Quantum-algorithm-specific calibration and optimization

Abstract

Systems and methods for algorithm-specific calibration of quantum systems are provided. In one example, a method may include obtaining, by one or more computing devices, data indicative of one or more quantum computing algorithms comprising a plurality of quantum computing operations. The method may include identifying, by the one or more computing devices, a plurality of respective calibration parameters, wherein each respective calibration parameter is associated with one or more algorithm-dependent interdependencies associated with one or more respective quantum computing operations of the plurality of quantum computing operations. The method may include obtaining, by the one or more computing devices, calibration data for each of the respective calibration parameters. The method may include determining, by the one or more computing devices based at least in part on the calibration data, a plurality of respective calibration values for the plurality of respective calibration parameters.

Description

QUANTUM-ALGORITHM-SPECIFIC CALIBRATION AND OPTIMIZATION PRIORITY CLAIM

[0001] The present application is based on and claims priority to United States Provisional Application Number 63 / 564,371 having a filing date of March 12, 2024 and United States Provisional Application Number 63 / 560,426 having a filing date of March 1, 2024. Application claims priority to and the benefit of each of such applications and incorporates all such applications herein by reference in their entirety. FIELD

[0002] The present disclosure relates generally to systems and methods for quantum computing. BACKGROUND

[0003] Quantum computing is a computing method that takes advantage of quantum effects, such as superposition of basis states and entanglement to perform certain computations more efficiently than a classical digital computer. In contrast to a digital computer, which stores and manipulates information in the form of bits, e.g., a “1” or “0,” quantum computing systems can manipulate information using quantum bits (“qubits”). A qubit can refer to a quantum device that enables the superposition of multiple states, e.g., data in both the “0” and “1” state, and / or to the superposition of data, itself, in the multiple states. In accordance with conventional terminology, the superposition of a “0” and “1” state in a quantum system may be represented, e.g., as a |0〉 + b |1〉 The “0” and “1” states of a digital computer are analogous to the |0〉 and |1〉 basis states, respectively of a qubit. SUMMARY

[0004] Aspects and advantages of embodiments of the present disclosure will be set forth in part in the following description, or can be learned from the description, or can be learned through practice of the embodiments.

[0005] Example aspects of the present disclosure provide an example method. In some implementations, the example method can include obtaining, by one or more computing devices, data indicative of one or more quantum computing algorithms comprising a plurality of quantum computing operations. In some implementations, the example method can include identifying, by the one or more computing devices, a plurality of respective calibrationparameters. In some implementations, each respective calibration parameter can be associated with one or more algorithm-dependent interdependencies associated with one or more respective quantum computing operations of the plurality of quantum computing operations. In some implementations, the example method can include obtaining, by the one or more computing devices, calibration data for each of the respective calibration parameters. In some implementations, the example method can include determining, by the one or more computing devices based at least in part on the calibration data, a plurality of respective calibration values for the plurality of respective calibration parameters.

[0006] 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 example embodiments of the present disclosure and, together with the description, explain the related principles. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] Detailed discussion of embodiments directed to one of ordinary skill in the art is set forth in the specification, which refers to the appended figures, in which:

[0008] FIG.1 depicts an example of a quantum computing system according to example aspects of the present disclosure;

[0009] FIG.2 depicts a block diagram of an example computing system for calibrating a quantum computing system according to example aspects of the present disclosure;

[0010] FIG.3 depicts a block diagram of an example computing device for calibrating a quantum computing system according to example aspects of the present disclosure;

[0011] FIG.4 depicts an example calibration stack for calibrating a quantum computing system according to example aspects of the present disclosure;

[0012] FIG.5 depicts an example calibration stack for calibrating a quantum computing system according to example aspects of the present disclosure;

[0013] FIG.6 depicts an example calibration stack for calibrating a quantum computing system according to example aspects of the present disclosure;

[0014] FIG.7 depicts an example execution of the quantum computing system according to example aspects of the present disclosure;

[0015] FIGS.8A-C depict an example parametrization procedure according to example aspects of the present disclosure;

[0016] FIG.9 depicts an example operation of a circuit to variable transformer according to example aspects of the present disclosure;

[0017] FIGS.10A-E depict example implementations of the processing step according to example aspects of the present disclosure; and

[0018] FIGS.11A-C depict example calibration flow diagrams according to example aspects of the present disclosure. DETAILED DESCRIPTION

[0019] Example embodiments according to some aspects of the present disclosure are directed to systems and methods for calibrating a quantum computing system. More particularly, the present disclosure is directed to calibration of quantum-algorithm-dependent calibration parameters. In some embodiments, a calibration stack comprising multiple calibration layers (e.g., algorithm-dependent calibration layers, algorithm-independent calibration layers) can be built.

[0020] In some embodiments, calibrating a quantum-algorithm-dependent calibration layer can include identifying an algorithmic context in which one or more quantum computing operations (e.g., quantum gates, etc.) will be performed, and identifying one or more calibration parameters (sometimes referred to herein as “parametric context”) based on the algorithmic context. In some embodiments, calibrating a quantum-algorithm-dependent calibration layer can include preprocessing the parametric context to simplify an algorithm- dependent optimization problem (e.g., by eliminating duplicate or sufficiently similar parameters to reduce a dimensionality of the optimization problem). In some embodiments, calibrating a quantum-algorithm-dependent calibration layer can include evaluating a performance metric based on one or more calibration parameter values for the processed parametric context, and selecting calibration parameter values based on the performance metric.

[0021] An algorithmic context for a particular quantum computing operation (e.g., quantum gate) can include, for example, the space-time neighborhood around the operation, and can include all interdependent operations. In some instances, the size, shape, and constituents of the neighborhood can be defined via the spatial, temporal, and spatiotemporal contexts of the operation. A spatial context can include the set of all interdependent operations within the same moment as the operation (i.e. concurrent operations). The underlying interdependencies can be derived from both engineered interactions (e.g., multi- qubit gates, etc.) and parasitic interactions (e.g., long-range, or short-range control crosstalk,long-range or short-range stray coupling, etc.) between quantum computational elements. Temporal context can include the set of all interdependent operations on the same qubits at different moments, which may include interdependencies derived from effects that manifest as a memory (e.g., echo microwave pulses, consecutive quantum gates operating on a qubit, etc.). Spatiotemporal context can include any other interdependency (e.g., different moments and different qubits, such as computational leakage that may persist and may transition between qubits).

[0022] Computational leakage may be a qubit in the |2^ state while the computationalbase is ^|0^, |1^^ can persist over multiple moments and can transition between qubits leadingto non-trivial spatiotemporal error mechanisms between operations.

[0023] A parametric context for a particular quantum computing operation can include all calibration parameters associated with each component of the operation’s algorithmic context. In some instances, a parametric context can be determined based on a data structure (e.g., dictionary, database, lookup table, etc.) correlating each component of an algorithmic context with one or more calibration parameters.

[0024] Processing a parametric context can include equating parameters associated with identical or sufficiently similar contexts (e.g., parameters in blocks of repeated gates, etc.). In some embodiments, determining whether two contexts are sufficiently similar can be based on a strength of an interdependency associated with a difference between the two contexts. In some embodiments, if an interdependency strength is below a threshold (e.g., predefined threshold, adaptive threshold, etc.), then two contexts can be treated as identical, and two or more parameters associated with the contexts can be equated, thereby simplifying an optimization problem.

[0025] In some embodiments, selecting calibration parameter values can include model- free selection. In some embodiments, selecting calibration parameter values can include model-based selection.

[0026] In some embodiments, model-free selection can include running a quantum computation. In some embodiments, the quantum computation can be a proxy computation, which may be smaller or cheaper to run than a quantum algorithm of interest, and which may embed the proxy operations in a parametric context similar to (e.g., same as) a parametric context of a quantum algorithm of interest. In some embodiments, model-free selection can include measuring an output of the quantum computation. In some instances, a performance metric can be derived from one or more measurements associated with the quantum computation. For example, a plurality of measurements can be compared to an expectedvalue associated with a high-fidelity quantum computation, and a performance metric can be determined based on the comparison.

[0027] In some embodiments, model-based selection can include obtaining calibration data (e.g., by testing; measuring; retrieving or receiving earlier-collected data; etc.); combining or otherwise processing the calibration data to generate one or more performance metrics; and selecting calibration parameter values based on the one or more performance metrics. In some embodiments, processing the calibration data can include estimating an error rate (e.g., associated with a particular operation; associated with a final outcome; associated with a qubit state at a particular time; etc.). In some instances, an overall error rate can be determined based on a combination of lower-level calibration parameters (e.g., data indicative of lower-level errors or source of error). In some instances, a combination of lower-level calibration parameters can include a sum of lower-level errors (e.g., when errors interact additively) or other combination (e.g., product, machine-learned error estimation, heuristic error estimation, etc.). In some embodiments, selecting calibration parameter values can include implementing a global optimizer (e.g., basin hopping, differential evolution, simulated annealing, machine-learned optimization, etc.). In some embodiments, selecting calibration parameter values can include comparing a performance metric to a performance threshold (e.g., predefined threshold, adaptive threshold, etc.) and accepting a set of candidate parameter values if a performance of the candidate parameter values is adequate.

[0028] In some embodiments, example systems and methods can be extended or modified in various ways. For example, systems and methods according to aspects of the present disclosure can be extended to recalibration of an already-calibrated system (e.g., at reduced computational cost compared to fully calibrating a quantum computing system from scratch). For example, one or more expired or failing calibration parameters can be identified, along with one or more unexpired or succeeding calibration parameters. The unexpired calibration parameters can be retained, and expired calibration parameters can be recalibrated (e.g., according to methods described above). As another example, systems and methods according to aspects of the present disclosure can be extended to simultaneous calibration based on multiple algorithms (e.g., two algorithms, dozens of algorithms, etc.). For example, a plurality of quantum algorithms can be parameterized; a plurality of parametric contexts can be preprocessed; a plurality of performance metrics can be evaluated; and calibration parameter values can be selected based on the performance metrics (e.g., using a weighted average, etc.). Similarly, a plurality of quantum algorithms can be parametrized based on a single performance metric (e.g., comprising a weighted average of algorithm-dependentvalues, etc.) or a single parametric context (e.g., determined based on preprocessing a plurality of parametric contexts, etc.) in some instances.

[0029] In some embodiments systems and methods can be extended or modified in various ways. For example, systems and methods according to example aspects of the present disclosure can build a calibration stack in an algorithm-dependent way. In some instances, systems and methods according to example aspects of the present disclosure can build a calibration stack in an algorithm-dependent way at each of a plurality of algorithm-dependent calibration layers. As another example, systems and methods according to example aspects of the present disclosure can parametrize a calibration problem in an algorithm-dependent way. As another example, systems and methods according to example aspects of the present disclosure can process the calibration problem in an algorithm-dependent way. As another example, systems and methods according to example aspects of the present disclosure can solve the calibration problem in an algorithm-dependent way. As another example, systems and methods according to example aspects of the present disclosure can be extended to local re-calibration in an algorithm-dependent way. As another example, systems and methods according to example aspects of the present disclosure can be extended to calibrating for multiple algorithms in an algorithm-dependent way.

[0030] Example embodiments according to some aspects of the present disclosure can provide for a number of technical effects and benefits, such as improvements to computing technology (e.g., quantum computing technology). In some instances, example systems and methods can provide improved calibration compared to alternative systems and methods, thereby providing more efficient and accurate quantum computing operations. In some instances, example systems and methods can provide similar calibration results at a reduced computational cost (e.g., electricity cost, memory usage, processor usage, etc.) compared to prior systems and methods.

[0031] For example, parameters associated with some quantum operations (e.g. single- and / or two-qubit gates) have traditionally or typically been calibrated via simple benchmarks (e.g. randomized benchmarking and / or cross-entropy benchmarking) within convenient algorithmic contexts (e.g. with all gates in isolation or with all single- or two-qubit gates running in parallel) that do not consider the target quantum algorithm within which they will eventually be executed. An advantage of this approach is that the calibration problem can in some instances be easy to compute, as each operation to be calibrated (e.g., each quantum gate, etc.) can be reduced to a low-dimensional optimization problem and computed separately from any neighboring operations.

[0032] However, due to hardware and control imperfections, the optimal calibrated parameters of a quantum operation implemented within a quantum algorithm can depend on the operations happening around it in both space and time (i.e. the algorithmic context). Therefore, calibration approaches that do not consider algorithmic context when calibrating quantum operations can in some instances lead to suboptimal calibration choices.

[0033] However, modeling all spatial and temporal interdependencies of a quantum algorithm can in some instances be computationally expensive or otherwise difficult. For example, an algorithm-dependent calibration optimization problem can in some instances be a high-dimensional problem, which may not factorize. In some instances, a high-dimensional problem may be difficult to compute and may not scale well, even becoming computationally intractable for some problem sizes (e.g., quantum algorithm sizes). Thus, formally optimizing all spatial and temporal interdependencies in a quantum algorithm may become impractical or significantly difficult as quantum computing systems scale to larger sizes. In some example embodiments, systems and methods of the present disclosure can efficiently explore a space of possible algorithm-dependent calibration parameter values, thereby accounting for spatial and temporal interdependencies at a reduced computational cost compared to alternative methods. In this manner, for instance, example systems and methods according to aspects of the present disclosure can provide improved calibration and / or reduced computational cost compared to alternative systems and methods.

[0034] With reference now to the Figures, example embodiments of the present disclosure will be discussed in further detail.

[0035] FIG.1 depicts an example quantum computing system 100. The example system 100 is an example of a system on one or more classical computers or quantum computing devices in one or more locations, in which the systems, components, and techniques described below can be implemented. Those of ordinary skill in the art, using the disclosures provided herein, will understand that other quantum computing structures or systems can be used without deviating from the scope of the present disclosure.

[0036] The system 100 includes quantum hardware 102 in data communication with one or more classical processors 104. The quantum hardware 102 includes components for performing quantum computation. For example, the quantum hardware 102 includes a quantum system 110, control device(s) 112, and readout device(s) 114 (e.g., readout resonator(s)). The quantum system 110 can include one or more multi-level quantum subsystems, such as a register of qubits. In some implementations, the multi-level quantumsubsystems can include superconducting qubits, such as flux qubits, charge qubits, transmon qubits, gmon qubits, etc.

[0037] The type of multi-level quantum subsystems that the system 100 utilizes may vary. For example, in some cases it may be convenient to include one or more readout device(s) 114 attached to one or more superconducting qubits, e.g., transmon, flux, gmon, xmon, or other qubits. In other cases, ion traps, photonic devices, or superconducting cavities (e.g., with which states may be prepared without requiring qubits) may be used. Further examples of realizations of multi-level quantum subsystems include fluxmon qubits, silicon quantum dots or phosphorus impurity qubits.

[0038] Quantum circuits may be constructed and applied to the register of qubits included in the quantum system 110 via multiple control lines that are coupled to one or more control devices 112. Example control devices 112 that operate on the register of qubits can be used to implement quantum gates or quantum circuits having a plurality 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 the quantum system 110 through one or more respective control parameters (e.g., one or more physical control parameters). For example, in some implementations, the multi-level quantum subsystems may be superconducting qubits and the control devices 112 may be configured to provide control pulses to control lines to generate magnetic fields to adjust the frequency of the qubits.

[0039] The quantum hardware 102 may further include readout devices 114 (e.g., readout resonators). Measurement results 108 obtained via measurement devices may be provided to the classical processors 104 for processing and analyzing. In some implementations, the quantum hardware 102 may include a quantum circuit and the control device(s) 112 and readout devices(s) 114 may implement one or more quantum logic gates that operate on the quantum system 102 through physical control parameters (e.g., microwave pulses) that are sent through wires included in the quantum hardware 102. Further examples of control devices include arbitrary waveform generators, wherein a DAC (digital to analog converter) creates the signal.

[0040] The readout device(s) 114 may be configured to perform quantum measurements on the quantum system 110 and send measurement results 108 to the classical processors 104. In addition, the quantum hardware 102 may be configured to receive data specifying physical control qubit parameter values 106 from the classical processors 104. The quantum hardware 102 may use the received physical control qubit parameter values 106 to update the action ofthe control device(s) 112 and readout devices(s) 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 devices 112 and may update the action of the DACs on the quantum system 110 accordingly. The classical processors 104 may be configured to initialize the quantum system 110 in an initial quantum state, e.g., by sending data to the quantum hardware 102 specifying an initial set of parameters 106.

[0041] The readout device(s) 114 can take advantage of a difference in the impedance for the |0〉 and |1〉 states of an element of the quantum system, such as a qubit, to measure the state of the element (e.g., the qubit). For example, the resonance frequency of a readout resonator can take on different values when a qubit is in the state |0〉 or the state |1〉, due to the nonlinearity of the qubit. Therefore, a microwave pulse reflected from the readout device 114 carries an amplitude and phase shift that depend on the qubit state. In some implementations, a Purcell filter can be used in conjunction with the readout device(s) 114 to impede microwave propagation at the qubit frequency.

[0042] In some implementations, the quantum system 110 can include a plurality of qubits 120 arranged, for instance, in a two-dimensional grid 122. For clarity, the two- dimensional grid 122 depicted in FIG.1 includes 16 qubits arranged in a square formation, however in some implementations the system 110 may include a smaller or a larger number of qubits. In some embodiments, the multiple qubits 120 can interact with each other through multiple qubit couplers, e.g., qubit coupler 124. The qubit couplers can define nearest neighbor interactions between the multiple qubits 120. In some implementations, the strengths of the multiple qubit couplers are tunable parameters. In some cases, the multiple qubit couplers included in the quantum computing system 100 may be couplers with a fixed coupling strength. In some implementations, the multiple 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 the system 100. A measurement qubit is a qubit that may be used to determine an outcome of a computation performed by the data qubit. That is, during a computation an unknown state of the data qubit is transferred to the measurement qubit using a suitable physical operation and measured via a suitable measurement operation performed on the measurement qubit.

[0043] In some implementations, each qubit in the multiple qubits 120 can be operated using respective operating frequencies, such as an idling frequency and / or an interaction frequency and / or readout frequency and / or reset frequency. The operating frequencies can vary from qubit to qubit. For instance, each qubit may idle at a different operating frequency.The operating frequencies for the qubits 120 can be chosen before a computation is performed by the calibration system. Some operating frequencies are better than other operating frequencies. One metric for assessing how good a particular operating frequency is for a particular qubit is energy relaxation time (T1) for the qubit at the frequency. Lower energy relaxation times can lead to larger quantum computational errors.

[0044] In various implementations, the example system 100 can be implemented as a client device, a server device, or both. The example system 100 can be implemented as part of a distributed computing system. The example system 100 can be implemented along with other example systems, which may be the same or different. The example system 100 can be implemented in a server farm or other facility that operates multiple computing systems to provide computational services to or on behalf of a plurality of client systems. Advantageously, techniques according to example aspects of the present disclosure can provide for improved calibration and maintenance of computing facilities, increasing service uptime, decreasing failure rates, etc. Example Computing Systems

[0045] FIG.2 depicts a block diagram of an example computing system 5 that can perform aspects of example embodiments of the present disclosure. The system 5 includes a computing device 50, a server computing system 60, and a third-party system 70 that are communicatively coupled over a network 49. The system 5 also includes a quantum computing system 80 that is communicatively coupled to the server computing system.

[0046] The computing device 50 can be any type of computing device (e.g., classical computing device), such as, for example, a mobile computing device (e.g., smartphone or tablet), a personal computing device (e.g., laptop or desktop), a workstation, a cluster, a gaming console or controller, a wearable computing device, an embedded computing device, or any other type of computing device. In some embodiments, the computing device 50 can be a client computing device or a server computing device. The computing device 50 can include one or more processors 51 and a memory 52. The one or more processors 51 can be any suitable processing device (e.g., a processor core, a microprocessor, an ASIC, an FPGA, a controller, a microcontroller, etc.) and can be one processor or a plurality of processors that are operatively connected. The memory 52 can 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 52 can store data 53 andinstructions 54 which are executed by the processor 51 to cause the user computing device 50 to perform operations as described herein.

[0047] The computing device 50 can also include one or more input components that receive user input. For example, a user input component can be a touch-sensitive component (e.g., a touch-sensitive display screen or a touch pad) that is sensitive to the touch of a user input object (e.g., a finger or a stylus). The touch-sensitive component can serve to implement a virtual keyboard. Other example user input components include a microphone, a traditional keyboard, or other means by which a user can provide user input.

[0048] The quantum computing system 80 can include one or more processors 81 (e.g., classical processor(s) 104) and a memory 82. The one or more processors 81 can be any suitable processing device (e.g., a processor core, a microprocessor, an ASIC, an FPGA, a controller, a microcontroller, etc.) and can be one processor or a plurality of processors that are operatively connected. The memory 82 can 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 82 can store data 83 and instructions 84 which are executed by the processor 81 to cause the quantum computing system 80 to perform operations as described herein.

[0049] The quantum computing system 80 can also include a quantum system 85 for performing quantum computations. In some instances, the quantum system 85 can be, comprise, or be comprised by quantum hardware 102, described above with reference to FIG. 1.

[0050] In some implementations, the quantum computing system can 80 include or be otherwise implemented by one or more server computing systems 60. In instances in which the quantum computing system 80 includes plural server computing devices, such server computing devices can operate according to sequential computing architectures, parallel computing architectures, or some combination thereof.

[0051] The third-party system 70 can include one or more processors 71 and a memory 72. The one or more processors 71 can be any suitable processing device (e.g., a processor core, a microprocessor, an ASIC, an FPGA, a controller, a microcontroller, etc.) and can be one processor or a plurality of processors that are operatively connected. The memory 72 can 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 72 can store data 73 and instructions 74 which are executed by the processor 71 to cause the third-party system 70 to perform operations. In some implementations, the third-party system 70 includes or is otherwise implemented by one or more server computing devices.

[0052] The server computing system 60 can include one or more processors 61 and a memory 62. The one or more processors 61 can be any suitable processing device (e.g., a processor core, a microprocessor, an ASIC, an FPGA, a controller, a microcontroller, etc.) and can be one processor or a plurality of processors that are operatively connected. The memory 62 can 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 62 can store data 63 and instructions 64 which are executed by the processor 61 to cause the server computing system 60 to perform operations. In some implementations, the server computing system 60 includes or is otherwise implemented by one or more server computing devices.

[0053] The network 49 can be any type of communications network (e.g., classical or quantum), such as a local area network (e.g., intranet), wide area network (e.g., Internet), or some combination thereof and can include any number of wired or wireless links. In general, communication over the network 49 can be carried via any type of wired or wireless connection, using a wide variety of communication protocols (e.g., TCP / IP, HTTP, SMTP, FTP), encodings or formats (e.g., HTML, XML), or protection schemes (e.g., VPN, secure HTTP, SSL).

[0054] FIG.2 illustrates one example computing system that can be used to implement the present disclosure. Other computing systems can be used as well. For example, in some implementations, the quantum computing system 80 can include the server computing system 60 or vice versa. In some implementations, the quantum computing system 80 may be communicatively coupled through the network 49 to the computing device 50, third-party system 70, or server computing system 60.

[0055] FIG.3 depicts a block diagram of an example computing device 90 that performs according to example embodiments of the present disclosure. The computing device 90 can be a client computing device or a server computing device. The computing device 90 can include a number of applications (e.g., applications 1 through N). Each application can contain its own machine learning library and machine-learned model(s). For example, each application can include a machine-learned model. Example applications include a word processing application, an email application, a browser application, an application configured for scientific computation, an application configured to communicate with one or more quantum computing systems, etc. As illustrated in FIG.3, each application can communicatewith a number of other components of the computing device, such as, for example, one or more sensors, a context manager, a device state component, or additional components. In some implementations, each application can communicate with each device component using an API (e.g., a public API). In some implementations, the API used by each application is specific to that application. Example Calibration Techniques

[0056] FIG.4 depicts a calibration stack 200 for frequency-tunable superconducting qubits. The calibration stack 200 may include a plurality of layers (e.g., 202, 204, 206, 208) including a first layer 202, layer i 204, layer i+1206, and a last layer 208.

[0057] The first layer 202 may include, for example, an algorithm-independent calibration layer. In some instances, a first layer 202 can include one or more operations for obtaining (e.g., obtaining directly from the quantum computing system, etc.) algorithm- independent data regarding operation of the quantum computing system (e.g., readout circuit parameters, qubit circuit parameters, qubit rabi oscillations, etc.) or one or more operations for determining (e.g., selecting, etc.) one or more algorithm-independent operating parameters. The information may include experimental data from the quantum computing system and / or experimental data from one or more qubits.

[0058] Layer i 204 may be one layer (e.g., algorithm-dependent calibration layer, etc.) of a plurality of layers, where the computing system is calibrating the quantum computing system. As shown in FIG.4, the computing system may obtain data indicative of a quantum algorithm 216 to be performed and may parameterize 210 the algorithm 216 to generate a parametric context. The computing system may then process 212 the parametric context and use the processed data to calibrate 214 one or more parameters of the quantum computing system. The calibrated data (e.g., selected parameter(s), etc.) may then be used in one or more operations of the next layer 206 (which may include, for example, a next algorithm- dependent layer comprising one or more parametrize 210, process 212, and calibrate 214 operations) to perform one or more additional calibration operations (e.g., selecting additional algorithm-dependent operating parameters, etc. The computing system can repeat the process, for example, until a last calibration layer 208 has been executed. In some instances, the quantum computing system can then execute the quantum algorithm 216 (e.g., using one or more operating parameters selected in one or more of calibration layers 202 through 208, etc.).

[0059] It should be understood that the number of layers depicted in FIG.4 are for illustrative purposes only, and that there may be any number of layers (e.g., 2, 3, 5, 7, 17, etc.) within the calibration stack 200. It should be understood that the functions and / or steps of layer i 204 may be performed by any of the plurality of layers.

[0060] It should be understood that each of the plurality of layers may be a step in the calibration process. A person having ordinary skill in the art would understand that the layers may build on the results of other layers and / or be performed in a sequential manner. Operations performed in a later layer can be based on parameters selected in an earlier layer or data obtained in an earlier layer; for example, an evaluate (e.g., 320 of FIG.5) operation can include performing one or more quantum operations to measure an error rate, wherein one or more parameters of the quantum operation can include parameters selected in an earlier calibration layer.

[0061] It should be understood that FIG.4 may depict a procedure for injecting algorithmic context into a calibration. The procedure may build an algorithm-dependent calibration stack. Then at each algorithm-dependent calibration layer parameterize the calibration problem, process the calibration problem and solve the calibration problem.

[0062] FIG.5 depicts a calibration stack 300 for frequency-tunable superconducting qubits. The calibration stack 300 may include a plurality of layers (e.g., 302, 304, 306, 308) including a first layer 302, layer i 304, layer i+1306 and a last layer 308.

[0063] In some instances, a layer 302, 304, 306, 308 can be, comprise, be comprised by, or otherwise share one or more properties with a layer 202, 204, 206, 208. For example, in some instances, a layer 302, 304, 306, 308 can have any property described herein with respect to a layer 202, 204, 206, 208, and vice versa.

[0064] The calibrate step 314 may include a select step 318, an evaluate step 320, a calibration check step 322 and a push step 324. The select step 318 may include selecting a candidate parameter value, (P). The candidate parameter value may be, but is not limited to, waveforms (e.g., DC and / or AC electronics waveforms), qubit-frequency trajectories, coupler frequency trajectories, a single-qubit gate temporal moment, idle frequency, interaction frequency, readout frequency, readout-pulse amplitude, readout-pulse length, gate-frequency trajectories, etc.

[0065] The candidate parameter values may be chosen by an arbitrary calculation. The candidate parameter values may be chosen by an arbitrary optimization strategy. The candidate parameter values may be chosen by a non-arbitrary optimization strategy. The candidate parameter values may be in a calibration parameter value set and / or a calibrationparameter set. The candidate parameter values may be candidate calibration values. The candidate parameter values may be context dependent and / or context independent, either in whole or in part. The sequence of the candidate parameter values may correspond to the path through the parameter space. The calibration strategy may use arbitrary data when choosing the candidate parameter values. The calibration strategy may use historical candidate parameters and / or performance metrics (e.g., performance metrics associated with historical candidate parameters) when choosing the candidate parameter values. The calibration strategy may be a context-dependent calibration strategy. The calibration strategy may be a context-independent calibration strategy. In the scenarios where the computing system recalibrates the data, the recalibration may stick with the same calibration strategy or a different calibration strategy. The calibration strategy may be a mix of calibration strategies.

[0066] One example calibration strategy is a global optimizer (e.g., basin hopping, differential evolution, simulated annealing, L-BFGS, a reinforcement learning algorithm, etc.).

[0067] The evaluate step 320 may acquire the calibration data (D), process the calibration data (C), and evaluate the candidate parameters C(P|D, A, L). Where P represents the set of parameters and / or optimization variables scheduled for calibration. A represents the quantum algorithm. L represents the current calibration layer. D represents the calibration data that may be used to evaluate algorithm performance. C may represent a performance metric over P. Where the calibrated set of parameters and / or optimized variables sought can be represented by P*. The calibration may be an arbitrary calibration and / or optimization strategy that maximizes C over P.

[0068] The evaluate step 320 may evaluate candidate parameter values based on a measurement (e.g., model-free performance measurement, measurement used for model- based performance estimation, etc.) of some proxy of the quantum algorithm’s performance. The calibration circuit, executed at the candidate parameter values may serve as a proxy of the target algorithm’s performance. For example, the computing system may convert raw readout signals into a fidelity signal that is nominally and / or believed to be correlated with the fidelity of the target quantum algorithm. The calibration circuit may embed the parameters of interest within their algorithmic and / or parametric contexts within the quantum algorithm. In some embodiments, the calibration circuit may be easier to execute and / or cheaper than the target algorithm. As a non-limiting illustrative example, an example proxy algorithm for the evaluate step 320 (e.g., model-free performance evaluation, etc.) caninclude a context aware fidelity estimation operation (CAFE) operation, such as a CAFE operation described by Debroy et al. in https: / / arxiv.org / pdf / 2303.17565.

[0069] In some instances, evaluation (e.g., model-based evaluation, etc.) of candidate parameter values can include acquiring calibration data, processing the calibration data, and evaluating candidate parameters based on the processed calibration data. When acquiring the calibration data, the system may use, but is not limited to, decoherence time, the frequency of the qubit, crosstalk parameters, the frequency between operations “a” and “b”, ^^^,^, ^^^,^^, ^^^^,^^and ∆^^. The system may also use any data associated with the classical and quantum hardware (e.g., control electronics, qubits, couplers, readout resonators, particle traps, etc.). It should be understood that the system may evaluate any two of the previous lists against each other. It should be understood that some of the list may be evaluated alone. The calibration data may be any other lower-level metrics associated with the classical (e.g., control electronics) and quantum hardware (e.g., qubits, couplers, readout resonators). These metrics may be taken at earlier stages of the calibration process and may be dependent on the performance metric used.

[0070] ^^^,^may be the frequency between two single-qubit gates on qubits “i” and “j”. ^^^,^,^may frequency between a single-qubit gate on qubit “i” and a two-qubit gate onqubits “j” and “k”. ^^^,^,^^may be the frequency between a two-qubit gate on qubits “i” and “j” and a two-qubit gate on qubits "k” and “l”. ∆^^may be the frequency-pulse distortion parameters versus the frequency for qubits“j” executing a two-qubit gate.

[0071] After acquiring the data, the evaluate step 320 may process the calibration data. The system may model the performance of the algorithm’s constituent operations (e.g., single, and / or two-qubit gates via e.g. analytics, theory, quantum simulation). The computing system may combine the operations into a performance metric (e.g., model-based performance metric) of the quantum algorithm (e.g., FIG.10). One example of this is illustrated below: 1. C: A sum of the estimated error of each operation in the circuit. a. C(P|D, A, L) = ∑operations Coperation(Poperation| D, A, L) b. Poperation ⊆ P: subset of frequencies relevant to estimating the error of the operation Coperation. 2. Coperation: Estimated error of one operation, which may be considered the sum over various error components, for example decoherence, crosstalk, and frequency-pulse distortion. a. Decoherence i. εD,i(fi|Ti): Decoherence error on single-qubit gate on qubit “i”ii. εD,ij(fi,fj,fij|Ti,Tj): Decoherence error on two-qubit gate on qubits “i” & “j” b. Crosstalk i. εX,ij(fi,fj |χij): Crosstalk error on two single-qubit gates on qubits “i” and “j” ii. εX,i,jk(fi,fj,fk,fjk |χi,jk): Crosstalk error on a single-qubit gate on qubit “i” and two-qubit gate on qubits “j” and “k” iii. εX,ij,kl(fi,fj,fk,fl,fij,fkl|χij,kl): Crosstalk error on a two-qubit gate on qubits “i” and “j” and a two-qubit gate on qubits “k” and “l” c. Frequency-pulse distortion i. εΔ,i,j(fi,fj,fk,fl |Δ): Frequency-pulse distortion error on a two-qubit gate on qubits “i” and “j”frequency) dependencies of all of its error components may define the interdependencies between operations / parameters and thus encode the algorithmic and / or parametric contexts. For example, we consider operation “E”, which has a non-trivial spatio-temporal context:

[0072] The evaluate step 320 may now evaluate the candidate parameter values based on the constructed model (e.g. C(P|D, A, L). It should be understood that the example above isonly one way of performing the evaluate step 320. In this example, the evaluate step 320 performed one version of a model based way to perform the evaluate step 320.

[0073] The check calibration step 322 may check whether the candidate parameters have sufficiently performed (e.g., passed a threshold performance metric, decreased a threshold number of errors, identified a threshold number of causes of errors, identified the cause of one or more errors, estimated a threshold number of error values, etc.). If the candidate parameters have sufficiently performed, then the candidate parameters may be sent to push step 324. If the candidate parameters have not sufficiently performed then the computing system may return to the select candidate parameter values step 318 and loop the process again. In other words, the computing system may recalibrate the candidate parameter value set.

[0074] The push step 324 may set the modified parameters (P*) as the new parameter values (P) and push these parameter values to the quantum computer control system. Layer i 304 may then be deemed to be calibrated and the system may move to layer i+1306 to perform the calibration steps. After all of the plurality of layers have been calibrated the quantum computer control system may control the quantum computing system according to the pushed parameter values, and may cause the quantum computing system to perform the quantum algorithm 316.

[0075] It should be understood that the number of layers depicted in FIG.5 are for illustrative purposes only, and that there may be any number of layers (e.g., 2, 3, 5, 7, 17, etc.) within the calibration stack 300. It should be understood that the functions and / or steps of layer i 304 may be performed by any of the plurality of layers.

[0076] It should be understood that each of the plurality of layers may be a step in the calibration process. A person having ordinary skill in the art would understand that the layers may build on the results of other layers and / or be performed in a sequential manner. Operations performed in a later layer can be based on parameters selected in an earlier layer or data obtained in an earlier layer; for example, an evaluate 320 operation can include performing one or more quantum operations to measure an error rate, wherein one or more parameters of the quantum operation can include parameters selected in an earlier calibration layer.

[0077] When selecting candidate parameter values the computing system may modify the selection and / or selection process. The computing system may modify the selection based on solving the smallest calibration problem possible around expired and / or failing parameters. The computing system may leverage algorithmic and / or parametric contexts. Thecomputing system may identify the expired and / or failing parameters Pexp. The computing system may target fewer parameters during this step, which may suppress optimization complexity and runtime while boosting scalability. The computing system may fix the unexpired parameters to their previously calibrated values, which may be assumed to be calibrated. The computing system may then repeat the calibration process once more. In the scenario where the computing system cannot find sufficiently optimal calibration parameters all parameters within the parametric contexts of the targeted parameters (i.e. all dependencies) should additionally be scheduled for calibration. These parameters may trade off directly against each other. This procedure may be repeated indefinitely until all parameters of the processor are under calibration as in the initial calibration step. This procedure may be part of the build process within later layers.

[0078] When evaluating candidate parameter values the computing system may modify the evaluation and / or evaluation process. The previously calibrated parameters may serve as optimization constraints. For sufficiently local constraints, the evaluation step may disregard the cost functions beyond dependencies of the parameters under calibration (i.e. they are constants for all different candidate parameter values). In the scenario where these cost functions are disregarded the computational overhead may be reduced. The computing system may also perform an extension. For example, sufficiently isolated parameters (i.e. ones that do not share parametric contexts) may be calibrated in parallel. For example, parameters corresponding to operations at opposite ends of a processor. This procedure may be part of the build process within later layers.

[0079] It should be understood that FIG.5 may depict a procedure for injecting algorithmic context into a calibration. The procedure may build an algorithm-dependent calibration stack. Then at each algorithm-dependent calibration layer parameterize the calibration problem, process the calibration problem and solve the calibration problem.

[0080] FIG.6 depicts a calibration stack 400 for frequency-tunable superconducting qubits. The calibration stack 400 may include a plurality of layers (e.g., 402, 404, 406, 408, 410, 412, 414, 416). The calibration stack 400 may include an uncalibrated layer 402, group of measure layers (e.g., 404, 406, 408) and a group of optimization layers (e.g., 410, 412, 414, 416). The calibration stack 400 may parametrize the calibration problem at one algorithm-dependent layer, the procedure may be applied separately to the algorithm- independent layers.

[0081] The uncalibrated layer 402 or the first layer 402 may include obtaining operational data (e.g., algorithm-independent operational data, etc.) from a quantumcomputing system. The information may include experimental data from the quantum computing system and / or experimental data from one or more qubits.

[0082] The measure layers may include a second layer 404, a third layer 406 and a fourth layer 408. The second layer 404 may measure the readout circuit parameters. The third layer 406 may measure the qubit circuit parameters. The fourth layer 408 may measure the qubit rabi oscillations. The measure layers may be algorithm-independent. The calibration parameters within the measure layers may be algorithm-independent. The calibration values within the measure layers may be algorithm-independent.

[0083] The optimization layers may include a fifth layer 410, a sixth layer 412, seventh layer 414 and an eighth layer 416. The fifth layer 410 may optimize gate-frequency trajectories. The sixth layer 412 may optimize coupler-off frequencies. The seventh layer 414 may optimize single-qubit gate control pulses. The eighth layer 416 may optimize two-qubit control pulses. The optimization layers may be algorithm-dependent. The calibration parameters within the optimization layers may be algorithm-dependent. The calibration values within the optimization layers may be algorithm-dependent. The calibration parameters within the optimization layers may be algorithm-independent. The calibration values within the optimization layers may be algorithm-independent.

[0084] After the eighth layer 416 has been fully performed the computing system may send the calibrated parameter values to the quantum computing control system, which can control the quantum computing system according to the calibrated parameter values to execute the quantum algorithm. The computing system may also repeat the optimization layers if the layers fail a performance metric. The computing system may also perform the steps shown in FIG.5.

[0085] Algorithm-dependent refers to layers that perform characterizations, calibrations, control-optimizations, etc. These actions may correspond directly to the quantum operations within the quantum algorithm. The calibrations in the algorithmic dependent layers may be algorithm-dependent calibrations and use algorithm-dependent calibration values and / or parameters.

[0086] One example of an algorithm-dependent action includes optimizing the qubit frequency trajectories used to implement quantum operations (e.g., single and / or two qubit gates) over the course of quantum algorithms in a way that mitigates computational errors. Another example is optimizing control waveforms (e.g., DC and / or AC electronics waveforms) used to implement quantum operations (e.g., single and / or two qubit gates). Another example is optimizing the coupler-frequency trajectories used to dynamicallyextinguish interactions between parasitically coupled qubits over quantum algorithms. Another example is interactions between computing elements (e.g., qubits, resonators, couplers). Another example is interactions between computing elements within their respective algorithmic contexts. Another example are interdependent calibrations, including ones that happen in later stages of calibration and ones that map to high dimensional optimization problems.

[0087] Algorithm-independent refers to layers that perform basic characterizations and calibrations. As opposed to algorithm-dependent layers, these layers do not correspond directly to the quantum operations within the algorithm.

[0088] One example of an algorithm-independent action is characterizing the specifications of computing devices and / or control electronics (e.g., DACs, ADCs, and / or FPGAs). Another example is characterizing the operating limits of computing systems and / or control electronics. Another example is characterizing the electrical circuit parameters of computational elements including qubits, resonators, and couplers (e.g., capacitances, mutual inductances, josephson junction resistances, qubit operating bandwidths, etc.). Another example is characterizing basic quantum control parameters (e.g., a map from the amplitude of a fixed-width AC voltage pulse to a qubit rabi oscillation curve, a map from the amplitude of a DC flux-bias voltage pulse to a qubit operating frequency, etc.). Another example is characterizing the electronic control signals (e.g. DC and / or AC waveforms). Another example is illustrated in FIG.8C.

[0089] It should be understood that the number of layers depicted in FIG.6 are for illustrative purposes only, and that there may be any number of layers (e.g., 2, 3, 5, 7, 17, etc.). It should be further understood that the measure layers (e.g., 404, 406, 408) may be done in any order and / or measure any number of parameters or experimental data related to quantum computing. It should be further understood that the optimization layers (e.g., 410, 412, 414, 416) may be performed in any order and / or optimize any number of parameters or experimental data related to quantum computing. It should be further understood, that the number of layers depicted in the measure layers and optimize layers are for illustrative purposes only and that there may be any number of layers (e.g., 2, 3, 5, 7, 17, etc.) within the measure layers and the optimization layers.

[0090] It should be understood that each of the plurality of layers may be a step in the calibration process. A person having ordinary skill in the art would understand that the layers may build on the results of other layers and / or be performed in a sequential manner. Operations performed in a later layer can be based on parameters selected in an earlier layeror data obtained in an earlier layer; for example, an evaluate (e.g., 320 of FIG.5) operation can include performing one or more quantum operations to measure an error rate, wherein one or more parameters of the quantum operation can include parameters selected in an earlier calibration layer.

[0091] It should be understood that FIG.6 may depict a procedure for injecting algorithmic context into a calibration. The procedure may build an algorithm-dependent calibration stack. Then at each algorithm-dependent calibration layer parameterize the calibration problem, process the calibration problem and solve the calibration problem.

[0092] FIG.7 depicts an example execution of the quantum algorithm 500. The quantum algorithm 500 includes a quantum processor 502, and a quantum circuit 504 (e.g., a quantum circuit of operations). The quantum processor 502 may include one or more qubits (e.g., qubit 0, qubit 1, qubit 2).

[0093] The one or more qubits may be any of the qubits discussed above. The one or more qubits may all be the same type of qubit, all different qubits, or a combination of similar and different qubits. The number of qubits illustrated in FIG.8 is for example purposes only, and there may be more or less qubits than shown. The qubits may couple to form multi-qubit operations (e.g., a two-qubit gate) or remain separate. The qubits may couple and / or decouple at different moments in time.

[0094] The quantum circuit 504 may include one or more operations. The operations may include a single qubit operation and / or a two-qubit operation. The operations may include several single qubit operations (e.g., operations A, C, E, F, G, H, I, K, L, M, N,O). The operations may include several two qubit operations (e.g., operations B, D, J). It should be understood that the order of operations depicted in FIG.7is for illustrative purposes only and that the operations may happen in any order. It should be understood that if there were four or more qubits then the operations may comprise a step with two, two qubit operations at a single moment. It should be understood that as the number of qubits increases so do the possibilities for combining two or single qubit operations.

[0095] The operations may happen at different moments in time. For example, single qubit operation A may happen at moment 0, and two qubit operation B may happen at moment 1. The operations may progress through time until the final operation is performed at which point the quantum circuit 504 may repeat the operations. The operations may not be repeated in some instances (e.g., the operations meet a performance metric, the operations pass a quality check, the operations are above a threshold, a period of time has passed, etc.). It should be understood that a moment is a single time slice of a quantum algorithm in whichoperations and / or the proxy quantum computation are executed and may be a multitude of time periods (e.g., one microsecond, one millisecond, one second, one minute, 10 minutes, etc.).

[0096] FIGS.8A-8C depict an example parametrization procedure for determining a parametric context based on an algorithmic context of one or more operations of interest. FIG.8A depicts the transformation of the circuit of operations into an algorithmic context. FIG.8B depicts the splitting of the algorithmic context into spatial, temporal, and / or spatiotemporal contexts. FIG.8C depicts the transformation of the circuit of operations into a parametric context and / or a circuit of calibration parameters.

[0097] Referring to FIG.8A, the circuit of operations 602 may be transformed by the computing system (e.g., by a parametrize 310 component of an ithlayer 304 of FIG.5; by an algorithm-dependent optimization layer 410, 412, 414, 416 of FIG.6; etc.) into an algorithmic context 604. The current layer of the computing system may be targeting operations including operation M 606. The computing system can determine that operation M 606 has a temporal context of operations L and N. The computing system can determine that operation M 606 has a spatial context comprising operation H. The computing system can determine that operation M 606 has a spatiotemporal context comprising operation B and operation D may provide spatiotemporal context. Operations B, D, H, L and N may be interdependent operations.

[0098] Interdependent operations may be the context surrounding the target operation 606. The size, shape and / or constituents of the context may be defined by the spatial, temporal, and / or spatiotemporal contexts.

[0099] Spatial contexts may be the set of all interdependent operations within a given moment (e.g., concurrent operations). The underlying interdependencies may be derived from engineered and / or parasitic interactions between quantum computational elements. An example of an engineered interaction is a multi-qubit gate (e.g., two-qubit gate, a SWAP gate, a CZ gate, etc.). An example of a parasitic interaction is control cross talk (e.g., long range or short range). Another example of a parasitic interaction is a stray coupling (e.g., long range or short range).

[0100] It should be understood that long range may refer to qubits not in close spatial proximity on a chip but their control wiring is in close spatial proximity at another part of the control stack (e.g. on the printed-circuit board (PCB) that houses the chip). It should be understood that long range may refer to two qubits that are not in close proximity on a chip interact through an electromagnetic mode established by the packaging hardware. It shouldbe understood that short range may refer to qubits in close spatial proximity on a chip. It should be understood that short range may refer to two qubits that are in close proximity on a chip but between which no multi-qubit gates exist interact through weak parasitic coupling due to design limitations.

[0101] Temporal contexts may be the set of all interdependent operations on the same qubits at different moments. The underlying interdependencies may be derived from memory and / or effects that manifest as such. One example is single qubit gates followed by two qubit gates, or vice versa. In this example, they may be interdependent due to how qubits may be continuously swept from idle frequencies to interaction frequencies and back. Another example is successive operations which may be executed within close temporal proximity. In this example, the successive operations may be in close temporal proximity due to short padding between them. The operations may overlap due to dispersion from imperfect control calibration (e.g., imperfect deconvolution which causes a square pulse to appear as an elongated and distorted pulse). Another example is microwave pulse reflections or echoes in the control circuitry. In this example, the microwave pulse reflections may occur due to poor microwave impedance matching. The poor microwave impedance matching can generate echo microwave pulses that may link operations at distant moments.

[0102] Spatiotemporal contexts may be the set of all interdependent operations at different moments and / or different qubits. An example of a spatiotemporal context is an interdependency (e.g., different moments and different qubits, such as computational leakage that may persist and may transition between qubits). Another example is an effect that manifests as a memory (e.g., microwave pulses, consecutive quantum gates operating on a qubit etc.).

[0103] It should be understood that spatial contexts, temporal contexts, and spatiotemporal contexts may refer to spatial proximity, temporal proximity, and spatiotemporal proximity. The contextual aspects may include the proximity or solely refer to the proximity of operations.

[0104] It should be noted that although FIG.8A refers to only one operation, M, being targeted, the calibration layer may be targeting multiple operations, and would perform the steps shown for each operation (e.g., determining each operations algorithmic context, parametric context, etc.). For example, if the layer shown in 9A was targeting single qubit operations these steps would be performed for operations A, C, E, F, G, H, I, K, L, M, N and O.

[0105] Referring to FIG.8B, the algorithmic context 604 may be split into a spatial context 612, a temporal context 614 and a spatiotemporal context 616 by the computing system. Where the computing system has determined, in this example, that the spatial context is H, the temporal context is L and N and the spatiotemporal context is B and D.

[0106] Interdependent operations may be the context surrounding the target operation 606. The size, shape and / or constituents of the context may be defined by the spatial, temporal, and / or spatiotemporal contexts.

[0107] Spatial contexts may be the set of all interdependent operations within a given moment (e.g., concurrent operations). The underlying interdependencies may be derived from engineered and / or parasitic interactions between quantum computational elements. An example of an engineered interaction is a multi-qubit gate (e.g., two-qubit gate, a SWAP gate, a CZ gate, etc.). An example of a parasitic interaction is control cross talk (e.g., long range or short range). Another example of a parasitic interaction is a stray coupling (e.g., long range or short range).

[0108] It should be understood that long range may refer to qubits not in close spatial proximity on a chip but their control wiring is in close spatial proximity at another part of the control stack (e.g. on the printed-circuit board (PCB) that houses the chip). It should be understood that long range may refer to two qubits that are not in close proximity on a chip interact through an electromagnetic mode established by the packaging hardware. It should be understood that short range may refer to qubits in close spatial proximity on a chip. It should be understood that short range may refer to two qubits that are in close proximity on a chip but between which no multi-qubit gates exist interact through weak parasitic coupling due to design limitations.

[0109] Temporal contexts may be the set of all interdependent operations on the same qubits at different moments. The underlying interdependencies may be derived from memory and / or effects that manifest as such. One example is single qubit gates followed by two qubit gates, or vice versa. In this example, they may be interdependent due to how qubits may be continuously swept from idle frequencies to interaction frequencies and back. Another example is successive operations which may be executed within close temporal proximity. In this example, the successive operations may be in close temporal proximity due to short padding between them. The operations may overlap due to dispersion from imperfect control calibration (e.g., imperfect deconvolution which causes a square pulse to appear as an elongated and distorted pulse). Another example is microwave pulse reflections or echoes in the control circuitry. In this example, the microwave pulse reflections may occur due to poormicrowave impedance matching. The poor microwave impedance matching can generate echo microwave pulses that may link operations at distant moments.

[0110] Spatiotemporal contexts may be the set of all interdependent operations at different moments and / or different qubits. An example of a spatiotemporal context is an interdependency (e.g., different moments and different qubits, such as computational leakage that may persist and may transition between qubits). Another example is an effect that manifests as a memory (e.g., microwave pulses, consecutive quantum gates operating on a qubit etc.).

[0111] It should be understood that spatial contexts, temporal contexts, and spatiotemporal contexts may refer to spatial proximity, temporal proximity, and spatiotemporal proximity. The contextual aspects may include the proximity or solely refer to the proximity of operations.

[0112] Referring to FIG.8C, the circuit of parameters 622 may be parameterized by the computing system (e.g., step 210, 310 of FIGS.4-5, by layer i 204, 320 of FIGS.4-5 etc.) into a parametric context 624. The parametric context 624 may include target parameters 626 and constraint parameters 628. The target parameters 626 may be the parameters that the current layer is calibrating. The constraint parameters 628 may be previously calibrated parameters. The previously calibrated parameters may serve as optimization constraints. It should be understood that multiple parameter types may serve as target parameters 626 within the same layer. The transformer may act as a dictionary that maps operations to one or more calibration parameters and / or optimization variables (e.g., p00which may act as an array).

[0113] Referring to FIG.9, FIG.9 depicts an operation of a circuit to variable transformer (e.g., operation-to-variable transformer). The operation-to-variable transformer 704 may convert the circuit of operations 702 into a circuit of variables 706. The quantum circuit of operations 702 may run operations based on data needed for the calibration process, the proxy quantum computation, and / or a request by the user. After the operations are fully run, including any repetitions, the operation-to-variable transformer 704 may transform the data from the experimental data into variables. The transformation may happen as described within other places of this specification. Once the operations are transformed, the computing system may input the variables into the quantum circuit of variables 706.

[0114] The operations within the quantum circuit of operations 702 may repeat. The repetitions may stop after the repetitions meet a performance metric (e.g., number of repetitions, desired amount of data, passing a threshold, passing a quality check, apredetermined period of time, fulfillment of a user’s request, identified a threshold number of errors, identified a threshold number of error values, decreased a threshold number of errors, etc.). After the repetitions stop the computing system (i.e. layer i 204 of FIG.4) may transform 704 the data into the quantum circuit of variables 706. The data may go through several layers and processes of the computing system before it gets transformed. The data may be transformed one or more times. The one or more times may be before the data currently gets transformed and / or after the data currently gets transformed. The data may also only be transformed at the current layer, depending on the need for calibration.

[0115] The transformer 704 may map operations to one or more calibration parameters and / or optimization variables. For example, operation A may be mapped onto optimization variable ^^^^, which may be an array. As shown in FIG.9 the calibration parameters and optimization variables are denoted by P.

[0116] It should be understood that the transformation of the operations into the variables may be a part of or all of the process step. It should be understood that the quantum circuit of variable 706 may be what is input into the calibration step. It should be understood that there may be other inputs into the calibration step (e.g., experimental data).

[0117] One example, of how the operation to variable transformer may be implemented for the gate frequency trajectory optimization layer (e.g., 410 of FIG.6) is reproduced below: 1. Transformation: SQti→ ptia. SQti: Single-qubit gate for qubit “i” in temporal moment “t”. i. We note that here SQ can be one of many gate types, including an X, Y, or Z gate or an arbitrary single-qubit rotation. b. pti: “idle frequency” at which qubit “i” in temporal moment “t” idles and performs single-qubit gates. 2. Transformation: SQti → ptij a. TQtij: two-qubit gate (TQ) for qubits “i” and “j” in temporal moment “t”. b. ptij: “interaction frequency” at which qubits “i” and “j” interact (e.g. are swept into resonance) in temporal moment “t” perform a two-qubit gate. Example: For the readout parameter optimization layer: 1. Operation: ROti→ pti: a. ROti: Readout for qubit “i” in temporal moment “t”. b. pti: i. “Readout” frequency at which qubits are measured. ii. “Readout-pulse amplitude” of the MW pulse used to measure qubits. iii. “Readout-pulse length” of the MW pulse used to measure qubits.

[0118] FIGS.10A-E depict one example implementation of the processing step.

[0119] Referring to FIG.10A, the process step may include equating parameters in blocks of repeated gates. In this example, the circuit starts with 15*R, where R is the number of repeats, unique operations 802. It should be understood that 15 refers to the number of qubits multiplied by the number of moments in time in a given circuit. In this example, there are three qubits and five moments of time. The quantum algorithm may remove repeated blocks 804, where the circuit is partially unrolled and the operations in 808 are all considered equivalent to the operations in 806. It should be understood that the repeated gates may be part of a recalibration process, the initial calibration process or the user’s input. It should be understood that the part of the processing procedure that leverages the parametric context to simplify the calibration program may happen after the transformation step depicted in FIG.9.

[0120] Referring to FIG.10B, after the operations go through the equating parameters step illustrated in 9A, the parameters may then be equated with parametric contexts. As shown in FIG.10B the computing system considers all of the connectivity 810 with the operations 806. After the connectivity 810 is considered the computing system may determine that the contexts of some operations are the same as others. For example, the contexts of B and L may be determined to be equivalent to D and N. In this scenario, the circuit may now be reduced to 13 unique operations 812.

[0121] Referring to FIG.10C, the 13 unique operations 812 of FIG.10B may go through a spatial connectivity check 814. The process in FIG.10C may happen at the same time, before or alternatively to the process in FIG.8D. The parameters or 13 unique operations 812 may be equated with sufficiently similar parametric contexts. As shown in FIG.10C, the computing system may disregard temporal and / or spatiotemporal interdependencies 814. The computing system may favor this method if the interdependencies are weaker. In the example shown in FIG.9C the unique operations may be reduced to seven 816. Once only the spatial connectivity is considered the quantum algorithm may determine that operations C, H, M, E, I, O are the same as A, G, K. This may narrow down the unique operations. This step may be done before or after parametrization.

[0122] Referring to FIG.10D, the 13 unique operations 812 of FIG.8B may go through an interdependency removal process. The process in FIG.10D may happen at the same time, after or alternatively to the process in FIG.8C. The calibration process may remove all temporal, spatial and spatiotemporal interdependencies. In other words, the computing system may consider no connectivity 818 between the operations and look for equivalents. In the example shown in FIG.11D this may reduce the unique operations to five. The computing system may determine that operations L, M, L, and O are the equivalent tooperation K. The computing system may determine that operations H and I are the same as operation G. The computing system may determine that operations C, E and F are the equivalent to operation A. This may narrow down the unique operations. This step may be done before or after parametrization.

[0123] In some cases, the calibration process may determine that the parametric context associated with one of the operations and / or calibration parameters is unshared with another of the operations. In this case, the computing system may determine whether the interdependency of the two parameters passes a threshold. If the interdependency is below the threshold the computing system may determine that the parametric context is similar and may determine that the operations are equivalent.

[0124] In the case where the process in 10D happens after the process in 8C the computing system may have determined that the spatial interdependencies are weak after disregarding the temporal and spatiotemporal interdependencies.

[0125] The process illustrated in FIGS.10A-E may be to narrow the parameters for one layer of the plurality of layers (e.g., 414 of FIG.6). For example, the parameters may be narrowed to optimize the single-qubit control pulses. The parameters after optimized may calibrate the quantum computing system or be saved by the computing system to calibrate the quantum computing system after the calibration process is completed. The parameters may be separately narrowed and optimized in other layers depending on what is currently being calibrated.

[0126] FIG.10E depicts an example implementation 800 of steps 210-214 of FIG.4. At a first moment 822 of time, qubits 0-2 may each perform a single qubit operation. At a second moment 824 of time qubit 0 and qubit 1 may form a two-qubit gate and qubit 2 may perform a single qubit operation. The operations may repeat. The repetitions may stop after the repetitions meet a performance metric (e.g., number of repetitions, desired amount of data, passing a threshold, passing a quality check, a predetermined period of time, fulfillment of a user’s request, identified a threshold number of errors, identified a threshold number of error values, decreased a threshold number of errors, etc.). After the repetitions stop the computing system (i.e. layer i 204 of FIG.4) may parameterize 826 the data. The data may go through several layers and processes of the quantum algorithm before it gets parameterized. The data may be parameterized one or more times. The one or more times may be before the data currently gets parameterized and / or after the data currently gets parameterized. The data may also only be parameterized at the current layer, depending on the need for calibration.

[0127] As shown in FIG.10E, P may include f00, f01, f02, f101, f12. fti may refer to a single- qubit idle frequency for qubit “i” at moment “t”. ftijmay refer to a two-qubit interaction frequency for qubits “i” and “j” at moment “t”. Although not shown in FIG.10 the circuit may be further processed by equating f02and f12. In this case, this would employ the extension processing step by assuming that contexts of “D” and “E” are sufficiently similar.

[0128] As shown in FIG.10E, the parametrized data 828 may be based on the frequencies. the frequencies may be DC and / or AC electronics waveforms, qubit frequency trajectories, coupler frequency trajectories, idle frequency trajectories, interaction frequencies, readout frequencies, etc. However, as discussed above, the parameters may be any number of parameters and are not limited to frequencies.

[0129] After the data is parameterized 826 the data may then be processed 830. Such that the data is calibrated. The data may also be processed 830 in that it is separated based on frequency type (i.e.832 as idle frequency and 834 as interaction frequency).

[0130] FIGS.11A-C depict example calibration flow diagrams in the case where there are multiple quantum algorithms. FIG.11A depicts the original multi-user method 1000. FIG. 11B depicts the extension multi-user method 1100. FIG.11C depicts the general multi-user method 1200.

[0131] Referring to FIG.11A, there may be a first user 1001 and a second user 1002 of the quantum computing system. The first user 1001 may run a first circuit 1003 and the second user 1002 may run a second circuit 1004 with the quantum computing system. The first circuit 1003 may go through a first calibration 1005. The second circuit 1004 may go through a second calibration 1006. Once the first calibration 1005 and the second calibration 1006 have been run the quantum computing system may schedule the execution 1010 of the quantum process.

[0132] The first circuit 1003 and the second circuit 1004 may be quantum circuits. Both the first 1003 and second circuit 1004 may run simultaneously. Both the first 1005 and second calibration 1006 may run simultaneously. The first 1005 and second calibration 1006 may run on the same computing system, quantum computing system and / or quantum algorithm or different computing systems, quantum computing systems and / or algorithms.

[0133] Referring to FIG.11B, the first user 1001 and the second user 1002 may each run a first circuit 1003 and a second circuit 1004. The first circuit 1003 and the second circuit 1004 may run a single calibration 1008 which in turn may schedule the execution 1010 of the quantum process after the calibration 1008 has run.

[0134] The first circuit 1003 and the second circuit 1004 may be quantum circuits. Both the first 1003 and second circuit 1004 may run simultaneously.

[0135] Referring to FIG.11C, an nth user 1012 may run an nth circuit 1014 on a calibration 1016. The calibration 1016, once fully calibrated, may schedule the execution 1010 of the quantum process.

[0136] The calibration 1016 may be a combined calibration, like in FIG.11B, where the calibration 1016 may be a combination of the first circuit 1003 to the nth circuit 1014 data. For example, in some instances, a performance P* associated with a calibration 1016 can include a weighted sum of a plurality of performance values associated with a plurality of circuits 1003, 1004, 1014, wherein one or more weights of the weighted sum can be selected to prioritize performance of particular quantum circuits 1003, 1004, 1014.

[0137] Implementations of the digital, classical, and / or quantum subject matter and the digital functional operations and quantum operations described in this specification can be implemented in digital electronic circuitry, suitable quantum circuitry or, more generally, quantum computational systems, in tangibly-implemented digital and / or quantum computer software or firmware, in digital and / or quantum computer hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. The term “quantum computing systems” may include, but is not limited to, quantum computers / computing systems, quantum information processing systems, quantum cryptography systems, or quantum simulators.

[0138] Implementations of the digital and / or quantum subject matter described in this specification can be implemented as one or more digital and / or quantum computer programs (e.g., 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, data processing apparatus). The digital and / or quantum computer storage medium can 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.

[0139] Alternatively or in addition, the program instructions can be encoded on an artificially-generated propagated signal that is capable of encoding digital and / or quantum information (e.g., a machine-generated electrical, optical, or electromagnetic signal) that is generated to encode digital and / or quantum information for transmission to suitable receiver apparatus for execution by a data processing apparatus.

[0140] The terms quantum information and quantum data refer to information or data that is carried by, held, or stored in quantum systems, where the smallest non-trivial system is a qubit (i.e., a system that defines the unit of quantum information). It is understood that the term “qubit” encompasses all quantum systems that may be suitably 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 can include atoms, electrons, photons, ions or superconducting qubits. In many implementations the computational basis states are identified with the ground and first excited states, however it is understood that other setups where the computational states are identified with higher level excited states (e.g., qubits) are possible.

[0141] The term “data 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 can also be, or further include, special purpose logic circuitry, e.g., an FPGA (field programmable gate array), or an ASIC (application-specific integrated circuit), or a quantum simulator, i.e., a quantum data processing apparatus that is designed to simulate or produce information about a specific quantum system. In particular, a quantum simulator is a special purpose quantum computer that does not have the capability to perform universal quantum computation. The apparatus can optionally include, in addition to hardware, code that creates an execution environment for digital and / or quantum computer programs, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them.

[0142] A digital or classical computer program, which may also be referred to or described as a program, software, a software application, a module, a software module, a script, or code, can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and it can 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 also be referred to or described as a program, software, a software application, a module, a software module, a script, or code, can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedurallanguages, and translated into a suitable quantum programming language, or can be written in a quantum programming language, e.g., QCL, Quipper, Cirq, etc.

[0143] A digital and / or quantum computer program may, but need not, correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data, e.g., 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., files that store one or more modules, sub-programs, or portions of code. A digital and / or quantum computer program can be deployed to be executed on one digital or one quantum computer or on multiple digital and / or quantum computers that are located at one site or distributed across multiple sites 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. Generally, a digital data communication network cannot transmit quantum data, however a quantum data communication network may transmit both quantum data and digital data.

[0144] The processes and logic flows described in this specification can be performed by one or more programmable digital and / or quantum computers, operating 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 and generating output. The processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, e.g., an FPGA or an ASIC, or a quantum simulator, or by a combination of special purpose logic circuitry or quantum simulators and one or more programmed digital and / or quantum computers.

[0145] For a system of one or more digital and / or quantum computers or processors to be “configured to” or “operable to” perform particular operations or actions means that the system has installed on it software, firmware, hardware, or a combination of them that in operation cause the system to perform the operations or actions. For one or more digital and / or quantum computer programs to be configured to perform particular operations or actions means that the one or more programs include instructions that, when executed by digital and / or quantum data processing apparatus, cause the apparatus to perform the operations or actions. A quantum computer may receive instructions from a digital computer that, when executed by the quantum computing apparatus, cause the apparatus to perform the operations or actions.

[0146] Digital and / or quantum computers suitable for the execution of a digital and / or quantum computer program can be based on general or special purpose digital and / orquantum microprocessors or both, or any other kind of central digital and / or quantum processing unit. Generally, a central digital and / or quantum processing unit will receive instructions and digital and / or quantum data from a read-only memory, or a random access memory, or quantum systems suitable for transmitting quantum data, e.g. photons, or combinations thereof.

[0147] Some example elements of a digital and / or quantum computer are a central processing unit for performing or executing instructions and one or more memory devices for storing instructions and digital and / or quantum data. The central processing unit and the memory can be supplemented by, or incorporated in, special purpose logic circuitry or quantum simulators. Generally, a digital and / or quantum computer will also include, or be operatively coupled to receive digital and / or quantum data from or transfer digital and / or quantum data to, or both, one or more mass storage devices for storing digital and / or quantum data, e.g., magnetic, magneto-optical disks, or optical disks, or quantum systems suitable for storing quantum information. However, a digital and / or quantum computer need not have such devices.

[0148] Digital and / or quantum computer-readable media suitable for storing digital and / or quantum computer program instructions and digital and / or quantum data include all forms of non-volatile digital and / or quantum memory, media and memory devices, including by way of example 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; and quantum systems, e.g., trapped atoms or electrons. It is understood that quantum memories are devices that can store quantum data for a long time with high fidelity and efficiency, e.g., light-matter interfaces where light is used for transmission and matter for storing and preserving the quantum features of quantum data such as superposition or quantum coherence.

[0149] Control of the various systems described in this specification, or portions of them, can be implemented in a digital and / or quantum computer program product that includes instructions that are stored on one or more tangible, non-transitory machine-readable storage media, and that are executable on one or more digital and / or quantum processing devices. The systems described in this specification, or portions of them, can each be implemented as an apparatus, method, or electronic system that may include one or more digital and / or quantum processing devices and memory to store executable instructions to perform the operations described in this specification.

[0150] While this specification contains many specific implementation details, these should not be construed as limitations on the scope of what may be claimed, but rather as descriptions of features that may be specific to particular implementations. Certain features that are described in this specification in the context of separate implementations can also be implemented in combination in a single implementation. Conversely, various features that are described in the context of a single implementation can also be implemented in multiple implementations separately or in any suitable sub combination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a sub-combination or variation of a sub-combination.

[0151] Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, 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 described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.

[0152] Particular implementations of the 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 one 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.

[0153] Aspects of the disclosure have been described in terms of illustrative implementations thereof. Numerous other implementations, modifications, or variations within the scope and spirit of the appended claims can occur to persons of ordinary skill in the art from a review of this disclosure. Any and all features in the following claims can be combined or rearranged in any way possible. Accordingly, the scope of the present disclosure is by way of example rather than by way of limitation, and the subject disclosure does not preclude inclusion of such modifications, variations or additions to the present subject matter as would be readily apparent to one of ordinary skill in the art. Moreover, terms are describedherein using lists of example elements joined by conjunctions such as “and,” “or,” “but,” etc. It should be understood that such conjunctions are provided for explanatory purposes only. Lists joined by a particular conjunction such as “or,” for example, can refer to “at least one of” or “any combination of” example elements listed therein, with “or” being understood as “and / or” unless otherwise indicated. Also, terms such as “based on” should be understood as “based at least in part on.”

[0154] Those of ordinary skill in the art, using the disclosures provided herein, will understand that the elements of any of the claims, operations, or processes discussed herein can be adapted, rearranged, expanded, omitted, combined, or modified in various ways without deviating from the scope of the present disclosure. Some of the claims are described with a letter reference to a claim element for exemplary illustrated purposes and is not meant to be limiting. The letter references do not imply a particular order of operations. For instance, letter identifiers such as (a), (b), (c),..., (i), (ii), (iii),..., etc. can be used to illustrate operations. Such identifiers are provided for the ease of the reader and do not denote a particular order of steps or operations. An operation illustrated by a list identifier of (a), (i), etc. can be performed before, after, or in parallel with another operation illustrated by a list identifier of (b), (ii), etc.

Claims

WHAT IS CLAIMED IS:

1. A method for context-dependent calibration of quantum computing systems, comprising: obtaining, by one or more computing devices, data indicative of one or more quantum computing algorithms comprising a plurality of quantum computing operations; identifying, by the one or more computing devices, a plurality of respective calibration parameters, wherein each respective calibration parameter is associated with one or more algorithm-dependent interdependencies associated with one or more respective quantum computing operations of the plurality of quantum computing operations; obtaining, by the one or more computing devices, calibration data for each of the respective calibration parameters; and determining, by the one or more computing devices based at least in part on the calibration data, a plurality of respective calibration values for the plurality of respective calibration parameters.

2. The method of claim 1, further comprising generating, based at least in part on at least one respective calibration value of the plurality of respective calibration values, one or more quantum computing control pulses.

3. The method of claim 1, wherein identifying a plurality of respective calibration parameters comprises: identifying, by the one or more computing devices, a first parametric context comprising one or more first calibration parameters associated with one or more algorithm- dependent interdependencies of a first quantum computing operation of the plurality of quantum computing operations; identifying, by the one or more computing devices, a second parametric context comprising one or more second calibration parameters associated with one or more algorithm-dependent interdependencies of a second quantum computing operation of the plurality of quantum computing operations; determining, by the one or more computing devices, that the first parametric context is sufficiently similar to the second parametric context to be treated as identical to the second parametric context;including, in the plurality of respective calibration parameters, the one or more first calibration parameters; and not including, in the plurality of respective calibration parameters, the one or more second calibration parameters.

4. The method of claim 3, wherein determining that the first parametric context is sufficiently similar to the second parametric context to be treated as identical to the second parametric context comprises: identifying one or more unshared calibration parameters associated with at least one, but not both, of the first parametric context and the second parametric context; determining, by the one or more computing devices, that a strength of an interdependency associated with the unshared calibration parameter is below a threshold.

5. The method of claim 1, wherein the identifying a plurality of respective calibration parameters comprises: identifying, by the one or more computing devices for each of the one or more respective quantum computing operations, one or more contextual operations in spatial, temporal, or spatiotemporal proximity to the respective quantum computing operation; and determining, by the one or more computing devices for each of the one or more respective quantum computing operations based on the one or more contextual operations, one or more calibration parameters associated with the one or more contextual operations.

6. The method of claim 5, wherein determining the one or more calibration parameters comprises: identifying, by the one or more computing devices, one or more operation types associated with the one or more contextual operations; and determining, based on the one or more operation types and a data structure mapping a plurality of operation types to a plurality of calibration parameter sets, the one or more calibration parameters.

7. The method of claim 1, wherein the plurality of respective calibration values are algorithm-dependent calibration values, and further comprising: determining a plurality of algorithm-independent calibration values associated with a plurality of algorithm-independent calibration parameters;wherein the algorithm-dependent calibration values are determined based at least in part on the algorithm-independent calibration values.

8. The method of claim 1, wherein obtaining calibration data comprises executing a proxy quantum computation comprising a number of quantum operations that is smaller than a number of quantum operations of the one or more quantum computing algorithms.

9. The method of claim 8, wherein the calibration data comprises a performance metric indicative of a performance of the proxy quantum computation.

10. The method of claim 1, wherein determining a plurality of respective calibration values comprises: selecting, by the one or more computing devices, a first plurality of candidate calibration values; evaluating, by the one or more computing devices, a performance metric associated with the first plurality of candidate calibration values; and determining, based at least in part on the performance metric, whether to accept the first plurality of candidate calibration values as the plurality of respective calibration values.

11. The method of claim 10, wherein evaluating a performance metric comprises: determining, by the one or more computing devices based on the calibration data and the first plurality of candidate calibration values, one or more estimated error values; and determining, by the one or more computing devices based on the one or more estimated error values, the performance metric.

12. The method of claim 1, wherein: the one or more quantum computing algorithms comprise a first quantum computing algorithm and a second quantum computing algorithm; and the plurality of respective calibration values are determined based at least in part on calibration data associated with the first quantum computing algorithm and based at least in part on calibration data associated with the second quantum computing algorithm.

13. The method of claim 1, wherein the plurality of respective calibration parameters comprises one or more calibration parameters associated with at least one of:one or more control waveforms; one or more qubit-frequency trajectories; one or more gate-frequency trajectories; and one or more coupler-frequency trajectories.

14. A method for context-dependent recalibration of quantum computing systems, comprising: obtaining, by one or more computing devices, data indicative of one or more quantum computing algorithms comprising a plurality of quantum computing operations; obtaining, by the one or more computing devices, first calibration data associated with a quantum computing system previously calibrated to execute the one or more quantum computing algorithms; identifying, by the one or more computing devices based on the first calibration data, one or more insufficiently calibrated operations of the quantum computing system and one or more sufficiently calibrated operations of the quantum computing system; retaining, by the one or more computing devices, one or more first calibration values associated with the sufficiently calibrated operations; identifying, by the one or more computing devices, a plurality of respective calibration parameters, wherein each respective calibration parameter is associated with one or more algorithm-dependent interdependencies associated with one or more respective insufficiently calibrated operations; obtaining, by the one or more computing devices, second calibration data for each of the respective calibration parameters; and determining, by the one or more computing devices based at least in part on the second calibration data, a plurality of respective second calibration values for the plurality of respective calibration parameters.

15. The method of claim 14: wherein the insufficiently calibrated operations comprise a first plurality of operations having interdependencies with each other; wherein the insufficiently calibrated operations comprise a second plurality of operations having interdependencies with each other;further comprising determining, by the one or more computing devices, that the first plurality of operations and second plurality of operations are sufficiently isolated from each other to be calibrated separately; and wherein determining a plurality of respective second calibration values comprises calibrating the first plurality of operations in parallel with the second plurality of operations.

16. The method of claim 14, wherein obtaining second calibration data comprises executing a proxy quantum computation comprising a number of quantum operations that is smaller than a number of quantum operations of the one or more quantum computing algorithms.

17. The method of claim 14, wherein determining a plurality of respective second calibration values comprises: selecting, by the one or more computing devices, a first plurality of candidate calibration values; evaluating, by the one or more computing devices, a performance metric associated with the first plurality of candidate calibration values; and determining, based at least in part on the performance metric, whether to accept the first plurality of candidate calibration values as the plurality of respective second calibration values.

18. One or more non-transitory computer-readable media storing instructions that are executable by a computing system to perform operations, the operations comprising: obtaining, by one or more computing devices, data indicative of one or more quantum computing algorithms comprising a plurality of quantum computing operations; identifying, by the one or more computing devices, a plurality of respective calibration parameters, wherein each respective calibration parameter is associated with one or more algorithm-dependent interdependencies associated with one or more respective quantum computing operations of the plurality of quantum computing operations; obtaining, by the one or more computing devices, calibration data for each of the respective calibration parameters; and determining, by the one or more computing devices based at least in part on the calibration data, a plurality of respective calibration values for the plurality of respective calibration parameters.

19. The non-transitory computer-readable media of claim 18, wherein the operations further comprise generating, based at least in part on at least one respective calibration value of the plurality of respective calibration values, one or more quantum computing control pulses.

20. The non-transitory computer-readable media of claim 18, wherein the plurality of respective calibration values are algorithm-dependent calibration values, and the operations further comprise: determining a plurality of algorithm-independent calibration values associated with a plurality of algorithm-independent calibration parameters; wherein the algorithm-dependent calibration values are determined based at least in part on the algorithm-independent calibration values.

Images