Patent Description:
This invention was made with Government support under Contract No. <NUM>. The Government has certain rights in this invention.

The present invention relates generally to superconducting circuits, and more particularly to robust tunable coupling between superconducting circuits.

The fundamental challenge for quantum computation and simulation is to construct a large-scale system of highly connected coherent qubits to perform various operations. Superconducting qubits utilize macroscopic circuits to process quantum information and are a promising candidate towards this end. Recently, materials research and circuit optimization has led to significant progress in qubit coherence. Superconducting qubits can now perform hundreds of operations within their coherence times, allowing for research into complex algorithms such as error correction. In many applications, it is desirable to combine these high-coherence qubits with tunable inter-qubit coupling, since it would allow for both coherent local operations and dynamically varying qubit interactions. For quantum computation, this would provide isolation for single-qubit gates while at the same time enabling fast two-qubit gates that minimize errors from decoherence. Despite previous attempts at tunable coupling, these applications have yet to be realized due to the challenge of incorporating tunable, long-distance coupling with high coherence devices.

<NPL>] discloses tunable filters and matching networks.

The present disclosure relates generally to coupling superconducting circuits, and more particularly to proving tunable coupling between components that is robust against fabrication error and errors in a provided control flux. A tunable coupling component is placed between two components in a superconducting circuit. The tunable coupling component can be adjusted to provide a strongly coupled state or a decoupled (or isolation) state between the components. In one example, manipulation can be performed on state information of an isolated qubits in the decoupled state, while the state information can be passed to other components of the superconducting circuit during a strongly coupled state.

Couplers of prior art have a linear dependence on control flux at the off point, that is, at the value of a control parameter that is intended to isolate the coupled components. This makes the off state of the coupler very sensitive to control flux and any changes in the off point, and the off point can change when the impedance of the circuits being coupled changes, such as when a second coupler coupled to one of the same circuits changes its coupling value. The inventive coupler is comprised of a chain of inductively coupled tunable LC resonators, whose lowest frequency collective mode can be tuned via bias flux over a wide range, such as <NUM> - <NUM>. When the lowest frequency coupler mode is at its highest frequency, the coupler is turned off, isolating the components linked by the tunable coupler. At an appropriate value for the control signal, the coupler mode frequencies decrease and the lowest mode approaches frequencies of the components linked by the tunable coupler, providing strong coupling between the two components. In other words, rather than an off point, the inventive coupler provides substantial isolation for a range of control flux values. In one example, when no control signal is applied to the tunable oscillator, the coupler remains in the "off" state. This state persists for small values of the control signal, and is thus insensitive to variations in the control flux. The residual coupling provided in the off state decreases approximately exponentially as the number of tunable oscillator "legs" in the coupler is increased.

In one example, a chain of coupled compound Josephson junction resonators is used as the coupling component. Near zero control flux, the effective inductances of the compound Josephson junctions are small and cause currents travelling along the backbone of the coupler to decay approximately exponentially. This shuts off the coupler for DC currents. When the control flux is near half a flux quantum in each compound Josephson junction loop, the effective inductances of each compound Josephson junction is large, and the current along the backbone decays more slowly, allowing coupling. For AC operation, the compound Josephson junctions act as tunable LC resonators that are much higher in frequency in the "off" state than the modes of the quantum circuits to be coupled. The off coupling decreases approximately exponentially in the number of compound Josephson junction resonator stages. One advantage of using detuning of the mode frequencies to turn off the coupling is that there is a threshold behavior where the coupler is off if the detuning is sufficiently large. This is favorable compared to the typical case where the off state is at a specific control flux value.

<FIG> illustrates a block diagram of an example of a superconducting system <NUM>. The superconducting system includes a first circuit component <NUM> coupled to a second circuit component <NUM> through a tunable coupler <NUM>. It will be appreciated that each of the first and second circuit components <NUM> and <NUM> can represent a qubit, a resonator, such as a lumped-element LC oscillator or a distributed resonator, a dissipative sub-circuit (e.g., a circuit containing resistive elements), or any other appropriate component for a superconducting system. It will also be appreciated that the term qubit is a shorthand for any system that contains two or more quantum states that can store quantum information. Exemplary implementations of superconducting qubits include the transmon, flux qubit, quantronium, the cooper pair box, and fluxonium, and typically include one or more of a Josephson junction, capacitor and inductor. It will be further appreciated that the term "coupled" is intended to encompass any means by which two systems can exchange energy or information.

The tunable coupler <NUM> includes a circuit path <NUM> between the first and second components <NUM> and <NUM> having a plurality of inductive and/or capacitive circuit elements (CEs). A given circuit element for the circuit path <NUM> can be inductors, capacitors, Josephson junctions, or a combination of these elements. A plurality of tunable oscillators <NUM> and <NUM> are connected along the circuit path <NUM>. The tunable oscillators <NUM> and <NUM> can be any sub-circuit having a resonant frequency that changes with a provided control signal. For example, the tunable oscillators <NUM> and <NUM> can be implemented as a compound Josephson junction. Each tunable oscillator <NUM> and <NUM> is responsive to a control signal, provided by an associated controller <NUM> to tune an associated resonant frequency of the oscillator. For example, the control signal can be a control flux provided to the tunable oscillator <NUM>. In one implementation, each of the plurality of tunable oscillators <NUM> and <NUM> connect points on the circuit path <NUM> to ground.

In one example, the tunable coupler <NUM> is configured such that the two circuit components <NUM> and <NUM> are isolated in the absence of a control signal. To couple the two components <NUM> and <NUM>, the control signal is provided to the tunable oscillators <NUM> and <NUM> within a relatively narrow range of values determined by the configuration of the oscillator to tune a frequency of a coupling mode of the tunable coupler close to a frequency associated with one or both of the circuit components <NUM> and <NUM>. In one example, utilizing a control flux, the range of values is centered at or near one-half of the magnetic flux quantum, Φ<NUM>, and can range between <NUM>Φ<NUM> and <NUM>Φ<NUM>. As a result, when the control flux is not in this narrow range, the tunable coupler <NUM> has a robust off-state, and can maintain substantial isolation between the two circuit components across a broad range of values for the control signal. Further, the off-state is very robust to variations in fabrication parameters.

<FIG> illustrates one example of a superconducting system <NUM> comprising two transmon qubits <NUM> and <NUM> and a tunable coupler <NUM>. The tunable coupler <NUM> includes a circuit path <NUM>, comprising a plurality of circuit elements <NUM>-<NUM>, and a plurality of tunable resonators <NUM>-<NUM> connected from the circuit path <NUM>. In the illustrated example, the circuit elements <NUM>-<NUM> are inductors, although it will be appreciated that a given circuit element can be an inductor, a capacitor, or a Josephson junction. In the illustrated implementation, the plurality of tunable resonators <NUM>-<NUM> connect the circuit path <NUM> to ground, although it will be appreciated that the tunable coupler <NUM> can be implemented in a floating implementation, with the tunable resonators connected to a second circuit path (not shown) comprising, for example, a second plurality of inductors and/or capacitors. In the illustrated implementation, each of the plurality of resonators <NUM>-<NUM> is implemented as a compound Josephson junction comprising two paths to ground, each interrupted by a Josephson junction. The plurality of tunable resonators <NUM>-<NUM> are tunable via a common bias line <NUM> to provide a control flux to the circuit loops containing the compound Josephson junctions.

It will be appreciated that each of the transmon qubits <NUM> and <NUM> has at least one characteristic frequency, representing spacing between two energy levels of each transmon qubit. In one implementation, a characteristic frequency of each of the transmon qubits <NUM> and <NUM>, representing a spacing between the ground and first excited states, can be around <NUM>, although it will be appreciated that the spacing can vary with the implementation of the qubits. A frequency associated with one or more coupling modes of the tunable coupler <NUM> is a function of the control flux provided to the plurality of compound Josephson junctions <NUM>-<NUM>. In accordance with an aspect of the present invention, when no control flux is provided to the plurality of compound Josephson junctions <NUM>-<NUM>, a lowest frequency coupling mode of the tunable coupler <NUM> remains at a frequency far from the characteristic frequencies of the transmon qubits <NUM> and <NUM> and the transmon qubits remain substantially isolated. The specific values of the coupler mode frequency vary with parameters of the coupler components, particularly the critical currents of the Josephson junctions in the compound Josephson junctions <NUM>-<NUM>, however, in practice, they are selected to maintain a broad range of values for the control flux for which substantial isolation of the two qubits can be maintained.

The coupler <NUM> has a relatively narrow range of values for the control flux for which the coupler is active and the transmon qubits <NUM> and <NUM> are strongly coupled. In general, the coupler <NUM> provides a maximum coupling strength when the provided control flux is around <NUM>Φ<NUM>. The behavior of the tunable coupler <NUM> can be analogized to that of a repeated current divider. When the compound Josephson junctions <NUM>-<NUM> are provided with a control flux outside of the predetermined range, an inductance of the compound Josephson remains low relative to an inductance of the circuit path <NUM>. Accordingly, each of the compound Josephson junctions <NUM>-<NUM> provide an alternate, low-impedance path to ground, restricting current flow between the two transmon qubits <NUM> and <NUM>. In practice, this isolation is improved (i.e., the residual coupling between the two transmon qubits is reduced) as the number of connected compound Josephson junctions is increased, providing more of these alternative paths to ground. When the compound Josephson junctions <NUM>-<NUM> are provided with control flux within the relatively narrow range of "on" values, the inductance of each compound Josephson junction increases, and becomes high relative to the inductance of the circuit path <NUM>. As a result, the two transmon qubits <NUM> and <NUM> become coupled along the circuit path <NUM>.

An approximate variance of the coupling strength of the tunable coupler <NUM> with the control flux can be described as: <MAT>
where <MAT>, L is the size of the inductances <NUM>-<NUM> along the circuit path <NUM>, Ic is a critical current of each compound Josephson junction, which is a function of the control flux, a, and N is a number of compound Josephson junctions in the tunable coupler <NUM>.

As can be seen from Eq. <NUM>, when the current through the compound Josephson junctions is high, the coupling drops exponentially with the number of compound Josephson junction, N, in the coupler. When the current through the compound Josephson junctions is low, y approaches <NUM>, and the coupling becomes polynomially small with the number of compound Josephson junctions, allowing for meaningful coupling between the two transmon qubits.

In one implementation, using Josephson junctions with relatively low critical currents, the coupler <NUM> includes six compound Josephson junctions. In this implementation, the critical current of the junctions in the two transmon qubits <NUM> and <NUM> is <NUM> nA, the inductance of the inductors in the two transmon qubits is <NUM> pH, the critical current of the junctions in the plurality of compound Josephson junctions <NUM>-<NUM> is <NUM> nA, and the inductance of the inductors <NUM>-<NUM> in the circuit path is <NUM> pH. <FIG> illustrates, for this implementation, a chart <NUM> showing a lowest frequency coupler mode for the tunable coupler, represented in gigahertz on a vertical axis <NUM>, as a function of an applied flux, represented in fractions of the magnetic flux quantum on a horizontal axis <NUM>.

As can be seen from the plotted line <NUM>, the coupler mode frequency stays well above the <NUM> characteristic frequency of the two transmon qubits <NUM> and <NUM> for a broad range of values. When the coupler mode is at the <NUM> maximum, the coupling between the two components is minimal, at approximately <NUM>, and it remains below <NUM> for a range of <NUM> Φ<NUM>. At this point, the coupler frequency exhibits a slope of <NUM> x <NUM>-<NUM> MHz/ m Φ<NUM>, such that the variance of the frequency with the control flux has a minimal effect on the coupling. When the control flux approaches <NUM>Φ<NUM>, the frequency of the coupler mode approaches the <NUM> characteristic frequency of the qubits <NUM> and <NUM>. At a value around <NUM>Φ<NUM>, the coupler <NUM> provides a coupling of around <NUM>, with a slope of around <NUM>/ m Φ<NUM>. While couplings well above <NUM> can be achieved for this implementation, in practice, the applied flux may be kept below <NUM>Φ<NUM> so that the coupler mode remains more than <NUM> away from the qubit modes.

For contrast, the behavior of an implementation of a similar coupler, also with six compound Josephson junctions, but using Josephson junctions with relatively high critical currents is illustrated as a chart <NUM> in <FIG>. In this implementation, the critical current of the junctions in the two transmon qubits <NUM> and <NUM> is <NUM> nA, the inductance of the inductors in the two transmon qubits is <NUM> pH, the critical current of the junctions in the plurality of compound Josephson junctions <NUM>-<NUM> is <NUM> nA, and the inductance of the inductors <NUM>-<NUM> in the circuit path is <NUM> pH. In <FIG>, a lowest frequency coupler mode for the tunable coupler, represented in gigahertz on a vertical axis <NUM>, is plotted as a function of an applied flux, represented in fractions of the magnetic flux quantum on a horizontal axis <NUM>.

As can be seen from the plotted line <NUM>, the coupler mode frequency both starts and remains significantly higher than the low critical current implementation of <FIG>. When the coupler mode is at the <NUM> maximum, the coupling between the two components is minimal, at approximately <NUM>, and the coupling remains low over the control flux range <NUM> - <NUM>Φ<NUM>. At the coupler mode frequency maximum, at zero control flux, the coupler frequency exhibits a slope of <NUM> x <NUM>-<NUM> MHz/ m Φ<NUM>, such that the variance of the frequency with the control flux has a minimal effect on the coupling. With standard couplers, the "off" flux of a given coupler can depend on flux applied to another coupler coupling the same quantum object, and the insensitivity to extraneous flux in this implementation provides a significant advantage. When the control flux approaches <NUM>. 5Φ<NUM>, the frequency of the coupler mode dips sharply toward the <NUM> characteristic frequency of the qubits <NUM> and <NUM>, although the minimum value is on the order of <NUM>. At this value, the coupler <NUM> provides a coupling of around <NUM>, with a slope of around <NUM>/ m Φ<NUM>.

The benefit of designing a coupler with a small coupler capacitance limit, as shown in <FIG>, is that the coupler frequencies can remain well above the qubit frequencies over the full range of tuning flux. This limit can be reached, for example, by utilizing small area junctions with high plasma frequencies. In this regime, the coupler in the "off" state can be described as a repeated current divider with the amount of qubit induced current decreasing in each successive leg by a factor of approximately <MAT>, where LL is the inductance at each of the Josephson junctions in the compound Josephson junctions <NUM>-<NUM> and LB is an inductance of each of the plurality of inductors <NUM>-<NUM> in the circuit path <NUM>, and Φ is the applied flux. The current-current coupling between the qubits is thus exponentially suppressed in the length of the coupler. Alternatively, the maximum "on" coupling is achieved when the flux applied to each of the plurality of compound Josephson junctions <NUM>-<NUM> is tuned to <NUM>Φ<NUM>, with the maximum coupling being approximately equal to a product of a maximum mutual inductance between the qubits, Mmax, and a square of the qubit currents, and <MAT>, is the inductance at the two qubits <NUM> and <NUM>, and NL is the number of compound Josephson junctions.

<FIG> is a chart <NUM> illustrating a variance of a turn-off behavior of the tunable coupler of <FIG> with variation in the critical currents of the Josephson junctions comprising the compound Josephson junctions. In the chart, a coupling strength of the coupler is represented logarithmically in MHz on the vertical axis <NUM>, and the control flux provided to the compound Josephson junctions is represented in fractions of the magnetic flux quantum on the horizontal axis <NUM>. It will be appreciated that the fabrication of Josephson junctions is not always exact, and that a degree of variation will be present in the critical current of a given junction. To represent this, the chart <NUM> includes a first curve <NUM>, representing a mean value for coupling given a <NUM>% variation in critical currents for each junction, a second curve <NUM>, representing a value for the coupling one standard deviation above the mean given a <NUM>% variation in critical currents for each junction, and a third curve <NUM>, representing a value for the coupling one standard deviation below the mean given a <NUM>% variation in critical currents for each junction. As can be seen from the plots, the degree of residual coupling varies slightly with the junction fabrication, but there is little change in the relatively large range of values for which the coupling remains minimal.

<FIG> is a chart <NUM> illustrating a variance of a turn-on behavior of the tunable coupler of <FIG> with variation in the critical currents of the Josephson junctions comprising the compound Josephson junctions. In the chart, a coupling strength of the coupler is represented in MHz on the vertical axis <NUM>, and the control flux provided to the compound Josephson junctions is represented in fractions of the magnetic flux quantum on the horizontal axis <NUM>. The chart <NUM> includes a first curve <NUM>, representing the mean value for the coupling given a <NUM>% variation in critical currents for each junction, a second curve <NUM>, representing a value for the coupling one standard deviation above the mean given a <NUM>% variation in critical currents for each junction, and a third curve <NUM>, representing a value for the coupling one standard deviation below the mean given a <NUM>% variation in critical currents for each junction. As can be seen from the plots, the turn-on behavior does exhibit variation with variations in the critical currents of the Josephson junctions, although it simply changes the setpoint for the on-coupling.

To allow for tuning for the set point for the on-coupling, for example, due to fabrication variations, <FIG> illustrates another example of a superconducting system <NUM> comprising two transmon qubits <NUM> and <NUM> and a tunable coupler <NUM>. The tunable coupler <NUM> includes a circuit path <NUM>, comprising a plurality of inductors <NUM>-<NUM>, and a plurality of compound Josephson junctions <NUM>-<NUM> connected from the circuit path <NUM> to ground. In the illustrated implementation, each compound Josephson junction comprises three paths to ground, each interrupted by a Josephson junction. Two of the three paths are inductively coupled to a common current bias line <NUM> to provide a control flux to the compound Josephson junctions. The bias line <NUM> controls the state of the coupler in a manner similar to that described for <FIG>.

The third path of each compound Josephson junction <NUM>-<NUM> is tunable by using a combination of respective direct current (DC) bias lines <NUM>-<NUM> to tune, within limits, a setpoint for the on-coupling of the tunable coupler. It will be appreciated that individual addressability of these bias lines is not necessary to the function of the device, and that they may be set by one or more common control lines. The DC bias allows the setpoint to be adjusted for errors in fabrication of the Josephson junctions, and allows for an on state that is relatively insensitive to minor variations in the control flux. This significantly relaxes constraints on flux pulses for controlling the coupler and reduces dephasing of the coupled components.

<FIG> illustrates a method <NUM> for coupling two superconducting circuit components. At <NUM>, first and second circuit paths are fabricated between the two superconducting components. The first circuit path comprises a plurality of circuit elements, which can include any of inductors, capacitors, and Josephson junction. The second circuit path can include one or more circuit elements or may be a common ground. At <NUM>, a plurality of tunable oscillators are fabricated forming connections between the first and second circuit paths. For example, the tunable oscillators can be fabricated as a plurality of compound Josephson junctions connecting the first circuit path to the second circuit path. Each tunable oscillator is designed to be responsive to a control signal to tune an associated frequency of the oscillator. In one implementation, a common bias line can be fabricated to be inductively coupled to each of plurality of tunable oscillators, such that the control signal can be provided via the common bias line.

At <NUM>, the control signal can be provided at a value within a predefined range to tune the plurality of tunable oscillators within a first frequency range, within which the two components are coupled. In one implementation, the control signal is provided as a control flux to each of the plurality of tunable oscillators. At <NUM>, the control signal is provided at a value outside of the predefined range to tune the plurality of tunable oscillators within a second frequency range, within which the two components are isolated. In one implementation, the predefined range does not include the value zero, such that the two components are isolated when no control signal is present.

Claim 1:
A tunable coupler (<NUM>, <NUM>, <NUM>) assembly for linking two components (<NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>) in a superconducting circuit (<NUM>, <NUM>, <NUM>), comprising:
a plurality of circuit elements, each implemented as one of an inductor, a capacitor, and a Josephson junction, connected in series on a first path (<NUM>, <NUM>, <NUM>) connecting the two components (<NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>); and
a plurality of tunable oscillators (<NUM>, <NUM>, <NUM> - <NUM>, <NUM> - <NUM>), each tunable oscillator (<NUM>, <NUM>, <NUM> - <NUM>, <NUM> - <NUM>) connecting the first path (<NUM>, <NUM>, <NUM>) which is connecting the two components (<NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>) to a second path (<NUM>, <NUM>) which is connecting the two components (<NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>), each tunable oscillator (<NUM>, <NUM>, <NUM> - <NUM>, <NUM> - <NUM>) being responsive to a control signal to tune an associated resonance frequency of the tunable oscillator (<NUM>, <NUM>, <NUM> - <NUM>, <NUM> - <NUM>) within a first frequency range and within a second frequency range, wherein the two components (<NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>) are coupled when the plurality of tunable oscillators (<NUM>,<NUM>, <NUM>-<NUM>, <NUM> - <NUM>) is tuned within said first frequency range, and wherein the two components (<NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>) are isolated when the plurality of tunable oscillators (<NUM>,<NUM>, <NUM>-<NUM>, <NUM> - <NUM>) is tuned within said second frequency range.