# US 10,483,980 B2 · Parametrically activated quantum logic gates

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- Number: US 10,483,980 B2
- Document ID: US10483980B2
- Status: Granted
- Kind: B2
- Application number: 16/012,551
- Filed: 2018-06-19
- Published: 2019-01-03
- Granted: 2019-11-19
- Earliest claimed: 2017-06-19
- Assignees: Rigetti & Co, LLC
- Applicants: Rigetti & Co, Inc.
- Inventors: Eyob A. Sete; Nicolas Didier; Marcus Palmer da Silva; Chad Tyler Rigetti; Matthew J. Reagor; Shane Arthur Caldwell; Nikolas Anton Tezak; Colm Andrew Ryan; Sabrina Sae Byul Hong; Prasahnt Sivarajah; Alexander Papageorge; Deanna Margo Abrams
- Web page: https://patentgrep.com/patent/US10483980B2

## CPC

- H03K 19/195: using 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
- 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

## Abstract

In a general aspect, a quantum logic gate is performed in a quantum computing system. In some cases, a pair of qubits are defined in a quantum processor; the pair of qubits can include a first qubit defined by a first qubit device in the quantum processor and a second qubit defined by a tunable qubit device in the quantum processor. A quantum logic gate can be applied to the pair of qubits by communicating a control signal to a control line coupled to the tunable qubit device. The control signal can be configured to modulate a transition frequency of the tunable qubit device at a modulation frequency, and the modulation frequency can be determined based on a transition frequency of the first qubit device.

## Claims

### Claim 1

A method comprising:
obtaining operating parameters for one or more of a plurality of qubit devices in a quantum processor circuit, the plurality of qubit devices comprising a fixed-frequency qubit device and a tunable qubit device, the operating parameters based on measurements of the quantum processor circuit under an operating condition, the operating condition comprising a flux modulation applied to the tunable qubit device; and
based on the operating parameters, selecting gate parameters of a two-qubit quantum logic gate for application to a pair of qubits defined by the fixed-frequency qubit device and the tunable qubit device;
generating a control signal configured to modulate, at a modulation frequency, a transition frequency of the tunable qubit device, the modulation frequency being determined based on a transition frequency of the fixed-frequency qubit device; and
applying the two-qubit quantum logic gate to the pair of qubits by communicating the control signal to a control line coupled to the tunable qubit device;
wherein the control signal is a first control signal, the modulation frequency is a first modulation frequency, the fixed-frequency qubit device is a first fixed-frequency qubit device that defines a first qubit, the two-qubit quantum logic gate is a first two-qubit quantum logic gate, the pair of qubits is a first pair of qubits, and the method further comprises:
generating a second control signal configured to modulate the transition frequency of the tunable qubit device at a second modulation frequency, the second modulation frequency being determined based on a transition frequency of a second fixed-frequency qubit device in the quantum processor circuit; and
applying a second two-qubit quantum logic gate to a second pair of qubits in the quantum processor circuit by communicating the second control signal to the control line coupled to the tunable qubit device, the second pair of qubits comprising a second qubit defined by the tunable qubit device and a third qubit defined by the second fixed-frequency qubit device.

### Claim 2 (depends on 1)

The method of claim 1, wherein the operating parameters include an effective coupling strength between the qubit devices during the flux modulation.

### Claim 3 (depends on 1)

The method of claim 1, wherein the operating parameters are obtained for a range of modulation amplitude of the flux modulation.

### Claim 4 (depends on 1)

The method of claim 1, wherein selecting gate parameters comprises selecting initial gate parameters, and the method further comprises generating refined gate parameters from the initial gate parameters.

### Claim 5 (depends on 4)

The method of claim 4, wherein the refined gate parameters are generated based on spectroscopic measurements of the two-qubit quantum logic gate applied to the quantum processor circuit.

### Claim 6 (depends on 1)

The method of claim 1, wherein the gate parameters include a flux modulation amplitude and a flux modulation frequency.

### Claim 7 (depends on 6)

The method of claim 6, further comprising selecting a filter for a flux modulation control line based on the flux modulation frequency.

### Claim 8 (depends on 1)

The method of claim 1, wherein selecting gate parameters of a two-qubit quantum logic gate comprises selecting parameters of the control signal for delivery to the control line coupled to the tunable qubit device, and the gate parameters correspond to:
a modulation amplitude of the flux modulation produced by the control signal;
the modulation frequency of the flux modulation produced by the control signal; and
a duration of the control signal.

### Claim 9 (depends on 8)

The method of claim 8, further comprising identifying single-qubit phase corrections for the two-qubit quantum logic gate.

### Claim 10 (depends on 1)

The method of claim 1, wherein selecting gate parameters of a two-qubit quantum logic gate comprises selecting gate parameters of a Bell-Rabi gate, a controlled-Z gate, an iSWAP gate or a square-root-of-iSWAP gate.

### Claim 11 (depends on 1)

The method of claim 1, further comprising benchmarking the two-qubit quantum logic gate based on the selected gate parameters.

### Claim 12 (depends on 1)

The method of claim 1, wherein:
the tunable qubit device comprises a superconducting circuit loop that receives a first magnetic flux that tunes the transition frequency of the tunable qubit device, and the control line comprises a flux-bias device that is inductively coupled to the superconducting circuit loop to control the first magnetic flux; and
generating the control signal to modulate the transition frequency of the tunable qubit device at the modulation frequency comprises generating the control signal to modulate the first magnetic flux at half the modulation frequency.

### Claim 13 (depends on 1)

The method of claim 1, wherein:
the tunable qubit device comprises a superconducting circuit loop that receives a first magnetic flux that tunes the transition frequency of the tunable qubit device, and the control line comprises a flux-bias device that is inductively coupled to the superconducting circuit loop to control the first magnetic flux; and
generating the control signal to modulate the transition frequency of the tunable qubit device at the modulation frequency comprises generating the control signal to modulate the first magnetic flux at the modulation frequency.

### Claim 14 (depends on 1)

The method of claim 1, wherein the operating condition comprises the flux modulation applied to the tunable qubit device at a flux modulation frequency between 0.02 GigaHertz and 0.40 GigaHertz.

### Claim 15 (depends on 1)

The method of claim 1, wherein the operating condition comprises the flux modulation applied to the tunable qubit device at a flux modulation frequency between 40 MegaHertz and 160 MegaHertz.

### Claim 16

A method comprising:
obtaining measurements of a coherence time of a qubit defined by a tunable qubit device in a quantum processor circuit comprising a plurality of qubit devices, the plurality of qubit devices comprising a fixed-frequency qubit device coupled to the tunable qubit device, the measurements representing values of the coherence time during a flux modulation applied to the tunable qubit device, the measurements corresponding to a range of modulation amplitudes of the flux modulation;
based on the measurements, identifying a modulation amplitude control value associated with a maximum coherence time of the qubit; and
based on the identified modulation amplitude control value, selecting a gate parameter of a two-qubit quantum logic gate for the fixed-frequency qubit device and the tunable qubit device;
wherein identifying the modulation amplitude control value comprises identifying a first modulation amplitude control value corresponding to the maximum measurement of the coherence time.

### Claim 17 (depends on 16)

The method of claim 16, wherein the tunable qubit device comprises a superconducting circuit loop that defines a flux quantum Φ0 and receives a first magnetic flux that tunes a transition frequency of the tunable qubit device, and the flux modulation comprises a modulation of the first magnetic flux at a modulation frequency.

### Claim 18 (depends on 17)

The method of claim 17, wherein the modulation amplitude control value represents a voltage amplitude of a control signal that produces the modulation of the first magnetic flux.

### Claim 19 (depends on 17)

The method of claim 17, wherein the modulation amplitude control value corresponds to a flux modulation amplitude between 0.45Φ0 and 0.65Φ0.

### Claim 20 (depends on 16)

The method of claim 16, wherein the fixed-frequency qubit device is a first fixed-frequency qubit device, and the plurality of qubit devices comprises:
the tunable qubit device; and
a plurality of fixed-frequency qubit devices each capacitively coupled to the tunable qubit device, wherein the plurality of fixed-frequency qubit devices includes the first fixed-frequency qubit device.

### Claim 21 (depends on 16)

The method of claim 16, wherein the gate parameters include the first modulation amplitude control value.

### Claim 22 (depends on 16)

The method of claim 16, wherein:
the tunable qubit device comprises a superconducting circuit loop that defines a flux quantum;
the first modulation amplitude control value corresponds to a first flux modulation amplitude; and
the gate parameters include a second modulation amplitude control value that corresponds to a second flux modulation amplitude, wherein the magnitude of difference between the first flux modulation amplitude and the second flux modulation amplitude is less than 0.1 of the flux quantum.

### Claim 23 (depends on 22)

The method of claim 22, comprising:
after identifying the first modulation amplitude, obtaining spectroscopic measurements of the two-qubit quantum logic gate applied to a pair of qubits defined by the fixed-frequency qubit device and the tunable qubit device; and
identifying the second modulation amplitude control value based on the spectroscopic measurements.

### Claim 24 (depends on 16)

The method of claim 16, wherein the coherence time is a transverse coherence time T2.

### Claim 25 (depends on 16)

The method of claim 16, further comprising obtaining measurements of a transition frequency shift of the tunable qubit device during a flux modulation applied to the tunable qubit device, the measurements of the transition frequency shift corresponding to a range of modulation amplitudes of the flux modulation, wherein the gate parameters are selected based in part on the measurements of the transition frequency shift.

### Claim 26

A method comprising:
obtaining measurements of a quantum processor circuit comprising a plurality of qubit devices, the plurality of qubit devices comprising a fixed-frequency qubit device and a tunable qubit device;
based on the measurements and by operation of one or more processors, computing multiple distinct gate conditions for applying a two-qubit quantum logic gate to a pair of qubits defined by the fixed-frequency qubit device and the tunable qubit device;
identifying one or more of the distinct gate conditions that satisfy an operating criterion associated with the two-qubit quantum logic gate;
based on the one or more gate conditions that satisfy the operating criterion, selecting gate parameters for the two-qubit quantum logic gate;
wherein:
obtaining measurements of the quantum processor circuit includes obtaining measurements of a mean transition frequency of the tunable qubit device during a flux modulation applied to the tunable qubit device, the measurements of the mean transition frequency corresponding to a range of modulation amplitudes of the flux modulation, and
the gate parameters are selected based in part on the measurements of the mean transition frequency;
generating a first control signal configured to modulate a transition frequency of the tunable qubit device at a first modulation frequency; and
applying the two-qubit quantum logic gate to the pair of qubits by communicating the control signal to a control line coupled to the tunable qubit device;
wherein the fixed-frequency qubit device is a first fixed-frequency qubit device that defines a first qubit, the two-qubit quantum logic gate is a first two-qubit quantum logic gate, the pair of qubits is a first pair of qubits, and the method further comprises:
generating a second control signal configured to modulate the transition frequency of the tunable qubit device at a second modulation frequency; and
applying a second two-qubit quantum logic gate to a second pair of qubits in the quantum processor circuit by communicating the second control signal to the control line coupled to the tunable qubit device, the second pair of qubits comprising a second qubit defined by the tunable qubit device and a third qubit defined by a second fixed-frequency qubit device.

### Claim 27 (depends on 26)

The method of claim 26, further comprising identifying resonant conditions for a plurality of transitions to be suppressed in the quantum processor circuit during application of the two-qubit quantum logic gate, wherein the one or more gate conditions that satisfy the operating criterion are identified based on avoiding the resonant conditions.

### Claim 28 (depends on 26)

The method of claim 26, wherein identifying one or more of the distinct gate conditions that satisfy the operating criterion comprises identifying a gate condition that is at least a minimum distance, in a modulation frequency and modulation amplitude domain, from resonant conditions of transitions to be suppressed in the quantum processor circuit during application of the two-qubit quantum logic gate.

### Claim 29 (depends on 26)

The method of claim 26, wherein the tunable qubit device comprises a superconducting circuit loop that defines a flux quantum Φ0 and receives a first magnetic flux that tunes a transition frequency of the tunable qubit device, and applying the two-qubit quantum logic gate comprises modulating the first magnetic flux at a modulation frequency.

### Claim 30 (depends on 26)

The method of claim 26, wherein the multiple distinct gate conditions are computed for a range of modulation amplitudes, and each distinct gate condition includes:
a modulation amplitude of a flux modulation;
a modulation frequency of the flux modulation; and
a duration of the flux modulation.

### Claim 31 (depends on 30)

The method of claim 30, wherein identifying one or more of the distinct gate conditions that satisfy an operating criterion associated with the two-qubit quantum logic gate comprises identifying the gate condition that includes the minimum duration.

### Claim 32 (depends on 26)

The method of claim 26, comprising identifying one or more of the distinct gate conditions that satisfy multiple operating criteria associated with the two-qubit quantum logic gate.

### Claim 33 (depends on 26)

The method of claim 26, wherein each of distinct gate conditions includes a modulation frequency that is based on:
a transition frequency of the tunable qubit device; and
a transition frequency of the fixed-frequency qubit device.

### Claim 34 (depends on 33)

The method of claim 33, wherein each of the distinct gate conditions further includes a modulation amplitude, and the modulation frequency in each gate condition is based on a transition frequency shift of the tunable qubit device under the modulation amplitude included in the gate condition.

### Claim 35 (depends on 26)

The method of claim 26, wherein selecting gate parameters for the two-qubit quantum logic gate comprises selecting parameters of a control signal for delivery to the control line coupled to the tunable qubit device, and the gate parameters correspond to:
a modulation amplitude of a flux modulation produced by the control signal;
a modulation frequency of the flux modulation produced by the control signal; and
a duration of the control signal.

### Claim 36 (depends on 35)

The method of claim 35, further comprising identifying single-qubit phase corrections for the two-qubit quantum logic gate.

### Claim 37 (depends on 26)

The method of claim 26, wherein selecting gate parameters for the two-qubit quantum logic gate comprises selecting gate parameters of a Bell-Rabi gate, a controlled-Z gate, an iSWAP gate or a square-root-of-iSWAP gate.

### Claim 38 (depends on 26)

The method of claim 26, further comprising benchmarking the two-qubit quantum logic gate based on the selected gate parameters.

### Claim 39

A method comprising:
obtaining measurements of a quantum processor circuit comprising a plurality of qubit devices, the plurality of qubit devices comprising a fixed-frequency qubit device and a tunable qubit device;
based on the measurements and by operation of one or more processors, computing multiple distinct gate conditions for applying a two-qubit quantum logic gate to a pair of qubits defined by the fixed-frequency qubit device and the tunable qubit device;
identifying one or more of the distinct gate conditions that satisfy an operating criterion associated with the two-qubit quantum logic gate;
based on the one or more gate conditions that satisfy the operating criterion, selecting gate parameters for the two-qubit quantum logic gate;
wherein the multiple distinct gate conditions are computed for a range of modulation amplitudes, and each distinct gate condition includes:
a modulation amplitude of a flux modulation;
a modulation frequency of the flux modulation; and
a duration of the flux modulation,
generating a first control signal configured to modulate a transition frequency of the tunable qubit device at a first modulation frequency; and
applying the two-qubit quantum logic gate to the pair of qubits by communicating the control signal to a control line coupled to the tunable qubit device;
wherein the fixed-frequency qubit device is a first fixed-frequency qubit device that defines a first qubit, the two-qubit quantum logic gate is a first two-qubit quantum logic gate, the pair of qubits is a first pair of qubits, and the method further comprises:
generating a second control signal configured to modulate the transition frequency of the tunable qubit device at a second modulation frequency; and
applying a second two-qubit quantum logic gate to a second pair of qubits in the quantum processor circuit by communicating the second control signal to the control line coupled to the tunable qubit device, the second pair of qubits comprising a second qubit defined by the tunable qubit device and a third qubit defined by a second fixed-frequency qubit device.

### Claim 40 (depends on 39)

The method of claim 39, further comprising identifying resonant conditions for a plurality of transitions to be suppressed in the quantum processor circuit during application of the two-qubit quantum logic gate, wherein the one or more gate conditions that satisfy the operating criterion are identified based on avoiding the resonant conditions.

### Claim 41 (depends on 39)

The method of claim 39, wherein identifying one or more of the distinct gate conditions that satisfy the operating criterion comprises identifying a gate condition that is at least a minimum distance, in a modulation frequency and modulation amplitude domain, from resonant conditions of transitions to be suppressed in the quantum processor circuit during application of the two-qubit quantum logic gate.

### Claim 42 (depends on 39)

The method of claim 39, wherein the tunable qubit device comprises a superconducting circuit loop that defines a flux quantum Φ0 and receives a first magnetic flux that tunes a transition frequency of the tunable qubit device, and applying the two-qubit quantum logic gate comprises modulating the first magnetic flux at a modulation frequency.

### Claim 43 (depends on 39)

The method of claim 39, wherein:
obtaining measurements of the quantum processor circuit includes obtaining measurements of a mean transition frequency of the tunable qubit device during a flux modulation applied to the tunable qubit device, the measurements of the mean transition frequency corresponding to a range of modulation amplitudes of the flux modulation, and
the gate parameters are selected based in part on the measurements of the mean transition frequency.

### Claim 44 (depends on 39)

The method of claim 39, wherein identifying one or more of the distinct gate conditions that satisfy an operating criterion associated with the two-qubit quantum logic gate comprises identifying the gate condition that includes the minimum duration.

### Claim 45 (depends on 39)

The method of claim 39, comprising identifying one or more of the distinct gate conditions that satisfy multiple operating criteria associated with the two-qubit quantum logic gate.

### Claim 46 (depends on 39)

The method of claim 39, wherein each of distinct gate conditions includes a modulation frequency that is based on:
a transition frequency of the tunable qubit device; and
a transition frequency of the fixed-frequency qubit device.

### Claim 47 (depends on 46)

The method of claim 46, wherein each of the distinct gate conditions further includes a modulation amplitude, and the modulation frequency in each gate condition is based on a transition frequency shift of the tunable qubit device under the modulation amplitude included in the gate condition.

### Claim 48 (depends on 39)

The method of claim 39, wherein selecting gate parameters for the two-qubit quantum logic gate comprises selecting parameters of a control signal for delivery to the control line coupled to the tunable qubit device, and the gate parameters correspond to:
a modulation amplitude of a flux modulation produced by the control signal;
a modulation frequency of the flux modulation produced by the control signal; and
a duration of the control signal.

### Claim 49 (depends on 48)

The method of claim 48, further comprising identifying single-qubit phase corrections for the two-qubit quantum logic gate.

### Claim 50 (depends on 39)

The method of claim 39, wherein selecting gate parameters for the two-qubit quantum logic gate comprises selecting gate parameters of a Bell-Rabi gate, a controlled-Z gate, an iSWAP gate or a square-root-of-iSWAP gate.

### Claim 51 (depends on 39)

The method of claim 39, further comprising benchmarking the two-qubit quantum logic gate based on the selected gate parameters.

### Claim 52

A method comprising:
obtaining measurements of a quantum processor circuit comprising a plurality of qubit devices, the plurality of qubit devices comprising a fixed-frequency qubit device and a tunable qubit device;
based on the measurements and by operation of one or more processors, computing multiple distinct gate conditions for applying a two-qubit quantum logic gate to a pair of qubits defined by the fixed-frequency qubit device and the tunable qubit device;
identifying one or more of the distinct gate conditions that satisfy an operating criterion associated with the two-qubit quantum logic gate;
based on the one or more gate conditions that satisfy the operating criterion, selecting gate parameters for the two-qubit quantum logic gate;
wherein selecting gate parameters for the two-qubit quantum logic gate comprises selecting parameters of a control signal for delivery to a control line coupled to the tunable qubit device, and the gate parameters correspond to:
a modulation amplitude of a flux modulation produced by the control signal;
a modulation frequency of the flux modulation produced by the control signal; and
a duration of the control signal,
generating a first control signal configured to modulate a transition frequency of the tunable qubit device at a first modulation frequency; and
applying the two-qubit quantum logic gate to the pair of qubits by communicating the first control signal to the control line coupled to the tunable qubit device;
wherein the fixed-frequency qubit device is a first fixed-frequency qubit device that defines a first qubit, the two-qubit quantum logic gate is a first two-qubit quantum logic gate, the pair of qubits is a first pair of qubits, and the method further comprises:
generating a second control signal configured to modulate the transition frequency of the tunable qubit device at a second modulation frequency; and
applying a second two-qubit quantum logic gate to a second pair of qubits in the quantum processor circuit by communicating the second control signal to the control line coupled to the tunable qubit device, the second pair of qubits comprising a second qubit defined by the tunable qubit device and a third qubit defined by a second fixed-frequency qubit device.

### Claim 53 (depends on 52)

The method of claim 52, further comprising identifying resonant conditions for a plurality of transitions to be suppressed in the quantum processor circuit during application of the two-qubit quantum logic gate, wherein the one or more gate conditions that satisfy the operating criterion are identified based on avoiding the resonant conditions.

### Claim 54 (depends on 52)

The method of claim 52, wherein identifying one or more of the distinct gate conditions that satisfy the operating criterion comprises identifying a gate condition that is at least a minimum distance, in a modulation frequency and modulation amplitude domain, from resonant conditions of transitions to be suppressed in the quantum processor circuit during application of the two-qubit quantum logic gate.

### Claim 55 (depends on 52)

The method of claim 52, wherein the tunable qubit device comprises a superconducting circuit loop that defines a flux quantum Φ0 and receives a first magnetic flux that tunes a transition frequency of the tunable qubit device, and applying the two-qubit quantum logic gate comprises modulating the first magnetic flux at a modulation frequency.

### Claim 56 (depends on 52)

The method of claim 52, wherein:
obtaining measurements of the quantum processor circuit includes obtaining measurements of a mean transition frequency of the tunable qubit device during a flux modulation applied to the tunable qubit device, the measurements of the mean transition frequency corresponding to a range of modulation amplitudes of the flux modulation, and
the gate parameters are selected based in part on the measurements of the mean transition frequency.

### Claim 57 (depends on 52)

The method of claim 52, wherein the multiple distinct gate conditions are computed for a range of modulation amplitudes, and each distinct gate condition includes:
a modulation amplitude of a flux modulation;
a modulation frequency of the flux modulation; and
a duration of the flux modulation.

### Claim 58 (depends on 57)

The method of claim 57, wherein identifying one or more of the distinct gate conditions that satisfy an operating criterion associated with the two-qubit quantum logic gate comprises identifying the gate condition that includes the minimum duration.

### Claim 59 (depends on 52)

The method of claim 52, comprising identifying one or more of the distinct gate conditions that satisfy multiple operating criteria associated with the two-qubit quantum logic gate.

### Claim 60 (depends on 52)

The method of claim 52, wherein each of distinct gate conditions includes a modulation frequency that is based on:
a transition frequency of the tunable qubit device; and
a transition frequency of the fixed-frequency qubit device.

### Claim 61 (depends on 60)

The method of claim 60, wherein each of the distinct gate conditions further includes a modulation amplitude, and the modulation frequency in each gate condition is based on a transition frequency shift of the tunable qubit device under the modulation amplitude included in the gate condition.

### Claim 62 (depends on 52)

The method of claim 52, further comprising identifying single-qubit phase corrections for the two-qubit quantum logic gate.

### Claim 63 (depends on 52)

The method of claim 52, wherein selecting gate parameters for the two-qubit quantum logic gate comprises selecting gate parameters of a Bell-Rabi gate, a controlled-Z gate, an iSWAP gate or a square-root-of-iSWAP gate.

### Claim 64 (depends on 52)

The method of claim 52, further comprising benchmarking the two-qubit quantum logic gate based on the selected gate parameters.