Superconducting qubit and resonator system based on Josephson ring modulator

Abstract

The superconducting quantum mechanical device includes first, second, third, and fourth Josephson junctions connected in a bridge circuit having first, second, and third resonant eigenmodes. The device also includes first and second capacitor pads. The first and second capacitor pads and the bridge circuit form a superconducting qubit having a resonant frequency corresponding to the first resonant eigenmode. The device further includes first and second resonator sections. The first and second resonator sections and the bridge circuit form a resonator having a resonant frequency corresponding to the second resonant eigenmode. The device also includes a magnetic flux source disposed near the bridge circuit. The magnetic flux source is configured to provide a magnetic flux through the bridge circuit during operation such that, when the third resonant eigenmode is excited, coupling occurs between the first, second, and third resonant eigenmodes.

Description

[Technical field]

[0001] SUMMARY OF THE DISCLOSURE The presently claimed embodiments of the invention relate to superconducting quantum mechanical devices, and more particularly to superconducting quantum mechanical devices having superconducting qubits coupled to superconducting resonators within the device. [Background technology]

[0002] Circuit quantum electrodynamics (cQED) is a fundamental and common building block in quantum processor architectures. cQED consists of a superconducting qubit coupled to a superconducting resonator. The resonant frequencies of the qubit and the resonator are usually different. For example, the qubit frequency can be around 5 GHz, while the resonator frequency can be around 7 GHz. When the frequencies are different, the coupling is called dispersive coupling. There are various types of qubits that can be used, such as transmon, fluxonium, and capacitively-shunted qubits. There are also various geometries of superconducting resonators that can be used, such as coplanar waveguide resonators, stripline resonators, microstrip resonators, and three-dimensional cavities. Examples of superconducting materials that can be used for the resonators include, but are not limited to, Nb, Al, TiN, NbTiN, and NbN. Various mechanisms can be employed to couple the qubit to the resonator, including electrostatic coupling (eg, via a capacitor) or inductive coupling (eg, via mutual inductance).

[0003] cQEDs have many applications: 1) the resonator acts as a bandpass filter between the qubit and the external circuitry, filtering out noise coming through the line at the qubit frequency; 2) the qubit can be driven and controlled by injecting qubit pulses through the resonator port; and 3) the qubit state can be measured by detecting changes in the resonator frequency that affect the qubit state.

[0004] To measure the state of a qubit using a cQED architecture, a readout signal close to the readout resonator frequency is sent to the resonator. Due to the (electrostatic or inductive) coupling between the qubit and the resonator, the resonator frequency depends on the qubit state. In other words, the resonant frequency of the readout resonator when the qubit is in the ground state is different from when the qubit is in the excited state. Due to the readout resonator resonant frequency dependence of the qubit state, the frequency of the readout signal is set to be halfway between these two resonant frequencies. Since the phase shift of the reflected readout signal differs depending on the readout resonator resonant frequency, which depends on the qubit state, it is possible to determine the qubit state by monitoring or measuring this phase shift.

[0005] Thus, in cQED, the readout resonator can protect the qubits from electromagnetic noise from the external environment. cQED also allows for relatively accurate and sensitive measurements of the qubit states using the resonator. cQED allows for performing quantum non-demolition measurements of the qubit states. In general, the theory of cQED is well developed, and cQED architectures are relatively easy to implement and scale up.

[0006] However, in cQED, the coupling between the qubit and the readout resonator is always ON. As a result, any noise photons (thermal or non-thermal) present in the readout resonator can dephasing the qubit state and cause it to lose its phase coherence. One way to circumvent this problem is to increase the resonator bandwidth and shorten the time it takes to measure the qubit. However, increasing the resonator bandwidth and shortening the time it takes to measure the qubit can also lead to a shorter qubit lifetime (due to the Purcell effect). To overcome the Purcell effect and still provide a relatively fast readout, a Purcell filter is usually added to the readout resonator. The Purcell filter is a microwave filter that has nearly uniform transparency at the readout frequency but large attenuation at the qubit frequency. As a result, this solution adds hardware complexity to the quantum processor architecture.

[0007] For qubits coupled to a relatively slow readout cavity (with narrow bandwidth), the dephasing of the qubit caused by a long-lived readout photon (which is part of the readout pulse) can be reduced by quickly emptying the readout cavity of photons using a specific pulse sequence applied to the readout cavity (e.g., the CLEAR technique). This solution also adds software, pulse, and timing complexity to the quantum processor architecture.

[0008] In conventional devices, the coupling between the qubit and the readout resonator and the presence of noise photons set stringent requirements on the qubit setup in order to reduce the population of photons in the readout resonator and thus the dephasing of the qubit. For example, the readout resonator must be fully thermalized to the base-temperature stage, the power of the applied pulses must be as low as possible to prevent heating effects, the heat dissipation in the environment coupled to the readout resonator should also be minimized, and cryogenic isolators and circulators are added to the output line to protect against noise, including electromagnetic noise such as amplification noise or thermal noise such as blackbody radiation at the readout frequency. These cryogenic circulators and isolators are bulky, difficult to thermalize, expensive and heavy, and the use of magnetic materials and strong magnetic fields can have negative effects on the superconducting circuits. Summary of the Invention

[0009] One aspect of the present invention is to provide a superconducting quantum mechanical device, the superconducting quantum mechanical device including a first Josephson junction, a second Josephson junction electrically connected to the first Josephson junction, a third Josephson junction electrically connected to the second Josephson junction, and a fourth Josephson junction electrically connected to the third Josephson junction and the first Josephson junction, where the first, second, third, and fourth Josephson junctions are connected in a bridge circuit having a first resonant eigenmode, a second resonant eigenmode, and a third resonant eigenmode. The superconducting quantum mechanical device also includes a first capacitor pad electrically connected to the first and fourth Josephson junctions at a node between the first and fourth Josephson junctions, and a second capacitor pad electrically connected to the second and third Josephson junctions at a node between the second and third Josephson junctions, wherein the first capacitor pad, the second capacitor pad, and the bridge circuit form a superconducting quantum bit, the superconducting quantum bit having a resonant frequency corresponding to a first resonant eigenmode of the bridge circuit. The superconducting quantum mechanical device further includes a first resonator section electrically connected to the first and second Josephson junctions at a node between the first and second Josephson junctions, and a second resonator section electrically connected to the third and fourth Josephson junctions at a node between the third and fourth Josephson junctions, where the first resonator section, the second resonator section, and the bridge circuit form a resonator having a resonant frequency corresponding to a second resonant eigenmode. The superconducting quantum mechanical device also includes a magnetic flux source disposed in proximity to the bridge circuit. The magnetic flux source is configured, in operation, to provide a magnetic flux through the bridge circuit such that, when the third resonant eigenmode is excited, coupling occurs between the first, second, and third resonant eigenmodes.

[0010] In one embodiment, the flux source is a conductive element for providing an electromagnetic flux source for flux biasing the bridge circuit. In one embodiment, the flux source is a magnetic material for providing an electromagnetic flux source for flux biasing the bridge circuit. In one embodiment, the flux source is controllable. In one embodiment, the flux source provides one-half a flux quantum (φ0 / 2).

[0011] In one embodiment, the superconducting qubit is a transmon-like qubit. In one embodiment, both the first resonator section and the second resonator section are resonator lines of substantially equal length. In one embodiment, the first resonator section and the second resonator section include resonator lines disposed between electrically grounded pads.

[0012] In one embodiment, the superconducting quantum mechanical device further includes a resonator feedline configured to electromagnetically couple to the resonator during operation to provide excitation of the second resonant eigenmode, hi one embodiment, the resonator feedline is separated from the resonator such that a capacitor is formed between the resonator feedline and the resonator.

[0013] In one embodiment, the superconducting quantum mechanical device further includes a qubit feedline configured to electromagnetically couple to the superconducting qubit to provide excitation of the first resonant eigenmode during operation. In one embodiment, the qubit feedline is isolated from the superconducting qubit so as to form a capacitor between the qubit feedline and the superconducting qubit. In one embodiment, the superconducting qubit and the resonator are formed on the same substrate and the bridge circuit is located at a substantially common center of the superconducting qubit and the resonator.

[0014] In one embodiment, the first resonator section, the second resonator section, the first Josephson junction, the second Josephson junction, the third Josephson junction, and the fourth Josephson junction comprise a superconducting material selected from the group consisting of Al, Nb, NbTiN, NbN, and TiN.

[0015] In one embodiment, the third resonant eigenmode is excited using a control drive applied to the superconducting qubit or resonator. In one embodiment, the frequency of the control drive is set to the difference between the qubit frequency of the superconducting qubit and the resonator resonant frequency. In one embodiment, the amplitude of the control drive is set to provide a full frequency conversion between the superconducting qubit and the resonator. In one embodiment, the amplitude of the control drive is set to provide a 50:50 beam split, where half the qubit information is swapped with half the resonator information. In one embodiment, the frequency of the control drive is set to the sum of the qubit frequency of the superconducting qubit and the resonator resonant frequency, and the amplitude of the control drive is set to provide a two-mode squeezing of the qubit mode and the resonator mode. In one embodiment, the frequency of the control drive is in the microwave frequency range.

[0016] The quantum mechanical device has many advantages including protecting the qubits from dephasing due to photons or photon noise in the resonator during qubit initialization, single qubit gates, or multi-qubit gates or combinations thereof. This is because the quantum mode (X mode) and the resonator mode (Y mode) are orthogonal. The X mode is orthogonal to the Y mode, and these two modes can only couple or interact through the third mode (Z mode) when the control drive signal is ON. As a result, this protection feature allows the device to reduce the number of cryogenic isolators and circulators required in the output lines. In addition, the qubits can be subject to photon noise in the normal third mode (Z mode) of the circuit. However, since the Z mode is at a different frequency than the readout resonator frequency (Y mode), the input and output lines can be filtered within a frequency band around this unique frequency without the use of circulators and / or isolators.

[0017] The concept of the invention, as well as its method of operation and function of the associated elements of construction and combination of parts and economies of manufacture will become more apparent from a consideration of the following description and appended claims, taken in conjunction with the accompanying drawings, all of which form a part of this specification, and in which like reference characters refer to corresponding parts in the various drawings, It is to be expressly understood, however, that the drawings are for the purpose of illustration and description only and are not intended as a definition of the limits of the invention. [Brief description of the drawings]

[0018] [Figure 1] 1 is a schematic diagram of a superconducting quantum mechanical device according to an embodiment of the present invention. [Diagram 2] FIG. 2 is a schematic diagram of a superconducting quantum mechanical device according to another embodiment of the present invention. [Diagram 3] 1A illustrates a bridge circuit having a first resonant eigenmode, FIG. 1B illustrates a bridge circuit having a second resonant eigenmode, and FIG. 1C illustrates a bridge circuit having a third resonant eigenmode, in accordance with an embodiment of the present invention; DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0019] 1 is a schematic diagram of a superconducting quantum mechanical device 100 according to an embodiment of the present invention. The superconducting quantum mechanical device 100 includes a first Josephson junction 102, a second Josephson junction 104 electrically connecting to the first Josephson junction 102, a third Josephson junction 106 electrically connecting to the second Josephson junction 104, and a fourth Josephson junction 108 electrically connecting to the third Josephson junction 106 and the first Josephson junction 102, such that the first Josephson junction 102, the second Josephson junction 104, the third Josephson junction 106, and the fourth Josephson junction 108 are connected in a bridge circuit 110. The bridge circuit 110 has a first resonant eigenmode, a second resonant eigenmode, and a third resonant eigenmode. The bridge circuit 110 is similar to a conventional Wheatstone bridge. However, instead of resistors in a conventional Wheatstone bridge, bridge circuit 110 has at least four Josephson junctions arranged in a similar configuration.

[0020] 3A-3C show a bridge circuit diagram 110 having a first resonant eigenmode, a second resonant eigenmode, and a third resonant eigenmode, according to an embodiment of the present invention. For example, FIGS. 3A-3C show rf voltage polarities at bridge nodes corresponding to the first, second, and third eigenmodes. FIG. 3A shows the bridge circuit 110 operating in the first eigenmode (X-mode). FIG. 3B shows the bridge circuit 110 operating in the second eigenmode (Y-mode). FIG. 3C shows the bridge circuit 110 operating in the third eigenmode (Z-mode). In some embodiments, the first, second, and third eigenmodes are mutually orthogonal to each other. In some embodiments, the bridge circuit 110, which may be a Josephson Ring Modulator (JRM), is a nonlinear, dispersive circuit based on Josephson tunnel junctions (e.g., four Josephson junctions) capable of three-wave mixing of electromagnetic signals (e.g., microwave signals) at the quantum limit. However, the broad concepts of the present invention are not limited to only four Josephson junctions, and according to some embodiments, additional Josephson junctions can be included in one or more of the legs of the bridge circuit 110.

[0021] Superconducting quantum mechanical device 100 also includes a first capacitor pad 112 electrically connected to first Josephson junction 102 and fourth Josephson junction 108 at node 1 therebetween. Superconducting quantum mechanical device 100 also includes a second capacitor pad 114 electrically connected to second Josephson junction 104 and third Josephson junction 106 at node 2 therebetween. First capacitor pad 112, second capacitor pad 114, and bridge circuit 110 form a superconducting qubit 116. Superconducting qubit 116 has a resonant frequency (f Q ).

[0022] The superconducting quantum mechanical device 100 further includes a first resonator section 120 electrically connected to the first Josephson junction 102 and the second Josephson junction 104 at a node 3 therebetween. The superconducting quantum mechanical device 100 also includes a second resonator section 122 electrically connected to the third Josephson junction 106 and the fourth Josephson junction 108 at a node 4 therebetween. The first resonator section 120, the second resonator section 122, and the bridge circuit 110 are configured to have a resonant frequency (f R ) to form a resonator 126.

[0023] The superconducting quantum mechanical device 100 also includes a magnetic flux source 128 disposed proximate the bridge circuit 110. The magnetic flux source 128 is configured, during operation, to provide a magnetic flux through the bridge circuit 110 such that coupling occurs between the first, second, and third resonant eigenmodes (X-mode, Y-mode, and Z-mode) when the third resonant eigenmode (Z-mode) is excited by an external drive.

[0024] In one embodiment, the magnetic flux source 128 is a conductive element to provide an electromagnetic magnetic flux source that provides a magnetic flux bias to the bridge circuit (loop) 110. In another embodiment, the magnetic flux source 128 is a magnetic material to provide an electromagnetic magnetic flux source that provides a magnetic flux bias to the bridge circuit (loop) 110. The magnetic flux source 128 is not limited to only these specific examples. It may be one or more conductive elements, or one or more magnets formed from a magnetic material, or a combination thereof. In one embodiment, the magnetic flux source 128 is controllable and may be set to provide zero magnetic flux. When there is no magnetic flux through the bridge circuit (loop) 110, the coupling constant between the three eigenmodes vanishes. In another embodiment, the magnetic flux source 128 may be set to provide half a magnetic flux quantum (φ0 / 2), in which case coupling is generated between the three eigenmodes.

[0025] In one embodiment, superconducting qubit 116 is a transmon-like qubit. For example, superconducting qubit 116 can be a transmon-like qubit.

[0026] In one embodiment, the first resonator section 120 includes a resonator line 120A and the second resonator section 122 includes a resonator line 122A. In one embodiment, the lines 120A and 122A are substantially equal in length. In one embodiment, the first resonator section 120 and the second resonator section 122 are coplanar. In one embodiment, the first resonator section 120 and the second resonator section 122 include microstrip or stripline. In one embodiment, the first resonator section 120 and the second resonator section 122 include resonator lines 120A and 122A that are disposed between electrically grounded pads 130.

[0027] In one embodiment, the first resonator section 120, the second resonator section 122, the first Josephson junction 102, the second Josephson junction 104, the third Josephson junction 106, and the fourth Josephson junction 108 include a superconducting material such as, but not limited to, Al, Nb, NbTiN, NbN, and TiN.

[0028] In one embodiment, superconducting qubit 116 and resonator 126 are formed on the same substrate, and bridge circuit 110 is integrated and located at a substantially common center of superconducting qubit 116 and resonator 126 .

[0029] In one embodiment, the superconducting quantum mechanical device 100 further includes a resonator feed line 132 configured to be electromagnetically coupled to the resonator 126 and to carry input and output readout signals at a readout frequency that excites a second resonant eigenmode (Y mode). In one embodiment, the resonator feed line 132 and the resonator 126 are separated to form a capacitor 134 therebetween. In one embodiment, the capacitor 134 is defined by providing a space between the resonator feed line 132 and the first resonator section 120 of the resonator 126. The capacitor 134 can electromagnetically couple the resonator feed line 132 to the resonator 126. Excitation of the second resonant eigenmode (Y mode) can be achieved by sending a drive signal through the resonator feed line 132 to the resonator 126. For example, in one embodiment, the drive signal can have a frequency in the microwave range. However, the drive signal can also have a frequency in a higher or lower frequency range.

[0030] In one embodiment, superconducting quantum mechanical device 100 further includes qubit feedline 136 configured to electromagnetically couple to superconducting qubit 116 to provide excitation of a first resonant eigenmode (X mode) during operation. In one embodiment, qubit feedline 136 and superconducting qubit 116 are separated to form a capacitor 138 therebetween. In one embodiment, capacitor 138 is defined by providing a space between qubit feedline 136 and first capacitor pad 114 of qubit 116. Capacitor 138 can electromagnetically couple qubit feedline 136 to qubit 116. Excitation of the first resonant eigenmode (X mode) can be achieved by sending a drive signal through qubit feedline 136 to qubit 116. Excitation of the first, second, or third eigenmodes can be achieved by applying a drive signal (e.g., a drive signal in the microwave frequency range) through either the resonator feedline 132 or the qubit feedline 136.

[0031] In one embodiment, the third resonant eigenmode (the Z mode) is excited using a control drive signal applied to the superconducting qubit 116 through qubit feedline 136 or to the resonator 126 through resonator feedline 132. In one embodiment, the frequency of the control drive is equal to the qubit frequency (f Q ) and the resonator frequency (f R ) In one embodiment, the amplitude of the control drive is set to provide full frequency conversion between the superconducting qubit 116 and the resonator 126. In another embodiment, the amplitude of the control drive is set to provide a 50:50 beam split, where half of the qubit information is swapped with half the resonator information.

[0032] Figure 2 is a schematic electrical diagram of a superconducting quantum mechanical device 200 according to another embodiment of the present invention. Superconducting quantum mechanical device 200 is similar in many aspects to superconducting quantum mechanical device 100 described in the paragraph above. Thus, the same reference numerals are used in Figure 2 to indicate components that are common between superconducting quantum mechanical devices 100 and 200, and the following paragraphs will focus only on the different features.

[0033] In one embodiment, the superconducting quantum mechanical device 200 further includes a pad 202 connected to node 3 and the first resonator section 120 of the bridge circuit 110, and a pad 204 connected to node 4 and the second resonator section 122 of the bridge circuit 110. For example, the pad 202 can be provided and connected to the end of the line 120A of the first resonator section 120 following node 3, and the pad 204 can be connected to the end of the line 122A of the second resonator section 122 following node 4. In another embodiment, instead of using pads 202 and 204, the width of the end of the line 120A and the width of the end of the line 122A can be increased. Providing pads 202 and 204 or increasing the width of the ends of the lines 120A and 122A can reduce charge distribution at nodes 3 and 4 by increasing the shunt capacitance across the Josephson junctions 102, 104, 106, and 108.

[0034] The superconducting quantum mechanical devices 100 and 200 have several advantages including protecting the qubit 116 from dephasing due to photons or photon noise in the resonator 126 during qubit initialization, single qubit gating, or multi-qubit gating, or a combination thereof. This is because the qubit mode (X mode) and the resonator mode (Y mode) are orthogonal. The X mode is orthogonal to the Y mode, and these two modes can only couple or interact via the Z mode when the control drive signal is ON. As a result, this protection feature allows for a reduction in the number of cryogenic isolators and circulators on the output lines. In addition, the qubit 116 may be subject to photon noise in the normal mode (Z mode) of the circuit. However, since the Z mode is at a different frequency than the readout resonator frequency (Y mode), the input and output lines can be filtered within a frequency band around this unique frequency without the use of circulators and / or isolators.

[0035] As mentioned in the paragraph above, in one embodiment, the control drive (f D ) is the qubit frequency (f Q ) and the resonator frequency (f R ), the difference between D =|f Q -f R | and the drive amplitude / power can be set to give full frequency conversion between the qubit and the resonator. Using this mode of operation, the qubit state can be measured. By applying a control drive (excitation or no excitation), the qubit state is swapped with the resonator readout photon. By measuring the output readout photon, the qubit state can be inferred. It is worth noting that the resonator 120 can be used as a storage resonator (i.e., memory) instead of a readout resonator.

[0036] As mentioned in the paragraph above, in another embodiment, the amplitude of the control drive can be set to provide a 50:50 beam split, where half the qubit information is swapped with half the resonator information. In this case, the control drive frequency is still f D =|f Q -f R |. However, the amplitude or power is set to give a 50:50 beam splitter point, where half of the qubit information is swapped with half of the resonator information, while the other half is kept in the qubit and resonator. By measuring the output readout photon, the qubit state can be entangled with the photon in flight, the output readout photon. Thus, by measuring the output readout photon, it is possible to infer the qubit state.

[0037] In another embodiment, the controlled drive frequency f D is the qubit frequency f Q and the resonator frequency f R It is possible to set it to be equal to the sum of f D =|f Q +fR | and the drive amplitude or power can be set to give two-mode squeezing of the qubit and resonator modes. Due to longitudinal coupling between the resonator and the qubit, this mode of operation can provide ultrafast and reliable readout of the qubit state (faster than cQED, which uses transverse coupling). This mode of operation can eliminate the need for quantum-limited Josephson amplifiers in the readout chain, as well as the overhead and losses of required intermediate stages.

[0038] In yet another embodiment, it is possible to implement a full conversion mode (single-mode squeezing or amplification) followed by a four-wave mixing operation. In this mode, the qubit and resonator information are swapped, and then the resonator is fed with the resonator frequency f R (or twice the resonator frequency, 2f R By applying a relatively strong pump (relatively high power) at 100 MHz (at 100 MHz), the reflected readout signal can be squeezed or amplified, thereby increasing the measurement signal-to-noise ratio (SNR). Such single-mode squeezing or amplification can be useful in implementing certain error-correcting bosonic codes. In another embodiment, in four-wave operation (single-mode squeezing), the vacuum noise inside the readout resonator is squeezed before swapping information between the qubit and the resonator.

[0039] The description of various embodiments of the present invention has been presented for illustrative purposes, but is not intended to be exhaustive or limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used in this specification is selected to best explain the principles of the embodiments, practical applications or technical improvements to the technology found in the market, or to allow others skilled in the art to understand the embodiments disclosed herein.

Claims

1. 1. A superconducting quantum mechanical device, comprising: a first Josephson junction, a second Josephson junction electrically connected to the first Josephson junction, a third Josephson junction electrically connected to the second Josephson junction, and a fourth Josephson junction electrically connected to the third Josephson junction and the first Josephson junction, the first Josephson junction, the second Josephson junction, the third Josephson junction, and the fourth Josephson junction being connected in a bridge circuit such that the first Josephson junction, the second Josephson junction, the third Josephson junction, and the fourth Josephson junction have a first resonant eigenmode, a second resonant eigenmode, and a third resonant eigenmode; a first capacitor pad electrically connected to the first Josephson junction and the fourth Josephson junction at a first node between the first Josephson junction and the fourth Josephson junction, and a second capacitor pad electrically connected to the second Josephson junction and the third Josephson junction at a second node between the second Josephson junction and the third Josephson junction, wherein the first capacitor pad, the second capacitor pad, and the bridge circuit are configured to form a superconducting qubit having a first resonant frequency corresponding to the first resonant eigenmode of the bridge circuit; a first resonator section electrically connected to the first Josephson junction and the second Josephson junction at a third node between the first Josephson junction and the second Josephson junction, and a second resonator section electrically connected to the third Josephson junction and the fourth Josephson junction at a fourth node between the third Josephson junction and the fourth Josephson junction, wherein the first resonator section, the second resonator section and the bridge circuit are configured to form a resonator having a second resonant frequency corresponding to the second resonant eigenmode; a magnetic flux source disposed proximate the bridge circuit; the magnetic flux source is configured, during operation, to provide a magnetic flux through the bridge circuit such that, when the third resonant eigenmode is excited, coupling occurs between the first resonant eigenmode, the second resonant eigenmode, and the third resonant eigenmode.

2. A grounded pad surrounding three sides of the first capacitor pad. The superconducting quantum mechanical device of claim 1 further comprising:

3. A superconducting quantum mechanical device as described in claim 1 or 2, wherein the first resonator section includes a first resonator line, a first end of the first resonator line that electromagnetically connects to the third node of the first resonator line being wider than other portions of the first resonator line.

4. 4. The superconducting quantum mechanical device of claim 1, wherein the magnetic flux source is a magnetic material or a conductive element for providing an electromagnetic flux source that is controllable and provides a flux bias to the bridge circuit.

5. The magnetic flux source has a width of half a magnetic flux quantum (φ ０ 5. The superconducting quantum mechanical device according to claim 1 , wherein:

6. 6. The superconducting quantum mechanical device of claim 1, wherein the superconducting qubit is a transmon-like qubit.

7. A superconducting quantum mechanical device as described in claim 3, wherein the second resonator section includes a second resonator line of equal length to the first resonator line of the first resonator section.

8. 8. The superconducting quantum mechanical device of claim 3 or 7, wherein the first resonator line of the first resonator section is disposed between electrically grounded pads.

9. 9. The superconducting quantum mechanical device of claim 1, further comprising a resonator feedline configured to electromagnetically couple to the resonator during operation to provide excitation of the second resonant eigenmode.

10. 10. The superconducting quantum mechanical device of claim 9, wherein the resonator feedline is separated from the resonator so as to form a capacitor between the resonator feedline and the resonator.

11. 11. The superconducting quantum mechanical device of claim 1, further comprising a qubit feedline configured to electromagnetically couple to the superconducting qubit during operation to provide excitation of the first resonant eigenmode.

12. 12. The superconducting quantum mechanical device of claim 11, wherein the qubit feedline is separated from the superconducting qubit so as to form a capacitor between the qubit feedline and the superconducting qubit.

13. 13. The superconducting quantum mechanical device of claim 1, wherein the superconducting quantum bit and the resonator are formed on the same substrate, and the bridge circuit is located at a common center of the superconducting quantum bit and the resonator.

14. 14. The superconducting quantum mechanical device of claim 1, wherein the first resonator section, the second resonator section, the first Josephson junction, the second Josephson junction, the third Josephson junction, and the fourth Josephson junction comprise a superconducting material selected from the group consisting of Al, Nb, NbTiN, NbN, and TiN.

15. 15. The superconducting quantum mechanical device of claim 1, wherein the third resonant eigenmode is excited using a control drive signal applied to the superconducting qubit or the resonator.

16. 16. The superconducting quantum mechanical device of claim 15, wherein a frequency of the control drive signal is set to the difference between a qubit frequency of the superconducting qubit and the second resonant frequency of the resonator.

17. 17. A superconducting quantum mechanical device according to claim 15 or 16, wherein the amplitude of the control drive signal is set to provide full frequency conversion between the superconducting qubit and the resonator.

18. 18. A superconducting quantum mechanical device according to any one of claims 15 to 17, wherein the amplitude of the control drive signal is set to provide a 50:50 beam split, with half of the qubit information swapped with half of the resonator information.

19. 16. The superconducting quantum mechanical device of claim 15, wherein a frequency of the control drive signal is set to the sum of a qubit frequency of the superconducting qubit and the second resonant frequency of the resonator, and an amplitude of the control drive signal is set to provide two-mode squeezing of a qubit mode and a resonator mode.

20. 20. A superconducting quantum mechanical device according to any one of claims 15 to 19, wherein the frequency of the control drive signal is in the microwave frequency range.

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