential-SWAP (e-SWAP) gate and the method comprises:
performing a first c-SWAP operation between the first cavity and the second cavity;
performing a second c-SWAP operation between the first cavity and the second cavity; and
performing a rotation operation on the ancilla transmon between the first c-SWAP operation and the second c-SWAP operation.

### Claim 5 (depends on 2)

The method of claim 2, wherein the quantum logic gate comprises an exponential-SWAP (e-SWAP) gate, the CPS operation is a first CPS operation and the method comprises:
performing a second CPS operation between the second cavity and the ancilla transmon after the first CPS operation and before the second BS operation; and
performing a rotation operation on the ancilla transmon between the first CPS operation and the second CPS operation.

### Claim 6 (depends on 5)

The method of claim 5, further comprising:
performing a first Hadamard operation before the first CPS operation and after the first BS operation; and
performing a second Hadamard operation after the second CPS operation and before the second BS operation.

### Claim 7 (depends on 6)

The method of claim 6, further comprising measuring the ancilla transmon.

### Claim 8 (depends on 7)

The method of claim 7, further comprising determining that a dephasing error a dephasing error occurred based on a result of measuring the ancilla transmon.

### Claim 9 (depends on 7)

The method of claim 7, wherein:
at least four energy levels of the ancilla transmon are used;
a first energy level of the ancilla transmon is associated with a first decay error type;
a second energy level of the ancilla transmon is associated with a second decay error type; and
the method further comprises correcting for decay errors based on a result of measuring the ancilla transmon.

### Claim 10 (depends on 1)

The method of claim 1, wherein at least one local quantum logic gate is performed on the ancilla transmon before and/or after the CPS operation.

### Claim 11 (depends on 10)

The method of claim 10, wherein:
the at least one local quantum logic gate comprises a first Hadamard operation performed after the BS operation and before the CPS operation; and
the method further comprises measuring the state of the ancilla transmon to compare the a first quantum state of the first cavity to a second quantum state of the second cavity.

### Claim 12 (depends on 2)

The method of claim 2, wherein:
the plurality of cavities further comprises a third cavity and a fourth cavity;
the coupling transmon is a first coupling transmon;
the ancilla transmon is dispersively coupled to the third cavity by not dispersively coupled to the fourth cavity;
the CPS operation is a first CPS operation; and
the method further comprises:
performing a third BS operation between the third cavity and the fourth cavity using a second coupling transmon that is dispersively coupled to both the third cavity and the fourth cavity; and
performing a second CPS operation between the third cavity and the ancilla transmon.

### Claim 13 (depends on 12)

The method of claim 12, wherein the method further comprises:
performing a fourth BS operation between the third cavity and the fourth cavity using the second coupling transmon, wherein the fourth BS operation is performed before the second CPS operation and the second BS operation is performed after the second CPS operation;
performing a third CPS operation between the third cavity and the ancilla transmon after the second CPS operation and before the fourth BS operation;
performing a rotation operation on the ancilla transmon between the second CPS operation and the third CPS operation; and
performing a fourth CPS operation between the second cavity and the ancilla transmon after the third CPS operation and before the second BS operation.

### Claim 14 (depends on 13)

The method of claim 13, wherein the method further comprises:
performing a first Hadamard operation before the first CPS operation and after the first and third BS operations; and
performing a second Hadamard operation after the fourth CPS operation and before the second and fourth BS operations.

### Claim 15

A multi-cavity quantum information system comprising:
a first cavity configured to support microwave radiation;
a second cavity configured to support microwave radiation;
a first transmon dispersively coupled to the first cavity;
a second transmon dispersively coupled to the second cavity;
a third transmon dispersively coupled to both the first cavity and the second cavity; and
a microwave source configured to:
apply microwave radiation to the third transmon to implement beam splitter operations between the first cavity and the second cavity and transmon rotation operations, and
apply microwave radiation to the first transmon and the second transmon to implement controlled phase shift operations on the first cavity and the second cavity, respectively.

### Claim 16 (depends on 15)

The multi-cavity quantum information system of claim 15, wherein the microwave source is further configured to apply microwave radiation to the first transmon and the second transmon to implement arbitrary rotation operation on the first transmon and the second transmon, respectively.

### Claim 17 (depends on 16)

The multi-cavity quantum information system of claim 16, wherein the microwave source is further configured to apply microwave radiation to the first, second and third transmon to implement a set of universal quantum gates between the first cavity and the second cavity.

### Claim 18 (depends on 15)

The multi-cavity quantum information system of claim 15, wherein the microwave source is further configured to apply microwave radiation to the first, second and third transmon to implement a controlled-SWAP gate between the first cavity and the second cavity.

### Claim 19 (depends on 15)

The multi-cavity quantum information system of claim 15, wherein the microwave source is further configured to apply microwave radiation to the first, second and third transmon to implement an exponential-SWAP gate between the first cavity and the second cavity.

### Claim 20 (depends on 15)

The multi-cavity quantum information system of claim 15, wherein the microwave source is further configured to:
apply microwave radiation to the first and/or second transmon to measure the first and/or second transmon; and
apply microwave radiation to the first, second, and/or third transmon to implement a quantum gate based on a result of measuring the first and/or second transmon.