Using time scales to operate quantum devices

Abstract

Systems and methods are provided for operating one or more qubits in a quantum computing system. In some examples, the methods may include obtaining historical time data associated with a time scale of an operational parameter of a qubit of a quantum device. The methods may include selecting an operational parameter value based at least in part on the historical time data associated with the time scale of the operational parameter to reduce a probability of occurrence of a time-dependent defect. The time-dependent defect may exhibit a time-dependent behavior. The methods may include operating the qubit of the quantum device at the operational parameter value.

Description

[Technical field]

[0001] This application claims the benefit of priority to U.S. Provisional Application No. 63 / 243,427, entitled “Operating Quantum Devices Using a Temporal Metric,” filed September 13, 2021, which is incorporated herein by reference.

[0002] The present disclosure relates generally to quantum computing systems. [Background technology]

[0003] Quantum computing is a computing method that exploits quantum effects such as superposition and entanglement of basis states to perform some calculations more efficiently than classical digital computers. In contrast to digital computers, which store and manipulate information in the form of bits, e.g., "1" or "0," quantum computing systems can manipulate information using quantum bits ("qubits"). A qubit may refer to a quantum device that allows for the superposition of data in multiple states, e.g., both "0" and "1" states, and / or the superposition of data in multiple states itself. Following conventional terminology, the superposition of "0" and "1" states in a quantum system may be represented, for example, as |0>+b|1>. The "0" and "1" states of a digital computer are analogous to the |0> and |1> basis states of a qubit, respectively. Summary of the Invention [Means for solving the problem]

[0004] Aspects and advantages of embodiments of the disclosure will be set forth in part in the description that follows, or may be learned from the description, or may be learned by practice of the embodiments.

[0005] One exemplary aspect of the present disclosure is directed to a method of operating a qubit of a quantum device. The method may include obtaining historical time data associated with a time scale of an operational parameter of the qubit of the quantum device. The method may include selecting an operational parameter value based at least in part on the historical time data associated with the time scale of the operational parameter to reduce a probability of occurrence of a time-dependent defect. The time-dependent defect may exhibit a time-dependent behavior. The method may include operating the qubit of the quantum device at the operational parameter value.

[0006] Other aspects of the present disclosure are directed to various systems, methods, apparatus, non-transitory computer-readable media, computer-readable instructions, and computing devices.

[0007] These and other features, aspects, and advantages of various embodiments of the present disclosure will become better understood with reference to the following description and appended claims. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the present disclosure and, together with the description, explain the associated principles.

[0008] A detailed discussion of embodiments directed to one of ordinary skill in the art is set forth herein, which refers to the accompanying figures. [Brief description of the drawings]

[0009] [Figure 1] FIG. 1 illustrates an exemplary quantum computing system in accordance with an exemplary embodiment of the present disclosure. [Diagram 2] FIG. 2 illustrates an exemplary plot of operating frequency of a qubit versus energy relaxation time. [Diagram 3] FIG. 1 illustrates an exemplary telegraphic behavior of the energy relaxation time of a qubit over time. [Figure 4] FIG. 1 illustrates an exemplary diffusive behavior of the energy relaxation time of a qubit over time. [Diagram 5] FIG. 1 illustrates an exemplary system for determining operational parameters of each of one or more qubits in a quantum computing system, according to an exemplary embodiment of the present disclosure. [Figure 6] 1 is a flow diagram of an example method for determining operational parameters of each of one or more qubits in a quantum computing system, according to an example embodiment of the present disclosure. [Figure 7] 1 is a flow diagram of an exemplary method for selecting operating parameters of each of one or more qubits in a quantum computing system, in accordance with an exemplary embodiment of the present disclosure. [Figure 8] FIG. 1 illustrates an example approach for generating a cost function to address telegraphic behavior of operational parameters, according to an example embodiment of the present disclosure. [Figure 9] FIG. 1 illustrates an exemplary generation of weighted cost terms according to an exemplary embodiment of the present disclosure. [Figure 10] FIG. 1 illustrates an example approach for generating a cost function to address diffusive behavior of an operating parameter, according to an example embodiment of the present disclosure. [Figure 11] FIG. 1 illustrates an example approach for generating a cost function to address diffusive and telegraphic behavior of operational parameters, according to an example embodiment of the present disclosure. [Figure 12] FIG. 1 illustrates an example training of a machine learned model for predicting future defect conditions according to an example embodiment of the present disclosure. [Figure 13] FIG. 1 illustrates an example application of a machine learning model to predict future defect conditions, according to an example embodiment of the present disclosure. [Figure 14] FIG. 1 illustrates an exemplary classical computing environment that can be used to implement aspects of the present disclosure, according to an exemplary embodiment of the present disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0010] Exemplary aspects of the present disclosure are directed to systems and methods for operating qubits in a quantum computing system. One problem with operating quantum devices is that qubits can decoherence (e.g., become dephased and / or undergo undesired state transitions). Decoherence that occurs before a computation is complete can lead to errors.

[0011] For example, a quantum computing device may include a quantum processor having multiple qubits (e.g., superconducting qubits). Each qubit may be operated according to an operating parameter. The effectiveness of the operating parameter may depend on a time scale (e.g., the scale may change with time). The time scale may change as a function of the operating parameter and may change over time. In some cases, the time scale may be associated with a time-dependent material defect, for example due to collision or coincidence with a defect, such as a two-level system (TLS) defect, in a material used to implement the multiple qubits.

[0012] For example, a quantum processor may include multiple qubits arranged, for example, in a two-dimensional lattice, with adjacent qubits permitted to interact. Each qubit may be operated using a respective operating frequency (e.g., a respective idle frequency, and / or interaction frequency, and / or readout frequency, and / or reset frequency). The operating frequencies may differ for each qubit (e.g., each qubit may idle at a different operating frequency).

[0013] Some operating frequencies are better than others. The time scale for evaluating a particular operating frequency for a qubit may be the energy relaxation time for the operating frequency. It may be desirable to operate the qubit at a frequency with a long energy relaxation time, since a shorter energy relaxation time may lead to larger quantum computation errors.

[0014] However, the energy relaxation time of a qubit can vary by several orders of magnitude based on the operating frequency and time. In this regard, the time-based variation of the energy relaxation time can be an obstacle to the scaling up of quantum computers. Some variations in the energy relaxation time can be caused by transitions of two-level defects in the material colliding (e.g., going in and out of resonance) or occurring simultaneously with transitions of the qubit. In some cases, the fluctuations can exhibit telegraphic behavior, where the defect moves between multiple discrete states. Alternatively, the fluctuations can exhibit diffusive behavior, where the defect fluctuates semi-continuously. In yet another form, the defect can exhibit some of each of telegraphic and diffusive behavior.

[0015] In frequency-tunable qubit architectures, two-level system defects can be reduced by optimizing the frequencies at which single-qubit gates, multi-qubit gates, resets, and readouts occur. However, this optimization of frequency does not take into account the time-dependent behavior of time scales (e.g., energy relaxation times) and associated time-dependent defects such as the time dependence of collisions with two-level system transitions.

[0016] Aspects of the present disclosure describe systems and methods that leverage past time data to predict and avoid future defects. The past time data can be used to enforce constraints in selecting operating parameters for a qubit. These constraints can reduce the probability of determining operating parameters for the operation of a qubit that coincide with a time-dependent defect.

[0017] For example, in some embodiments, a cost function may be constructed that is a sum of weighted cost terms. At least one of the weighted cost terms may be associated with past time data to enforce the constraints. The cost function may be optimized or otherwise used to select operational parameter values ​​for the operational parameters. The quantum device may be operated at determined operational parameters of the qubits to improve performance and reduce the occurrence of errors due to defects.

[0018] In some implementations, the cost function may include cost terms such that the cost function embeds past defect states into the cost function. This approach may be suitable for telegraphic defects. In some embodiments, the cost function may include cost terms that embed future predicted defect states into the cost function. The future predicted defect states may be extrapolated from past time data. This extrapolation may be accomplished, for example, using polynomial approximation or machine learning models (e.g., implemented using neural networks). This may be appropriate for defects that exhibit diffusive behavior. A hybrid approach using cost terms related to both past defect states and future predicted defect states extrapolated from past time data may be appropriate for other cases, such as defects that exhibit both telegraphic and diffusive behavior.

[0019] Systems and methods according to exemplary aspects of the present disclosure may have several technical effects and advantages. For example, a quantum computing device operated according to exemplary aspects of the present disclosure may perform calculations with fewer errors and greater accuracy. In addition, reduced errors may result in improved coherency of the quantum computing system and the ability to scale up the quantum computing system to include a larger number of qubits.

[0020] Referring now to the figures, exemplary embodiments of the present disclosure will be discussed in more detail. As used herein, the use of the term "about" in conjunction with a value refers to within 20% of that value.

[0021] 1 illustrates an exemplary quantum computing system 100. System 100 is one example of a system of one or more classical computers and / or quantum computing devices in one or more locations in which the systems, components, and techniques described below may be implemented. Using the disclosure provided herein, one of ordinary skill in the art will understand that other quantum computing devices or systems may be used without departing from the scope of the present disclosure.

[0022] The system 100 includes quantum hardware 102 in data communication with one or more classical processors 104. The classical processor 104 may be configured to execute computer-readable instructions stored in one or more memory devices to perform operations such as any of the operations described herein. The quantum hardware 102 includes components for performing quantum computations. For example, the quantum hardware 102 includes a quantum system 110, a control device 112, and a readout device 114 (e.g., a readout resonator). The quantum system 110 may include one or more multilevel quantum subsystems, such as a register of qubits (e.g., qubits 120). In some implementations, the multilevel quantum subsystem may include superconducting qubits, such as flux qubits, charge qubits, transmon qubits, gmon qubits, etc.

[0023] The type of multilevel quantum subsystem utilized by system 100 may vary. For example, in some cases it may be advantageous to include one or more readout devices 114 attached to one or more superconducting qubits, e.g., transmon qubits, flux qubits, gmon qubits, xmon qubits, or other qubits. In other cases, ion traps, photonic devices, or superconducting cavities (e.g., with which states may be prepared without the need for qubits) may be used. Further examples of implementations of multilevel quantum subsystems include fluxmon qubits, silicon quantum dots, or phosphorus impurity qubits.

[0024] A quantum circuit may be constructed that is applied to a register of qubits included in quantum system 110 via a number of control lines coupled to one or more control devices 112. An exemplary control device 112 operating on a register of qubits may be used to implement a quantum gate or a quantum circuit having a number of quantum gates, e.g., Pauli gates, Hadamard gates, controlled NOT (CNOT) gates, controlled phase gates, T-gates, multi-qubit quantum gates, coupler quantum gates, etc. The one or more control devices 112 may be configured to operate on quantum system 110 through one or more respective control parameters (e.g., one or more physical control parameters). For example, in some embodiments, the multi-level quantum subsystem may be a superconducting qubit, and the control device 112 may be configured to provide control pulses to the control lines to generate a magnetic field to tune the frequency of the qubit.

[0025] The quantum hardware 102 may further include a readout device 114 (e.g., a readout resonator). Measurement results 108 obtained via the measurement device may be provided to the classical processor 104 for processing and analysis. In some implementations, the quantum hardware 102 may include quantum circuits, and the control device 112 and readout device 114 may implement one or more quantum logic gates that operate on the quantum system 110 through physical control parameters (e.g., microwave pulses) transmitted through wires included in the quantum hardware 102. Further examples of control devices include arbitrary waveform generators, where a digital-to-analog converter (DAC) creates the signal.

[0026] The readout device 114 may be configured to perform a quantum measurement on the quantum system 110 and transmit the measurement result 108 to the classical processor 104. In addition, the quantum hardware 102 may be configured to receive data from the classical processor 104 specifying the physical control qubit parameter values ​​106. The quantum hardware 102 may use the received physical control qubit parameter values ​​106 to update the action of the control device 112 and the readout device 114 on the quantum system 110. For example, the quantum hardware 102 may receive data specifying new values ​​representing voltage strengths of one or more DACs included in the control device 112 and may update the action of the DACs on the quantum system 110 accordingly. The classical processor 104 may be configured to initialize the quantum system 110 to an initial quantum state, for example, by transmitting data specifying an initial set of parameters 106 to the quantum hardware 102.

[0027] In some implementations, the readout device 114 can measure the state of a quantum system, such as a qubit, by utilizing the difference in impedance for the |0> and |1> states of the element (e.g., a qubit). For example, the resonant frequency of the readout resonator may be different when the qubit is in state |0> and when it is in state |1> due to the nonlinearity of the qubit. Thus, microwave pulses reflected from the readout device 114 have amplitude and phase shifts that depend on the qubit state. In some implementations, a Purcell filter may be used with the readout device 114 to prevent microwave propagation at the qubit frequency.

[0028] In some embodiments, quantum system 110 may include a plurality of qubits 120 arranged, for example, in a two-dimensional lattice 122. For clarity, two-dimensional lattice 122 shown in FIG. 1 includes 4×4 qubits, but in some embodiments, system 110 may include fewer or more qubits. In some embodiments, the plurality of qubits 120 may interact with one another through a plurality of qubit couplers, for example, qubit coupler 124. The qubit coupler may define nearest-neighbor interactions between the plurality of qubits 120. In some implementations, the strength of the plurality of qubit couplers is a tunable parameter. In some cases, the plurality of qubit couplers included in quantum computing system 100 may be couplers with invariant coupling strengths.

[0029] In some implementations, the plurality of qubits 120 may include data qubits, such as qubit 126, and measurement qubits, such as qubit 128. A data qubit is a qubit that participates in a computation being performed by system 100. A measurement qubit is a qubit that may be used to determine the outcome of a computation performed by a data qubit. That is, during a computation, the unknown state of a data qubit is transferred to a measurement qubit using an appropriate physical operation and measured via an appropriate measurement operation performed on the measurement qubit.

[0030] In some implementations, each qubit in the plurality of qubits 120 may be operated using a respective operating frequency, such as an idle frequency, and / or an interaction frequency, and / or a readout frequency, and / or a reset frequency. The operating frequency may vary from qubit to qubit. For example, each qubit may be idle at a different operating frequency. The operating frequency of qubit 120 may be chosen before a computation is performed.

[0031] Some operating frequencies are better than others. One measure to evaluate how good a particular operating frequency is for a particular qubit is the energy relaxation time (T1) of that qubit at that frequency. A shorter energy relaxation time can lead to larger quantum computation errors. In that regard, it may be desirable to operate the qubit at a frequency with a longer energy relaxation time.

[0032] 2 shows a plot 130 illustrating an example relationship between qubit frequency 132 and energy relaxation time (T1) 134. Ideally, the energy relaxation time varies smoothly as a function of qubit frequency. However, as shown in plot 130, in reality, the energy relaxation time may vary sporadically as a function of qubit frequency due to imperfections, as demonstrated by the downward spike 136. The imperfections may be, for example, due to the transition frequency of a two-level system (TLS) defect becoming resonant with the operating frequency.

[0033] The energy relaxation time may also vary over time. In that regard, the energy relaxation time is a time scale related to the operating parameter of the operating frequency of the qubit. For example, FIG. 3 shows a plot 140 of operating frequency 142 and energy relaxation time 144 as a function of time 146. Darker pixels in the plot 140 represent shortening of the energy relaxation time that may be due to defects such as collisions with TLS defects. As shown, the operating frequency at which the defect occurs may vary over time and exhibit time-dependent behavior. In the example of FIG. 3, the defect moves between multiple discrete frequencies. In this regard, in the example of FIG. 3, the time-dependent defect exhibits telegraphic behavior (e.g., the defect moves between multiple discrete frequencies).

[0034] As another example, FIG. 4 illustrates a plot 150 of operating frequency 152 and energy relaxation time 154 as a function of time 156. Darker pixels in plot 150 represent shortened energy relaxation times that may be due to defects such as TLS defects. As shown, the operating frequency at which defects occur may vary with time and exhibit time-dependent behavior. In the example of FIG. 4, the defects fluctuate semi-continuously with time. In this regard, in the example of FIG. 4, the time-dependent defects exhibit diffusive behavior (e.g., the defects fluctuate with time).

[0035] Defects, as evidenced by shortened relaxation times, may exhibit telegraphic behavior, diffusive behavior, or both telegraphic and diffusive behavior, as demonstrated by Figures 3 and 4. Aspects of the present disclosure are directed to operating qubits in quantum devices to reduce errors that may result from the time-dependent behavior of defects, such as TLS defects.

[0036] Aspects of the present disclosure are directed to systems and methods for operating qubits in a manner that reduces the occurrence of time-dependent defects (e.g., impinging on TLS defects) by determining operating parameters of the qubits that have a low probability of introducing defects. For example, systems and methods according to example aspects of the present disclosure can determine an operating frequency of a qubit that avoids the degradation of energy relaxation time due to TLS.

[0037] In certain aspects, the operational parameters are determined based at least in part on past time data associated with the qubit. The past time data may indicate how a time scale (e.g., energy relaxation time) varies over time. The past time data may be used to enforce constraints in an optimization problem that incorporates knowledge of the past time data to reduce the probability of selecting operational parameters that may result in a qubit defect (e.g., colliding with a TLS defect).

[0038] Aspects of the present disclosure are discussed with reference to qubits (e.g., superconducting qubits) arranged in a two-dimensional lattice for purposes of illustration and discussion. The operating parameter is the qubit operating frequency. The time scale can be an energy relaxation time. The defect can be a collision with a two-level system defect.

[0039] Those skilled in the art will understand using the disclosure provided herein that aspects of the disclosure may be used with any type of qubit and architecture without departing from the scope of the disclosure For example, the qubits may be spin qubits in a spin qubit quantum processor, or ions in a trapped ion quantum processor.

[0040] The operating parameter may be any tunable parameter without departing from the scope of this disclosure, for example, in a spin qubit, the operating parameter may be an external magnetic field.

[0041] Any time-dependent behavior may be exhibited without departing from the scope of this disclosure. For example, when selecting an operating frequency for a superconducting qubit, the time-dependent behavior may be used to implement a single-qubit gate, a multi-qubit gate, a reset, and / or a readout. The dependencies between the operating parameters may vary without departing from the scope of this disclosure. For example, the frequency locus of a two-qubit gate may depend on the frequency locus of a single-qubit gate.

[0042] Any time scale may be used without departing from the scope of this disclosure. For example, the time scale may be based on single-qubit randomized benchmarking, single-qubit cross-entropy benchmarking, two-qubit randomized benchmarking, two-qubit cross-entropy benchmarking, dephasing time, or other suitable scale.

[0043] Any imperfections may be considered without departing from the scope of the present disclosure. For example, imperfections may result from changing microwave modes or nuclear spins.

[0044] 5 illustrates an example system 200 for determining an operating frequency of one or more qubits, according to an example embodiment of the present disclosure. System 200 may be an example of a system implemented as a quantum or classical computer program on one or more quantum or classical computers at one or more locations.

[0045] System 200 receives input data representative of a quantum computing device to be used to perform a computation, such as input data 206. For example, input data 206 may include data representative of characteristics of qubits included in the quantum computing device, such as the type of qubits included in the quantum computing device, the number of qubits included in the quantum computing device, the type of interaction between qubits included in the quantum computing device, the accessible frequency range of qubits included in the quantum computing device, predicted and / or measured relaxation times and / or coherence times of qubits included in the quantum computing device, etc.

[0046] The input data 206 may further include data representing optimization constraints that may be used to reduce the number of allowed qubit operating frequency configurations. The optimization constraints may be based on and vary based on the physical and engineering constraints of the quantum device (and its control system). For example, the optimization constraints may include a predetermined constraint on the difference in frequency between adjacent qubits, e.g., constraining the qubit frequencies so that adjacent qubits idle X GHz apart from each other, a predetermined constraint on the relationship between different types of operating frequencies, e.g., constraining adjacent qubits to interact at approximately the average of their idle frequencies, or a predetermined constraint on the tolerance of accepted frequencies.

[0047] According to certain aspects of the present disclosure, the optimization constraints may be based at least in part on past time data related to time scales (e.g., energy relaxation times) of one or more qubits in a quantum device. The past time data may demonstrate, for example, telegraphic and / or diffusive behavior of defects in the qubits at operating frequencies that vary over time.

[0048] The system 200 includes a cost function generator 202. The cost function generator 202 may be configured to receive input data 206 and define a first cost function that associates qubit operating frequency values ​​with costs corresponding to operational states of a quantum device specified by the input data 206. The operational states of a quantum device may be defined as a set of qubit operating frequencies used by the quantum device during execution of a quantum algorithm, e.g., an idle frequency and an interaction frequency.

[0049] According to an exemplary embodiment of the present disclosure, the cost function may include a plurality of weighted cost terms, at least one of which may be associated with past time data associated with the time scale. Defining such a cost function and exemplary cost function terms is described in detail below with reference to Figures 7 to 13.

[0050] The system may include a cost function adjuster 204. The cost function adjuster is configured to receive input data representing one or more optimization constraints and to apply the one or more constraints to the first cost function defined by the cost function generator 202 to define an adjusted cost function.

[0051] The system may include an optimizer 210. The optimizer 210 may be configured to adjust the qubit operating frequency values ​​to vary the cost according to an adjusted cost function defined by the cost function adjuster 204 such that the operating conditions of the quantum device specified by the input data 206 are improved, e.g., such that calculations performed by the quantum computing device using the adjusted qubit operating frequency values ​​are less prone to errors. The optimizer 210 may be configured to perform various standard optimization routines as part of adjusting the qubit operating frequency values ​​to vary the cost according to the adjusted cost function. Exemplary optimization routines are described below.

[0052] The system 200 generates as an output data representative of the qubit operating frequency, e.g., output data 208. The generated output data 208 may be used to operate a quantum device that includes the qubit / qubits and perform a computation.

[0053] 6 illustrates a flow diagram of an example method 300 for operating one or more qubits in a quantum computing device, according to an example embodiment of the present disclosure. The method 300 may be implemented using any suitable quantum and / or classical computing system, such as the system described in FIG. 1. FIG. 6 illustrates operations performed in a particular order for purposes of illustration and discussion. Those skilled in the art will appreciate, using the disclosure provided herein, that the operations of any of the methods described herein may be expanded to include steps not shown, omitted, reordered, and / or modified in various ways without departing from the scope of the present disclosure.

[0054] At 302, method 300 includes obtaining past time data associated with a time scale of an operational parameter of one or more qubits. In some embodiments, the past time data may be associated with energy relaxation times at different operating frequencies associated with the qubits. The operating frequencies may be, for example, idling frequencies and / or interaction frequencies at which nearest interacting qubits in a network of interacting qubits should be operated. Examples of past time data associated with energy relaxation times are provided in FIG. 3 and FIG. 4.

[0055] At 304, the method 300 includes selecting an operational parameter value based at least in part on historical time data associated with a time scale of the operational parameter to reduce a probability of occurrence of a time-dependent defect (e.g., colliding with a TLS defect). The time-dependent defect may exhibit time-dependent behavior (e.g., telegraphic behavior and / or diffuse behavior). In an exemplary embodiment, selecting the operational parameter may include constraining a cost function that enforces the constraint based on the historical time data. An optimization operation may be performed using the cost function to select the operational parameter value for the operational parameter. Details regarding constructing a cost function and performing an optimization operation are discussed in detail with reference to FIGS. 7 through 13.

[0056] At 306, method 300 includes operating the qubits of the quantum device at the selected operating parameter values. For example, multiple qubits in a two-dimensional lattice may be operated at an operating frequency determined for each of the qubits to perform a quantum operation (e.g., implement a quantum algorithm, implement a single-qubit gate, implement a multi-qubit gate, perform a readout, etc.).

[0057] 7-13, an exemplary implementation of selecting an operational parameter value based on historical time data is described. FIG. 7 illustrates a flow diagram of an exemplary method 400 for selecting an operational parameter value based at least in part on historical time data associated with a time scale of the operational parameter to reduce the probability of occurrence of a time-dependent defect according to an exemplary embodiment of the present disclosure. The method 400 may be implemented using any suitable quantum and / or classical computing system, such as the system described in FIG. 1. FIG. 7 illustrates operations performed in a particular order for purposes of illustration and discussion. Those skilled in the art will appreciate, using the disclosure provided herein, that the operations of any of the methods described herein may be expanded to include steps not shown, omitted, reordered, and / or modified in various ways without departing from the scope of the present disclosure.

[0058] In step 402, the method includes constructing a cost function having multiple weighted cost terms. The cost function may map costs (e.g., real numbers) corresponding to states of the quantum device to operational parameter values ​​(e.g., operating frequency values) of the qubits. A lower cost may correspond to better operational conditions for the quantum device (e.g., implementing a quantum algorithm with a lower error rate). The cost function may have multiple weighted cost terms. The cost function terms and weights may be determined, for example, based at least in part on data representative of characteristics of qubits included in the quantum computing device.

[0059] At 404, the method includes implementing cost terms in the cost function based on historical time data. For example, at least one of the weighted cost terms in the cost function may be based at least in part on historical time data. The weighted cost terms based on historical time data may be constructed taking into account time-dependent behavior of the defects. For example, the weighted cost terms may be constructed by considering whether the defects exhibit telegraphic behavior, diffuse behavior, or a combination of telegraphic and diffuse behavior. Details regarding exemplary cost functions are described below.

[0060] At 406, the method includes selecting operational parameter values ​​based on a cost function. For example, an optimization process may be performed on the cost function to determine operational parameter values ​​for one or more qubits. In some embodiments, operational parameters such as operating frequency may be determined for qubits arranged in a two-dimensional lattice. Details regarding an exemplary optimization process are described below.

[0061] 8 illustrates an example construction of a cost function 502 with weighted cost terms to address defects exhibiting telegraphic behavior. The weighted cost terms may be associated with past time data such that the cost function 502 embeds at least one past defect condition into the cost function.

[0062] More specifically, a telegraphic fault state may jump suddenly between multiple discrete fault states. An approach to reducing telegraphic faults may be to construct a cost function that is a weighted sum of current and past measured (e.g., unmodeled) cost functions shown in FIG. 8. More specifically, the cost function 502 is a function of a current cost function 504 associated with time t0, as well as a cost function 505 associated with time t0. -1 , t -2 , and t -3It can be a weighted sum of the past measured cost functions 506, 508, and 510 respectively associated therewith. In this way, a plurality of past defect states can be embedded in the cost function. By embedding the past defect states in the cost function, the cost function can implicitly prepare for the defect state to return to the past measured defect state.

[0063] An exemplary process for constructing a cost function to address telecommunication defect states is given below. Take the T1(f,t0) data at the current time t0. Retrieve the past T1(f,ti) data for time ti < t0. Construct the weighted relaxation cost function as follows. C(f)=Σi≦0 wi C(f,ti|T1(f,ti)) such that Σi wi = 1

[0064] The weights wi can be chosen by any function that can depend, for example, on qubits, defects (e.g., TLS), and the quantum processor architecture. In some embodiments, the weights wi can be chosen based on an arbitrary time constant Tc. For example, the weights can be chosen via a Gaussian function such that wi ∝ exp[-((t0 - ti) / Tc)^2]. As another example, the weights can be chosen via an exponential function that decays such that wi ∝ exp[-(t0 - ti) / Tc]. In some embodiments, the weights can be chosen according to a weight function that suppresses the weights as the weights are associated with times farther from the current time. The weight function can be any function and / or can depend on the qubit architecture and the type of defect being mitigated. FIG. 9 shows an exemplary weight function 520 for assigning weights based on the deviation of time from the current time. In some examples, the weight function weights the cost terms associated with time data in the more distant past less than the cost terms associated with time data in the more recent past.

[0065] 10 illustrates an example construction of a cost function 532 with weighted cost terms to address defects exhibiting diffuse behavior. The cost function 532 may include one or more weighted cost terms to embed future predicted defect states into the cost function. The future predicted defect states may be determined based at least in part on past time data (e.g., using a polynomial approximation of the past time data, using a machine learning algorithm, etc.).

[0066] The diffusive defect condition may have smoothly varying operational parameters. An approach to mitigate the diffusive defect condition may be to construct a cost function that is a weighted sum of a current cost function and one or more predicted cost functions for the future as shown in FIG. 10. The predicted cost function may be generated by extrapolating the defect condition based on past time data associated with the time scale, for example, via a simple polynomial approximation or using a neural network. More specifically, the cost function 532 may be a weighted sum of a current cost function 534 associated with time t0 and a future predicted cost function 535 at tk≧ti>t0. The prediction of the future may be calculated using a polynomial approximation, a machine learning algorithm, or some other method. TLS A future predicted cost function can be generated by extrapolating, for example, time t -1 , t -2 , and t -3 The cost function 532 may be determined from past measured time data in each (e.g., cost functions 536, 538, and 540). By embedding future predictions, the cost function 532 provides for the possibility that a TLS defect may move to a frequency that it has not moved to before. Embedding future predicted cost terms into the cost function may also be used to address the telegraphic behavior of the defect condition with appropriate extrapolation models.

[0067] In some embodiments, as shown in FIG. 11, a cost function can be constructed that includes a current cost function, one or more predicted cost functions, and one or more past measured cost functions. This cost function may be suitable for dealing with defective states that exhibit both telecommunication behavior and diffusivity behavior. For example, as shown in FIG. 11, the cost function 552 can be a weighted sum of the current and past measured cost functions 555 and the future predicted cost function 557 at tk≧ti>t0. The cost function 555 includes the cost function 554 for the current time t0, as well as the past measured cost functions 556, 558, and 560 associated with times t -1 , t -2 , and t -3 respectively. The future predicted cost function can be determined, for example, from past measured time data (e.g., cost functions 536, 538, and 540) at times t -1 , t -2 , and t -3 respectively.

[0068] An exemplary process for constructing a cost function under the approach of FIG. 11 is given below. Take the T1(f,t0) data at the current time t0. Retrieve the past T1(f,ti) data for time ti<t0. Predict the future T1(f,ti) data for time tk≧ti>t0 (e.g., using extrapolation, machine learning, etc.). Construct the weighted relaxation cost function as follows. C(f)=Σi≦0 wi C(f,ti|T1(f,ti))+Σk≧i>0 wi C(f,ti|T1(f,ti)) such that Σi wi=1

[0069] The weights wi may be chosen by any function that may depend, for example, on the qubits, the defects (e.g., TLS defects), and the quantum processor architecture. In some embodiments, the weights wi may be chosen based on any time constant Tc. For example, the weights may be chosen via a Gaussian function, such as wi∝exp[-((t0-ti) / Tc)^2]. As another example, the weights may be chosen via a decaying exponential function, such as wi∝exp[-(t0-ti) / Tc]. In some embodiments, the weights may be chosen according to a weighting function that dampens the weights as they are associated with times further away from the current time (e.g., as shown in FIG. 9).

[0070] Any suitable method may be used to generate the T1(f,ti) and / or C(f,ti|T1(f,ti)) cost function predictions. One approach is to fit the past time data trajectory to some function, such as a polynomial, and then use the polynomial to extrapolate where the defect may be at future times. Another approach is to use a machine learning (ML) model, such as a neural network, to predict the future location of the defect and / or the future T1(f,ti) spectrum. Assuming sufficient model capacity, this approach may be useful for mitigating diffuse and telegraphic defects.

[0071] More specifically, Figure 12 illustrates one exemplary embodiment for training a machine learning (ML) model 610 within a supervised learning framework. For example, the model 610 can be a polynomial regression model or any neural network model. The input 604 can be past time data and any portion of time. The label 602 can be any portion of data delayed by any arbitrary time with respect to the input 604.

[0072] FIG. 13 illustrates an example of how a trained ML model 610 may be used according to an exemplary embodiment of the present disclosure. At some current time t0, past time data may be provided to the model 610 as an input 614. The model 610 may generate predicted defect locations, and / or predicted T1(f,ti) spectra, and / or C(f,ti|T1(f,ti)) cost functions. This information may then be used to construct a cost function with weighted cost terms for future predicted states as discussed above. Details regarding an exemplary computing environment that may be used to train and / or apply the ML model 610 are discussed with reference to FIG. 14.

[0073] Additional details regarding an exemplary optimization process, and exemplary cost functions, and cost terms are described below. As discussed above, the exemplary cost terms may be associated with a current time, a past measured time, and / or a future predicted time. For purposes of illustration and discussion, an exemplary optimization process and exemplary cost terms are described for determining the idle and interaction frequencies at which nearest-neighbor interacting qubits in a superconducting quantum computing device should be operated, but the techniques described below may be equally applied to determining the operating parameters of any qubit architecture (e.g., quantum dots, defects spins, atoms) that comprises a network of interacting qubits (e.g., not limited to nearest-neighbor interactions).

[0074] More specifically, in some implementations (e.g., in a quantum computing device including a two-dimensional lattice of interacting superconducting qubits), the operating parameters may include an idle frequency and an interaction frequency. The idle frequency is the frequency at which a qubit is operated when the qubit is not involved in a computation or when the qubit is being used to perform a single-qubit gate. A corresponding idle qubit frequency may be specified for each qubit of the quantum computing device. The interaction frequency is a common frequency at which adjacent qubits in the two-dimensional lattice are operated when performing a two-qubit gate. A corresponding interaction frequency may be specified for each pair of adjacent qubits.

[0075] A cost function may be defined that maps costs (e.g., real numbers) corresponding to operational states of the quantum device to qubit operating frequency values ​​(e.g., the idle frequency of all qubits as described below). For example, a lower cost may correspond to a better operational state of the quantum device, e.g., an operational state that executes a given quantum algorithm with a lower error rate compared to other operational states. In some cases, the better operational state may depend on the quantum algorithm. Systems and methods according to example aspects of the present disclosure may take such dependencies into account by weighting individual cost terms differently in different optimization routines.

[0076] The cost function includes a weighted sum of cost terms corresponding to respective costs. The types of cost terms included in the first cost function may vary and depend on the type of quantum computing device. Some cost terms may be based on past time data and / or future predicted states as discussed above. As an example, the cost function may include an idling cost term for the current time, past measured times, and / or future predicted times that penalizes undesirable characteristics of qubit idling frequency. The idling cost term may penalize low qubit relaxation time (T1) idling frequency. Other cost terms may be used in the cost function without departing from the scope of this disclosure.

[0077] 14 shows a block diagram of an example computing system 700 for determining operational parameter values ​​of one or more qubits, according to an example embodiment of the present disclosure. System 700 includes a user computing device 702, a server computing device 730, and a training computing system 750 communicatively coupled via a network 780.

[0078] The user computing device 702 may be any type of computing device, such as, for example, a personal computing device (e.g., a laptop or desktop), a mobile computing device (e.g., a smartphone or tablet), a gaming console or controller, a wearable computing device, an embedded computing device, or any other type of computing device.

[0079] The user computing device 702 includes one or more processors 712 and memory 714. The one or more processors 712 may be any suitable processing device (e.g., a processor core, a microprocessor, an ASIC, an FPGA, a controller, a microcontroller, etc.) and may be one or more processors operably connected. The memory 714 may include one or more non-transitory computer-readable storage media, such as RAM, ROM, EEPROM, EPROM, flash memory devices, magnetic disks, etc., and combinations thereof. The memory 714 may store data 716 and instructions 718 that are executed by the processor 712 to cause the user computing device 702 to perform operations.

[0080] In some implementations, the user computing device 702 may store or include one or more predictive models 720. For example, the predictive models 720 may be or otherwise include various machine learning models, such as neural networks (e.g., deep neural networks), or other types of machine learning models including nonlinear and / or linear models. The neural networks may include feedforward neural networks, recurrent neural networks (e.g., long short-term memory recurrent neural networks), convolutional neural networks, or other forms of neural networks. Some exemplary machine learning models may leverage attention mechanisms such as self-attention. For example, some exemplary machine learning models may include multi-headed self-attention models (e.g., transformer models).

[0081] In some implementations, one or more predictive models 720 may be received from a server computing system 730 over a network 780, stored in a user computing device memory 714, and used or otherwise implemented by one or more processors 712. In some implementations, a user computing device 702 may implement multiple parallel instances of a single predictive model 720.

[0082] More specifically, predictive model 720 may be used to generate cost terms associated with future predicted defect states based on past time data, which may be taken into account in determining operational parameter values ​​for operating one or more qubits of a quantum device.

[0083] Additionally or alternatively, one or more predictive models 740 may be included in or otherwise stored and implemented by a server computing system 730 that communicates with the user computing device 702 according to a client-server relationship. Thus, one or more models 720 may be stored and implemented in the user computing device 702 and / or one or more models 740 may be stored and implemented in the server computing system 730.

[0084] The user computing device 702 may also include one or more user input components 722 that receive user input. For example, the user input component 722 may be a touch-sensitive component (e.g., a touch-sensitive display screen or touchpad) that senses the touch of a user input object (e.g., a finger or stylus). The touch-sensitive component may be responsible for implementing a virtual keyboard. Other exemplary user input components include a microphone, a traditional keyboard, or other means by which a user can provide user input.

[0085] The server computing system 730 includes one or more processors 732 and memory 734. The one or more processors 732 may be any suitable processing device (e.g., a processor core, a microprocessor, an ASIC, an FPGA, a controller, a microcontroller, etc.) and may be one or more processors operatively connected thereto. The memory 734 may include one or more non-transitory computer-readable storage media, such as RAM, ROM, EEPROM, EPROM, flash memory devices, magnetic disks, etc., and combinations thereof. The memory 734 may store data 736 and instructions 738 that are executed by the processor 732 to cause the server computing system 730 to perform operations.

[0086] In some implementations, the server computing system 730 includes or is otherwise implemented by one or more server computing devices. In instances in which the server computing system 730 includes multiple server computing devices, such server computing devices may operate according to a sequential computing architecture, a parallel computing architecture, or some combination thereof.

[0087] As described above, the server computing system 730 may store or otherwise include one or more predictive models 740. For example, the models 740 may be or otherwise include various machine learning models. Exemplary machine learning models include neural networks or other multi-layer nonlinear models. Exemplary neural networks include feed-forward neural networks, deep neural networks, recurrent neural networks, and convolutional neural networks. Some exemplary machine learning models may leverage attention mechanisms such as self-attention. For example, some exemplary machine learning models may include multi-headed self-attention models (e.g., Transformer models).

[0088] The user computing device 702 and / or the server computing system 730 can train the models 720 and / or 740 through interaction with a training computing system 750 that is communicatively coupled via a network 780. The training computing system 750 may be separate from the server computing system 730 or may be part of the server computing system 730.

[0089] The training computing system 750 includes one or more processors 752 and memory 754. The one or more processors 752 may be any suitable processing device (e.g., a processor core, a microprocessor, an ASIC, an FPGA, a controller, a microcontroller, etc.) and may be one or more processors operably connected thereto. The memory 754 may include one or more non-transitory computer-readable storage media, such as RAM, ROM, EEPROM, EPROM, flash memory devices, magnetic disks, etc., and combinations thereof. The memory 754 may store data 756 and instructions 758 that are executed by the processor 752 to cause the training computing system 750 to perform operations. In some implementations, the training computing system 750 includes or is otherwise implemented by one or more server computing devices.

[0090] The training computing system 750 may include a model trainer 760 that trains the machine learning models 720 and / or 740 stored on the user computing device 702 and / or the server computing system 730 using various training or learning techniques, such as, for example, backpropagation of errors. For example, a loss function may be backpropagated through the model to update one or more parameters of the model (e.g., based on the gradient of the loss function). Various loss functions may be used, such as mean squared error, likelihood loss, cross entropy loss, hinge loss, and / or various other loss functions. Gradient descent techniques may be used to iteratively update the parameters over a number of training iterations.

[0091] In some implementations, performing backpropagation of the error may include performing truncated backpropagation through time. The model trainer 760 can perform a number of generalization techniques (e.g., weight decay, dropout, etc.) to improve the generalization ability of the model being trained.

[0092] Specifically, model trainer 760 may train predictive models 720 and / or 740 based on a set of training data 762. Training data 762 may include, for example, past time data related to a time scale (e.g., energy relaxation time) and / or the presence of defects (e.g., TLS defects).

[0093] The model trainer 760 includes computer logic utilized to provide the desired functionality. The model trainer 760 may be implemented in hardware, firmware, and / or software controlling a general-purpose processor. For example, in some implementations, the model trainer 760 includes a program file that is stored in a storage device, loaded into memory, and executed by one or more processors. In other implementations, the model trainer 760 includes one or more sets of computer-executable instructions stored in a tangible computer-readable storage medium, such as a RAM, a hard disk, or an optical or magnetic medium.

[0094] Network 780 may be any type of communications network, such as a local area network (e.g., an intranet), a wide area network (e.g., the Internet), or some combination thereof, and may include any number of wired or wireless links. In general, communications over network 780 may be carried over any type of wired and / or wireless connections using a wide variety of communications protocols (e.g., TCP / IP, HTTP, SMTP, FTP), encodings or formats (e.g., HTML, XML), and / or protection schemes (e.g., VPN, Secure HTTP, SSL).

[0095] 14 illustrates one exemplary computing system that may be used to implement the present disclosure. Other computing systems may also be used. For example, in some implementations, a user computing device 702 may include a model trainer 760 and a training data set 762. In such implementations, the model 720 may be both trained and used locally at the user computing device 702.

[0096] The digital, classical, and / or quantum subject matter implementations, and the digital functions and quantum operations described herein may be implemented in digital electronic circuitry, in suitable quantum circuitry or more generally in a quantum computing system, in tangibly implemented digital and / or quantum computer software or firmware, in digital and / or quantum computer hardware including the structures disclosed herein and structural equivalents thereof, or in any combination of one or more of these. The term "quantum computing system" may include, but is not limited to, a quantum computer / computing system, a quantum information processing system, a quantum cryptography system, or a quantum simulator.

[0097] Implementations of the digital and / or quantum subject matter described herein may be implemented as one or more digital and / or quantum computer programs, i.e., one or more modules of digital and / or quantum computer program instructions encoded on a tangible, non-transitory storage medium for execution by or to control the operation of a data processing device. The digital and / or quantum computer storage medium may be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, one or more qubits / qubit structures, or a combination of one or more of them. Alternatively or additionally, the program instructions may be encoded on an artificially generated propagated signal (e.g., a machine-generated electrical, optical, or electromagnetic signal) capable of encoding digital and / or quantum information, which is generated to encode the digital and / or quantum information for transmission to an appropriate receiver device for execution by the data processing device.

[0098] The terms quantum information and quantum data refer to information or data carried, held, or stored by a quantum system, with the smallest non-trivial system being a qubit, i.e., a system that defines a unit of quantum information. The term "qubit" is understood to encompass all quantum systems that can be appropriately approximated as a two-level system in the corresponding context. Such quantum systems may include multi-level systems, e.g., with two or more levels. By way of example, such systems may include atoms, electrons, photons, ions, or superconducting qubits. In many implementations, the computational basis states are specified with the fundamental first excited states, but it is understood that other setups are possible in which the computational states are specified with higher-level excited states (e.g., qudits).

[0099] The term "digital processing apparatus" refers to digital and / or quantum data processing hardware and encompasses all kinds of apparatus, devices, and machines for processing digital and / or quantum data, including, by way of example, a programmable digital processor, a programmable quantum processor, a digital computer, a quantum computer, or multiple digital and quantum processors or computers, and combinations thereof. The apparatus may be or further include special-purpose logic circuitry, such as a field programmable gate array (FPGA), or an application specific integrated circuit (ASIC), or a quantum simulator, i.e., a quantum data processing apparatus designed to simulate or generate information about a particular quantum system. In particular, a quantum simulator is a special-purpose quantum computer that does not have the ability to perform general-purpose quantum computations. In addition to hardware, the apparatus may optionally include code that creates an execution environment for digital and / or quantum computer programs, such as code constituting a processor firmware, a protocol stack, a database management system, an operating system, or one or more combinations thereof.

[0100] A digital or classical computer program, which may be referred to or described as a program, software, software application, module, software module, script, or code, may be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and may be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a digital computing environment. A quantum computer program, which may be referred to or described as a program, software, software application, module, software module, script, or code, may be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and translated into a suitable quantum programming language, or written in a quantum programming language, e.g., QCL, Quipper, Cirq, etc.

[0101] A digital and / or quantum computer program may correspond to a file in a file system, but need not. A program may be stored in a portion of a file holding other programs or data, e.g., in one or more scripts stored in a markup language document, in a single file dedicated to the program in question, or in multiple coordinated files, e.g., in a file storing one or more modules, subprograms, or portions of code. A digital and / or quantum computer program may be deployed to run on one digital computer or one quantum computer, or on multiple digital and / or quantum computers located at one location or distributed across multiple locations and interconnected by a digital and / or quantum data communication network. A quantum data communication network is understood to be a network that may transmit quantum data using quantum systems, e.g., qubits. In general, a digital data communication network cannot transmit quantum data, but a quantum data communication network may transmit both quantum data and digital data.

[0102] The processes and logic flows described herein may be performed by one or more programmable digital computers and / or quantum computers, operating in conjunction with one or more digital and / or quantum processors as appropriate, executing one or more digital and / or quantum computer programs to perform functions by operating on input digital and quantum data to generate outputs. The processes and logic flows may also be performed, and apparatus implemented, as special purpose logic circuitry, e.g., an FPGA or ASIC, or as a quantum simulator, or a combination of special purpose logic circuitry or quantum simulators with one or more programmed digital computers and / or quantum computers.

[0103] A system of one or more digital and / or quantum computers or processors "configured to" or "operable to" perform a particular operation or action means that the system has installed thereon software, firmware, hardware, or a combination thereof that, when operated, causes the system to perform the operation or action. One or more digital and / or quantum computer programs are configured to perform a particular operation or action means that the one or more programs contain instructions that, when executed by a digital and / or quantum data processing device, cause the device to perform the operation or action. A quantum computer may receive instructions from a digital computer that, when executed by a quantum computing device, causes the device to perform the operation or action.

[0104] A digital and / or quantum computer suitable for executing a digital and / or quantum computer program may be based on a general purpose or dedicated digital microprocessor and / or quantum microprocessor, or on any other kind of central digital and / or quantum processing unit. In general, the central digital and / or quantum processing unit receives instructions and digital and / or quantum data from a read-only memory, or a random access memory, or a quantum system suitable for transmitting quantum data, e.g. photons, or a combination of these.

[0105] Some exemplary elements of a digital computer and / or quantum computer are a central processing unit for carrying out or executing instructions, and one or more memory devices for storing instructions and digital and / or quantum data. The central processing unit and memory may be supplemented by or incorporated in special-purpose logic circuits or quantum simulators. In general, a digital computer and / or quantum computer also includes one or more mass storage devices, such as magnetic, magneto-optical, or optical disks, for storing digital and / or quantum data, or a quantum system suitable for storing quantum information, or is operatively coupled to receive digital and / or quantum data from them, or transmit digital and / or quantum data to them, or both. However, a digital computer and / or quantum computer may not have such devices.

[0106] Digital and / or quantum computer readable media suitable for storing digital and / or quantum computer program instructions and digital and / or quantum data include, by way of example, all forms of non-volatile digital and / or quantum memories, media, and memory devices, including semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices, magnetic disks, e.g., internal hard disks or removable disks, magneto-optical disks, and CD-ROM and DVD-ROM disks, as well as quantum systems, e.g., trapped atoms or electrons. Quantum memories are devices that can store quantum data with high fidelity and efficiency for long periods of time, e.g., light-matter interfaces, where light is used for transmission and matter is used to store and retain the quantum characteristics of the quantum data, such as superposition or quantum coherence.

[0107] Control of the various systems described herein, or portions thereof, may be implemented in a digital and / or quantum computer program product that includes instructions stored on one or more tangible, non-transitory, machine-readable storage media and executable on one or more digital and / or quantum processing devices. The systems described herein, or portions thereof, may each be implemented as an apparatus, method, or electronic system that may include one or more digital and / or quantum processing devices and memory for storing executable instructions for performing the operations described herein.

[0108] Although this specification contains many specific implementation details, these should not be interpreted as limitations on the scope of what may be claimed, but rather as descriptions of features that may be specific to a particular implementation. Some features described in this specification in the context of separate implementations may be implemented in combination in a single implementation. Conversely, various features described in the context of a single implementation may be implemented in multiple implementations separately or in any suitable subcombination. Moreover, although features are described above as acting in some combinations and may even be initially claimed as such, one or more features from the claimed combination may in some cases be deleted from the combination, and the claimed combination may be directed to a subcombination or a variation of the subcombination.

[0109] Similarly, although operations are shown in the figures in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown, or in a sequential order, or that all of the shown operations be performed, to achieve desirable results. In some situations, multitasking and parallel processing may be advantageous. Moreover, the separation of various system modules and components in the implementations described above should not be understood as requiring such separation in all implementations, and it should be understood that the program components and systems described may generally be integrated together in a single software product or packaged into multiple software products.

[0110] Specific implementations of the present subject matter have been described. Other implementations are within the scope of the following claims. For example, the actions recited in the claims can be performed in a different order and still achieve desirable results. As an example, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In some cases, multitasking and parallel processing may be advantageous. [Explanation of symbols]

[0111] 100 Quantum Computing System, System 102 Quantum Hardware 104 Classical Processors 106 parameters, physical control qubit parameter values 108 Measurement results 110 Quantum Systems 112 Control Device 114 Readout Device 120 Cubits 122 2D lattice 124 Cubit Coupler 126 Cubits 128 Cubits 132 Qbit Frequency, Quantum Bit Frequency 134 Energy relaxation time 136 Defects, spikes 142 Operating Frequency 144 Energy Relaxation Time 146 hours 152 Operating Frequency 154 Energy Relaxation Time 156 hours 200 Systems 202 Cost Function Generator 204 Cost Function Adjuster 206 Input Data 208 Output Data 210 Optimizer 502 Cost Function 504 Current Cost Function 506 Measured Cost Function 508 Measured Cost Function 510 Measured Cost Function 532 Cost Function 534 Current Cost Function 535 Expected Cost Function 536 Cost Function 538 Cost Function 540 Cost Function 552 Cost Function 554 Cost Function 555 Measured Cost Function 556 Measured Cost Function 557 Expected Cost Function 558 Measured Cost Function 560 Measured Cost Function 602 Label 604 Input 610 Machine Learning (ML) Models 614 Input 620 Predictions 700 Computing System 702 User Computing Device 712 processor 714 Memory 716 Data 718 command 720 Machine learning models, predictive models 722 User Input Components 730 Server Computing System 732 processor 734 Memory 736 Data 738 command 740 Machine learning models, predictive models 750 Training Computing System 752 processor 754 Memory 756 Data 758 command 760 Model Trainer 762 Training data, training data set 780 Network

Claims

1. 1. A method of operating a qubit in a quantum device, comprising the steps of: obtaining past time data related to a time scale of an operating parameter of a qubit of a quantum device; selecting an operational parameter value based at least in part on the historical time data associated with the time scale of the operational parameter to reduce a probability of occurrence of a time-dependent defect, the time-dependent defect exhibiting a time-dependent behavior; operating the qubit of the quantum device at the operating parameter values; A method of operating a qubit in a quantum device, comprising:

2. The method of claim 1 , wherein the time scale of the operational parameter is an energy relaxation time of the operational parameter.

3. The method of claim 1 , wherein the operating parameter of the qubit is an operating frequency.

4. The method of claim 1 , wherein the time-dependent defect is a collision with a two-level defect.

5. The method of claim 1 , wherein the qubit is a superconducting qubit.

6. the step of selecting an operating parameter value comprises: constructing a cost function having a plurality of weighted cost terms, at least one of the weighted cost terms being associated with past time data; selecting the operational parameter values ​​based at least in part on the cost function; 2. The method of claim 1, comprising:

7. The method of claim 1 , wherein the time-dependent defects exhibit telegraphic behavior.

8. the step of selecting an operating parameter value comprises: constructing a cost function having a plurality of weighted cost terms, at least one of the weighted cost terms being associated with past time data such that the cost function embeds past defect conditions into the cost function; selecting the operational parameter values ​​based at least in part on the cost function; 8. The method of claim 7, comprising:

9. The method of claim 1 , wherein the time-dependent defects exhibit diffusive behavior.

10. the step of selecting an operating parameter value comprises: constructing a cost function having a plurality of weighted cost terms, at least one of the weighted cost terms being associated with past time data such that the cost function embeds future predicted defect conditions into the cost function; selecting the operational parameter values ​​based at least in part on the constructed cost function; 10. The method of claim 9, comprising:

11. The method of claim 10 , wherein the future predicted defect condition is determined based at least in part on an extrapolation of the past time data.

12. The method of claim 10 , wherein the future predicted defect condition is determined based at least in part on a machine learning model.

13. the step of selecting an operating parameter value comprises: constructing a cost function having a plurality of weighted cost terms, the weighted cost terms comprising a first cost term associated with past temporal data such that the cost function embeds future predicted defect conditions into the cost function, and the weighted cost terms comprising one or more second cost terms associated with past temporal data such that the cost function embeds past defect conditions into the cost function; selecting the operational parameter values ​​based at least in part on the constructed cost function; 2. The method of claim 1, comprising:

14. 14. The method of claim 6, 8, 10 or 13, wherein the cost function weights cost terms associated with more distant past time data more lightly than cost terms associated with more recent past time data.

15. a plurality of superconducting qubits, each qubit configured to be operated using an operating frequency, each operating frequency associated with an energy relaxation time; one or more processors configured to execute computer-readable instructions stored in one or more memory devices to perform operations; and wherein the operation comprises: determining a set of operating frequencies for the plurality of superconducting qubits based at least in part on past time data associated with an energy relaxation time for each operating frequency to reduce a probability of occurrence of a two-level state defect; operating the plurality of superconducting qubits at the set of operating frequencies; 1. A quantum computing system comprising:

16. 16. The quantum computing system of claim 15, wherein the operating frequency comprises an idle frequency, an interaction frequency, a readout frequency, or a reset frequency.

17. 16. The quantum computing system of claim 15, wherein adjacent qubits are operable to interact with each other.

18. A computer program comprising instructions executable by a classical or quantum processing device, such execution causing said classical or quantum processing device to: obtaining past time data related to a time scale of an operating parameter of a qubit of a quantum device; selecting an operational parameter value based at least in part on the historical time data associated with the time scale of the operational parameter to reduce a probability of occurrence of a time-dependent defect, the time-dependent defect exhibiting a time-dependent behavior; operating the qubit of the quantum device at the operating parameter values; A computer program product for causing a computer to perform operations including:

19. said act of selecting an operating parameter value comprising: constructing a cost function having a plurality of weighted cost terms, at least one of the weighted cost terms being associated with past time data; selecting the operational parameter values ​​based at least in part on the cost function; and 20. The computer program of claim 18, comprising:

20. said act of selecting an operating parameter value comprising: constructing a cost function having a plurality of weighted cost terms, the weighted cost terms comprising a first cost term associated with past temporal data such that the cost function embeds future predicted defect conditions into the cost function, and the weighted cost terms comprising one or more second cost terms related to past temporal data such that the cost function embeds past defect conditions into the cost function; selecting the operational parameter values ​​based at least in part on the cost function; and 20. The computer program of claim 18, comprising:

Images