# US 9,438,245 B2 · Reducing spontaneous emission in circuit quantum electrodynamics by a combined readout and filter technique

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- Number: US 9,438,245 B2
- Document ID: US9438245B2
- Status: Granted
- Kind: B2
- Application number: 14/512,489
- Filed: 2014-10-13
- Published: 2016-06-02
- Granted: 2016-09-06
- Earliest claimed: 2014-10-13
- Assignees: International Business Machines Corporation
- Applicants: International Business Machines Corporation
- Inventors: Nicholas T. Bronn; Jerry M. Chow; Jay M. Gambetta; Nicholas A. Masluk; Matthias Steffen
- Web page: https://patentgrep.com/patent/US9438245B2

## CPC

- H03K 19/00346: {Modifications for eliminating interference or parasitic voltages or currents}
- B82Y 10/00: Nanotechnology for information processing, storage or transmission, e.g. quantum computing or single electron logic
- 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
- H03K 19/195: using superconductive devices
- 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
- G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS

## Abstract

A mechanism relates a superconductor circuit. A Δ circuit includes a first node connecting a Purcell capacitor to a qubit coupling capacitor, a second node connecting the Purcell capacitor to a readout coupling capacitor, and a third node connecting the qubit coupling capacitor to the readout coupling capacitor. A qubit is connected to the first node and has a qubit frequency. A readout resonator connects to the third node combining with the Purcell capacitor to form a filter. Capacitance of the Purcell capacitor is determined as a factor of the qubit frequency of the qubit and blocks emissions of the qubit at the qubit frequency. Capacitance of the Purcell capacitor causes destructive interference, between a first path containing Purcell capacitor and a second path containing both the qubit coupling capacitor and readout coupling capacitor, in order to block emissions of the qubit at the qubit frequency to the external environment.

## Claims

### Claim 1

A superconductor circuit comprising:
a delta (Δ) circuit comprising a first node connecting a Purcell capacitor (CP) to a qubit coupling capacitor (Cq), a second node connecting the Purcell capacitor (CP) to a readout coupling capacitor (Cc), and a third node connecting the qubit coupling capacitor (Cq) to the readout coupling capacitor (Cc);
a qubit connected to the first node, wherein the qubit has a qubit frequency;
a readout resonator connected to the third node, wherein the readout resonator combines with the Purcell capacitor (CP) to form a filter; and
the second node configured for connection to an external environment;
wherein capacitance of the Purcell capacitor (CP) is determined as a factor of the qubit frequency of the qubit, such that the capacitance of the Purcell capacitor (CP) blocks emissions of the qubit at the qubit frequency to the external environment; and
wherein the capacitance of the Purcell capacitor (CP) is set to cause destructive interference, between a first path containing the Purcell capacitor (CP) and a second path containing both the qubit coupling capacitor (Cq) and the readout coupling capacitor (Cc), at the qubit frequency in order to block the emissions of the qubit at the qubit frequency to the external environment.

### Claim 2 (depends on 1)

The superconductor circuit of claim 1, wherein the capacitance of the Purcell capacitor (CP) has a direct relationship to the qubit frequency of the qubit in which the capacitance of the Purcell capacitor (CP) is to be increased when a value of the qubit frequency is increased in order to block the qubit frequency to the external environment.

### Claim 3 (depends on 1)

The superconductor circuit of claim 1, wherein the readout resonator further possesses an inductance and a capacitance connected in parallel together.

### Claim 4 (depends on 1)

The superconductor circuit of claim 1, wherein the readout resonator provides dispersive readout of the qubit to the external environment.

### Claim 5 (depends on 4)

The superconductor circuit of claim 4, wherein the readout resonator combined with the Purcell capacitor (CP) provides filtering at the qubit frequency of radiation from the qubit to the external environment.

### Claim 6 (depends on 3)

The superconductor circuit of claim 3, wherein the capacitance of the Purcell capacitor (CP) is determined based on factors which include the qubit frequency of the qubit, the inductance of the readout resonator, and the capacitance of the readout resonator such that the capacitance of the Purcell capacitor (CP) blocks emissions of the qubit at the qubit frequency to the external environment while allowing dispersive readout of a state of the qubit.

### Claim 7 (depends on 1)

The superconductor circuit of claim 1, wherein the qubit includes a Josephson junction.

### Claim 8 (depends on 1)

The superconductor circuit of claim 1, wherein the Δ circuit has a relationship to a Y circuit;
wherein the capacitance of the Purcell capacitor (CP) is determined based on the relationship between the Δ circuit and the Y circuit.

### Claim 9

A method of providing a superconductor circuit, the method comprising:
providing a delta (Δ) circuit comprising a first node connecting a Purcell capacitor (CP) to a qubit coupling capacitor (Cq), a second node connecting the Purcell capacitor (CP) to a readout coupling capacitor (Cc), and a third node connecting the qubit coupling capacitor (Cq) to the readout coupling capacitor (Cc);
providing a qubit connected to the first node, wherein the qubit has a qubit frequency; and
forming a readout resonator connected to the third node, wherein the readout resonator combines with the Purcell capacitor (CP) to form a filter;
wherein the second node is configured for connection to an external environment;
wherein capacitance of the Purcell capacitor (CP) is determined as a factor of the qubit frequency of the qubit, such that the capacitance of the Purcell capacitor (CP) blocks emissions of the qubit at the qubit frequency to the external environment; and
wherein the capacitance of the Purcell capacitor (CP) is set to cause destructive interference, between a first path containing the Purcell capacitor (CP) and a second path containing both the qubit coupling capacitor (Cq) and the readout coupling capacitor (Cc), at the qubit frequency in order to block the emissions of the qubit at the qubit frequency to the external environment.

### Claim 10 (depends on 9)

The method of claim 9, wherein the capacitance of the Purcell capacitor (CP) has a direct relationship to the qubit frequency of the qubit in which the capacitance of the Purcell capacitor (CP) is to be increased when a value of the qubit frequency is increased in order to block the qubit frequency to the external environment.

### Claim 11 (depends on 9)

The method of claim 9, wherein the readout resonator further possesses an inductance and a capacitance connected in parallel together.

### Claim 12 (depends on 9)

The method of claim 9, wherein the readout resonator provides dispersive readout of the qubit to the external environment.

### Claim 13 (depends on 12)

The method of claim 12, wherein the readout resonator combined with the Purcell capacitor (CP) provides filtering at the qubit frequency of radiation from the qubit to the external environment.

### Claim 14 (depends on 12)

The method of claim 12, wherein the capacitance of the Purcell capacitor (CP) is determined based on factors which include the qubit frequency of the qubit, an inductance of the readout resonator, and a capacitance of the readout resonator such that the capacitance of the Purcell capacitor (CP) blocks emissions of the qubit at the qubit frequency to the external environment while allowing dispersive readout of a state of the qubit.

### Claim 15 (depends on 9)

The method of claim 9, wherein the qubit includes a Josephson junction.

### Claim 16 (depends on 9)

The method of claim 9, wherein the Δ circuit has a relationship to a Y circuit;
wherein the capacitance of the Purcell capacitor (CP) is determined based on the relationship between the Δ circuit and the Y circuit.

### Claim 17

A superconductor circuit comprising:
a qubit connected to a qubit coupling capacitor (C′q), wherein the qubit has a qubit frequency;
a combination readout resonator and filter including a Purcell capacitor (C′P), the Purcell capacitor (C′P) being connected to the qubit coupling capacitor (C′q);
a readout coupling capacitor (C′c) connected to the Purcell capacitor (C′P) and the qubit coupling capacitor (C′q), the readout coupling capacitor (C′c) configured for connection to an external environment;
wherein capacitance of the Purcell capacitor (C′P) is determined as a factor of the qubit frequency of the qubit, such that the capacitance of the Purcell capacitor (C′P) blocks emissions of the qubit at the qubit frequency to the external environment; and
wherein the capacitance of the Purcell capacitor (C′P) is set to short the combination readout resonator and filter including the Purcell capacitor (C′P) to ground at the qubit frequency in order to block the emissions of the qubit at the qubit frequency to the external environment.

### Claim 18 (depends on 17)

The superconductor circuit of claim 17, wherein the capacitance of the Purcell capacitor (C′P) has an inverse relationship to the qubit frequency of the qubit in which the capacitance of the Purcell capacitor (C′P) is to be decreased when a value of the qubit frequency is increased in order to block the qubit frequency to the external environment.

### Claim 19 (depends on 17)

The superconductor circuit of claim 17, wherein the combination readout resonator and filter further includes a readout resonator inductance and a readout resonator capacitance connected in parallel together;
wherein the readout resonator is connected in series to the Purcell capacitor (C′P), thereby forming the combination readout resonator and filter.

### Claim 20 (depends on 17)

The superconductor circuit of claim 17, wherein the combination readout resonator and filter provides dispersive readout of the qubit to the external environment.

### Claim 21

A method for a superconductor circuit, the method comprising:
providing a qubit connected to a qubit coupling capacitor (C′q), wherein the qubit has a qubit frequency;
forming a combination readout resonator and filter including a Purcell capacitor (C′P), the Purcell capacitor (C′P) being connected to the qubit coupling capacitor (C′q); and
providing a readout coupling capacitor (C′c) connected to the Purcell capacitor (C′P) and the qubit coupling capacitor (C′q), the readout coupling capacitor (C′c) configured for connection to an external environment;
wherein capacitance of the Purcell capacitor (C′P) is determined as a factor of the qubit frequency of the qubit, such that the capacitance of the Purcell capacitor (C′P) blocks emissions of the qubit at the qubit frequency to the external environment; and
wherein the capacitance of the Purcell capacitor (C′P) is set to short the combination readout resonator and filter to ground at the qubit frequency in order to block the emissions of the qubit at the qubit frequency to the external environment.

### Claim 22 (depends on 21)

The method of claim 21, wherein the capacitance of the Purcell capacitor (C′P) has an inverse relationship to the qubit frequency of the qubit in which the capacitance of the Purcell capacitor (C′P) is to be decreased when a value of the qubit frequency is increased in order to block the qubit frequency to the external environment.

### Claim 23 (depends on 21)

The method of claim 21, wherein the combination readout resonator and filter further includes a readout resonator inductance and a readout resonator capacitance connected in parallel together;
wherein the readout resonator is connected in series to the Purcell capacitor (C′P), thereby forming the combination readout resonator and filter.

### Claim 24 (depends on 21)

The method of claim 21, wherein the combination readout resonator and filter provides dispersive readout of the qubit to the external environment.

### Claim 25

A superconductor circuit comprising:
a delta (Δ) circuit comprising a first node connecting a Purcell capacitor (CP) to a qubit coupling capacitor (Cq), a second node connecting the Purcell capacitor (CP) to a readout coupling capacitor (Cc), and a third node connecting the qubit coupling capacitor (Cq) to the readout coupling capacitor (Cc);
a qubit connected to the first node, wherein the qubit has a qubit frequency;
a readout resonator connected to the third node, wherein the readout resonator combines with the Purcell capacitor (CP) to form a filter; and
the second node configured for connection to the external environment;
wherein the delta circuit is equivalent to a Y circuit;
wherein the Y circuit includes a qubit coupling capacitor (C′q), a Purcell capacitor (C′P), and a readout coupling capacitor (C′c);
wherein capacitances of the Purcell capacitor (CP), the qubit coupling capacitor (Cq), and the readout coupling capacitor (Cc) are determined by a Δ-Y transformation as follows:
C
q
=
C
q
′
⁢
C
c
′
+
C
c
′
⁢
C
P
′
+
C
P
′
⁢
C
q
′
C
c
′
;
C
c
=
C
q
′
⁢
C
c
′
+
C
c
′
⁢
C
P
′
+
C
P
′
⁢
C
q
′
C
q
′
;
⁢
and
C
P
=
C
q
′
⁢
C
c
′
+
C
c
′
⁢
C
P
′
+
C
P
′
⁢
C
q
′
C
P
′
.