Flux bias system and method for superconducting quantum circuits

Abstract

Quantum computing systems require methods for controlling the energy of qubits and couplers for quantum operations. Flux biasing of qubits and quantum couplers is provided for superconducting quantum computers using single flux quantum (SFQ) technology. The method is applicable to a wide range of superconducting qubit structures and couplers, including transmons, flaxonium, flux qubits, phase qubits, and other superconducting qubits. The method allows for arbitrary amplitude time-varying flux biasing of qubits and couplers due to a sequence of fast SFQ pulses. Several preferred embodiments are disclosed that provide high fidelity control of fast single-qubit and multi-qubit operations.

Description

[Technical field]

[0001] The present invention relates to the field of superconducting circuits, and more particularly to superconducting circuits for quantum computing applications. [Background technology]

[0002] Each patent, patent publication, and other reference cited herein is expressly incorporated herein by reference in its entirety for all purposes.

[0003] Superconducting integrated circuits based on Josephson junctions (JJ) are capable of operating at very low power and high speeds, far beyond those possible using conventional semiconductor circuits. It has long been known that superconducting integrated circuits can be used for digital logic circuits based on single flux quantum (SFQ) pulses. These SFQ pulses have a pulse length of Φ 1, each containing one fluxon of magnetic flux, typically corresponding to a pulse height of about 1 mV and a pulse width of about 2 ps. 0 =h / 2e=2.07mV·ps. Several logic families based on SFQ pulses are known in the prior art, including Rapid Single Flux Quantum (RSFQ), Energy Efficient RSFQ (EERSFQ), Reciprocal Quantum Logic (RQL), and Quantum Flux Parametron (QFP). Despite the word "quantum", all of these logic families involve classical digital computing using classical bits. See, for example, the following U.S. Patents: 8,571,614, 9,473,124, 9,853,645, 10,917,096, 10,528,886, 10,748,079, 7,969,178, 8,138,784, 9,646,682, and 10,084,454.

[0004] Recently, superconducting integrated circuits composed of multiple JJs have also been applied to true quantum computing using quantum bits (qubits), which may enable calculations that cannot be achieved using classical computers. There are several types of superconducting qubits disclosed in the prior art, such as flux qubits, phase qubits, charge qubits, topological qubits, flaxonium qubits, and transmon qubits. See, for example, the following U.S. patents and published application numbers: 6,459,097; 6,504,172; 6,576,951; 6,627,915; 6,784,451; 6,838,694; 6,984,846; 7,268,576; 7,335,909; 7,843,209; 8,648,331; Nos. 8,654,578, 9,524,470, 9,685,935, 10,068,184, 10,176,432, 10,255,557, 10,256,392, 10,622,998, 10,789,123, 10,840,295, 10,949,769 and 2020 / 0280316.

[0005] Each qubit has an infinite number of different potential quantum mechanical states. When the state of a qubit is physically measured, the measurement produces one of two different basis states that are resolved from the state of the qubit. Hence, a single qubit can represent one, zero, or any quantum superposition of those two qubit states, a pair of qubits can be in any quantum superposition of four orthogonal basis states, and three qubits can be in any superposition of eight orthogonal basis states. The function that defines the quantum mechanical state of a qubit is known as the wave function of the qubit. The wave function also specifies the probability distribution of the outcome of a given measurement.

[0006] Although particular descriptions of qubits herein may describe such qubits in terms of the mathematical properties of the qubit, each such qubit may be implemented in a physical medium in any of a variety of different ways. Examples of such physical media include superconducting materials, trapped ions, photons, optical cavities, individual electrons trapped in quantum dots, point defects in solids (e.g., phosphorus donors in silicon or nitrogen vacancy centers in diamond), molecules (e.g., alanine, vanadium complexes), or aggregates of any of the foregoing that exhibit qubit behavior (i.e., including quantum states and transitions between them that can be controllably induced or detected).

[0007] For any given medium implementing a qubit, any of a variety of properties of that medium may be selected to implement the qubit. For example, if an electron is selected to implement a qubit, then the x-component of the electron's spin degree of freedom may be selected as the property of such electron to represent the state of such qubit. Alternatively, the y-component, or the z-component of the spin degree of freedom may be selected as the property of such electron to represent the state of such qubit. This is merely a specific example of the general characteristics that for any physical medium selected to implement a qubit, there may be multiple physical degrees of freedom (e.g., the x-, y-, and z-components in the electron spin example) that may be selected to represent 0 and 1. For any particular degree of freedom, the physical medium may be controllably placed in a superposition and then a measurement may be made at the selected degree of freedom to obtain a reading of the qubit value.

[0008] A particular implementation of a quantum computer, referred to as a gate model quantum computer, includes quantum gates. In contrast to classical gates, there are an infinite number of possible single-qubit quantum gates that change the state vector of a qubit. Changing the state of a qubit state vector is typically referred to as a single-qubit rotation, and may also be referred to herein as a state change or single-qubit quantum gate operation. A rotation, state change, or single-qubit quantum gate operation may be mathematically represented by a unitary 2×2 matrix with complex elements. A rotation corresponds to a rotation of a qubit state in the Hilbert space of qubit states, which may be conceptualized as a rotation of the Bloch sphere. (As is well known to those skilled in the art, the Bloch sphere is a geometric representation of the space of pure states of qubits.) A multi-qubit gate changes the quantum state of a set of qubits. For example, a two-qubit gate rotates the state of two qubits as a rotation in the four-dimensional Hilbert space of the two qubits. Hilbert space is an abstract vector space with a structure of inner products that allows for measuring lengths and angles. Moreover, Hilbert spaces are complete: there are sufficient limits in this space that make it possible to use the techniques of calculus.

[0009] A quantum circuit may be specified as a sequence of quantum gates. The term "quantum gate" may refer to the application of a gate control signal (defined below) to one or more qubits that implements a logical gate operation by subjecting those qubits to a particular physical transformation. To conceptualize a quantum circuit, consider a set of matrices corresponding to component quantum gates that, when multiplied together in the order specified by the gate sequence, produce a 2 n ×2 nA quantum circuit may therefore be represented as a single composition operator. However, designing a quantum circuit in terms of its constituent gates allows the design to fit a standard set of gates and thus makes it easier to deploy. A quantum circuit therefore corresponds to the design of actions to be taken on the physical components of a quantum computer.

[0010] A given variational quantum circuit may be parameterized in a suitable device-specific manner. More generally, the quantum gates that make up a quantum circuit may have multiple tuning parameters associated with them. For example, in an embodiment based on optical switching, the tuning parameters may correspond to the angles of individual optical elements.

[0011] In certain embodiments of quantum circuits, the quantum circuit includes both one or more gates and one or more measurement operations. A quantum computer implemented using such a quantum circuit is referred to herein as implementing "measurement feedback." For example, a quantum computer implementing measurement feedback may execute a gate in the quantum circuit, then measure only a subset (i.e., less than all) of the qubits in the quantum computer, and determine which gate(s) to execute next based on the result(s) of the measurement(s). Specifically, the measurement(s) may indicate the degree of error in the gate operation(s), and the quantum computer may determine which gate(s) to execute next based on the degree of error. The quantum computer may then execute the gate(s) indicated by the determination. This process of executing a gate, measuring a subset of the qubits, and determining which gate(s) to execute next may be repeated any number of times. Measurement feedback may be useful for performing quantum error correction, but is not limited to use in performing quantum error correction. For any quantum circuit, there are error-corrected implementations of the circuit with or without measurement feedback.

[0012] Each superconducting qubit is characterized by a ground quantum state and an excited quantum state separated by an energy E, such that E=hf. The transition between the ground and excited states is mediated by a narrowband microwave signal with a frequency f, which is typically on the order of 10 GHz. Such a microwave signal may have a shaped envelope, sometimes referred to as a "microwave pulse", with a width that may be on the order of 100 cycles. However, such a "microwave pulse" is quite different from the above-mentioned SFQ pulses, which have a broadband spectral content up to several hundred GHz. Most prior art control systems are based on these narrowband microwave pulses. See U.S. Pat. Nos. 7,932,514, 8,294,138, 8,872,360, 10,572,816, and 10,650,319.

[0013] It is known in the prior art that any quantum computing system requires an interface with a classical computer for control and readout. In most of the prior art, the classical control computer may comprise a conventional semiconductor computer at room temperature, with control lines to the cryogenic qubits. However, for at least the first stage of control of the quantum computer, it may be advantageous to employ cryogenic control circuitry close to the quantum computer. Such a control system in close proximity to the quantum computer would reduce latency and allow for more rapid and flexible control of the quantum computer. Furthermore, superconducting quantum computing requires ultra-low temperatures of about 0.01 K, typically using helium dilution refrigerators, where the available cooling capacity is very small. The primary heat load in a cryogenic computer involves a set of input / output (I / O) lines, which would be impractically large for a quantum computer of any significant scale. The inclusion of a local source of classical control circuitry would reduce the number of I / O lines, and therefore make large systems more practical, provided that the dissipation of the cryogenic classical control circuitry is also very small.

[0014] Some prior art discloses the use of conventional semiconductor circuitry at cryogenic temperatures to control cryogenic qubits. See, for example, U.S. Patents and Published Applications: 10,671,559, 2020 / 0394548, and 2020 / 0160205. However, the power levels of the semiconductor control circuitry are generally much higher than those comparable to the cryogenic environment of a quantum computer.

[0015] One type of superconducting circuit that can be used to control superconducting qubits is an induction circuit that applies a magnetic flux, including circuits based on superconducting quantum interference devices or SQUIDs. See, for example, U.S. Patents and Published Applications: Nos. 7,847,615, 7,932,514, 8,854,074, 9,996,801, 10,665,635, 10,969,443, and 2021 / 0033683. These control methods are generally fairly slow.

[0016] All superconducting logic circuits are low dissipative, but some variants, such as those identified as ERSFQ, eSFQ, RQL, and QFP, are particularly low energy. They are based on SFQ pulses, which are quite different from the more commonly used resonant narrowband microwave signals. Such circuits can be placed near superconducting qubits, assuming a common cryogenic environment and low power consumption. There have been several previous proposals for SFQ logic circuits to control or read out superconducting qubits. For example, trains of precisely timed SFQ pulses can be used to induce quantum transitions in superconducting qubits or measure the quantum state of the qubits. See, for example, U.S. Patent Nos. 7,969,178, 8,138,784, 8,508,280, 9,425,804, 9,787,312, 10,726,351, and 10,748,079.

[0017] Although SFQ pulses are very fast by themselves, the prior art does not teach a method for rapid, programmable SFQ control over the very large numbers of qubits that would be required for a practical quantum computer. In particular, the prior art does not teach a method for using SFQ circuits to tune the parameters of the various qubits and the coupling between these parameters.

[0018] Quantum computers (QCs) containing qubits promise exponential speedup in solving certain problems. Qubits can be implemented in physical systems with two distinct energy levels representing |0> and |1> states, e.g., up and down spin states of an electron. Qubit states can be manipulated with microwave pulses whose frequency f matches the energy level spacing E=hf. Qubit manipulations can be represented as rotations in the Bloch sphere. The axis of rotation is set by the phase of the microwave signal relative to the qubit phase, which must be tracked for coherent manipulation. The pulse amplitude and pulse duration determine the rotation angle.

[0019] The singular value decomposition allows the visualization of the two-qubit state through a pair of Bloch spheres for each subsystem. Bloch vectors TIFF2024526085000002.tif7140 and TIFF2024526085000003.tif7140 is inscribed in the sphere of each of these Bloch vectors, and represents the six degrees of freedom that can be detected by local measurements. The nine degrees of freedom that can only be detected nonlocally are contained in Σ, M, and N, or equivalently, in two matrix products MΣ and NΣ. The columns of these two products are, respectively, TIFF2024526085000004.tif6140 and The scaled correlation axes are given in TIFF2024526085000005.tif7142. To complete the geometric representation of the quantum state, three scaled correlation axes for each system can be added to their respective Bloch spheres, where they represent the magnitude and direction of the correlation. The scaled correlation axes in the two systems are paired by a shared index i.

[0020] The spin along two such axes with the same index is the shared length x of these axes. i While spins are correlated proportionally to i, spins along axes with different indices are uncorrelated. That is, simultaneously measuring two spins on multiple copies of the system, each along its scaled correlation axis i, yields an expectation value equal to the length of the axis. Simultaneously measuring two spins along correlation axes with different indices i ≠ j yields an expectation value of zero.

[0021] Quantum channels and operations, described by trace-preserving completely positive maps, are at the heart of quantum information science research. The case of a single quantum bit (qubit) has a particularly attractive geometric interpretation in terms of a particular deformation of the Bloch sphere. This geometric picture largely guides our intuition for the higher dimensional cases.

[0022] Viewing quantum operations as operators acting on operators leads to a clean geometric decomposition in the single-qubit case: a completely positive map that preserves traces. Given any 2 × 2 complex matrix, eight degrees of freedom can be identified, for example via the real and imaginary parts of the four entries. For Hermitian matrices, these eight degrees of freedom are reduced to four, since the specification of any one of the off-diagonal terms fixes one of the other terms, and each of the diagonal terms must be real. As a result, the linear map from a 2 × 2 Hermitian matrix to a 2 × 2 Hermitian matrix can be fully characterized by 16 parameters. It is easy to verify that any Hermitian matrix can be written as a linear combination of an identity matrix with real coefficients and three Pauli matrices. Thus, any Hermitian 2×2 matrix can be expressed as a 4-component real vector in the Pauli basis {1,σx,σy,σz}, and any linear map on a Hermitian 2×2 matrix can be expressed as a 4×4 real matrix in the same basis.

[0023] We shift our attention to a subset of 2 × 2 Hermitian matrices, namely single-qubit density matrices, and add the condition that the matrices must be positive and have a trace equal to 1. The trace condition forces the coefficient of the identity matrix to be 1 / 2, reducing the characterization to a three-dimensional real subspace. Positivity then shows that every density matrix can be represented by a point within a radius of 1 / 2 of the origin in this three-dimensional real subspace. Using the standard convention of factoring 1 / 2 out of each component, we obtain the familiar Bloch vector representation of density matrices, and the set of admissible density matrices is the sphere ||r||, which is the Bloch sphere. 2 ≦1. By considering density matrices and quantum operations on density matrices, the form of this linear map can be further refined, since quantum operations are described by completely positive maps that preserve traces. (Equivalently, the Hilbert-Schmidt dual of the map is completely positive definite and unital.)

[0024] The effect of any trace-preserving completely positive mapping on the Bloch sphere can therefore be characterized as a composition of a rotation with possible inversion, a compression to an ellipsoid, a second rotation with possible inversion, and a translation. Summary of the Invention [Problem to be solved by the invention]

[0025] Quantum computers require many qubits and couplers with well-defined and precise energies. Superconducting quantum computers are fabricated from integrated circuits with multiple Josephson junctions. In practice, due to differences in the manufacturing process of Josephson junctions, the fabricated qubits have slightly different energies from the design parameters. Such variations in the energies of qubits and couplers make it difficult to precisely perform single-qubit and multi-qubit operations in quantum computers, especially as the number of coupled qubits increases. External energy tuning of qubits via flux biasing can compensate for the inherent variations in the manufacturing process and allow an additional degree of control. Precisely controlled flux biasing of superconducting circuits is necessary to achieve the desired quantum behavior in scalable quantum computing systems. [Means for solving the problem]

[0026] In addition to compensating for manufacturing variations, the controllability of the energy of quantum circuits such as qubits and quantum couplers enables certain functions and properties. As an example, by varying the energy of qubits and quantum couplers, one can increase or decrease their interaction with other components in the quantum circuit. This allows for deliberate coupling and decoupling of different quantum components based on the desired functionality. For example, to enable two-qubit or multi-qubit gate operations, the energy of a coupler or qubit can be adjusted to enable interactions between them. Similarly, a qubit can be decoupled from other qubits or couplers by decoupling the energy via a flux bias application. Varying the flux bias application to increase coupling enables multi-qubit and coupler gate operations, whereas varying the flux bias application to decouple quantum components allows maintaining quantum coherence by decreasing the interactions.

[0027] Finally, single-qubit or two-qubit gate operations can be performed by applying the generated fast flux bias pulses to perform high-fidelity qubit control. Such control can be performed using a universal set of flux pulses where the qubit gate is completed within a single or multiple Larmor periods. The basic principle of SFQ flux bias application according to the present invention is as follows: A superconducting storage loop is magnetically coupled to a quantum circuit. As shown in FIG. 1, SFQ pulses are added to or removed from the storage loop to vary the amount of flux bias application of the qubit or coupler.

[0028] The resolution, amount of coupling, and rate of change of flux bias application are different design parameters of the transformer, namely L in , L out , M, and the SFQ circuitry and / or qubits / couplers.

[0029] Li, X., T. Cai, H. Yan, Z. Wang, X. Pan, Y. Ma, W. Cai et al. “Tunable coupler for realizing a controlled-phase gate with dynamically decoupled regime in a superconducting circuit.” Physical Review Applied 14, no. 2 (2020): 024070 discloses a tunable and switchable qubit coupler. Controllable interactions between superconducting qubits are desirable for large-scale quantum computing and simulations. Based on Yan et al. [Phys. Rev. Appl. 10, 054061 (2018)], we tested a flux-controlled tunable coupler with continuous tunability by adjusting the coupler frequency, which can completely turn off adjacent superconducting qubit coupling. Taking advantage of the tunable interaction between two qubits via a coupler, a controlled-phase (CZ) gate with a dynamically decoupled regime allows the qubit-qubit coupling to be dynamically "off" during the tuning process of one qubit frequency to and from the operating point, while only being "on" at the normal operating point, which effectively suppresses leakage from the computational subspace, but also allows the obtained two-qubit phase to be geometric at the operating point.

[0030] The circuits that add or remove magnetic flux can be designed in many ways. The simplest approach is to use Josephson transmission lines (JTLs), as shown in Figure 2. In Figure 2, if we have a chain of JTLs, we can amplify the JTLs and add L in This allows the number of fluxons that can be stored in the

[0031] A more scalable approach would be to use parallel JTLs to increase the capacity of the fluxons stored in the loop, thus reducing the inductor L shown in Figure 3. inIn the circuit shown in Figure 4, the number of JTLs in parallel can be arbitrarily large, from 1 to n, depending on the specifics of the flux biasing design. A circuit simulation of this circuit is shown in Figure 4.

[0032] Using this technique, it is possible to create different profiles of flux bias application over time. In FIG. 5, sample times and flux bias application of varying amplitudes are shown. The flux bias application can be either positive or negative. An SFQ circuit that adds or removes flux to the flux bias application circuit of FIG. 1 could be designed for a particular profile or time dependence of the flux bias application. The slew rate of the rising and falling edges of the flux bias application waveform or flux bias pulse (FBP) can be achieved by varying the SFQ circuit clock, a sub-multiple of the SFQ circuit clock, and / or the SFQ pulse repetition rate set by a special on-chip SFQ pulse generator circuit (flux pump). In the general case, the SFQ pulse repetition rate can be non-uniform.

[0033] As an example, a flux pump could be used for fast variation of flux biasing by injecting or removing a fast pulse train for coarse flux biasing as shown in Figure 6. One example of a flux pump is a relaxation oscillator or circuit that uses an underdamped Josephson junction. As the underdamped Josephson junction switches, it creates a SFQ pulse train with the number of pulses determined by the resistive and inductive load of the circuit.

[0034] Flux biasing using SFQ pulses can be further refined for specific purposes including fast but high resolution biasing over large intervals by combining coarse and fine biasing as shown in Figure 7. In Figure 7, the coarse biasing could be used for fast steps of biasing and the fine biasing could be used for initial and / or final high resolution adjustments. In general, the specific sequence, duration, pulse rate and other parameters of the coarse and fine biasing, and thus the shape of the flux bias pulses generated, their number and polarity, are selected based on specific functions and optimizations to achieve the highest gate fidelity.

[0035] The initial flux stored in the flux-biased storage loop can be reset by adding a reset circuit as shown in Figure 8. In Figure 8, a SQUID in series with the input transformer can be used as the reset mechanism. When the critical current of the SQUID is suppressed by applying a reset current to the input transformer, L in The magnetic flux stored in is completely removed.

[0036] SFQ pulse control can be used not only for tuning qubits, as proposed in the prior art, but also to initiate quantum transitions between qubit states. In this scheme, SFQ pulses are applied resonantly (uniformly) over many qubit Larmor periods, or use more complex non-uniform pulse patterns derived using optimal control theory methods.

[0037] A central control unit (which can be a SFQ digital logic circuit) can be used to coordinate and synchronize the combination and timing of these two control mechanisms, as suggested by the block diagram in Figure 9A. Rapid flux biasing of the qubits and couplers also enables novel and improved multi-qubit operations, as shown in Figure 10A. This can be used to increase the speed of multi-qubit gate operations or improve the fidelity of gate operations by exploiting novel modes of multi-qubit interaction.

[0038] Here, a central control unit is capable of precise timing and control of the SFQ pulse trains acting on each qubit, as well as flux biasing of all the qubits and couplers to achieve faster multi-qubit operations with higher fidelity.

[0039] Alternatively, quantum transitions can be performed using FBP waveforms generated by SFQ circuits, as shown in Figure 9B. In this case, the qubit rotation is driven exclusively by the flux bias applied to the qubits, while the SFQ circuit is used to generate a specific FBP corresponding to the desired gate. This method can potentially lead to faster gate execution, since the applied FBP can execute the gate within a single or a few Larmor periods, as opposed to SFQ pulse trains or microwave pulses, which are typically applied over many qubit Larmor periods.

[0040] Figure 10B shows a block diagram of multi-qubit operations using only flux bias application control. In this case, separate FBPs are generated to control the qubits and the couplers connecting the qubits. The SFQ flux bias to adjust the qubit energy (qubit frequency) is combined with the qubit-controlled flux bias application. See the SFQ flux bias offset in Figure 10B.

[0041] An example of application of SFQ flux biasing to change the energy of a qubit during a SFQ single qubit operation is shown in Figure 11. In this example, the energy of the qubit can be rapidly reduced during a single qubit operation, allowing for faster single qubit operation. At the end of the single qubit rotation, the flux biasing can change the energy of the qubit again to isolate the qubit from the rest of the circuit.

[0042] This type of flux bias control can be applied to vary the superconducting critical current of a SQUID loop incorporated into a qubit, instead of a single Josephson junction (sometimes called a split junction) that is the central component of a superconducting qubit or coupler, which in turn affects the energy and coupling strength of the quantum device. Applicable qubits include flux qubits, phase qubits, and transmons, among others. For fluxonium and similar qubits with large inductors (superinductors), the flux bias can be applied to the superinductor, which may be fabricated using a Josephson junction array. Other applications of rapid time-varying superconducting digital flux control for quantum computing are described in more detail below or may become apparent to those skilled in the art.

[0043] It is therefore an object to provide a flux control system comprising: a superconducting circuit configured to convert each successive single flux quantum pulse into a magnetic flux; a superconducting inductor configured to integrate magnetic flux from the superconducting circuit to define an integrated magnetic flux; and a control system comprising a plurality of Josephson junctions, the control system configured to generate at least one output control signal for controlling the superconducting circuit, the output control signal comprising at least one sequence of single flux quantum pulses adapted to selectively vary the integrated magnetic flux.

[0044] It is also an object to provide a flux control system comprising: at least one superconducting circuit configured to generate single flux quantum pulses; a coupling circuit configured to couple the single flux quantum pulses into a corresponding magnetic flux; a superconducting inductor configured to integrate the magnetic flux corresponding to the single flux quantum pulse to define an integrated magnetic flux; a qubit having a resonant frequency responsive to the integrated magnetic flux; a sensor having a sensor output, the sensor configured to determine at least one of the resonant frequency and the integrated magnetic flux; and a control system comprising a plurality of Josephson junctions, the control system configured to control a value of the integrated magnetic flux responsive to the sensor output.

[0045] It is a further object to provide a flux control method for controlling a superconducting system comprising a superconducting circuit configured to convert each successive single flux quantum pulse into a magnetic flux, a superconducting inductor configured to integrate the magnetic flux from the superconducting circuit to define an integrated magnetic flux, and a control circuit comprising a plurality of Josephson junctions, the method comprising: defining a target magnetic flux; controlling the superconducting circuit to generate a sequence of single flux quantum pulses to monotonically vary the integrated flux to reduce a difference between the target magnetic flux and the integrated magnetic flux; and controlling the superconducting circuit to stop monotonically varying the integrated flux by stopping generating the sequence of single flux quantum pulses to monotonically vary the integrated flux, wherein said controlling the superconducting circuit to stop generating the sequence of single flux quantum pulses is responsive to a value of the integrated flux.

[0046] The flux control system may further comprise a quantum computing circuit comprising at least one qubit having at least one physical property tunable in response to at least an integrated flux, the integrated flux being coupled to the at least one qubit. The at least one physical property may comprise a microwave resonance. The control system may be configured to control dynamic changes in the at least one physical property of the at least one qubit over time. The at least one physical property may comprise at least one of a microwave resonance, an energy, and a phase of the qubit, and may control each of the microwave resonance, the energy, and the phase of the qubit. The control system may be configured to control dynamic changes in the at least one physical property of at least one of the qubits and the tunable qubit coupler. At least one of the qubits and the tunable qubit coupler may comprise a switching qubit coupler configured to selectively control the presence and absence of an interaction of multiple qubits.

[0047] The flux control system may be provided in a first integrated circuit and at least one of the qubits and the tunable qubit coupler are provided in a second integrated circuit, where the first integrated circuit and the second integrated circuit are provided on a common substrate.

[0048] The flux control system may further comprise at least one of a qubit and a tunable qubit coupler associated with the qubit coupled to the integral flux, wherein a state of the qubit Bloch sphere of the qubit is responsive to at least one output control signal.

[0049] The flux control system may further comprise a qubit coupled to the integrated flux, the qubit having a state represented by a phase and an amplitude of the Bloch sphere, the phase and amplitude of the Bloch sphere responsive to at least one output control signal.

[0050] The flux control system may be provided on a first integrated circuit and at least one of the qubits and the tunable qubit coupler are provided on a second integrated circuit, where the first integrated circuit and the second integrated circuit are inductively coupled and provided on separate substrates having a flip-chip geometry.

[0051] The control system may further comprise an input port configured to receive at least one feedback signal related to the magnitude of the integrated magnetic flux.

[0052] The control system may further comprise a pair of output ports configured to generate a first signal adapted to increase the integral magnetic flux and a second signal adapted to decrease the integral magnetic flux.

[0053] The control system may be configured to implement at least one of a phase-locked loop control and a frequency-locked loop control.

[0054] The control system may be configured to receive a photon input control signal.

[0055] The flux control system may further comprise a frequency mixer and a detector configured to receive the output of the at least one qubit and to generate an input control signal for the control system.

[0056] The flux control system may further comprise a superconducting oscillator configured to generate a microwave signal that interacts with the qubit.

[0057] The superconducting inductor may be further configured to couple the integrated magnetic flux to a quantum computing circuit comprising a transmon qubit circuit having a microwave resonance tunable according to at least the integrated magnetic flux. The control system may be configured to define a first microwave resonant frequency of the transmon qubit within a quantum computation period of the transmon qubit and thereafter define a second microwave resonant frequency of the transmon qubit, the first microwave resonant frequency and the second microwave resonant frequency being different.

[0058] The superconducting inductor may be further configured to couple the integrated magnetic flux to a quantum computing circuit comprising a transmon qubit circuit having a microwave resonance tunable in response to at least the integrated magnetic flux, and the control system may be configured to adjust the microwave resonance of the transmon qubit circuit with the integrated magnetic flux in response to a microwave resonance state of the transmon qubit circuit.

[0059] The flux control system may further comprise a superconducting quantum interference device responsive to the integrated magnetic flux adapted to generate a magnetometer output, the control system comprising a control system input responsive to the magnetometer output.

[0060] The control system may further comprise a first input port configured to receive a reference frequency signal, a second input port configured to receive a microwave resonator signal, and a comparison circuit configured to generate a comparison output configured to control the integrated magnetic flux and to selectively vary the integrated magnetic flux in response to the comparison output.

[0061] The control system is further configured to receive at least one input control signal selectively responsive to a signal from the qubit during a quantum computing computation representative of a computational state of the qubit during a subsequent stage of quantum computing, and to control the integrated flux selectively responsive to a computational state of the qubit during a subsequent stage of quantum computing.

[0062] The flux control system may further comprise an error input port configured to receive the error signal and at least one memory configured to persistently store a calibration value responsive to the error signal, wherein the control system generates the output control signal selectively responsive to the persistently stored calibration value.

[0063] The flux control system may further comprise a superconducting circuit configured to reset the integrated flux to a predetermined value.

[0064] The control system is further configured to generate at least one sequence of at least two types of single flux quantum pulses including a first type of sequence adapted to change the integrated magnetic flux by a first amount and a second type of sequence adapted to change the integrated magnetic flux by a second amount, where the first amount may be different from the second amount, the control system being configured to receive at least one input control signal representative of the amount of change of the integrated magnetic flux, and to generate the first type of sequence and the second type of sequence in selective response to the at least one input control signal.

[0065] The control system is further configured to generate at least two different types of output control signals comprising at least one sequence of single flux quantum pulses, including a first type of sequence associated with a first positive integer number of single flux quantum pulses and a second type of sequence associated with a second positive integer number of single flux quantum pulses, where the first positive integer and the second positive integer may be different.

[0066] The flux control system may further comprise a counter responsive to the target value configured to count each single flux quantum pulse and selectively generate a signal when an accumulated value of the at least one sequence of single flux quantum pulses corresponds to the target value, wherein the superconducting circuit comprises a superconducting transformer primary inductor coupled to a superconducting inductor as a superconducting transformer secondary inductor, the at least one sequence of single flux quantum pulses includes a first pulse and a second pulse, the superconducting transformer primary inductor having a first terminal and a second terminal, the first pulse entering the superconducting transformer primary inductor at the first terminal and the second pulse entering the superconducting transformer primary inductor at the second terminal, whereby the first pulse acts with opposite polarity relative to the second pulse on a change in integrated flux.

[0067] The control system may further comprise a gate configured to receive a feedback signal based on the magnitude of the integrated magnetic flux and configured to stop the at least one sequence of single flux quantum pulses when the feedback signal indicates a sufficient correction of the integrated magnetic flux.

[0068] The flux control system may further comprise a control system input representative of a feedback signal, the control system configured to generate at least one output control signal selectively responsive to the feedback signal to generate an output representative of a first type of train of successive single flux quantum pulses to increase the integrated flux, or a second type of train of successive single flux quantum pulses to decrease the integrated flux, or no net single flux quantum pulses to maintain the integrated flux.

[0069] The flux control system may further comprise a counter, wherein the control system is configured to receive a target value and, in response to the target value, selectively increment the counter based on successive trains of single flux quantum pulses adapted to increase the integrated flux and decrement the counter based on successive trains of single flux quantum pulses adapted to decrease the integrated flux, and suppress net single flux quantum pulses while a count value of the counter corresponds to an error margin of the target value.

[0070] The flux control system may further comprise a reset circuit configured to establish the magnetic flux at a predetermined value, the reset circuit may comprise a reset inductor coupled to a superconducting quantum interference device (SQUID) having a critical current in series with the superconducting inductor, such that a current in the reset inductor is sufficient to drive the SQUID above the critical current and become resistive, and energy stored in the superconducting inductor becomes dissipative.

[0071] It is another object of the present invention to provide a method for controlling a superconducting quantum computing circuit, the method comprising: generating different types of flux bias applied pulses using a superconducting digital SFQ control circuit in response to at least one control signal over time; converting single flux quantum voltage pulses into magnetic flux in response selectively to a history of the at least one control signal; using the generated flux bias pulses with or without a single flux quantum voltage pulse applied to the superconducting quantum circuit, where the different types of single flux quantum voltage pulses cause increases and decreases in magnetic flux; coupling magnetic flux to the quantum computing circuit with tunable characteristics in response to the coupled magnetic flux; and defining at least one control signal over time in response to a performance of the quantum computing circuit.

[0072] It is also an object of the present invention to provide a method for controlling a superconducting quantum computing circuit, the method comprising: generating a single flux quantum voltage pulse with a superconducting digital control circuit in response to at least one control signal over time; converting the single flux quantum voltage pulse into a magnetic flux in response to a history of the at least one control signal; coupling the magnetic flux to the quantum computing circuit, the quantum computing circuit comprising at least one component having a characteristic that is adjustable in response to the coupled magnetic flux; and defining the at least one control signal over time to selectively define the magnetic flux to modify a characteristic of the at least one component. The coupled magnetic flux may, for example, control a frequency, phase, rate, precision, or dynamic range of the at least one component.

[0073] It is a further object to provide a method of magnetic flux control including a control system comprising a plurality of Josephson junctions, the control system configured to generate a sequence of single flux quantum pulses, a superconducting circuit configured to convert the sequence of single flux quantum pulses into magnetic flux, and a superconducting inductor configured to couple the magnetic flux to a quantum computing circuit comprising at least one qubit coupler circuit having physical properties tunable in response to the magnetic flux.

[0074] It is also an object to provide a flux control system comprising a control system comprising a plurality of Josephson junctions configured to generate a sequence of single flux quantum pulses, a superconducting circuit configured to convert each pulse of the sequence of single flux quantum pulses into a magnetic flux, and a superconducting inductor configured to integrate the magnetic flux, wherein the integrated magnetic flux is controlled to increase and decrease in response to at least one control signal of the control system.

[0075] The superconducting inductor may be further configured to couple the integrated magnetic flux to a quantum computing circuit comprising at least one qubit circuit having a physical property tunable as a function of at least the magnetic flux.

[0076] The flux control system may further comprise a quantum computing circuit comprising at least one qubit circuit having a physical property tunable at least in response to the magnetic flux.

[0077] The control system may have at least one control mode adapted to maintain a constant physical property of the at least one qubit.

[0078] The control system may have at least one control mode adapted to dynamically vary a physical property of at least one qubit over time.

[0079] The superconducting inductor may be further configured to couple the integrated magnetic flux to a qubit circuit having physical properties tunable in response to at least the magnetic flux.

[0080] The flux control system may be provided with or integrated with a qubit circuit having a physical property that is tunable in response to at least the magnetic flux.

[0081] The control system may have at least one control mode adapted to maintain constant physical properties of the qubits.

[0082] The control system may have at least one control mode adapted to dynamically vary a physical property of the qubit over time.

[0083] The control system may include an input configured to receive a feedback signal.

[0084] The control system may include a pair of inputs configured to receive feedback signals indicative of the magnetic flux excess and the magnetic flux deficiency.

[0085] The control system may include a pair of outputs configured to generate signals representative of an increase in magnetic flux and a decrease in magnetic flux.

[0086] The control system may be configured to implement a phase-locked loop control, see en.wikipedia.org / wiki / Phase-locked_loop.

[0087] The control system may be configured to implement a frequency locked loop control, see en.wikipedia.org / wiki / Frequency-locked_loop.

[0088] The control system may be configured to receive a light control signal.

[0089] The control system may be configured to receive a photon control signal.

[0090] The control system may further include an optical output signal.

[0091] The modulation of the signal may be detected by using a receiver with a heterodyne or homodyne architecture. In a homodyne, the modulated signal is typically 1 +f 2 , f 1 -f 2 Such as input frequency f 1 and f 2 The signals are mixed in a mixer, a nonlinear device that produces a modulation product of f 1 =f 2 For the homodyne condition where f 1 ≠f 2 In this case, the modulating signal is f 1 and f 2The mixer has the advantage of producing an intermediate frequency that appears at the output biased at the offset frequency of 100 MHz, which can be bandpass filtered and subjected to other processes, and is converted above the baseband frequency. Mixers allow frequency conversion of the output even when the modulation of one or both of the signals is not important. A detector is a device that determines the characteristics of a modulated signal.

[0092] The flux control system may further include a heterodyne detector. See, for example, Ilves, Jesper, Shingo Kono, Yoshiki Sunada, Shota Yamazaki, Minkyu Kim, Kazuki Koshino, and Yasunobu Nakamura. “On-demand generation and characterization of a microwave time-bin qubit.” npj Quantum Information 6, no. 1 (2020): 1-7.

[0093] The flux control system may further comprise a homodyne detector.

[0094] The flux control system may further comprise a phase sensitive amplifier configured to amplify a microwave signal interacting with the at least one qubit.

[0095] The flux control system may further comprise a Josephson parametric amplifier configured to amplify a signal associated with the at least one qubit.

[0096] The flux control system may further comprise a quadrature oscillator.

[0097] The flux control system may further comprise a quadrature signal demodulator.

[0098] The control system may be configured to maintain a first magnetic flux associated with the qubit and to maintain a second magnetic flux associated with the qubit within a decoherence time of the qubit, the first magnetic flux and the second magnetic flux being different.

[0099] The superconducting inductor may be further configured to couple the integrated magnetic flux to a quantum computing circuit comprising at least one qubit circuit having a physical property adjustable in response to at least the magnetic flux, and the control system may be configured to maintain a first state of the physical property of the at least one qubit within a decoherence time of the at least one qubit, and thereafter maintain a second state of the physical property of the at least one qubit, the first state and the second state being distinct.

[0100] The physical property may include microwave resonance.

[0101] The superconducting inductor may be further configured to couple the integrated magnetic flux to a quantum computing circuit comprising a transmon qubit circuit having a microwave resonance adjustable according to at least the magnetic flux, and the control system may be configured to define a first microwave resonant frequency of the transmon qubit within a quantum computing period of the transmon qubit, and thereafter to define a second microwave resonant frequency of the transmon qubit, the first microwave resonant frequency and the second microwave resonant frequency being different.

[0102] The flux control system may further comprise a magnetometer configured to measure integrated magnetic flux. The magnetometer may comprise a Superconducting Quantum Interference Detector (SQUID) magnetometer. The magnetometer may comprise a Superconducting Quantum Interference Filter (SQIF) magnetometer. The control system may further comprise an input for receiving a signal responsive to an output of the magnetometer.

[0103] The control system may further comprise an input for receiving a reference frequency signal, an input for receiving a microwave resonant signal, and a comparison circuit for generating an output for controlling the magnetic flux to increase or decrease.

[0104] The control system may further comprise a comparison circuit that receives a control signal including the reference frequency signal and the microwave resonant signal, and generates an output for the control system to control the magnetic flux to increase or decrease depending on the output of the comparison circuit.

[0105] The control system may receive at least one control signal selectively responsive to a signal from the qubit during a quantum computing computation representative of a computational state of the qubit during a stage of quantum computing, and controls the magnetic flux selectively responsive to a computational state of the qubit during a subsequent stage of quantum computing.

[0106] The flux control system may further comprise at least one memory configured to persistently store a calibration value, and the control system generates the sequence of single flux quantum pulses according to the persistently stored calibration value. An input may be provided for receiving the calibration value. A circuit may be provided for determining the calibration value.

[0107] The flux control system may further comprise circuitry configured to reset the integrated flux to a predetermined value, for example by providing an element that temporarily transitions from a superconducting state to a non-superconducting state to dissipate energy stored in the superconducting inductor.

[0108] The control system is configured to generate sequences of at least two types of single flux quantum pulses including a first type having a first number of single flux quantum pulses for changing the integrated flux by a first amount and a second type having a second number of single flux quantum pulses for changing the integrated flux by a second amount, where the first number may be different from the second number.

[0109] The control system is configured to generate at least two types of sequences of single flux quantum pulses: a first type that changes the integrated magnetic flux by a first amount and a second type that changes the integrated magnetic flux by a second amount, where the first amount and the second amount may be different.

[0110] The control system is configured to generate sequences of at least four types of single flux quantum pulses including a first type having a first number of single flux quantum pulses for increasing the integral flux by a first amount, a second type having a second number of single flux quantum pulses for increasing the integral flux by a second amount, a third type having a third number of single flux quantum pulses for decreasing the integral flux by a third amount, and a fourth type having a fourth number of single flux quantum pulses for decreasing the integral flux by the second amount, where the first number may be different from the second number and the third number may be different from the fourth number.

[0111] The control system is configured to generate at least four types of sequences of single flux quantum pulses: a first type that increases the integral flux by a first amount, a second type that increases the integral flux by a second amount, a third type that decreases the integral flux by a third amount, and a fourth type that decreases the integral flux by a fourth amount, where the first amount and the second amount may be different and the third amount and the fourth amount may be different.

[0112] The control system may be configured to generate at least three different types of sequences of single flux quantum pulses: a first type that changes the integrated flux by a first amount, a second type that changes the integrated flux by a second amount, and a third type that changes the integrated flux by a third amount.

[0113] The control system may receive at least one control signal representative of an amount of change in integral magnetic flux, and the control system may be configured to generate at least a first type, a second type, and a third type in selective response to the at least one control signal representative of the amount of change in integral magnetic flux.

[0114] The control system may be configured to generate at least two different types of sequences of single flux quantum pulses to increase the integrated flux: a first type that generates a single single flux quantum pulse and a second type that generates multiple single flux quantum pulses.

[0115] The control system may be configured to generate at least two additional different types of sequences of single flux quantum pulses to reduce the integrated flux: a third type that generates a single single flux quantum pulse, and a fourth type that generates multiple single flux quantum pulses.

[0116] The control system may be configured to generate at least three different types of sequences of single flux quantum pulses for increasing the integral flux: a first type generating a single single flux quantum pulse, a second type generating a plurality of single flux quantum pulses including a first range, and a third type generating a plurality of single flux quantum pulses including a second range. The first and second ranges may be different. The control system may be configured to generate at least three additional different types of sequences of single flux quantum pulses for decreasing the integral flux: a fourth type generating a single single flux quantum pulse, a fifth type generating a plurality of single flux quantum pulses including a third range, and a sixth type generating a plurality of single flux quantum pulses including a fourth range. The first and second ranges are different and the third and fourth ranges are different.

[0117] It is also an object to provide a method of flux bias control that includes generating a sequence of single flux quantum pulses using a control system having a plurality of Josephson junctions, converting each pulse of the sequence of single flux quantum pulses into magnetic flux using a superconducting circuit, and integrating the magnetic flux using a superconducting inductor, where the integrated magnetic flux can be increased or decreased in response to at least one control signal of the control system.

[0118] The superconducting inductor may couple the integrated magnetic flux to a quantum computing circuit that includes at least one qubit circuit having a physical property tunable in response to at least the magnetic flux.

[0119] The control system may maintain constant physical properties of at least one qubit over a period of time.

[0120] The control system may dynamically vary a physical property of at least one qubit over time.

[0121] The superconducting inductor may couple the integrated magnetic flux to a qubit circuit having physical properties that are tunable depending at least on the magnetic flux.

[0122] The control system may maintain constant physical properties of the qubits over a period of time.

[0123] The control system may dynamically vary the physical properties of the qubits over time.

[0124] A control system feedback signal may be received. A pair of feedback signals may be received, each indicative of a flux excess and a flux deficiency.

[0125] A pair of outputs may be provided which generate signals representative of an increase in magnetic flux and a decrease in magnetic flux.

[0126] The control system implements a phase-locked loop control and / or a frequency-locked loop control.

[0127] The flux control method may receive optical and / or photon control signals and may generate optical and / or photon output signals.

[0128] The microwave signal may be detected using a heterodyne or homodyne detector.

[0129] A phase sensitive amplifier may be provided for amplifying a microwave signal that interacts with the at least one qubit. A Josephson parametric amplifier may be provided for amplifying a signal associated with the at least one qubit. The microwave signal is an output of the qubit and may have characteristics depending on the qubit. In some cases, multiple qubits may be combined and an output signal derived from one qubit may be used to affect another qubit.

[0130] Quadrature oscillators may be used to generate the quadrature microwave signals.

[0131] The microwave signal may be demodulated using a quadrature signal demodulator.

[0132] During a decoherence time of the qubit, a first magnetic flux associated with the qubit may be maintained, and then a second magnetic flux associated with the qubit may be maintained, where the first magnetic flux and the second magnetic flux are different.

[0133] The flux control method may further include coupling the integrated flux to a quantum computing circuit comprising at least one qubit circuit having a physical property tunable in response to at least the magnetic flux, maintaining a first state of the physical property of the at least one qubit within a decoherence time of the at least one qubit, and thereafter maintaining a second state of the physical property of the at least one qubit, the first state and the second state being different.

[0134] The physical property may include microwave resonance.

[0135] The superconducting inductor may couple the integrated magnetic flux to a quantum computing circuit comprising a transmon qubit circuit having a microwave resonance tunable in response to at least the magnetic flux, and may further include defining a first microwave resonant frequency of the transmon qubit within a quantum computation period of the transmon qubit, and thereafter defining a second microwave resonant frequency of the transmon qubit, the first microwave resonant frequency and the second microwave resonant frequency being different.

[0136] A magnetometer sensor may be provided for measuring integrated magnetic flux. The magnetometer may include a Superconducting Quantum Interference Detector (SQUID) magnetometer. The magnetometer may include a Superconducting Quantum Interference Filter (SQIF) magnetometer. A control system input signal may be provided in response to an output of the magnetometer.

[0137] The magnetic flux control method may further include comparing a reference frequency signal to the microwave resonant signal and controlling the magnetic flux to increase or decrease in response to the comparison.

[0138] The magnetic flux control method may further include receiving a control signal including a reference frequency signal and a microwave resonance signal, comparing the reference frequency signal with the microwave resonance signal to generate a comparison output, and controlling the magnetic flux to increase or decrease according to the comparison output.

[0139] The flux control method may further include receiving at least one control signal selectively responsive to a signal from the qubit during a quantum computing computation representative of a computational state of the qubit during a subsequent stage of quantum computing, and controlling the flux selectively responsive to a computational state of the qubit during a subsequent stage of quantum computing.

[0140] The flux control method may further include storing a calibration value in a memory, a register, or an analog storage device, and generating a sequence of single flux quantum pulses in response to the persistently stored calibration value. The calibration value may be received from an external input. The calibration value may be determined within the control system.

[0141] The integrated flux may be reset to a predetermined value. The integrated flux may be reset by temporarily making at least one superconducting element associated with the superconducting inductor resistive while a portion of the superconducting inductor remains superconducting. The at least one superconducting element may include a superconducting quantum interference device (SQUID) that is induced to enter a non-superconducting state by exceeding a critical current.

[0142] At least two types of sequences of single flux quantum pulses are generated, including a first type having a first number of single flux quantum pulses for changing the integrated flux by a first amount and a second type having a second number of single flux quantum pulses for changing the integrated flux by a second amount, where the first number may be different from the second number.

[0143] At least two types of sequences of single flux quantum pulses are generated, including a first type that changes the integrated flux by a first amount and a second type that changes the integrated flux by a second amount, where the first amount and the second amount may be different.

[0144] At least four types of sequences of single flux quantum pulses are generated, including a first type having a first number of single flux quantum pulses for increasing the integrated flux by a first amount, a second type having a second number of single flux quantum pulses for increasing the integrated flux by a second amount, a third type having a third number of single flux quantum pulses for decreasing the integrated flux by a third amount, and a fourth type having a fourth number of single flux quantum pulses for decreasing the integrated flux by the second amount, where the first number may be different from the second number and the third number may be different from the fourth number.

[0145] At least four types of sequences of single flux quantum pulses are generated: a first type that increases the integrated flux by a first amount, a second type that increases the integrated flux by a second amount, a third type that decreases the integrated flux by a third amount, and a fourth type that decreases the integrated flux by a fourth amount, where the first amount and the second amount may be different and the third amount and the fourth amount may be different.

[0146] The flux control method may further include generating at least three different types of sequences of single flux quantum pulses: a first type that changes the integrated flux by a first amount, a second type that changes the integrated flux by a second amount, and a third type that changes the integrated flux by a third amount. The method may further include receiving at least one control signal indicative of the amount of change of the integrated flux, and the control system may be configured to generate at least the first type, second type, and third type in selective response to the at least one control signal indicative of the amount of change of the integrated flux.

[0147] The flux control method may further include generating at least two different types of sequences of single flux quantum pulses to increase the integrated flux, a first type that generates a single single flux quantum pulse and a second type that generates multiple single flux quantum pulses. The method may further include generating at least two additional different types of sequences of single flux quantum pulses to decrease the integrated flux, a third type that generates a single single flux quantum pulse and a fourth type that generates multiple single flux quantum pulses.

[0148] The method of flux control may further include generating at least three different types of sequences of single flux quantum pulses for increasing the integral flux: a first type generating a single single flux quantum pulse, a second type generating a plurality of single flux quantum pulses including a first range, and a third type generating a plurality of single flux quantum pulses including a second range. The first and second ranges may be different. At least three additional different types of sequences of single flux quantum pulses for decreasing the integral flux may be generated: a fourth type generating a single single flux quantum pulse, a fifth type generating a plurality of single flux quantum pulses including a third range, and a sixth type generating a plurality of single flux quantum pulses including a fourth range. The first and second ranges may be different, and the third and fourth ranges may be different.

[0149] The flux from a sequence of single flux quantum pulses may be integrated by a superconducting inductor such that successive single flux quantum pulses cause a change in the current in the superconducting inductor by a quantized amount.

[0150] The control system may selectively generate single flux quantum pulses representing different polarities.

[0151] The control system may selectively generate a first type single flux quantum pulse and a second type single flux quantum pulse, where the first type single flux quantum pulse causes an increase in current in the superconducting inductor and the second type single flux quantum pulse causes a decrease in current in the superconducting inductor. The superconducting circuit may include a superconducting transformer primary inductor coupled to the superconducting inductor as a superconducting transformer secondary inductor. The superconducting transformer primary inductor may have a first terminal and a second terminal, where the first type single flux quantum pulse enters the superconducting transformer primary inductor at the first terminal and the second type single flux quantum pulse enters the superconducting transformer primary inductor at the second terminal, whereby the first type single flux quantum pulse acts on the change in magnetic flux with an opposite polarity to the first type single flux quantum pulse.

[0152] The control system may be configured to receive a target value of the magnetic flux, the system further comprising a counter configured to count the single flux quantum pulses and to stop the sequence of single flux quantum pulses when the counter value corresponds to the target value.

[0153] The control system may be configured to receive a feedback signal about the magnetic flux, the system further comprising a gate configured to stop the sequence of single flux quantum pulses (or the effect of the flux quantum pulses on the integrated magnetic flux) when the feedback signal indicates sufficient correction of the magnetic flux.

[0154] The control system may receive a feedback signal and, in response to the feedback signal, selectively generate a first type of train of successive single flux quantum pulses or a second type of train of successive single flux quantum pulses, where the first type of single flux quantum pulses cause an increase in current in the superconducting inductor and the second type of single flux quantum pulses cause a decrease in current in the superconducting inductor.

[0155] The control system may receive a target value and, in response to the target value, selectively generate and count a train of successive single flux quantum pulses of a first type or a second type, where the single flux quantum pulses of the first type cause an increase in the current in the superconducting inductor and the single flux quantum pulses of the second type cause a decrease in the current in the superconducting inductor. The counter acts as a numerical integrator of the pulses. Because the pulses are quantized, the cumulative effect of the pulses correlates with the increasing number of pulses.

[0156] The control system may receive a feedback signal and selectively generate an output representative of a first type of train of consecutive single flux quantum pulses, or a second type of train of consecutive single flux quantum pulses, or no net single flux quantum pulses, in response to the feedback signal, where the first type of single flux quantum pulses cause an increase in current in the superconducting inductor and the second type of single flux quantum pulses cause a decrease in current in the superconducting inductor, and the output representative of no net single flux quantum pulses results in no net change in current in the superconducting inductor. The output representative of no net single flux quantum pulses may not include single flux quantum pulses. The output representative of no net single flux quantum pulses may include offsetting the first type of single flux quantum pulses and the second type of single flux quantum pulses.

[0157] The control system may receive a target value and, in response to the target value, selectively increment a counter based on a train of successive single flux quantum pulses of a first type until the count increases to the target value, decrement a counter based on a train of successive single flux quantum pulses of a second type until the count decreases to the target value, or suppress net single flux quantum pulses while the counter corresponds to an error margin of the target value, where the first type of single flux quantum pulses cause an increase in current in the superconducting inductor and the second type of single flux quantum pulses cause a decrease in current in the superconducting inductor. The suppressed net single flux quantum pulses may include no single flux quantum pulses and / or offsetting the first type of single flux quantum pulses and the second type of single flux quantum pulses.

[0158] The system may further include a sensor configured to measure magnetic flux, a sensor configured to measure a physical property, and / or an input configured to receive a feedback signal responsive to performance of the plurality of qubits.

[0159] The at least one qubit may include a plurality of qubits having a physical property tunable in response to a magnetic flux, and a coupler between the plurality of qubits. The qubits may be superconducting qubits.

[0160] The control system may selectively generate a first type single flux quantum pulse and a second type single flux quantum pulse, where the first type single flux quantum pulse causes a change in the current of the superconducting inductor of a first amplitude and the second type single flux quantum pulse causes a change in the current of the superconducting inductor of a second amplitude, and where the first type single flux quantum pulse is generated independently of the second type single flux quantum pulse. The first type single flux quantum pulse may cause a change in the current of the superconducting inductor having a smaller absolute value than a change in the current of the superconducting inductor caused by the second type single flux quantum pulse.

[0161] A reset may be provided that is configured to establish the magnetic flux at a predetermined value, e.g., zero. The reset may include a reset inductor coupled to a superconducting quantum interference device (SQUID) in series with the superconducting inductor, such that a current in the reset inductor is sufficient to drive the SQUID beyond its critical current and become resistive and therefore dissipative of energy stored in the superconducting inductor.

[0162] It is also an object to provide a flux bias control method that includes generating a sequence of single flux quantum pulses using a control system including a plurality of Josephson junctions, converting the sequence of single flux quantum pulses into a magnetic flux, coupling the magnetic flux with a quantum computing circuit including at least one qubit circuit using a superconducting inductor, and adjusting a physical property of the qubit in response to the magnetic flux.

[0163] The flux from a sequence of single flux quantum pulses may be integrated by a superconducting inductor such that successive single flux quantum pulses cause a change in the current in the superconducting inductor by a quantized amount.

[0164] The generating may include selectively generating single flux quantum pulses representing different polarities with a control system.

[0165] A first type of single flux quantum pulse and a second type of single flux quantum pulse may be selectively generated, the first type of single flux quantum pulse causing an increase in current in the superconducting inductor and the second type of single flux quantum pulse causing a decrease in current in the superconducting inductor.

[0166] The sequence of single flux quantum pulses may be converted into a magnetic flux by a superconducting circuit comprising a superconducting transformer primary inductor coupled to a superconducting inductor as a superconducting transformer secondary inductor.

[0167] The superconducting transformer primary inductor may have a first terminal and a second terminal, where a first type of single flux quantum pulse enters the superconducting transformer primary inductor at the first terminal and a second type of single flux quantum pulse enters the superconducting transformer primary inductor at the second terminal, such that the first type of single flux quantum pulse acts on the change in magnetic flux with an opposite polarity to the first type of single flux quantum pulse.

[0168] The method may further include receiving a target value of the magnetic flux, counting a sequence of single flux quantum pulses, and stopping the single flux quantum pulses after the counter value corresponds to the target value.

[0169] The method may further include receiving a feedback signal for the magnetic flux responsive to a required correction of the magnetic flux, and gating the sequence of single flux quantum pulses when the feedback signal indicates sufficient correction of the magnetic flux.

[0170] The method may further include receiving a feedback signal and generating a train of successive single flux quantum pulses of a first type or a second type selectively responsive to the feedback signal, the first type of single flux quantum pulses causing an increase in current in the superconducting inductor and the second type of single flux quantum pulses causing a decrease in current in the superconducting inductor.

[0171] The method may further include receiving a target value and counting successive trains of single flux quantum pulses of a first type or a second type until the count corresponds to the target value, where the first type single flux quantum pulses cause an increase in a current in the superconducting inductor and the second type single flux quantum pulses cause a decrease in a current in the superconducting inductor.

[0172] The method may further include receiving a feedback signal and selectively generating, in response to the feedback signal, an output representative of a first type or a second type of successive single flux quantum pulse train or no net single flux quantum pulse, where the first type of single flux quantum pulse causes an increase in current in the superconducting inductor and the second type of single flux quantum pulse causes a decrease in current in the superconducting inductor, and the output representative of no net single flux quantum pulse results in no net change in current in the superconducting inductor.

[0173] The output representative of no net single flux quantum pulses may include no single flux quantum pulses and / or offsetting the first type single flux quantum pulses with the second type single flux quantum pulses.

[0174] The method may further include receiving a target value, selectively incrementing a counter based on a first type of train of successive single flux quantum pulses if the count is below the target value, selectively decrementing the counter based on a second type of train of successive single flux quantum pulses if the count is above the target value, and selectively suppressing a net single flux quantum pulse if the count corresponds to an error margin of the target value, where the first type of single flux quantum pulse causes an increase in current in the superconducting inductor and the second type of single flux quantum pulse causes a decrease in current in the superconducting inductor. The suppressed net single flux quantum pulse may include no single flux quantum pulses and / or offsetting the first type of single flux quantum pulses and the second type of single flux quantum pulses.

[0175] The method may further include measuring the magnetic flux or the integrated magnetic flux using a sensor, and / or measuring a physical property using a sensor, and / or receiving a feedback signal responsive to performance of the plurality of qubits.

[0176] The at least one qubit may include a plurality of qubits having a physical property tunable in response to a magnetic flux, and a coupler between the plurality of qubits. The qubits may be superconducting qubits.

[0177] The method may further include selectively generating a first type single flux quantum pulse and selectively generating a second type single flux quantum pulse, where the first type single flux quantum pulse causes a change in the current of the superconducting inductor of a first amplitude and the second type single flux quantum pulse causes a change in the current of the superconducting inductor of a second amplitude, and where the first type single flux quantum pulse is generated independently of the second type single flux quantum pulse. The first type single flux quantum pulse may cause a change in the current of the superconducting inductor having a smaller absolute value than a change in the current of the superconducting inductor caused by the second type single flux quantum pulse.

[0178] The method may further include resetting the magnetic flux to a predetermined value. The resetting may include passing a pulse through a reset inductor coupled to a superconducting quantum interference device (SQUID) in series with the superconducting inductor, such that the pulse induced current in the reset inductor is sufficient to drive the SQUID above a critical current of the SQUID and cause it to become resistive and thus the energy stored in the superconducting inductor to become dissipative. [Brief description of the drawings]

[0179] [Figure 1] The SFQ magnetic flux bias application circuit is shown. [Diagram 2] SFQ flux biasing using a chain of JTL is shown. [Diagram 3] 1 shows flux biasing using parallel JTLs. [Figure 4] 13 shows a simulation of magnetic flux biasing by adding or removing magnetic fluxons. [Diagram 5] 13 illustrates a time-varying magnetic flux bias application of an arbitrary shape. [Figure 6] 1 shows a circuit for coarse flux biasing using a flux pump. [Figure 7] A combination of coarse and fine biasing is shown. [Figure 8] 1 shows a circuit for resetting the flux stored in the flux biasing circuit. [Figure 9A] FIG. 1 shows a block diagram of a single qubit gate operation using time-varying flux biasing. [Figure 10B] FIG. 1 shows a block diagram of single-qubit gate operation using time- and pulse-rate-variable flux biasing. [Figure 10A] FIG. 1 shows a block diagram of a multi-qubit gate operation using time-varying flux biasing of the qubits and couplers. [Figure 10B]FIG. 1 shows a block diagram of multi-qubit gate operation using time- and pulse-rate-variable flux biasing of the qubits and couplers. [Figure 11] We demonstrate single-qubit manipulation by combining SFQ pulses for single-qubit control and flux biasing. [Figure 12A] 1 shows a block diagram of a prototype SFQ flux bias circuit employing a counter. [Figure 12B] 1 shows a block diagram of a prototype SFQ flux bias circuit employing feedback. [Figure 12C] FIG. 1 shows a block diagram of a prototype SFQ flux bias circuit for generating net zero flux bias pulses for fluxonium control. [Figure 12D] FIG. 1 shows a block diagram of a prototype low-hardware-overhead SFQ flux bias circuit for generating net-zero flux bias pulses for fluxonium control. [Figure 13] 1 shows an outline of the amplified JTL. [Figure 14A] 1 shows a block diagram of a relaxation oscillator flux pump. [Figure 14B] 1 shows a circuit schematic of a relaxation oscillator flux pump. [Figure 14C] 1 shows a graph of a simulation of the operation of a relaxation oscillator, with the dotted curve showing the voltage output and the solid curve representing the total flux output. [Figure 15] FIG. 1 shows a block diagram of a programmable pulse counter. [Figure 16A] A top-level schematic of a prototype SFQ flux bias circuit is shown. [Figure 16B] 16B shows a schematic diagram of the magnetic flux generating circuit from FIG. 16A. [Figure 16C] FIG. 16C shows a schematic diagram of the switch from FIG. 16B. [Figure 16D] FIG. 16D shows a schematic diagram of the synchronizer component of the switch from FIG. 16C. [Figure 17] The circuit layout of the prototype SFQ flux bias circuit is shown. [Figure 18] A simulation of the operation of the prototype SFQ flux bias circuit is presented. [Figure 19] Experimental measurements of the prototype SFQ bias circuit are presented. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0180] FIG. 1 shows a conceptual diagram of a preferred embodiment of the flux biasing circuit. The diagram includes the flux biasing circuit itself, which generates a time-varying flux that is inductively coupled to a superconducting qubit or to a superconducting coupler between two qubits (qubit / coupler). The inductive coupling is performed by a primary inductance L in , secondary inductance L out , and a mutual inductance M. The transformer lines preferably comprise a superconducting material such as niobium or aluminum at cryogenic operating temperatures, so that they have a fluxon Φ 0 The flux biasing circuitry and the qubit / coupler are essentially lossless, with the flux being quantized as a multiple of . Both the flux biasing circuitry and the qubit / coupler comprise multiple Josephson junctions. The flux biasing circuitry and the qubit / coupler may be integrated circuits that may be fabricated on the same chip, or may be fabricated on separate chips that are inductively coupled in a flip-chip geometry.

[0181] FIG. 1 also includes two digital SFQ generation circuits, which may be nominally identical, but have primary inductances L1 and L2 with opposite polarities to correspond to magnetic fluxes of opposite signs. in is connected to

[0182] This schematic is further elaborated in Figure 2 to include a Josephson transmission line (JTL) in each of the two channels. The JTLs are used to transport and shape the SFQ pulses, and may also be configured in parallel to achieve current gain, as shown in Figure 3. The JTLs themselves propagate the SFQ pulses in series, but the parallel output configuration acts as a digital pulse multiplier that increases the total flux by a factor of n for the parallel unit cells.

[0183] Figures 4 and 5 show two examples of time-varying flux profiles that can be generated by such positive and negative fluxon generators. Figure 4 shows a simple profile that rises linearly, remains constant, and then ramps down again, while Figure 5 represents an arbitrary change over time. Although no time axis is specified in either case, the characteristic ramp time can be anything from 10 ps to 1 ns or more, since individual SFQ pulses have characteristic pulse widths of 1-2 ps. This can be equated to the period of a qubit resonance, which can be on the order of 100 ps. Hence, the flux bias change can occur within a single resonance period or over multiple resonance periods. Note also that although SFQ pulses contain very high frequency components, the circuit can be configured to filter out the highest frequency components to produce a smooth flux profile. Such a smooth flux profile is also one that does not excite quasiparticles in the quantum portion of the circuit, which in this case tends to reduce the quantum coherence time.

[0184] Further embodiments of the flux bias application circuit are shown in Figures 6 and 7 and include two stages of coarse and fine control. The coarse control may include a flux pump that multiplies the flux by a known factor. One embodiment of the flux pump is a SQUID relaxation oscillator, shown in Figures 14A-14C and described further below. The two stages of flux bias control allow for high precision, high speed, and large dynamic range.

[0185] A further refinement of resetting the flux in the control loop to zero is shown in Figure 8. This is achieved using a SQUID in series with an inductive memory loop. When a control SFQ pulse drives the SQUID above its critical current into its normal state, the loop becomes resistive and the stored flux of either sign quickly escapes the loop.

[0186] The block diagram in FIG. 9A shows various ways in which SFQ digital control can be applied to qubit control. In a preferred embodiment, all of these blocks include superconducting circuits mounted at cryogenic temperatures. The top block is a central control unit that provides a centralized source of clock pulses for synchronization and sequential timing. These clock pulses are also SFQ pulses. The SFQ control signals include flux biases for the qubits, but also other SFQ pulse sequences that can be used, for example, to induce quantum transitions. These include blocks labeled "SFQ pattern generation," "SFQ amplitude control," and "SFQ-qubit coupler." These are similar to prior art circuits for SFQ control, but here they can be appropriately synchronized with the flux bias application circuitry for improved control.

[0187] The block diagram of Figure 9B shows another embodiment in which the qubits are exclusively controlled using flux bias pulses (FBP). The shape of the pulses is controlled using the blocks "SFQ FBP amplitude control" and "SFQ FBP ramp control". The specific control functions of these blocks are generated by the "SFQ flux bias (FBP) pattern generation" block.

[0188] Figures 10A and 10B take this further for two coupled qubits and others. Two tunable qubits linked by a coupler, shown in the center of the figure, contain the superconducting quantum circuitry itself. These can be linked to other qubits and couplers, as shown at the bottom. Fully synchronized digital control at all levels enables new opportunities for precision control while minimizing decoherence of quantum operations.

[0189] An illustrative example of these two types of SFQ control is shown in Figure 11. The bottom pulses (corresponding to opposite polarities) provide a flux bias that first tunes and then detunes the energy of the qubit shown in the center. The top pulses represent a resonant pulse train coupled to induce a transition of the qubit during which its energy is appropriately tuned.

[0190] In addition to presenting concepts and methods for superconducting digital flux biasing of qubits, portions of preferred embodiments have been designed, simulated, fabricated, and demonstrated experimentally.

[0191] Figure 12A shows a block diagram of a flux bias control circuit similar to that shown in Figure 3. This circuit includes positive and negative flux generating circuits, each having an amplifying JTL (AJTL), a switch, and a counter. It also includes a single coupled inductor L1 that couples the flux to a qubit or coupler labeled Q, and a superconducting clock source that sets the rate at which the SFQ pulses are generated.

[0192] Alternatively, as shown in FIG. 12B, a flux bias control circuit similar to that shown in FIG. 3 is provided with a feedback input based on a sensor measurement or performance indicator in response to the output of the qubit. This circuit also includes positive and negative flux generating circuits, each having an amplified JTL (AJTL), a switch, a comparator to determine if the flux is above or below a target or set point provided by the controller, and an inverter to drive the opposite phase (flux on vs. flux off). The comparator may also have unique complementary outputs. It also includes a single coupled inductor L1 that couples the flux to the qubit or coupler labeled Q, and a superconducting clock source that sets the rate of generation of the SFQ pulses. Not shown in 12B is the option to suppress all pulses, for example when the sensor output or performance indicator indicates sufficient proximity to the target that no adjustment is required. Typically, this is generated by a digital control, a deadband control circuit, or a hysteresis circuit, and may be advantageously implemented by adjusting a set point. The null regulation zone may be implemented by suppression of the pulses or by the presence of both flux-on and flux-off pulses. In the former case, power dissipation is reduced. Typically, the comparator is implemented in digital logic, but an analog implementation is possible as long as power dissipation is kept at a low level. The comparator may be digital in magnitude and analog in time, operating in a phase relationship. For example, if the comparator is clocked, the output may selectively depend on whether one input leads the clock and the other trails the clock. If both lead or trail, the comparator may produce a null output.

[0193] FIG. 12C shows an example of an SFQ circuit for generating net zero flux bias pulses that can be used for fluxonium control within a single qubit cycle (Larmor period). The net zero pulses are generated over an interval Δt ZIt consists of two opposite polarity triangular flux bias pulses applied to the qubit at 1 V. The amplitude of each pulse is programmed using a SFQ counter, whose carry signal triggers a polarity switch implemented using a toggle flip-flop (TFF). A non-destructive readout switch (ND) is used to control the initiation and completion of the pulse generation.

[0194] FIG. 12D shows an example of a simplified SFQ circuit for generating net zero flux bias pulses similar to those described in FIG. 12C. The reduction in complexity is achieved by reducing the spacing □t between flux bias pulses of opposite polarity. Z This is achieved by using a dc / SFQ converter to generate a control SFQ pulse to set the dc / SFQ frequency. Although this scheme is simpler on the SFQ side, it requires a control signal for the dc / SFQ converter, which can be generated by cryo-CMOS or conventional room temperature electronics.

[0195] The AJTL can be a parallel JTL with six JTL stages in parallel, as shown in FIG. 13. Alternatively, a flux pump based on a relaxation oscillator (ROS) can be used, as shown in FIG. 14A-C. FIG. 14A shows a block diagram of a total flux bias circuit with two ROS circuits for both positive and negative flux. FIG. 14B shows a schematic of a ROS built around a hysteretic Josephson junction Jm2. When this junction switches, it is held at a voltage stage that generates a long period of time, typically several hundred fluxons or more. A simulation of the operation of the ROS is shown in FIG. 14C, where the oscillating dotted curve shows the voltage output and the solid curve with a long tail represents the total flux output. This ROS flux bias circuit would be particularly useful for the coarse channels of the two-stage flux bias circuit, as suggested in FIG. 6 and FIG. 7.

[0196] The counter is 2. NThe divider may be a fixed divider based on a simple chain of N T flip-flops (TFFs) as known in the prior art to generate SFQ pulses. Alternatively, a programmable counter as shown in FIG. 15 may be used, which can be programmed to generate up to 2 N An arbitrary programmable number of SFQ pulses can be generated using the SFQ-based FET. It also includes a string of N TFFs (N=6 in FIG. 14C) linked to a serially programmable non-destructive readout (NDRO) register.

[0197] A portion of the schematic hierarchy of a prototype flux bias control circuit based on Figure 12 is shown in Figures 16A, 16B, 16C, and 16D. Figure 16A shows the components of the overall bipolar flux control circuit, including positive and negative flux channels (flux on and flux off), two identical flux bias drivers (FB_DRV), a synchronous clock generator with splitters for clock distribution, and an output flux bias inductor LFB. This output inductor would couple the flux to the qubits or couplers, but quantum circuits are not included in this prototype demonstration circuit.

[0198] Figure 16B provides a more detailed schematic diagram of the flux bias driver FB_DRV, including a switch, a 16-bit counter, and an amplifier JTL, as shown in the block of Figure 11. The switch is further expanded in Figure 16C, comprising a synchronizer circuit SYNC and a storage register NDRO. Finally, in Figure 16D, the SYNC circuit is shown to include two D flip-flops (DFF), which are well known in the prior art.

[0199] The circuit of Figures 16A-16D was placed on a chip using standard integrated circuit design tools. A portion of the chip layout is shown in Figure 17. It includes a flux-on and flux-off bias driver with component counter 171 (x16), switch 172, and JTL current amplifier 173.

[0200] The operation of the circuit of Figure 16 has been simulated. Some inputs and outputs are shown in Figure 18. The top plot shows several periods of the output current (and therefore the flux bias) ramping up and down. Below this are a clock signal, alternating flux pulses (positive and negative flux) from the left and right sides, and trigger pulses for the two sides.

[0201] A chip based on the layout of Figure 17 was fabricated using niobium Josephson junction technology, cooled to about 4K below the superconducting critical temperature, and tested. Preliminary results are shown in Figure 19, showing the clock input, flux pump input, and flux output measured by a DC SQUID. Although this was a preliminary low frequency test, the circuit demonstrated the expected functionality.

[0202] Similar superconducting circuits, with flux bias linked to superconducting qubits or interqubit couplers, would be expected to exhibit similar performance at high speeds and at cryogenic temperatures in the mK range.

Claims

1. A magnetic flux control system comprising: A control system including a plurality of Josephson junctions configured to generate a sequence of single flux quantum pulses; A superconducting circuit configured to convert each pulse of the sequence of single flux quantum pulses into magnetic flux; A superconducting inductor configured to integrate the magnetic flux; The magnetic flux control system, wherein the integrated magnetic flux is controlled to increase and decrease in correspondence with at least one control signal of the control system.

2. The magnetic flux control system according to claim 1, wherein the superconducting inductor is further configured to couple the integrated magnetic flux to a quantum computing circuit comprising at least one qubit circuit having at least one physical property adjustable according to at least the magnetic flux.

3. The magnetic flux control system according to claim 2, wherein the control system has at least one control mode adapted to dynamically change the adjustable physical property of the at least one qubit over time.

4. The magnetic flux control system according to claim 1, wherein the control system has at least one control mode adapted to maintain a certain physical property of the qubit.

5. The magnetic flux control system according to claim 1, wherein the control system has at least one control mode adapted to dynamically change the physical property of the qubit over time.

6. The magnetic flux control system according to claim 1, wherein the control system comprises an input configured to receive a feedback signal.

7. The magnetic flux control system according to claim 1, wherein the control system comprises a pair of inputs configured to receive feedback signals representing excess and deficiency of magnetic flux.

8. The magnetic flux control system according to claim 1, wherein the control system is configured to implement phase-locked loop control.

9. The magnetic flux control system according to claim 1, wherein the control system is configured to receive a photon control signal.

10. The magnetic flux control system according to claim 1, further comprising a heterodyne detector.

11. The magnetic flux control system according to claim 1, further comprising a phase-sensitive amplifier configured to amplify a microwave signal interacting with at least one qubit.

12. The qubit comprises a transmon qubit, the control system is further configured to couple the integral flux to a transmon qubit circuit having a microwave resonance adjustable at least according to the flux within the decoherence time of the qubit, maintain a first flux associated with the transmon qubit, define a first microwave resonance frequency of the transmon qubit, define a second microwave resonance frequency of the transmon qubit, and then maintain a second flux associated with the transmon qubit and be configured to define the second microwave resonance frequency of the transmon qubit, wherein the first flux is different from the second flux and the first microwave resonance frequency is different from the second microwave resonance frequency, the flux control system according to claim 1.

13. the control system is configured to receive at least one control signal selectively in response to a signal from the qubit during quantum computing representing a computational state of the qubit during a stage of quantum computing, and to control the flux selectively in response to the computational state of the qubit during a subsequent stage of quantum computing, the flux control system according to claim 1.

14. A flux bias control method, comprising: generating a sequence of single flux quantum pulses using a control system comprising a plurality of Josephson junctions; converting the sequence of single flux quantum pulses into a flux; coupling the flux to a quantum computing circuit comprising at least one qubit coupler circuit using a superconducting inductor; and adjusting a physical property of the qubit according to the flux.

15. further comprising selectively generating a first type of single flux quantum pulse and a second type of single flux quantum pulse, wherein the first type of single flux quantum pulse causes an increase in the current of the superconducting inductor and the second type of single flux quantum pulse causes a decrease in the current of the superconducting inductor, the flux bias control method according to claim 14.

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