Full microwave ZZ control

Abstract

A technique for facilitating dynamic control of ZZ interaction for quantum computing devices. In one example, a quantum coupling device can include a bias component operably coupled to first and second qubits via respective first and second drive lines. The bias component can facilitate dynamic control of the ZZ interaction between the first and second qubits using a non-resonant microwave signal applied via the respective first and second drive lines.

Description

[Technical field]

[0001] The present disclosure relates to quantum computing, and more particularly to techniques that facilitate dynamic control of ZZ interactions for quantum computing devices. Summary of the Invention

[0002] The following presents a summary to provide a basic understanding of one or more embodiments of the present invention. This summary is not intended to identify key or critical elements, nor is it intended to delineate the scope of particular embodiments or claims. Its sole purpose is to present concepts in a simplified form as a prelude to the more detailed description that is presented later. In one or more embodiments described herein, a system, device, computer-implemented method, or computer program product, or combination thereof, that facilitates dynamic control of ZZ interactions for quantum computing devices is described.

[0003] According to an embodiment, a quantum coupling device can include a bias component operably coupled to the first and second quantum bits via respective first and second drive lines. The bias component can facilitate dynamic control of the ZZ interaction between the first and second quantum bits using a non-resonant microwave signal applied via the respective first and second drive lines.

[0004] According to another embodiment, the computer-implemented method can include operably coupling, by a system operably coupled to the processor, a bias component to the first and second quantum bits via respective first and second drive lines. The computer-implemented method can further include dynamically controlling, by the system, a ZZ interaction between the first and second quantum bits with a non-resonant microwave signal applied via the respective first and second drive lines using the bias component.

[0005] According to another embodiment, a computer program product may comprise a computer-readable storage medium having program instructions embodied thereon. The program instructions are executable by a processor to cause the processor to perform operations. The operations may include operably coupling, by the processor, a bias component to the first and second quantum bits via respective first and second drive lines. The operations may further include, by the processor, using the bias component to facilitate dynamic control of the ZZ interaction between the first and second quantum bits with a non-resonant microwave signal applied via the respective first and second drive lines. [Brief description of the drawings]

[0006] [Figure 1] FIG. 1 illustrates a block diagram of an example non-limiting device that can facilitate dynamic control of ZZ interactions for quantum computing devices in accordance with one or more embodiments described herein. [Diagram 2] FIG. 1 shows an example non-limiting graph with a logarithmic scale plotting ZZ coupling versus the relative phase difference between non-resonant microwave signals and the Rabi rate in accordance with one or more embodiments described herein. [Diagram 3] FIG. 2 shows an example non-limiting graph depicting the relative phase difference between non-resonant microwave signals as a function of time in accordance with one or more embodiments described herein. [Figure 4] FIG. 13 shows an example non-limiting graph depicting the shift in qubit frequency versus drive phase and Rabi rate, in accordance with one or more embodiments described herein. [Diagram 5] FIG. 13 illustrates another example, non-limiting graph depicting the shift in qubit frequency versus drive phase and Rabi rate, in accordance with one or more embodiments described herein. [Figure 6]FIG. 2 illustrates an example non-limiting non-resonant microwave signal including an echo π pulse in accordance with one or more embodiments described herein. [Figure 7] FIG. 2 illustrates an example non-limiting non-resonant microwave signal including frame change pulses in accordance with one or more embodiments described herein. [Figure 8] FIG. 1 illustrates a block diagram of an exemplary non-limiting quantum coupling device that can facilitate dynamic control of ZZ interactions for quantum computing devices in accordance with one or more embodiments described herein. [Figure 9] FIG. 2 shows an example non-limiting graph depicting the relative phase difference between non-resonant microwave signals as a function of time in accordance with one or more embodiments described herein. [Figure 10] FIG. 13 illustrates an example non-limiting graph on a logarithmic scale plotting ZZ coupling versus non-resonant microwave signal frequency and non-resonant microwave signal amplitude in accordance with one or more embodiments described herein. [Figure 11] FIG. 2 illustrates an example non-limiting graph depicting the amplitude of a non-resonant microwave signal as a function of time in accordance with one or more embodiments described herein. [Figure 12] FIG. 2 illustrates an example non-limiting non-resonant microwave signal including an echo π pulse in accordance with one or more embodiments described herein. [Figure 13] FIG. 2 illustrates an example non-limiting non-resonant microwave signal including a frame altering pulse in accordance with one or more embodiments described herein. [Figure 14] FIG. 2 illustrates an example non-limiting graph depicting the amplitude of a non-resonant microwave signal as a function of time in accordance with one or more embodiments described herein. [Figure 15] FIG. 13 shows an example non-limiting graph depicting ZZ coupling as a function of the amplitude of an additional non-resonant microwave signal in accordance with one or more embodiments described herein. [Figure 16] FIG. 1 illustrates a flow diagram of an exemplary non-limiting computer-implemented methodology that facilitates dynamic control of ZZ interactions for quantum computing devices in accordance with one or more embodiments described herein. [Figure 17] FIG. 1 illustrates a block diagram of an exemplary non-limiting operating environment that can facilitate one or more embodiments described herein. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0007] The following detailed description is merely exemplary and is not intended to limit the embodiments or the application and / or uses of the embodiments, nor is it intended to be bound by any express or implied information presented in the preceding "Technical Field" or "Summary" sections, or in the "Description of the Preferred Embodiments" section.

[0008] One or more embodiments are now described with reference to the drawings, in which like reference numerals are used to refer to like elements throughout. In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of one or more embodiments. However, it will be apparent that in various instances, one or more embodiments may be practiced without these specific details.

[0009] Classical computers operate on binary numbers (or bits), which store or represent information as binary states, to perform computations and information processing functions. In contrast, quantum computing devices operate on quantum bits (or qubits), which store or represent information as both binary states and superpositions of binary states. As such, quantum computing devices exploit quantum mechanical phenomena such as entanglement and interference.

[0010] Quantum computing uses quantum bits as its fundamental units, instead of classical computational bits. A quantum bit (e.g., a quantum binary digit) is the quantum mechanical analogue of a classical bit. While a classical bit can only be in one of two basis states (e.g., 0 or 1), a quantum bit can be in any superposition of these basis states (e.g., α|0>+β|1>, where α and β are |α| 2 +|β| 2 = 1). Multiple qubits can be in an exponentially large number of states simultaneously, but when the state of a qubit is measured, the result is either 0 or 1. During the operation of a quantum computer, the state of the qubits is transformed by operations known as gates. During their operation, there can be constructive and / or deconstructive interference of coefficients before the state (i.e., α and β). This dual property of superposition and interference allows quantum computers (e.g., computers that employ qubits rather than only classical bits) to theoretically solve certain problems more quickly than on classical computers. A typical quantum program requires the coordination of quantum mechanical and classical parts of the computation.

[0011] The following definitions are used throughout this disclosure unless otherwise indicated: "qubit" refers to a two-level quantum system. "CR" refers to a cross-resonant gate. "Anharmonicity" (α) refers to the difference between the energy levels of the second and first excited states and transitions of the qubit (e.g., the lowest two energy levels). "Resonant state" refers to when the driving magnetic field is at the same frequency as the transition frequency in the quantum system. "Hamiltonian" refers to the energy of a quantum system expressed in terms of quantum operations. "Stark shift" refers to a shift in the energy levels of a quantum system due to a non-resonant driving magnetic field. "Stark drive" refers to a non-resonant drive that causes an AC Stark shift. "ZZ" refers to a shift in the energy of a state when two qubits are excited. "Gate" refers to an operation on a quantum system that transforms a quantum state. "Single qubit gate" refers to a gate that transforms the state of a single qubit (e.g., typically using microwave drive). A "two-qubit gate" refers to a gate that transforms the combined state of two qubits and involves some form of interaction between the two qubits.

[0012] One common type of quantum circuit implemented in a quantum computing device comprises fixed-frequency transmon qubits with fixed coupling. Each qubit in such a quantum circuit may include a microwave drive line that operably couples the qubit to a bias component. In an embodiment, the Hamiltonian of such a quantum circuit may be approximated using the Hamiltonian defined by Equation 1:

[0013]

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[0014] According to equation 1 above, ω i denotes the qubit frequency of transmon i (i.e., the energy splitting between the two lowest levels), and α iis the anharmonicity of the transmon i (e.g., the energy splitting between the first and second energy levels and ω i (the difference between

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[0015] In some cases, a "resonant" drive signal (e.g., ω d,i =ω i ) can facilitate single-qubit gates. That is, by applying a drive signal that is "on-resonant," manipulation of the state of a particular qubit can be facilitated. For example, a particular qubit can be modulated between a ground state |0> and an excited state |1>. In some cases, cross-resonance can be performed by applying a drive signal that is on-resonance with an adjacent qubit. For example, ω d,0 Cross resonance can be implemented when ω = ω1 or vice versa. Implementing such cross resonance can facilitate an all-microwave method for implementing two-qubit gates.

[0016] In some cases, a "far off-resonance drive" (e.g., |ω d,i -ω i |>>Ω d ) can cause a “Stark shift”; that is, the application of far-resonant drive can cause a shift in the energy of a qubit. In embodiments, the shift in the energy of a qubit caused by the application of far-resonant drive can be approximated using the relationship defined by Equation 2:

[0017]

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[0018] According to equation 2 above, ω i,Starkdenotes the energy of the qubit after application of the non-resonant drive, Δ denotes the detuning of the non-resonant drive from the qubit frequency, and Ω denotes the strength of the non-resonant drive. One feature of the form of the fixed coupling Hamiltonian defined by Equation 1 is that there may be residual unwanted ZZ couplings in the "dressed frame" (e.g., the frame after diagonalizing the Hamiltonian to take into account the coupling terms). In an embodiment, the residual unwanted ZZ couplings may be approximated using the formula defined by Equation 3.

[0019]

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[0020] The ZZ coupling between qubits can be tuned by application of a single Stark drive, and in some cases Stark drive can be used to cancel such ZZ interactions. Furthermore, Stark-induced ZZ coupling can be implemented by using a dual Stark drive to simultaneously drive both qubits at the same frequency. In an embodiment, the ZZ coupling can be approximated within the high power limit using the formula defined by Equation 4:

[0021]

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[0022] Equation 4 shows that the Stark ZZ activation can be effectively set by the ratio of drive power to detune. Equation 4 further shows that the Stark can be a function of the relative phase between the drive tones and can also be proportional to the coupling. Note that this is not a resonant effect of higher transmon levels.

[0023] One element of quantum computing devices that is not trivial is a coupling element known as a two-qubit gate, which facilitates the exchange of information between adjacent qubits. In some cases, cross-resonance techniques have been used to implement such two-qubit gates. However, quantum computing devices that implement cross-resonance gates can encounter a variety of challenges, both in terms of fabrication constraints and gate fidelity.

[0024] As an example, a viable cross-resonant gate typically contains adjacent qubits that are relatively close in frequency (e.g., within anharmonicity) but do not actually overlap. If any resonance condition is met (e.g., adjacent qubits have the same resonant frequency), a frequency collision occurs and typically renders the quantum circuit inoperable. This represents a particularly stringent requirement on the frequency of each qubit coupled to a particular cross-resonant gate. As another example, the ZZ coupling described in Equation 3 (always valid ZZ interaction) can cause unwanted two-qubit coupling that can degrade the performance of the circuit.

[0025] FIG. 1 illustrates a block diagram of an exemplary non-limiting quantum coupling device 100 that can facilitate dynamic control of ZZ interactions for quantum computing devices in accordance with one or more embodiments described herein. As illustrated by the example embodiment depicted in FIG. 1, the device 100 includes a bias component 110, a first qubit 120, and a second qubit 130. The first qubit 120 and the second qubit 130 are operably coupled to the bias component 110 via a first drive line 125 and a second drive line 135, respectively. Examples of qubits suitable for implementing the first qubit 120 and / or the second qubit 130 include, but are not limited to, fixed frequency qubits, tunable qubits, transmon qubits, fixed frequency transmon qubits, tunable transmon qubits, etc. In an embodiment, the first qubit 120 and / or the second qubit 130 can be fixed frequency non-tunable qubits. As described in further detail below, bias component 110 can facilitate dynamic control of the ZZ interaction between qubits (e.g., first qubit 120 or second qubit 130 or both) using a non-resonant microwave signal applied via each drive line (e.g., first drive line 125 or second drive line 135 or both). By varying characteristics of such a non-resonant microwave signal, embodiments of bias component 110 can provide tunable coupling 140 between first qubit 120 and second qubit 130.

[0026] 2-3 illustrate an embodiment in which bias component 110 can facilitate dynamic control of the ZZ interaction between first qubit 120 and second qubit 130 by dynamically adjusting the relative phase difference between the non-resonant microwave signals. In the example embodiment illustrated by FIGS. 2-3, bias component 110 can apply a non-resonant microwave signal to first qubit 120 and second qubit 130 at a constant power value. In this embodiment, first qubit 120 and second qubit 130 can have resonant frequencies of 4900 megahertz (MHz) and 5300 MHz, respectively. In this embodiment, first qubit 120 and second qubit 130 have an exchange coupling strength J of 3 MHz. The non-resonant microwave signals may include a first non-resonant microwave signal applied to the first qubit 120 via the first drive line 125, and a second non-resonant microwave signal applied to the second qubit 130 via the second drive line 135. In an embodiment, the first and second non-resonant microwave signals may have frequency values ​​defined by the respective resonant frequencies of the first qubit 120 and the second qubit 130. For example, in FIGS. 2-3, the frequency value of the first and second non-resonant microwave signals is 5100 MHz. In an embodiment, the first and second non-resonant microwave signals may have equal amplitude values. For example, in FIGS. 2-3, the respective amplitude values ​​of the first and second non-resonant microwave signals are equal. In an embodiment, a common source may generate the first and second non-resonant microwave signals. For example, the bias component 110 may comprise a microwave source that generates the first and second non-resonant microwave signals.

[0027] The Y-axis of graph 200 (e.g., the vertical axis of graph 200) represents the relative phase difference between the non-resonant microwave signals that bias component 110 applies to first qubit 120 and second qubit 130. As illustrated by graph 200, the ZZ coupling between first qubit 120 and second qubit 130 can vary based on the relative phase difference between the non-resonant microwave signals consistent with Equation 4. For example, graph 200 includes a low ZZ coupling point 210 where the ZZ coupling between first qubit 120 and second qubit 130 can be substantially zero. Graph 200 illustrates that the relative phase difference between the non-resonant microwave signals at low ZZ coupling point 210 is approximately 1.7 radians. Graph 200 further includes a high ZZ coupling point 220 where the ZZ coupling between first qubit 120 and second qubit 130 is approximately 1.5 megahertz (MHz). Graph 200 shows that the relative phase difference between the non-resonant microwave signals at high ZZ coupling point 220 is approximately 3.0 radians.

[0028] 3 illustrates an exemplary, non-limiting graph 300 depicting the relative phase difference between non-resonant microwave signals as a function of time, in accordance with one or more embodiments described herein. As illustrated by graph 300, bias component 110 can facilitate dynamic control of ZZ coupling 140 between first qubit 120 and second qubit 130 by dynamically adjusting (or controlling) the relative phase difference. For example, bias component 110 can apply a non-resonant microwave signal at a constant power value to first qubit 120 and second qubit 130 with a relative phase difference of about 1.7 radians during a first time period 310 to cancel the ZZ interaction between first qubit 120 and second qubit 130. In this example, to induce ZZ interaction between the first qubit 120 and the second qubit 130, the bias component 110 can dynamically adjust the relative phase difference between the non-resonant microwave signals from about 1.7 radians to about 3.0 radians during the second time period 320. During the third time period 330, ZZ coupling 140 between the first qubit 120 and the second qubit 130 may be undesirable. Therefore, the bias component 110 can dynamically adjust the relative phase difference between the non-resonant microwave signals from about 3.0 radians to about 1.7 radians during the third time period 330.

[0029] 4-5 show example non-limiting graphs illustrating qubit frequency shift (e.g., Stark frequency shift) versus the relative phase difference between the non-resonant microwave signals and the Rabin factor of both signals, in accordance with one or more embodiments described herein. Specifically, example non-limiting graph 400 shows the qubit frequency shift of first qubit 120, and example non-limiting graph 500 shows the qubit frequency shift of second qubit 130. As shown by graphs 400 and 500, any shift in the qubit frequencies of first qubit 120 and second qubit 130 can be minimized because bias component 110 dynamically adjusts the relative phase difference between the non-resonant microwave signals.

[0030] In an embodiment, as shown in FIGS. 6-7, by introducing an echo π pulse or a frame change pulse into the pulse sequence corresponding to the non-resonant microwave signal, all single qubit Z errors resulting from that dynamic adjustment of the relative phase difference may be corrected. FIGS. 6-7 show exemplary non-limiting pulse sequences including an echo π pulse and a frame change pulse, respectively. Specifically, FIG. 6 shows a first pulse sequence 600 and a second pulse sequence 650. The first pulse sequence 600 corresponds to a first non-resonant microwave signal that the bias component 110 may apply to the first qubit 120 via the first drive line 125. The second pulse sequence 650 corresponds to a second non-resonant microwave signal that the bias component 110 may apply to the second qubit 130 via the second drive line 135.

[0031] 3, pulses 602 and 652 correspond to a non-resonant microwave signal that bias component 110 may apply during first time period 310 to cancel the ZZ interaction between first qubit 120 and second qubit 130. Pulses 610 and 660 correspond to a non-resonant microwave signal that bias component 110 may apply during third time period 330 to cancel the ZZ interaction between first qubit 120 and second qubit 130. Pulses 604 and 608 collectively correspond to a first non-resonant microwave signal that bias component 110 may apply to first qubit 120 during second time period 320 to induce a ZZ interaction between first qubit 120 and second qubit 130. Similarly, pulses 654 and 658 collectively correspond to a second non-resonant microwave signal that bias component 110 may apply to second qubit 130 during second time period 320.

[0032] To correct any single qubit Z errors (e.g., ZI interactions, IZ interactions, or qubit Stark shifts, or a combination thereof) resulting from the dynamic adjustment of the relative phase difference, bias component 110 can introduce an echo π pulse into the off-resonant microwave pulses. For example, bias component 110 can split pulses 604 and 608 into two separate pulses, as shown by FIG. 6. Bias component 110 can also introduce an echo π pulse 606 into the first off-resonant microwave signal such that echo π pulse 606 is interposed between pulse 604 and pulse 608. As another example, bias component 110 can split pulses 654 and 658 into two separate pulses, as shown by FIG. 6. Bias component 110 can also introduce an echo π pulse 656 into the second non-resonant microwave signal such that echo π pulse 656 is interposed between pulse 654 and pulse 658 .

[0033] 7 illustrates a first pulse sequence 700 and a second pulse sequence 750. The first pulse sequence 700 corresponds to a first non-resonant microwave signal that the bias component 110 may apply to the first qubit 120 via the first drive line 125. The second pulse sequence 750 corresponds to a second non-resonant microwave signal that the bias component 110 may apply to the second qubit 130 via the second drive line 135.

[0034] 3, pulses 702 and 752 correspond to a non-resonant microwave signal that bias component 110 may apply during first period 310 to cancel the ZZ interaction between first qubit 120 and second qubit 130. Pulses 708 and 758 correspond to a non-resonant microwave signal that bias component 110 may apply during third period 330 to cancel the ZZ interaction between first qubit 120 and second qubit 130. Pulses 704 and 754 correspond to first and second non-resonant microwave signals, respectively, that bias component 110 may apply during second period 320 to induce a ZZ interaction between first qubit 120 and second qubit 130.

[0035] To correct any single qubit Z errors (e.g., ZI interactions, IZ interactions, or qubit Stark shifts, or a combination thereof) resulting from the dynamic adjustment of the relative phase difference, bias component 110 can introduce a frame-changing pulse to the non-resonant microwave pulses. For example, bias component 110 can introduce a frame-changing pulse 706 to the first non-resonant microwave signal such that frame-changing pulse 706 is interposed between pulse 704 and pulse 708. As another example, bias component 110 can introduce a frame-changing pulse 756 to the second non-resonant microwave signal such that frame-changing pulse 756 is interposed between pulse 754 and pulse 758.

[0036] FIG. 8 illustrates a block diagram of an exemplary non-limiting quantum coupling device 800 that can facilitate dynamic control of ZZ interactions for quantum computing devices in accordance with one or more embodiments described herein. As illustrated by the example embodiment depicted in FIG. 8, the device 800 includes a bias component 110 operably coupled to a lattice of qubits. In FIG. 8, the lattice of qubits includes a first qubit 120, a second qubit 130, a third qubit 850, and a fourth qubit 870. The first qubit 120, the second qubit 130, the third qubit 850, and the fourth qubit 870 are operably coupled to the bias component 110 via a first drive line 125, a second drive line 135, a third drive line 855, and a fourth drive line 875, respectively. Examples of qubits suitable for implementing the first qubit 120, the second qubit 130, the third qubit 850, or the fourth qubit 870, or combinations thereof, include, but are not limited to, fixed frequency qubits, tunable qubits, transmon qubits, fixed frequency transmon qubits, tunable transmon qubits, etc. In an embodiment, the first qubit 120, the second qubit 130, the third qubit 850, or the fourth qubit 870, or combinations thereof, can be fixed frequency non-tunable qubits. As described in further detail below, the bias component 110 can facilitate dynamic control of ZZ interactions between qubits in the lattice using a non-resonant microwave signal applied via each drive line. In particular, the bias component 110 can facilitate dynamic control of pairwise ZZ interactions between selected pairs of qubits in the lattice using a non-resonant microwave signal applied via each drive line.

[0037] In an embodiment where first qubit 120 and second qubit 130 comprise a lattice of qubits including a third qubit (e.g., third qubit 850), facilitating dynamic control of the ZZ interaction between the first and second qubits using bias component 110 includes continuously applying pairwise ZZ interactions between selected pairs of qubits in the lattice to perform a quantum algorithm. In an embodiment where first qubit 120 and second qubit 130 comprise a lattice of qubits including a third qubit (e.g., third qubit 850), facilitating dynamic control of the ZZ interaction between the first and second qubits using bias component 110 includes applying pairwise ZZ interactions between selected pairs of qubits in the lattice to perform adiabatic quantum computing.

[0038] 9 illustrates an exemplary, non-limiting graph 900 depicting the relative phase difference between non-resonant microwave signals as a function of time, in accordance with one or more embodiments described herein. Graph 900 illustrates that bias component 110 can facilitate dynamic control of pairwise ZZ interactions between selected pairs of qubits in the lattice of qubits illustrated in FIG. 8 by dynamically adjusting (or controlling) the relative phase difference of the non-resonant microwave signals. In the example illustrated by FIG. 9, bias component 110 can cancel ZZ interactions between each pair of qubits in the lattice during a first period 910.

[0039] As such, the bias components can apply non-resonant microwave signals via each drive line with respective phase differences corresponding to the low ZZ coupling points (e.g., low ZZ coupling points 210 in FIG. 2). In an embodiment, the non-resonant microwave signals include a constant power value. As illustrated by graph 900, there is a phase difference between each non-resonant microwave signal applied during a first period 910. For example, there is a phase difference between a first non-resonant microwave signal 902 applied to the first qubit 120 via first drive line 125 and a third non-resonant microwave signal 904 applied to the third qubit 850 via third drive line 855. As another example, there is a phase difference between a second non-resonant microwave signal 906 applied to the second qubit 130 via second drive line 135 and a fourth non-resonant microwave signal 908 applied to the fourth qubit 870 via fourth drive line 875.

[0040] During the second period 920, a ZZ coupling 860 between the first qubit 120 and the third qubit 850 may be desired. As such, the bias component 110 may dynamically adjust the relative phase difference between the first non-resonant microwave signal 902 and the third non-resonant microwave signal 904 during the second period 920 to induce a ZZ interaction between the first qubit 120 and the third qubit 850. The bias component 110 may suppress the ZZ interaction between the other qubits in the lattice by maintaining the other respective phase differences such that only the relative phase difference between the first non-resonant microwave signal 902 and the third non-resonant microwave signal 904 changes during the second period 920. For example, the bias component 110 can suppress the ZZ interaction between the first quantum bit 120 and the second quantum bit 130 during the second time period 920 by maintaining a relative phase difference between the first non-resonant microwave signal 902 and the second non-resonant microwave signal 906.

[0041] During the third time period 930, a ZZ coupling 880 between the first qubit 120 and the fourth qubit 870 may be desired. As such, the bias component 110 may dynamically adjust the relative phase difference between the first non-resonant microwave signal 902 and the fourth non-resonant microwave signal 908 during the third time period 930 to induce a ZZ interaction between the first qubit 120 and the fourth qubit 870. The bias component 110 may suppress the ZZ interaction between the other qubits in the lattice by maintaining the other respective phase differences such that only the relative phase difference between the first non-resonant microwave signal 902 and the fourth non-resonant microwave signal 908 changes during the third time period 930. For example, the bias component 110 can suppress the ZZ interaction between the first qubit 120 and the third qubit 850 during the third time period 930 by restoring the relative phase difference between the first non-resonant microwave signal 902 and the third non-resonant microwave signal 904 that was present during the first time period 910.

[0042] During the fourth time period 940, ZZ coupling between any of the qubits of the lattice may be undesirable, so the bias component 110 can dynamically adjust the relative phase difference of the non-resonant microwave signals during the fourth time period such that the relative phase difference that existed between each of the non-resonant microwave signals during the first time period 910 is restored.

[0043] In an embodiment, the Hamiltonian of quantum coupling device 800 in the example described above with respect to FIG. 9 may be approximated using the Hamiltonian defined by Equation 5.

[0044]

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[0045] According to equation 5 above, ξ ij denotes the time-dependent ZZ coupling strength between qubits i and j,

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[0046] 10-11 illustrate an embodiment in which the bias component 110 of FIG. 1 can facilitate dynamic control of the ZZ interaction between the first qubit 120 and the second qubit 130 by dynamically adjusting the amplitude (or drive power) of at least one of the non-resonant microwave signals. In this embodiment, the first qubit 120 and the second qubit 130 can have resonant frequencies of 4900 MHz and 5300 MHz, respectively. In this embodiment, the first qubit 120 and the second qubit 130 have an exchange coupling strength J of 3 MHz. The non-resonant microwave signals can include a first non-resonant microwave signal applied to the first qubit 120 via a first drive line 125, and a second non-resonant microwave signal applied to the second qubit 130 via a second drive line 135. In an embodiment, the first and second non-resonant microwave signals can have a frequency value defined by the respective resonant frequencies of the first qubit 120 and the second qubit 130. For example, in FIGS. 10-11, the frequency value of the first and second non-resonant microwave signals is 5100 MHz. In an embodiment, the first and second non-resonant microwave signals can have equal amplitude values. For example, in FIGS. 10-11, the respective amplitude values ​​of the first and second non-resonant microwave signals are equal. In an embodiment, a phase difference between the first and second non-resonant microwave signals can be fixed. For example, in FIGS. 10-11, the phase difference between the first and second non-resonant microwave signals is fixed at π radians. In an embodiment, a common source can generate the first and second non-resonant microwave signals. For example, the bias component 110 can include a microwave source that generates the first and second non-resonant microwave signals.

[0047] The x-axis of graph 1000 (e.g., the horizontal axis of graph 1000) corresponds to the amplitude (or drive power) of the non-resonant microwave signal that bias component 110 applies to first qubit 120 and second qubit 130. As illustrated by graph 1000, the ZZ coupling between first qubit 120 and second qubit 130 can vary based on the amplitude of the non-resonant microwave signal. For example, graph 1000 includes a low ZZ coupling point 1010 where the ZZ coupling between first qubit 120 and second qubit 130 can be substantially zero. Graph 1000 illustrates that the amplitude of the non-resonant microwave signal at low ZZ coupling point 1010 is approximately 25 MHz. Graph 1000 further includes a high ZZ coupling point 1020 where the ZZ coupling between first qubit 120 and second qubit 130 is approximately 1.5 MHz. Graph 200 shows that the amplitude of the non-resonant microwave signal at high ZZ coupling point 1020 is approximately 95 MHz.

[0048] FIG. 11 illustrates an exemplary, non-limiting graph 1100 depicting the amplitude of a non-resonant microwave signal as a function of time, in accordance with one or more embodiments described herein. As illustrated by graph 1100, bias component 110 can facilitate dynamic control of ZZ coupling 140 between first qubit 120 and second qubit 130 by dynamically adjusting (or controlling) the amplitude of the non-resonant microwave signal. For example, bias component 110 can apply a non-resonant microwave signal to first qubit 120 and second qubit 130 at an amplitude of about 25 MHz during a first time period 1110 to cancel the ZZ interaction between first qubit 120 and second qubit 130. In this example, to induce the ZZ interaction between first qubit 120 and second qubit 130, bias component 110 can dynamically adjust the amplitude of the non-resonant microwave signal from about 25 MHz to about 95 MHz during a second time period 1120. During the third time period 1130, ZZ coupling 140 between the first qubit 120 and the second qubit 130 may be undesirable. Therefore, the bias component 110 can dynamically adjust the amplitude of the non-resonant microwave signal from about 95 MHz to about 25 MHz during the third time period 1130.

[0049] In an embodiment, as shown in FIGS. 12-13, by introducing an echo π pulse or a frame change pulse into the pulse sequence corresponding to the non-resonant microwave signal, all single qubit Z errors resulting from that dynamic adjustment of the amplitude of the non-resonant microwave signal may be corrected. FIGS. 12-13 show exemplary non-limiting pulse sequences including an echo π pulse and a frame change pulse, respectively. Specifically, FIG. 12 shows a first pulse sequence 1200 and a second pulse sequence 1250. The first pulse sequence 1200 corresponds to a first non-resonant microwave signal that the bias component 110 may apply to the first qubit 120 via the first drive line 125. The second pulse sequence 1250 corresponds to a second non-resonant microwave signal that the bias component 110 may apply to the second qubit 130 via the second drive line 135.

[0050] 11 , pulses 1202 and 1206 collectively correspond to a first non-resonant microwave signal that bias component 110 may apply to first qubit 120 during second period 1120 to induce a ZZ interaction between first qubit 120 and second qubit 130. Similarly, pulses 1252 and 1256 collectively correspond to a second non-resonant microwave signal that bias component 110 may apply to second qubit 130 during second period 1120.

[0051] To correct any single qubit Z errors (e.g., ZI interactions, IZ interactions, or qubit Stark shifts, or a combination thereof) resulting from dynamic adjustment of the amplitude of the non-resonant microwave signal, bias component 110 can introduce an echo π pulse into the non-resonant microwave pulse. For example, bias component 110 can split pulses 1202 and 1206 into two separate pulses, as shown by FIG. 12. Bias component 110 can also introduce an echo π pulse 1204 into the first non-resonant microwave signal such that echo π pulse 1204 is interposed between pulse 1202 and pulse 1206. As another example, bias component 110 can split pulses 1252 and 1256 into two separate pulses, as shown by FIG. 12. Bias component 110 can also introduce an echo π pulse 1254 into the second non-resonant microwave signal such that echo π pulse 1254 is interposed between pulse 1252 and pulse 1256 .

[0052] 13 illustrates a first pulse sequence 1300 and a second pulse sequence 1350. The first pulse sequence 1300 corresponds to a first non-resonant microwave signal that the bias component 110 may apply to the first qubit 120 via the first drive line 125. The second pulse sequence 1350 corresponds to a second non-resonant microwave signal that the bias component 110 may apply to the second qubit 130 via the second drive line 135. With reference to FIG. 11, pulses 1302 and 1352 correspond to first and second non-resonant microwave signals, respectively, that the bias component 110 may apply during the second time period 1120 to induce a ZZ interaction between the first qubit 120 and the second qubit 130.

[0053] To correct any single qubit Z errors (e.g., ZI interactions, IZ interactions, or qubit Stark shifts, or a combination thereof) resulting from dynamic adjustment of the amplitude of the non-resonant microwave signal, bias component 110 can introduce a frame-changing pulse to the non-resonant microwave pulse. For example, bias component 110 can introduce a frame-changing pulse 1304 to the first non-resonant microwave signal such that frame-changing pulse 1304 follows pulse 1302 in the first pulse sequence 1300. As another example, bias component 110 can introduce a frame-changing pulse 1354 to the second non-resonant microwave signal such that frame-changing pulse 1354 follows pulse 1352 in the second pulse sequence 1350.

[0054] 14 illustrates an exemplary, non-limiting graph 1400 depicting the amplitude (or drive power value) of a non-resonant microwave signal as a function of time, in accordance with one or more embodiments described herein. Graph 1400 illustrates that the bias component 110 can facilitate dynamic control of pairwise ZZ coupling between selected pairs of qubits in the lattice of qubits illustrated in FIG. 8 by dynamically adjusting (or controlling) the amplitude of at least one of the non-resonant microwave signals. In the example illustrated by FIG. 14, each pairwise ZZ coupling involves a non-resonant microwave signal having a different frequency. As such, the non-resonant microwave signals of FIG. 14 include (i) a first non-resonant microwave signal 1402 having a first frequency that may be applied to the first quantum bit 120 and the second quantum bit 130 via respective drive lines, (ii) a second non-resonant microwave signal 1404 having a second frequency that may be applied to the first quantum bit 120 and the third quantum bit 850 via respective drive lines, and (iii) a third non-resonant microwave signal 1406 having a third frequency that may be applied to the first quantum bit 120 and the fourth quantum bit 870 via respective drive lines.

[0055] During the first period 1410, ZZ coupling between any qubits in the lattice may be undesirable. Therefore, the bias component 110 cancels the ZZ interaction between each pair of qubits in the lattice during the first period 1410 by applying non-resonant microwave signals at amplitudes corresponding to low ZZ coupling points (e.g., low ZZ coupling points 1010 in FIG. 10).

[0056] During the second period 1420, ZZ coupling 140 between the first qubit 120 and the second qubit 130 may be desired. To that end, the bias component 110 may dynamically adjust (or pulse) the amplitude of the first non-resonant microwave signal 1402 from the amplitude that existed during the first period 1410 to an amplitude that corresponds to a high ZZ coupling point (e.g., high ZZ coupling point 1020 of FIG. 10) during the second period 1420 to induce ZZ interaction between the first qubit 120 and the second qubit 130. The bias component 110 may suppress ZZ interaction between other qubits in the lattice by maintaining the other non-resonant microwave signals at their respective amplitudes that existed during the first period 1410. For example, the bias component 110 can suppress the ZZ interaction between the first qubit 120 and the third qubit 850 during the second time period 1420 by maintaining the second non-resonant microwave signal 1404 at the amplitude that was present during the first time period 1410.

[0057] During the third period 1430, ZZ coupling 860 between the first qubit 120 and the third qubit 850 may be desired. To that end, the bias component 110 may dynamically adjust (or pulse) the amplitude of the second non-resonant microwave signal 1404 from the amplitude present during the first period 1410 and the second period 1420 to an amplitude corresponding to a high ZZ coupling point during the third period 1430 to induce ZZ interaction between the first qubit 120 and the third qubit 850. The bias component 110 may suppress ZZ interaction between other qubits in the lattice by adding other non-resonant microwave signals at the respective amplitudes present during the first period 1410. For example, the bias component 110 can suppress the ZZ interaction between the first quantum bit 120 and the second quantum bit 130 during the third period 1430 by dynamically adjusting the first non-resonant microwave signal 1402 from the amplitude that was present during the second period 1420 to the amplitude that was present during the first period 1410.

[0058] During the fourth period 1440, ZZ coupling 880 between the first qubit 120 and the fourth qubit 870 may be desirable. To that end, bias component 110 may dynamically adjust (or pulse) the amplitude of third non-resonant microwave signal 1406 from the amplitude present during the first period 1410-third period 1430 to an amplitude corresponding to a high ZZ coupling point during the fourth period 1440 to induce ZZ interaction between the first qubit 120 and the fourth qubit 870. Bias component 110 may suppress ZZ interaction between other qubits in the lattice by adding other non-resonant microwave signals at the respective amplitudes present during the first period 1410. For example, the bias component 110 can suppress the ZZ interaction between the first quantum bit 120 and the third quantum bit 850 during the fourth period 1440 by dynamically adjusting the second non-resonant microwave signal 1404 from the amplitude that was present during the third period 1430 to the amplitude that was present during the first period 1410 and the second period 1420.

[0059] During the fifth period 1450, ZZ coupling between any qubits in the lattice may be undesirable, so the bias component 110 can cancel the ZZ interaction between each pair of qubits in the lattice during the fifth period 1450 by applying non-resonant microwave signals at amplitudes corresponding to low ZZ coupling points.

[0060] FIG. 15 illustrates an exemplary, non-limiting graph 1500 depicting ZZ coupling as a function of the amplitude of an additional non-resonant microwave signal, according to one or more embodiments described herein. In the example of FIG. 15, the first qubit 120 and the second qubit 130 can have resonant frequencies of 4900 MHz and 5300 MHz, respectively. In the example of FIG. 15, the first qubit 120 and the second qubit 130 have an exchange coupling strength J of 3 MHz. To obtain the exemplary graph 1500, the bias component 110 applies a common non-resonant microwave signal having a frequency of 5100 MHz to the first qubit 120 and the second qubit 130. The bias component 110 also applies an additional non-resonant microwave signal having a frequency of 5250 MHz to the first qubit 120. The x-axis of the graph 1500 (e.g., the horizontal axis of the graph 1500) corresponds to the amplitude (or drive power) of the additional non-resonant microwave signal.

[0061] 16 illustrates a flow diagram of an exemplary non-limiting computer-implemented method 1600 for facilitating dynamic control of ZZ interactions for a quantum computing device in accordance with one or more embodiments described herein. Repetitive descriptions of similar elements employed in other embodiments described herein have been omitted for the sake of brevity.

[0062] At 1610, the computer-implemented method 1600 may include operably coupling, by a system operably coupled to the processor, a bias component (e.g., bias component 110 of FIG. 1 ) to first and second quantum bits (e.g., first quantum bit 120 and second quantum bit 130) via respective first and second drive lines (e.g., first drive line 125 and second drive line 135).

[0063] At 1620, the computer-implemented method 1600 may include dynamically controlling, by the system, a ZZ interaction between the first and second quantum bits with a non-resonant microwave signal applied via each of the first and second drive lines using a bias component. In an embodiment, dynamically controlling the ZZ interaction between the first and second quantum bits using a bias component may include dynamically adjusting, by the system, a relative phase difference between the non-resonant microwave signals. In an embodiment, a common source may generate the non-resonant microwave signals. In an embodiment, the non-resonant microwave signals may include a frequency value defined by a respective resonant frequency of the first and second quantum bits. In an embodiment, the non-resonant microwave signal may include a constant power value.

[0064] In an embodiment, dynamically controlling the ZZ interaction between the first and second qubits using the bias component can include dynamically adjusting the amplitude of at least one of the non-resonant microwave signals. In an embodiment, the first and second qubits comprise a lattice of qubits including a third qubit (e.g., third qubit 850 of FIG. 8). In an embodiment, facilitating dynamic control of the ZZ interaction between the first and second qubits using the bias component can include continuously applying pairwise ZZ interactions between selected pairs of qubits in the lattice to perform a quantum algorithm. In an embodiment, facilitating dynamic control of the ZZ interaction between the first and second qubits using the bias component can include applying pairwise ZZ interactions between selected pairs of qubits in the lattice to perform adiabatic quantum computing.

[0065] In an embodiment, the computer-implemented method 1600 may further include operably coupling, by the system, a third qubit (e.g., third qubit 850 of FIG. 8 ) to a bias component via a third drive line (e.g., third drive line 855). In an embodiment, the computer-implemented method 1600 may further include inducing, by the system, at the bias component, a ZZ interaction between the first and third qubits by adjusting the relative phase difference between the non-resonant microwave signals applied via the respective first and third drive lines.

[0066] In an embodiment, the computer-implemented method 1600 may further include operably coupling a third qubit (e.g., third qubit 850 of FIG. 8) to a bias component via a third drive line (e.g., third drive line 855). In an embodiment, the computer-implemented method 1600 may further include suppressing ZZ interaction between the third and first qubits by maintaining, at the bias component, a phase difference between the non-resonant microwave signals applied via the respective third and first drive lines.

[0067] To provide background for various aspects of the disclosed subject matter, FIG. 17 and the following discussion are intended to provide a general overview of a suitable environment in which various aspects of the disclosed subject matter may be implemented. Implementing various aspects of the present disclosure may include a computer 1712, so FIG. 17 illustrates a suitable operating environment 1700. The computer 1712 may include a processing unit 1714, a system memory 1716, and a system bus 1718. The system bus 1718 couples system components, including but not limited to the system memory 1716, to the processing unit 1714. The processing unit 1714 may be any of a variety of available processors. Dual microprocessors and other multi-processor architectures may also be employed as the processing unit 1714. The system bus 1718 can be any of several types of bus structures including a memory bus or memory controller, a peripheral bus or external bus, and / or a local bus using any of a variety of available bus architectures including, but not limited to, Industry Standard Architecture (ISA), Micro Channel Architecture (MCA), Enhanced ISA (EISA), Intelligent Drive Electronics (IDE), VESA Local Bus (VLB), Peripheral Component Interconnects (PCI), Cardbus, Universal Serial Bus (USB), Advanced Graphics Port (AGP), Firewire (IEEE 1094), and Small Computer Systems Interface (SCSI). The system memory 1716 can also include volatile memory 1720 and non-volatile memory 1722.The basic input / output system (BIOS), containing the basic routines for transferring information between elements within computer 1712, such as during start-up, is stored in nonvolatile memory 1722. Examples of nonvolatile memory 1722 include, but are not limited to, read only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), flash memory, or nonvolatile random access memory (RAM) such as ferroelectric RAM (FeRAM). Volatile memory 1720 can also include random access memory (RAM), which acts as external cache memory. For example, RAM is available in many forms, including, but not limited to, static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), direct Rambus RAM (DRRAM), direct Rambus dynamic RAM (DRDRAM), and Rambus dynamic RAM.

[0068] The computer 1712 may also include removable / non-removable, volatile / non-volatile computer storage media. For example, FIG. 17 shows disk storage 1724. Disk storage 1724 may include devices such as, but not limited to, a magnetic disk drive, a floppy disk drive, a tape drive, a Jaz drive, a Zip drive, an LS-100 drive, a flash memory card, or a memory stick. Disk storage 1724 may also include storage media, separately or in combination with other storage media, including, but not limited to, an optical disk drive, such as a compact disk ROM (CD-ROM) device, a CD recordable (CD-R) drive, a CD rewritable (CD-RW) drive, or a digital versatile disk ROM (DVD-ROM) drive. To facilitate connection of the disk storage 1724 to the system bus 1718, a removable or non-removable interface, such as interface 1726, is typically used. 17 also illustrates software that acts as an intermediary between a user and the basic computer resources described in suitable operating environment 1700. Such software may include, for example, an operating system 1728. The operating system 1728, which may be stored on disk storage 1724, operates to control and allocate resources of the computer 1712. System applications 1730 take advantage of the management of resources by the operating system 1728 through program modules 1732 and program data 1734 stored, for example, in either the system memory 1716 or on the disk storage 1724. It is to be understood that the present disclosure may be implemented using various operating systems or combinations of operating systems.A user inputs commands or information into the computer 1712 through the input devices 1736. The input devices 1736 include, but are not limited to, pointing devices such as a mouse, trackball, stylus, touch pad, keyboard, microphone, joystick, game pad, satellite dish, scanner, TV tuner card, digital camera, digital video camera, web camera, etc. These and other input devices connect to the processing unit 1714 through the system bus 1718 via interface ports 1738. The interface ports 1738 include, for example, serial ports, parallel ports, game ports, and universal serial bus (USB). The output devices 1740 use some of the same types of ports as the input devices 1736. In this manner, for example, a USB port can be used to provide input to the computer 1712 and to output information from the computer 1712 to the output devices 1740. Output adapter 1742 is provided to indicate the presence of any output devices 1740 such as monitors, speakers, and printers, among other output devices 1740 that require special adapters. Examples of output adapters 1742 include, but are not limited to, video cards and sound cards, which provide a means of connection between the output device(s) 1740 and the system bus 1718. Other devices and / or systems of devices, such as remote computer(s) 1744, may be said to provide both input and output capabilities.

[0069] The computer 1712 can operate in a networked environment using logical connections to one or more remote computers, such as a remote computer 1744. The remote computer 1744 can be a computer, a server, a router, a network PC, a workstation, a microprocessor-based device, a peer device, or other common network node, and can typically include many of the elements described in conjunction with the computer 1712. For simplicity, only a memory storage device 1746 is shown with the remote computer 1744. The remote computer 1744 is logically connected to the computer 1712 through a network interface 1748 and then physically connected through a communication connection 1750. The network interface 1748 encompasses wired and / or wireless communication networks, such as local-area networks (LANs), wide-area networks (WANs), cellular networks, and the like. LAN technologies include Fiber Distributed Data Interface (FDDI), Copper Distributed Data Interface (CDDI), Ethernet, Token Ring, and the like. WAN technologies include, but are not limited to, point-to-point links, circuit-switched networks such as Integrated Services Digital Networks (ISDN) and variations thereon, packet-switched networks, and Digital Subscriber Lines (DSL). Communications connection 1750 refers to the hardware / software employed to connect network interface 1748 to system bus 1718. Communications connection 1750 is shown within computer 1712 for clarity of illustration, but may also be external to computer 1712.The hardware / software for connecting to the network interface 1748 may include, by way of example only, internal and external technologies such as modems, including ordinary telephone grade modems, cable modems, and DSL modems, ISDN adapters, and Ethernet cards.

[0070] The present invention may be a system, a method, an apparatus, or a computer program product, or a combination thereof, at any possible level of technical detail of integration. The computer program product may include a computer readable storage medium containing computer readable program instructions for causing a processor to perform aspects of the present invention. The computer readable storage medium may be a tangible device that can hold and store instructions for use by an instruction execution device. The computer readable storage medium may be, for example, but not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination thereof. A non-exhaustive list of more specific examples of computer-readable storage media may include portable computer diskettes, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital versatile disk (DVD), memory sticks, floppy disks, mechanically encoded devices such as punch cards or raised structures in grooves in which the instructions are recorded, and any suitable combinations of these. As used herein, computer-readable storage media should not itself be construed as being ephemeral signals such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission medium (e.g., light pulses passing through a fiber optic cable), or electrical signals transmitted over wires.

[0071] The computer readable program instructions described herein may be downloaded from a computer readable storage medium to each computing device / processing device or to an external computer or storage device over a network (e.g., the Internet, a local area network, a wide area network, or a wireless network, or a combination thereof) that may comprise copper transmission cables, optical transmission fiber, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface within each computing device / processing device receives the computer readable program instructions from the network and forwards the computer readable program instructions for storage on a computer readable storage medium within each computing device / processing device. The computer readable program instructions for carrying out the operations of the present invention may be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state setting data, configuration data for an integrated circuit, or source or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk®, C++, and procedural programming languages ​​such as the "C" programming language or similar programming languages. The computer readable program instructions may execute entirely on the user's computer, partially on the user's computer as a stand-alone software package, partially on each of the user's computer and a remote computer, or entirely on the remote computer or server.In the latter scenario, the remote computer can be connected to the user's computer through any type of network, including a local area network (LAN) or wide area network (WAN), or the connection can be made to an external computer (e.g., through the Internet using an Internet Service Provider). In some embodiments, to perform aspects of the invention, electronic circuitry, including, for example, programmable logic circuits, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), can execute computer-readable program instructions to customize the electronic circuitry by utilizing state information of the computer-readable program instructions.

[0072] Aspects of the present invention are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks included in the flowchart illustrations and / or block diagrams, can be implemented by computer readable program instructions. These computer readable program instructions can be provided to a processor of a general purpose computer, a special purpose computer, or other programmable data processing apparatus to create a machine, where the instructions executed via a processor of the computer or other programmable data processing apparatus create means for performing the functions / operations specified in the blocks of the flowcharts and / or block diagrams. These computer readable program instructions can also be stored on a computer readable storage medium and can instruct a computer, programmable data processing apparatus, or other device, or combination thereof, to function in a particular manner, such that the computer readable storage medium on which the instructions are stored comprises an article of manufacture including instructions for performing aspects of the functions / operations specified in the blocks of the flowcharts and / or block diagrams. The computer-readable program instructions may be loaded into a computer, other programmable data processing apparatus, or other device to generate a computer-implemented process and cause a series of operable operations to be performed on the computer, other programmable apparatus, or other device, such that the instructions, which execute on the computer, other programmable apparatus, or other device, perform the functions / operations specified in the flowchart and / or block diagram blocks.

[0073] The flowcharts and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, including one or more executable instructions for implementing the specified logical function. In some alternative implementations, the functions shown in the blocks may occur in a different order than the order shown in the figures. For example, two blocks shown in succession may in fact be executed substantially simultaneously or in reverse order, depending on the functionality involved. It is also noted that each block in the block diagrams and / or flowchart illustrations, as well as combinations of blocks included in the block diagrams and / or flowchart illustrations, may be implemented by a dedicated hardware-based system that performs the specified functions or operations or executes a combination of dedicated hardware and computer instructions.

[0074] Although the subject matter has been described above in the general context of computer-executable instructions for a computer program product executed on one or more computers, or both, those skilled in the art will recognize that the present disclosure may be combined with or implemented in combination with other program modules. Typically, program modules include routines, programs, components, data structures, etc. that perform particular tasks and / or implement particular abstract data types. Furthermore, those skilled in the art will appreciate that the computer-implemented methods of the present invention may be practiced using other computer system configurations, including single-processor or multi-processor computer systems, minicomputing devices, mainframe computers, computers, handheld computing devices (e.g., PDAs, phones), microprocessor-based or programmable consumer or industrial electronics, and the like. The illustrated aspects may also be practiced in a distributed computing environment, where tasks are performed by remote processing devices linked through a communications network. However, some, if not all, aspects of the present disclosure may be practiced on stand-alone computers. In a distributed computing environment, program modules may be located in both local and remote memory storage devices. For example, in one or more embodiments, the computer-executable components may be executed from a memory, which may include or consist of one or more distributed memory units. As used herein, "memory" and "memory unit" are interchangeable. Furthermore, one or more embodiments described herein may execute the code of the computer-executable components in a distributed manner, e.g., with multiple processors coupled or acting in concert to execute the code from one or more distributed memory units.As used herein, the term "memory" can encompass a single memory or memory unit in one location or multiple memories or memory units in one or more locations.

[0075] As used in this application, terms such as "component," "system," "platform," "interface," and the like, can refer to and / or include a computer-related or operable machine-related entity that includes one or more specific functions. The entities disclosed herein can be either hardware, a combination of hardware and software, software, or software in execution. For example, a component can be, but is not limited to, a process running on a processor, a processor, an object, an executable, a thread of execution, a program, or a computer, or combinations thereof. As an example, both an application running on a server and the server can be a component. One or more components can reside within a process and / or a thread of execution, and a component can be localized on one computer or distributed between two or more computers, or / and. In another example, each component can execute from various computer readable media having various data structures stored thereon. A component may communicate via local and / or remote processes, such as according to signals containing one or more data packets (e.g., data from one component communicating with another component in a local or distributed system, or communicating with other systems via signals over a network such as the Internet, or both). As another example, a component may be a device having a specific function provided by mechanical parts operated by electrical or electronic circuits, and operated by a software or firmware application executed by a processor. In such cases, the processor may be internal or external to the device and may execute at least a portion of the software or firmware application.As yet another example, a component can be a device that provides a particular functionality through electronic components that do not include mechanical parts, and those electronic components can include a processor or other means for executing software or firmware that provides at least a portion of the functionality of the electronic component. In one aspect, a component can emulate an electronic component through a virtual machine, for example, in a cloud computing system.

[0076] In addition, the term "or" is intended to mean an inclusive or rather than an exclusive or. That is, unless otherwise specified or clear from the context, "X employs A or B" is intended to mean any of the natural inclusive permutations. That is, if X employs A, X employs B, or X employs both A and B, then "X employs A or B" is satisfied in any of the foregoing cases. Furthermore, the articles "a" and "an" used in this specification and the accompanying drawings should generally be construed to mean "one or more" unless otherwise specified or clear from the context to cover the singular form. As used herein, the terms "example" and / or "exemplary" are used to mean serving as an example, instance, or illustration. For the avoidance of doubt, the subject matter disclosed herein is not limited by such examples. Additionally, any aspect or design described herein as "example" and / or "exemplary" is not necessarily to be construed as preferred or advantageous over other aspects or designs, and is not intended to exclude equivalent exemplary structures and techniques known to those skilled in the art.

[0077] As used herein, the term "processor" may refer to virtually any computing unit or device, including, but not limited to, single-core processors, single processors with software multithreaded execution capabilities, multi-core processors, multi-core processors with software multithreaded execution capabilities, multi-core processors with hardware multithreading techniques, parallel platforms, and parallel platforms with distributed shared memory. Additionally, a processor may refer to an integrated circuit, an application specific integrated circuit (ASIC), a digital signal processor (DSP), a field programmable gate array (FPGA), a programmable logic controller (PLC), a complex programmable logic device (CPLD), discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. Additionally, a processor may utilize nanoscale architectures, such as, but not limited to, molecular and quantum dot-based transistors, switches, and gates, to optimize space utilization and improve performance of user equipment. A processor may be implemented as a combination of computing processing units. In this disclosure, terms such as "store," "storage," "data store," "data storage," "database," and substantially any other information storage component that relate to the operation and functionality of a component are used to refer to a "memory component," an entity embodied in a "memory," or a component that comprises a memory.It should be understood that the memory and / or memory components described herein can be either volatile or non-volatile memory, or can include both volatile and non-volatile memory. Examples of non-volatile memory include, but are not limited to, read only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable ROM (EEPROM), flash memory, or non-volatile random access memory (RAM) (e.g., ferroelectric RAM (FeRAM)). Volatile memory can include RAM, which can act as an external cache memory, for example. For example, RAM is available in many forms, including, but not limited to, synchronous RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), direct Rambus RAM (DRRAM), direct Rambus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM). Additionally, the memory components of the systems or computer-implemented methods disclosed herein are intended to include memory, including, but not limited to, these and any other suitable types of memory.

[0078] The foregoing includes merely examples of systems and computer-implemented methods. Of course, for purposes of describing this disclosure, it is not possible to describe every conceivable combination of components or computer-implemented methods, but one of ordinary skill in the art will recognize that many other combinations and permutations of the present disclosure are possible. Furthermore, to the extent that terms such as "including," "having," "possessing," and the like are used in the detailed description, claims, appendices, and drawings, such terms are intended to be inclusive in a similar manner to the term "comprising" as "comprising" is interpreted when used as a transitional term in the claims.

[0079] The description of various embodiments is presented for illustrative purposes, but is not intended to be exhaustive and is not limited to the disclosed embodiments. Many changes and modifications that do not depart from the scope and spirit of the described embodiments will be apparent to those skilled in the art. The terms used in this specification are selected to best explain the principles of the embodiments, practical applications, or technical improvements beyond the technology found in the market, or to enable other skilled in the art to understand the embodiments disclosed herein.

Claims

1. A quantum coupled device comprising a bias component operably coupled to a first quantum bit and a second quantum bit via a first drive line and a second drive line, respectively, wherein the bias component facilitates dynamic control of a ZZ interaction between the first quantum bit and the second quantum bit using a non-resonant microwave signal applied via the first drive line and the second drive line, respectively.

2. 10. The quantum coupling device of claim 1 , wherein the bias component facilitates dynamic control of a ZZ interaction between the first quantum bit and the second quantum bit by dynamically adjusting a relative phase difference between the non-resonant microwave signals.

3. 3. The quantum coupling device of claim 1, wherein a common source generates the non-resonant microwave signals.

4. 4. The quantum coupling device of claim 1, wherein the non-resonant microwave signal comprises a frequency value defined by a respective resonant frequency of the first quantum bit and the second quantum bit.

5. The quantum coupling device of claim 1 , wherein the non-resonant microwave signal comprises a constant power value.

6. 6. The quantum coupling device of claim 1, wherein single qubit Z errors are corrected by echo or frame change.

7. 7. The quantum coupling device of claim 1, further comprising a third quantum bit operably coupled to the bias component via a third drive line, the bias component inducing a ZZ interaction between the first quantum bit and the third quantum bit by adjusting a relative phase difference between the non-resonant microwave signals applied via each of the first drive line and the third drive line.

8. 8. The quantum coupled device of claim 1, further comprising a third quantum bit operably coupled to the bias component via a third drive line, the bias component suppressing ZZ interaction between the third quantum bit and the first quantum bit by maintaining a phase difference between the non-resonant microwave signals applied via the third drive line and the first drive line, respectively.

9. 9. The quantum coupling device of claim 1 , wherein the bias component controls a ZZ interaction between the first quantum bit and the second quantum bit by dynamically adjusting the amplitude of at least one of the non-resonant microwave signals.

10. 10. A quantum coupling device according to claim 1, wherein for ZZ gate operation, the Stark shift of the qubit is cancelled by echo or frame change.

11. operatively coupling, by a system operatively coupled to the processor, a bias component to the first qubit and the second qubit via a first drive line and a second drive line, respectively; and dynamically controlling, by the system, a ZZ interaction between the first qubit and the second qubit with a non-resonant microwave signal applied via each of the first drive line and the second drive line using the bias component.

12. dynamically controlling a ZZ interaction between the first qubit and the second qubit using the bias component; The computer-implemented method of claim 11 , comprising dynamically adjusting, by the system, a relative phase difference between the non-resonant microwave signals.

13. 13. The computer-implemented method of claim 11, wherein a common source generates the non-resonant microwave signals.

14. 14. The computer-implemented method of claim 11, wherein the non-resonant microwave signal comprises a frequency value defined by a respective resonant frequency of the first quantum bit and the second quantum bit.

15. 15. The computer-implemented method of claim 11, wherein the non-resonant microwave signal comprises a constant power value.

16. operably coupling, by the system, a third qubit to the bias component via a third drive line; 16. The computer-implemented method of claim 11, further comprising: inducing, by the system, a ZZ interaction between the first qubit and the third qubit by adjusting, with the bias component, a relative phase difference between the non-resonant microwave signals applied via each of the first drive line and the third drive line.

17. operably coupling, by the system, a third qubit to the bias component via a third drive line; 17. The computer-implemented method of claim 11, further comprising: suppressing ZZ interaction between the third qubit and the first qubit by maintaining a phase difference between the non-resonant microwave signals applied via the third drive line and the first drive line, respectively, with the bias component.

18. facilitating dynamic control of a ZZ interaction between the first qubit and the second qubit using the bias component; 18. The computer-implemented method of claim 11, comprising dynamically adjusting, by the system, an amplitude of at least one of the non-resonant microwave signals.

19. the first qubit and the second qubit comprise a lattice of qubits including a third qubit, and facilitating dynamic control of a ZZ interaction between the first qubit and the second qubit using the bias component; 19. The computer-implemented method of claim 11, comprising successively applying pairwise ZZ interactions between selected pairs of qubits in the lattice to perform a quantum algorithm.

20. the first qubit and the second qubit comprise a lattice of qubits including a third qubit, and facilitating dynamic control of a ZZ interaction between the first qubit and the second qubit using the bias component; 20. The computer-implemented method of claim 11, comprising applying pairwise ZZ interactions between selected pairs of qubits in the lattice to perform adiabatic quantum computing.

21. operably coupling, by the system, a third qubit to the bias component via a third drive line; dynamically adjusting a first non-resonant microwave signal applied via the first drive line and the third drive line to a first amplitude corresponding to a high ZZ coupling point; and applying a second non-resonant microwave signal applied via the first drive line and the second drive line at a second amplitude corresponding to a low ZZ coupling point, wherein the non-resonant microwave signals comprise the first non-resonant microwave signal and the second non-resonant microwave signal, the first non-resonant microwave signal comprising a first frequency and the second non-resonant microwave signal comprising a second frequency different from the first frequency.

22. A computer comprising: operatively coupling a bias component to the first qubit and the second qubit via a first drive line and a second drive line, respectively; and using the bias component to facilitate dynamic control of a ZZ interaction between the first quantum bit and the second quantum bit with a non-resonant microwave signal applied via each of the first drive line and the second drive line.

23. In the computer, 23. The computer program product of claim 22, further comprising: using the bias component to facilitate dynamic control of a ZZ interaction between the first quantum bit and the second quantum bit by dynamically adjusting a relative phase difference between the non-resonant microwave signals or by adjusting an amplitude of at least one of the non-resonant microwave signals.

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