Automatic device calibration

Abstract

This disclosure relates to a method for calibrating a quantum device comprising multiple physical circuit elements forming multiple qubits. The method comprises performing, by one or more classical processors, the steps of creating a digital representation of (i) units representing the multiple physical circuit elements of the quantum device and (ii) physical connections between the units in the quantum device; searching the digital representation to find sub-structures; determining for each sub-structure at least one experiment that is associated with that sub-structure; and calibrating the quantum device based on measurements from the experiments.

Description

"Automatic device calibration"Technical Field

[0001] This disclosure relates to quantum device calibration.Background

[0002] Calibration of quantum devices is important due to the sensitivity of quantum systems to various environmental factors and the imperfections in the manufacturing process of quantum components. Quantum devices, which rely on phenomena such as superposition and entanglement, use precise control over their qubits to function correctly. Any deviation in the expected behavior of qubits can lead to errors in quantum computations, which can significantly affect the performance and reliability of quantum algorithms. The calibration process ensures that each qubit is accurately tuned to its optimal operational state, minimizing errors caused by external disturbances and intrinsic noise.

[0003] The difficulties in calibrating quantum devices are manifold and stem from the intricate nature of quantum mechanics and the extreme precision required to manipulate qubits. One of the primary challenges is the decoherence of qubits, which occurs when they interact with their external environment, causing the loss of their quantum state. Decoherence can be induced by various factors such as temperature fluctuations, electromagnetic interference, and even cosmic radiation. For instance, superconducting qubits, which operate at cryogenic temperatures, are particularly sensitive to thermal noise. Achieving and maintaining the necessary near-absolute zero temperatures is difficult, demanding sophisticated refrigeration systems and shielding from external thermal sources.

[0004] Another significant obstacle is the control and measurement precision. Quantum gates, the fundamental building blocks of quantum algorithms, are executed accurately, often down to the level of single nanoseconds. Any slight deviation in timing or the amplitude of control pulses can introduce errors. For example, trapped ion qubits use precise laser control to manipulate their energy levels. Even minute imperfections in the laser's frequency or intensity can lead to faulty gate operations. Additionally, the cross-talk between qubits, where the operation on one qubit inadvertently affects its neighbors, complicates the calibrationprocess. This calls for complex error-correction protocols and sophisticated pulse shaping techniques to mitigate such interference.

[0005] The inherent variability in the manufacturing process of quantum devices further exacerbates calibration difficulties. Variations in material properties, such as the presence of microscopic defects in superconducting circuits or the inhomogeneity in semiconductor qubits, can significantly impact qubit performance. These imperfections are characterized and compensated for during calibration, requiring extensive computational resources and iterative optimization procedures. For example, in quantum dot qubits, the electrostatic potential landscape is finely tuned to ensure that each dot contains exactly one electron, a process that involves meticulous adjustment of gate voltages and the stabilization of charge configurations.

[0006] Noise is another pervasive issue that complicates the calibration of quantum devices. Quantum systems are inherently susceptible to both intrinsic noise, arising from the quantum components themselves, and extrinsic noise from the surrounding environment. Quantum noise can manifest as random fluctuations in qubit states, leading to errors in computation. Techniques such as dynamical decoupling, which involves the application of a sequence of control pulses to average out the effects of noise, are employed to mitigate this problem. However, these techniques add further complexity to the calibration process, as they rely on precise timing and coordination of pulses. In addition, another source of error is drift of device parameters over time (due to noise). This can be addressed by retuning, which should be performed rapidly so it does not significantly impact device up-time

[0007] Further, the scalability of quantum devices introduces additional calibration challenges. As the number of qubits increases, the complexity of the calibration process grows exponentially. Each qubit is individually characterized and tuned, and the interactions between qubits are managed to avoid cascading errors. There is a need for advanced algorithms to automate and optimize the calibration process, ensuring that the quantum device can operate reliably and efficiently.

[0008] Finally, qubits themselves are not atomic units in the sense that qubits are often implemented using a number of physical circuit elements. Therefore, each qubit may comprise filters, resonators and other elements that are in-line with the actual physicalquantum mechanical system, like a Josephson junction, quantum dot, photon, etc. As a result, there is a wide variety of different implementations even if they use the same physical quantum system and the physical quantum-mechanical system is often not directly accessible. Therefore, any calibration experiments are performed in consideration of the in-line nonquantum circuit elements. This will become more challenging as quantum devices become more integrated with an increase complexity of qubit structures.

[0009] Any discussion of documents, acts, materials, devices, articles or the like which has been included in the present specification is not to be taken as an admission that any or all of these matters form part of the prior art base or were common general knowledge in the field relevant to the present disclosure as it existed before the priority date of each of the appended claims.

[0010] Throughout this specification the word "comprise", or variations such as "comprises" or "comprising", will be understood to imply the inclusion of a stated element, integer or step, or group of elements, integers or steps, but not the exclusion of any other element, integer or step, or group of elements, integers or steps.Summary

[0011] Provided herein is a method for calibrating a quantum device comprising multiple physical circuit elements forming multiple qubits. The method comprises performing, by one or more classical processors, the steps of:creating a digital representation of (i) units representing the multiple physical circuit elements of the quantum device and (ii) physical connections between the units in the quantum device;searching the digital representation to find sub-structures;determining for each sub-structure at least one experiment that is associated with that sub-structure; andcalibrating the quantum device based on measurements from the experiments.

[0012] In some embodiments, searching the digital representation comprises applying a query to the digital representation and each sub-structure is a part of the digital representation for which the query is satisfied.

[0013] In some embodiments, the query defines the sub-structure dynamically.

[0014] In some embodiments, the sub-structure is defined at the point of satisfying the query.

[0015] In some embodiments, the query comprises a sequence of physical circuit element types.

[0016] In some embodiments, the physical circuit element types are purposive types.

[0017] In some embodiments, the query comprises one or more parameters representing a number of the physical circuit elements and corresponding types of the physical circuit elements.

[0018] In some embodiments, the query comprises a threshold on the number of the physical circuit elements.

[0019] In some embodiments, the experiment is parameterised by parameter values of the parameters upon satisfying the query.

[0020] In some embodiments, applying the query comprises executing a pattern-matching algorithm for recognizing calibration-relevant substructures.

[0021] In some embodiments, applying the query is based on a rule-based engine that dynamically selects optimal calibration parameters based on circuit topology.

[0022] In some embodiments, applying the query comprises optimizing calibration efficiency by prioritizing sub-structures with the highest expected error rates or selecting calibration sequences that minimize experimental overhead.

[0023] In some embodiments, the substructure comprises one or more quantum mechanical systems and one or more classical circuit elements in line with the one or more quantum mechanical systems.

[0024] In some embodiments, the query defines a qubit.

[0025] In some embodiments, searching the digital representation to find sub-structures comprises identifying qubits in the digital representation.

[0026] In some embodiments, identifying qubits comprises identifying logical qubits.

[0027] In some embodiments, the digital representation comprises multi-qubit interactions for detection of entanglement errors or identification of qubit clusters exhibiting correlated noise.

[0028] In some embodiments, the method further comprises creating a transformed digital representation by replacing the multiple physical circuit elements by the sub-structures identified in the representation.

[0029] In some embodiments, the sub-structures are directly connectable to physical hardware to conduct the experiments.

[0030] In some embodiments, determining the at least one experiment comprises retrieving the at least one experiment from a library of experiments.

[0031] In some embodiments, the method comprises using historical calibration data to predict future deviations in qubit performance or suggest corrective actions before performance degradation occurs.

[0032] In some embodiments, the multiple physical circuit elements comprise quantum mechanical systems and each experiment comprises control and read-out of the quantum mechanical systems.

[0033] In some embodiments, calibrating the quantum device comprises adjusting control parameters or readout parameters or both of the quantum device.

[0034] In some embodiments, the quantum mechanical systems comprise transmons.

[0035] A computer system comprises one or more processors configured to perform the above method.

[0036] Software, when executed by a computer, causes the computer to perform the method of any one of the preceding claims.

[0037] A quantum device comprises a classical controller configured to operate the quantum device according to operating parameters determined by the above method.Brief Description of Drawings

[0038] An example will now be described with reference to the following figures:Figure 1 illustrates an example quantum device.Figure 2 illustrates two sub-structures that are defined by two corresponding queries. Figure 3 illustrates a transformed representation for the circuit in Figure 1Figure 4 illustrates a method 400 for calibrating a quantum device.Figure 5 illustrates a computer system that is configured to perform the above method. Figure 6 is a micrograph of a 4-qubit transmon quantum processing unit.Figure 7 illustrates a graph representation of the QPU in Figure 6.Figure 8 illustrates feedline-resonator bus sub-structure matched against the graph in Figure 7 with example data tables for each element. The dotted elements (Purcell filters) are not relevant to the resonator spectroscopy experiment and their data tables are not captured.Figure 9 illustrates a 7-transmon QPU using bus-resonatorsFigure 10: (a) A graph representation of Figure 9 with additional feedlines not shown in the capture, (b), (c) matches for the feedline-resonator bus structures with four and three coupled resonators respectively.Figure 11 illustrates resonator spectroscopy results for a single resonator.Figure 12 illustrates resonator spectroscopy results over a feedline with 5 coupled resonatorsFigure 13 illustrates results of 2D power scan spectroscopy.Figure 14 illustrates results of 2D flux bias spectroscopy.Figure 15 illustrates experimental results from a feedline discovery experiment in which a spectroscopy scan was performed over a frequency range associated with a selected feedline.Figure 16 illustrates results of a two-dimensional power scan in which resonator transmission was measured as a function of frequency and power (resonator spectroscopy).Figure 17 illustrates experimental results in which a flux bias was applied while monitoring the resonator response.Figure 18 illustrates resonator spectroscopy results for a selected resonator, including a fitted resonance curve.Figure 19 illustrates experimental results from a transmon spectroscopy experiment, in which a resonance corresponding to a qubit transition was identified.Figure 20 illustrates results of a power Rabi experiment in which oscillations in the measured signal were observed as a function of control pulse amplitude.Figure 21 illustrates Ramsey interference results from which a residual detuning parameter was extracted.Figure 22 illustrates classifier training results based on measurement histograms obtained from the quantum device.Figure 23 illustrates experimental results from which an anharmonicity parameter was determined.Figure 24 illustrates experimental results from which a dispersive shift parameter was extracted.Figure 25 illustrates results of a relaxation experiment used to determine a T1 parameter.Figure 26 illustrates results of dephasing experiments used to determine T2 and echo-based T2 parameters.Figure 27 illustrates results from a T2 echo experiment.Figure 28 illustrates results of a fine amplitude calibration step of a transmon qubit and Sx gate.Figure 29 illustrates the results of a DRAG leakage calibration experiment.Figure 30 illustrates the results of checking the gate fidelity by running a randomized benchmarking experiment.Figure 31 illustrates experimental results from a CZ flux spectroscopy experiment. Figure 32 illustrates results from a CZ leakage calibration experiment.Figure 333 illustrates results of a quantum process tomography experiment used to characterise a two-qubit operation.Description of Embodiments

[0039] This disclosure relates to calibration of a quantum device, which means the determination of operating parameters for the use of the quantum device. As described above, the operating parameters depend on the circuit structure as well as a range of factors, including environmental factors as well as manufacturing and assembly factors. Since it is practically impossible to model these factors with sufficient accuracy, experiments are performed on the quantum device to measure the behaviour of the quantum device for selected input signals. In this context, the term “experiment” does not relate to a research task but denotes the difference to production use. So the experiment is used to characterise or calibrate a commercial quantum device before it is used during production. The experiments and the calibration can be re-run at any time to update the calibration and account for changing environmental parameters, for example.

[0040] Experiments, in many cases, include a definition of input signals (also referred to as stimuli), and the definition of measurements of the output or any other accessible ports of the quantum device. It is noted that the measurement of a quantum system is also referred to as read-out, and these terms are used herein interchangeably. There is then an association between the measurements of the experiments and the operating parameters in production. More particularly, a classical computer calculates the operating parameters from the received measurements.

[0041] Figure 1 illustrates an example quantum device, which is a superconducting quantum computer in this case comprising a first feedline 101 and six transmission line shunted plasma oscillation units (transmons), such as first transmon 102 and second transmon 103, which are connected. In the path of first transmon 102 and second transmon 103 there is a first resonator 104 and a second resonator 105 and a filter 106. It is noted that filter 106 is a non-quantum / classical circuit elements and is inline with the first transmon 102 and the second transmon 103 and then connected to second feedline 107.

[0042] In this case, input signals can only be applied to and measurements only taken from first feedline 101 and second feedline 107. Therefore, the filter 106, first resonator 104 and second resonator 105 are part of the calibration process together with the first transmon 102 and the second transmon 103, which are the actual quantum-mechanical systems that storequantum information. It is noted that the complete sub-structure comprising non-quantum elements, such as filter 106, quantum elements that do not store quantum information, such as first resonator 104 and second resonator 105, as well as quantum-mechanical systems that store quantum information, such as first transmon 102, second transmon 103 is referred to as a physical qubit, because this is the element that can be addressed physically and can be used for its qubit functionality and behaviour.

[0043] One problem is now that it is difficult to design a suitable experiment for this particular architecture efficiently. More particularly, in a complex design space that comprises many different variations of architectures, potentially with the same number and type of quantum-mechanical systems, it is difficult to design a suitable experiment for each element or each path between first feedline 101 and second feedline 107. These different architectures may be present in a single quantum device, which makes calibration of the entire device difficult.

[0044] Therefore, this disclosure provides a method for calibrating a quantum device 100, noting that the method can be used to calibrate other quantum devices. The quantum device may be a quantum computer, including ‘digital’ quantum computers using binary qubits or qudits etc., as well as ‘analog’, quantum computers that function by annealing and may be based on neural atoms or superconducting circuits comprising Josephson junctions. Other quantum devices include quantum sensors while further quantum devices can also be calibrated using this method. At the heart of these quantum devices is a physical quantum mechanical system, such as an electron spin, photon spin, number state, nitrogen vacancy, and others. As described with reference to Figure 1, quantum device 100 comprises multiple physical circuit elements forming multiple qubits. The multiple physical circuit elements comprise classical elements, such as filters, resonators, transmission lines and the like, as well as physical quantum mechanical systems.

[0045] Figure 4 illustrates a method 400 for calibrating a quantum device comprising multiple physical circuit elements forming multiple qubits. Figure 5 illustrates a computer system 500 that is configured to perform method 400. Computer system 500 comprises a processor 501, program memory 502 and data memory 503 as well as a communication port 504 and a control port 505, noting that the ports may be combined into a single port. Program memory 502 is a non-transitory, computer readable medium with program code stored thereonthat, when executed, causes processor 501 to perform the methods disclosed herein, including method 400. Processor 501 stores a digital representation, as well as other circuit parameters on data memory 503. Processor 501 may also store experiment details including measurements and calculated calibration data on data memory 503. Processor 501 may use historical calibration data to predict future deviations in qubit performance or suggest corrective actions before performance degradation occurs. This involves analyzing past calibration data to identify patterns and trends that may indicate potential future deviations in the performance of qubits. By leveraging this historical data, the method can forecast when a qubit might deviate from its optimal operational state due to factors such as environmental changes, manufacturing imperfections, or intrinsic noise. Additionally, the method can suggest corrective actions to be taken before any significant performance degradation occurs, ensuring that the quantum device remains reliable and efficient. These corrective actions may include adjusting control parameters, retuning qubits, or implementing error-correction protocols to mitigate the impact of predicted deviations.

[0046] Although a single processor 501 is shown, it is noted that computer system 500 may equally be implemented with multiple processors or in a cloud computing environment.Further, computer system 500 comprises a communication port configured to receive the digital representation of the circuit as well as other input data, such as from a user.Communication port 504 may further provide results back to the user for operating the quantum device. There is also control port 505 that is configured to output control signals to the quantum device. This includes input signals to perform the experiments determined for the particular quantum device. The control port 505 also receives measurements for the processor 501 to calculate the operating parameters of the quantum device. It is noted that the quantum device may be in communication with the computer system 500 over a network, such as the internet, such that the control of the quantum device can also occur over communication port 504.

[0047] According to method 400, processor 501 creates 401 a digital representation of (i) units representing the multiple physical circuit elements of the quantum device and (ii) physical connections between the units in the quantum device. This digital representation may be similar to a circuit diagram or circuit description. Therefore, the digital representation may be of the form of a graph comprising nodes and edges. It is noted that the graph is a data structure stored on computer memory in the sense that the nodes and edges are data elements.The graph can be implemented in software using various data structures to represent the nodes and edges that constitute the graph. One approach is to use an adjacency list, where each node has a list of its adjacent nodes, effectively capturing the connections between them. This method is efficient in terms of space, especially for sparse graphs, as it only stores edges that actually exist. Alternatively, an adjacency matrix can be used, which involves a 2D array where each cell indicates whether an edge exists between a pair of nodes. This method allows for quick lookup of connections but can be less space-efficient for large, sparse graphs.Another flexible approach is to use object-oriented programming, where nodes and edges are represented as objects, and their relationships are managed through references or pointers. This allows for a more complex and dynamic representation, accommodating additional properties or methods for nodes and edges. Each of these data structures offers different tradeoffs in terms of memory usage and performance, and the choice of data structure may depend on the specific requirements of the application, such as the need for efficient edge lookups or the ability to handle dynamic changes to the graph structure.

[0048] The physical circuit elements are represented by nodes while the connections between them are represented by edges. Other representations, such as incidence matrices, lists, structured text, data objects, database entries, etc. are equally possible and are also considered as alternative representations of graphs. Further, the digital representation may comprise multi-qubit interactions for detection of entanglement errors or identification of qubit clusters exhibiting correlated noise. This involves creating a digital representation of the quantum device that includes the interactions between multiple qubits. These interactions are useful for detecting entanglement errors, which occur when the quantum state of a qubit becomes correlated with the state of another qubit in an unintended manner. Additionally, the digital representation helps in identifying clusters of qubits that exhibit correlated noise, which is an issue in quantum devices due to environmental factors and imperfections in the manufacturing process. By accurately modelling these multi-qubit interactions, the method enhances the calibration process, ensuring that the quantum device operates reliably and efficiently.

[0049] Processor 501 then searches the digital representation to find sub-structures. In one example, searching the digital representation comprises applying a query to the digital representation and each sub-structure is a part of the digital representation for which the query is satisfied. That is, the processor applies a computational query mechanism to dynamicallyidentify functional sub-structures within the representation based on predefined or adaptive calibration criteria. The query may also be referred to as a definition of a trait and satisfying the query may also be referred to as identifying a sub-structure that matches the pattern defined by the query.

[0050] The method involves applying a query that executes a pattern-matching algorithm to recognize calibration-relevant substructures. This process uses a computational query mechanism to dynamically identify functional sub-structures within the digital representation of the quantum device based on predefined or adaptive calibration criteria. The patternmatching algorithm searches for specific sequences of physical circuit element types, such as resonators, filters, and transmons, that are relevant for calibration. These sub-structures are then labeled and used to parameterize the calibration experiments. Additionally, the method employs a rule-based engine that dynamically selects optimal calibration parameters based on circuit topology. This engine uses a set of predefined rules to analyze the circuit topology and dynamically select the most suitable calibration parameters. The engine takes into account the specific arrangement and connections of the physical circuit elements, such as the number and types of resonators, filters, and transmons, to determine the optimal calibration settings. Furthermore, the method optimizes calibration efficiency by prioritizing sub-structures with the highest expected error rates or selecting calibration sequences that minimize experimental overhead. This optimization process involves identifying sub-structures within the quantum device that are most likely to exhibit errors and prioritizing them for calibration. The method also includes selecting calibration sequences that reduce the overall experimental overhead, ensuring that the calibration process is efficient and effective. By focusing on the most error-prone sub-structures and minimizing the time and resources required for calibration, the method enhances the overall performance and reliability of the quantum device.

[0051] The query may be formulated in a query language and may follow a query grammar. One example for a language that can be used is pkl (pkl-lang.org), which is a declarative language comprising classes, functions, conditionals, and loops. It also facilitates abstraction layers, and the sharing of code by creating packages.

[0052] In this way, the query defines the sub-structure dynamically, which means that the actual sub-structure is defined at runtime, i.e. it is defined at runtime how many resonators, filters, transmons, etc. the sub-structure has and how they are connected. In other words, thesub-structure is defined in its components and connections at the point of satisfying the query. The query provides for the rule that needs to be satisfied for that sub-structure but there may be a wide range of different sub-structures that satisfy that rule.

[0053] To that end, the query may comprise a sequence of physical circuit element types and if parts of the circuit matches that sequence, that part is then labelled a sub-structure. In one example, the physical circuit element types are purposive types, which means that the physical circuit element types are not defined explicitly by specific characteristics, but by the purpose that they fulfill in the circuit. This way the query becomes more expressive and can match a wider range of sub-structures.

[0054] Further, the query may comprise one or more parameters representing a number of the physical circuit elements and corresponding types of the physical circuit elements, which may be a threshold on the number of the physical circuit elements. This way the query matches dynamically any number of elements that satisfy the threshold. At the same time, it is possible to store the number of elements in that specific match instance and then parameterise the experiment by the parameter values of the parameters upon satisfying the query. As a result, the experiment is parameterised and the actual instance of the experiment for a particular sub-structure is determined at run-time using the parameter values for the matched sub-structure.

[0055] Figure 2 illustrates two sub-structures that are defined by two corresponding queries, labelled as Cl and C2 (for component 1 and component 2). In the circuit of Figure 1, the first sub-structure matches the first and third ‘column’ in Figure 1 while the second sub-structure matches the middle column in Figure 1.

[0056] As can be seen in Figure 1, it is noted for clarity that the substructure comprises one or more quantum mechanical systems (such as transmons 102 and 103) and one or more classical circuit elements, such as filter 106 and resonators 103 / 105 in line with the one or more quantum mechanical systems. In that sense, the query may define a physical qubit and searching the digital representation to find sub-structures may comprise identifying qubits in the digital representation. In other words, the query identifies circuit structures in the circuit that act as qubits when the circuit is used as a quantum device.

[0057] It is noted that the queries above identify physical qubits, which means structures that can be controlled and read out as a physical multi-level quantum mechanical system. However, there may also be queries that identify higher level sub-structures, such as logical qubits, which may contain multiple physical qubits.

[0058] Returning to Figure 4, once the sub-structures are identified in step 402, processor 501 determines for each sub-structure an experiment that is associated with that sub-structure. In other words, the processor associates each identified sub-structure with at least one parameterized experiment tailored to its circuit topology and operational constraints. For example, processor 501 may access a library of experiments, that may be stored as a database of experiments comprising at least one experiment for each sub-structure. The library / database maybe searchable to search for experiments given the current sub-structure. As such, the library / database may be indexed to facilitate the search. This way, processor 501 retrieves the experiment for this sub-structure from the library of experiments.

[0059] As explained above, the sub-structures may be parameterised and the searching and satisfying of the query may yield parameter values. In that case, the processor 501 enters those parameter values in the experiment definition to determine each of the final experiments for that sub-structure, noting that one or more experiments may be run for any one substructure. Each experiment comprises an indication of input signals (stimuli), measurements (e.g. measurement basis of quantum measurements). The experiments may also comprise a mapping of the measurements to operating parameters of the quantum device.

[0060] Finally, processor 501 calibrates 404 the quantum device based on the measurements from the experiments. That is, processor 501 calculates operating parameters that enable the optimal operation of the quantum device in light of the obtain experimental measurements.

[0061] It is noted that processor 501 may further creating a transformed digital representation by replacing the multiple physical circuit elements by the sub-structures identified in the representation. This way, a simplified or abstracted circuit representation is created that can then be used for experimental design. In other words, instead of determining the experiments directly as described above, processor 501 may first create the transformed representation and then determine the experiments based on the transformed representation.

[0062] Figure 3 illustrates a transformed representation for the circuit in Figure 1, where the physical circuit elements are now replaced by the sub-structures Cl and C2. As can be seen, the experiments for all Cl sub-structures can be largely identical since both were identified by matching the Cl query shown in Figure 2.

[0063] As can also be seen in Figure 3, the sub-structures C1 / C2 are directly connectable to physical hardware to conduct the experiments. The physical hardware in this case are the first feedline 101 and the second feedline 107. This is useful because the hardware that conducts the experiments can physically access the feedlines 101 / 107 to conduct the experiments. This also means that the sub-structures form a direct edge between the connection ports of the quantum device.Example

[0064] The following description provides an example of the application of the disclosed method for a superconducting transmon architecture, noting that other architectures can equally be used. In this architecture, qubits are physically implemented with transmons coupled to microwave readout resonators. Characterization of the qubits is based on accurate determination of parameters associated to these physical elements. For feedline discovery, the first parameter determined for each qubit is the resonator frequency; the fundamental frequency of the readout resonator element coupled to the qubit’s transmon; the resonator frequency is detuned from the qubit’s frequency. This parameter is beneficial for high-fidelity qubit readout.

[0065] In a feedline frequency-multiplexed configuration, multiple readout resonators are coupled to a single feedline bus and each readout resonator is allocated a frequency band to prevent interference with other resonators, thus providing individual addressability to the qubits. However, this means that the internal resonator-transmon mappings may be invisible from the perspective of a control system since there is a single pair of readout ports for each feedline. So, the second challenge is to determine which frequency band is allocated to which qubit.

[0066] Thus, feedline discovery has two broad objectives:1. Determine the resonant frequency for each qubit’ s readout resonator.2. Determine an internal mapping of readout resonators to qubits.Calibration procedure

[0067] The steps for calibration include:1) Identify feedline-resonator bus sub-structures, by creating a graph representation of the QPU and matching against a query expression.2) Run experiments against each matched sub-structure:a) Determine resonant frequencies, by performing a spectroscopy experiment over the bandwidth of each matched feedline.b) Identify dead resonators, by performing an “alive test” that flags resonators that are not coupled to qubits in the given power regime.c) Map resonators to flux ports, by performing flux bias scans across feedline-resonator bus sub-structures that preclude dead resonators.Example processing unit

[0068] An example superconducting transmon QPU is shown in Figure 6. It has four tunable transmon qubits 601, each with their own charge (drive) lines 602 and flux lines 603. The QPU uses a frequency -multiplexed feedline configuration, where each qubit is coupled to a readout resonator element 604 for qubit measurement. The readout resonators are in turn coupled to a shared feedline 605. Frequency multiplexing allows a single microwave probe signal sent through the readout port to individually address each qubit. The response of each qubit will be reflected back through the feedline to the other readout port where measurements can be captured.Circuit model

[0069] Figure 7 illustrates an example graph structure used to create an circuit model of the chip. Here, a chip boundary is highlighted to emphasise that only control ports are accessible by the control system, and the internal resonator-transmon couplings are opaque to the control system. Corresponding data tables are instantiated and mapped to each element in the circuit model. These data tables contain both the calibration parameters that the method determines and additional internal information used for the calibration procedure.Feedline-resonator bus sub-structures

[0070] The feedline discovery calibration procedure is relevant to feedline-resonator buses. As such, experiments are defined against these sub-structures and the associated expected data-tables that result from it.Query expression

[0071] To identify the feedline-resonator bus sub-structure, a query expression is used. One purpose of the query expression is to capture a one-to-many relationship between feedline and coupled resonators, for every unique feedline for the targeted QPU. Because QPU designs may vary in both the number of feedlines and the number of resonators coupled to each feedline, the query expression supports the use of patterns with controls over how the pattern repeats in the query. In the case of a feedline— resonator bus substructure, the query encodes a mapping between a feedline element and a pattern expressing the readout resonator— transmon pairing that must repeat at least twice. That is, there must be at least two resonators coupled to the same feedline for it to be considered a feedline— resonator bus sub-structure. Additionally, the query ex-pression must robustly operate over variations in the feedline— resonator bus substructure configuration.

[0072] For example, Purcell filters are additional elements coupled between a feedline and a resonator to improve readout quality. The Purcell filter is an optional element; it can be seen in the QPU shown in Figure 8, and it is not seen in the QPU shown in Figure 9. The resonator— transmon pairing pattern therefore includes wildcard elements in the pattern that can incorporate these optional elements, in this case preceding the readout-resonator. The query expression also supports specifying constraints in wild-cards used in patterns, to prevent the query matching irrelevant or incorrect elements.

[0073] For example, consider a pattern intended to capture resonator— transmon pairings with an unconstrained wildcard preceding the resonator intended to capture optional readout filter elements. If a target QPU also includes transmon— resonator— transmon two-qubit substructure, the pattern would erroneously mistake one of the transmons in the two-qubit substructure as a filter element; such a two-qubit substructure can be seen in the QPU in Figure 9. As such, the original pattern should constrain the wildcard to ensure it only capture elements intended for readout filtering. Such constraints are expressed using predicate logic that check element traits.

[0074] One example query is provided below( : F) -- [ ( : ?, ' filter' readout T ) ] +

[0075] Here each element in the graph representation is described through a node identifier of the format (name:type, trait). Where,• the name for optionally matching on a specific element by its given reference (not used in this example),• the type is any of the available types for a given architecture (e.g. F for feedline, R for resonator, etc.), and• the trait is an additional expression that identifies additional markers that elements can be designated with to distinguish their purpose and other properties from other elements of the same type.

[0076] The query expression first identifies a granular sub -sub structure [ (?)-(:R, readout)— (:T) ], representing each qubit’s readout-transmon coupling. The additional (:?, filter)? element is an optional match for filters preceding the readout resonator that are not necessarily always present in transmon QPUs. Finally, using this sub-substructure, the query expression identifies a one-to-many relationship between the a single feedline and the readout-transmon coupling through the syntax: (:F)— +[ ... ].Match result

[0077] Figure 8 shows the matched feedline-resonator bus sub-structure from querying the QPU represented in Figure 7 with the query. The data-tables for each relevant matched item will also be attached, and given initial estimates of the relevant values, e.g. flmand fhigh. From here, the experiment routine can calculate necessary parameters such as the feedline bandwidth, and schedule experiments relevant to the sub-structure - in this case resonator spectroscopy, discussed below.Match on a different QPU

[0078] Transmon based QPUs may use similar physical components such as transmons, resonators, couplers, ports. However, their layouts - the arrangement of their individual components and how each are connected to one another - may not necessarily be the same.Furthermore, the configuration of sub-structures used by each QPU will likely be different too.

[0079] Figure 9 shows a different 7-qubit transmon based QPU using similar components as before. However, unlike the first QPU (Figure 6 / 7), it does not use individual Purcell filters for qubit readout. Further, as opposed to direct transmon-transmon couplers, the coupling between transmons in this second chip uses a transmon-resonator bus configuration, where multiple transmons are coupled through a single bus resonator.

[0080] Because of the query’s ability to express wildcards on the filters, (:?, filter)?, the absence of the Purcell filter does not affect the match. Additionally, the requirement that the sub-structure matches a feedline to one (or more) resonator-transmon couplings precludes matching on bus resonators as the element between the feedline and bus resonator is a transmon which does not have the required filter trait.

[0081] Finally, notice that the number of resonator-transmon couplings the feedline is coupled against will not affect the query’s ability to match, as the query expression allows matching against a variable number of sub -sub structures with the (:F)— [ ... ]+ syntax. Thus, the query is able to robustly match a multitude of feedline-resonator bus configurations against various QPU layouts, as seen in Figure 10.Experiments for feedline-resonator bus

[0082] Resonator spectroscopy

[0083] Resonator spectroscopy aims to identify the resonant frequency of a resonator.Figure 11 shows a Lorentzian fit over the frequency sweep, where the drop in feedline transmission S21identifies the fundamental frequency of the resonator. The method can sweep over the entire frequency bandwidth of a frequency-multiplexed feedline and identify all resonant frequencies for all coupled resonators, as seen in Figure 12. Once this experiment is complete, the results are stored against the feedline’s data table (resonances: [##, ...] entry).

[0084] Alive-test

[0085] 2D power scan spectroscopy as seen in Figure 13 allows to identify resonators that are not coupled to transmons. Resonators which do not have the bifurcated low-power / high-power regimes in their power scan are marked as “dead” with a trait that is later used in the 2D flux bias spectroscopy.

[0086] Bias scan

[0087] Once the resonator spectroscopy and alive-test results are captured, the method may update the query match to identify a more specific sub-structure used to complete the final objective of mapping resonators to qubits.( : F) --+ [ ( : ?, ' filter ' ) ? -- ( : R, ' readout & ! dead' ) -- ( : T) -- ( : port, ' Z ' ) ]

[0088] The resonator element trait expression is modified to also require that the resonator is not dead (Idead). And, an additional match to a port (:port) element with a Z trait identifies a coupled flux line to the transmon. This one-to-one mapping between flux port and transmon allows us to bias the flux port whilst performing spectroscopy on the readout port to identify the hidden resonator-transmon mappings.

[0089] A 2D flux bias spectroscopy, as seen in Figure 14, biases a flux port whilst performing resonator spectroscopy. The strongest response matching to one of the resonant frequencies discovered above, indicates a strong coupling between the resonator and transmon, and hence provides the required resonator-qubit mapping.

[0090] While the above section provides a specific example for a QPU circuit, it is noted that the methods disclosed herein equally apply to other QPU architectures. That is, for any architecture provided to the mothed, the method calibrates the quantum device, which includes multiple physical circuit elements forming multiple qubits. The classical processors creatings a digital representation of units representing the multiple physical circuit elements of the quantum device and the physical connections between these units, searches the digital representation to find sub-structures, determines at least one experiment associated with each sub-structure, and calibrates the quantum device based on the measurements obtained from these experiments. This method encompasses various types of quantum computerarchitectures, including superconducting qubits, trapped ions, photonic qubits, and topological qubits, ensuring that the calibration process is adaptable and applicable to different designs and configurations. For instance, in superconducting qubits, the method can be used to map resonators to qubits via 2D flux bias spectroscopy. In trapped ion architectures, the method can be adapted to calibrate ion positions and their interactions. Photonic qubits can utilize this method to align optical components and verify entanglement, while topological qubits can benefit from the method by identifying and stabilizing anyon pairs and their braiding operations.Experimental Results

[0091] The following experimental results illustrate implementation of the method for calibrating a quantum device comprising multiple physical circuit elements forming multiple qubits, as disclosed herein. In particular, the experiments demonstrate creating and operating on a digital representation of a quantum device, identifying sub-structures within that representation using queries, determining experiments associated with the identified sub-structures, and calibrating the quantum device based on measurements obtained from the experiments.Identification of feedline-resonator sub-structures

[0092] In a first stage, a digital representation of the quantum device was created, comprising units representing physical circuit elements of the quantum device and physical connections between those units. The digital representation was searched using a query to identify feedline-resonator bus sub-structures, each sub-structure comprising a feedline coupled to multiple resonators associated with respective transmons.

[0093] Based on identification of the feedline-resonator bus sub-structures, a feedline discovery experiment was determined for each identified sub-structure. Figure 15 illustrates experimental results from a feedline discovery experiment in which a spectroscopy scan was performed over a frequency range associated with a selected feedline. The resulting measurements reveal multiple resonant responses corresponding to resonators coupled to the feedline, thereby determining resonant frequencies associated with the sub-structure.Parameterised resonator experiments

[0094] Following identification of the feedline-resonator bus sub-structure, further experiments associated with that sub-structure were determined and executed. These experiments were parameterised based on parameters of the sub-structure identified by the query, including the number of resonators coupled to the feedline and their associated ports.

[0095] A resonator power spectroscopy experiment was performed to characterise resonator behaviour over different probe powers. Figure 16 illustrates results of a two-dimensional power scan in which feedline transmission was measured as a function of frequency and power. Measurements obtained from this experiment were used to classify resonators and to identify resonators suitable for subsequent calibration steps.

[0096] A resonator bias spectroscopy experiment was also performed. Figure 17 illustrates experimental results in which a flux bias was applied while monitoring the resonator response. This experiment provides measurements indicative of coupling between a resonator and an associated quantum mechanical system.

[0097] Figure 18 illustrates resonator spectroscopy results for a selected resonator, including a fitted resonance curve. From these measurements, resonator parameters were determined and stored in association with the corresponding unit in the digital representation.

[0098] In one example, parameters determined for a resonator coupled to a transmon include a resonator frequency, a low-power voltage parameter, and a corresponding transmon bias parameter. These parameters were subsequently used to determine experiments associated with the connected quantum mechanical system.

[0099] In this case, found the following properties were found for resonator rDl :Resonator rDl - Transmon qDl :Resonator mapped to frequency 7154.086 MHzResonator vp low: 0.042 VTransmon de bias : 0.026 VDetermination of experiments associated with a transmon sub-structure

[0100] Following determination of resonator parameters, the digital representation was searched to identify a refined sub-structure comprising a resonator coupled to a transmon.Based on identification of this sub-structure, one or more transmon-specific experiments were determined and executed.

[0101] A transmon spectroscopy experiment was performed to characterise the transition frequency of the quantum mechanical system. Figure 19 illustrates experimental results from a transmon spectroscopy experiment, in which a resonance corresponding to a qubit transition was identified. Measurements obtained from this experiment were used to determine a qubit operating frequency. Providing the following result:Transmon spectroscopy analysis successful .Found :- frequency_01 : (5363.485902573116 ± 0.053835266957575255) MHz

[0102] A power Rabi experiment was then determined and executed to calibrate control pulse amplitudes associated with single-qubit gate operations. Figure 20 illustrates results of a power Rabi experiment in which oscillations in the measured signal were observed as a function of control pulse amplitude. Based on these measurements, control parameters corresponding to X and SX gates were determined with the following result:Power Rabi analysis successful .FitParameter (value=0 . 13640638360524113,004132509996568732)FitParameter (value=0 . 06820319180262056,002066254998284366)

[0103] A Ramsey experiment was subsequently performed to refine the qubit frequency calibration. Figure 21 illustrates Ramsey interference results from which a residual detuning parameter was extracted. The operating parameters of the quantum device were updated based on this measurement as follows:Ramsey analysis successful .Found :- detuning : (0.14334325112733942 ± 0.005935877920265869) MHzUpdating the digital representation and further parameter determination

[0104] Based on the measurements obtained from the above experiments, the digital representation was updated to include calibrated parameters associated with the identified sub-structures. Using the updated representation, additional experiments were determined and executed.

[0105] A readout classification experiment was performed to characterise measurement outcomes associated with different quantum states. Figure 22 illustrates classifier training results based on measurement histograms obtained from the quantum device.

[0106] An anharmonicity spectroscopy experiment was performed to determine higher-order energy level parameters of the transmon. Figure 23 illustrates experimental results from which an anharmonicity parameter was determined. Result:Transmon anharmonicity spectroscopy analysis successful .Found :- anharmonicity: (-208.9719216080017 ± 0.05535942659010713) MHz,

[0107] A dispersive shift experiment was also determined and executed to characterise coupling between the transmon and its associated resonator. Figure 24 illustrates experimental results from which a dispersive shift parameter was extracted:ChiOl scan experiment has run successfully.Foun :- dispersive_shift : (-1.1895188263225556 ± 0.0887665771043304) MHzCoherence experiments associated with a transmon sub-structure

[0108] Further experiments associated with the transmon sub-structure were determined to characterise coherent properties of the quantum mechanical system. These experiments included relaxation and dephasing measurements.

[0109] Figure 25 illustrates results of a relaxation experiment used to determine a T1 parameter. Figure 26 illustrates results of dephasing experiments used to determine T2 and echo-based T2 parameters. Measurements from these experiments were stored in association with the corresponding sub-structure in the digital representation with the following values: T1 analysis successful .Found :- Tl : (22.71394709206913 ± 0.582619452767915) psCalibration of single-qubit gate operations

[0110] After determining operating parameters for the transmon sub-structure, further experiments were determined to calibrate single-qubit gate operations. These experiments included fine amplitude calibration and leakage-reduction experiments.Randomized benchmarking experiments were then executed to evaluate gate performance. Figure 27 illustrates experimental results from a single-qubit randomized benchmarking experiment. Based on these measurements, single-qubit gate fidelities were determined and associated with the calibrated operating parameters.T2: (23.51861600701475 ± 0.6062396491841803) ps.

[0111] Figure 28 illustrates results of a fine amplitude calibration step of a transmon qubit and Sx gate. Figure 29 illustrates the results of a DRAG leakage calibration experiment. In this context, DRAG stands for "Derivative Removal by Adiabatic Gate." It is a technique used in the calibration of single-qubit gate operations, particularly for transmon qubits, to reduce leakage and errors during quantum gate execution. The DRAG method involves shaping control pulses so that unwanted transitions to higher energy levels are suppressed, thereby improving gate fidelity and coherence performance in quantum experiments.

[0112] Figure 30 illustrates the results of checking the gate fidelity by running a randomized benchmarking experiment. The fidelity was found to be 99.85%. Similarly, an X gate was calibrated with the DRAG leakage calibration for the X gate. The following tables summarise the results:Gate Fidelity for Calibrated Transmon qDlTwo-qubit experiments and sub-structure calibration

[0113] The method was also applied to sub-structures comprising multiple quantum mechanical systems. Two-qubit calibration experiments were determined and executed, including controlled-Z (CZ) flux spectroscopy and leakage calibration.

[0114] Figure 31 illustrates experimental results from a CZ flux spectroscopy experiment. Figure 32 illustrates results from a CZ leakage calibration experiment. Figure 33 illustrates results of a quantum process tomography experiment used to characterise a two-qubit operation. Measurements obtained from these experiments were used to calibrate operating parameters associated with multi-qubit sub-structures in the quantum device.

[0115] It will be appreciated by persons skilled in the art that numerous variations and / or modifications may be made to the above-described embodiments, without departing from the broad general scope of the present disclosure. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive.

Claims

CLAIMS:

1. A method for calibrating a quantum device comprising multiple physical circuit elements forming multiple qubits, the method comprising performing, by one or more classical processors, the steps of:creating a digital representation of (i) units representing the multiple physical circuit elements of the quantum device and (ii) physical connections between the units in the quantum device;searching the digital representation to find sub-structures;determining for each sub-structure at least one experiment that is associated with that sub-structure; andcalibrating the quantum device based on measurements from the experiments.

2. The method of claim 1, wherein searching the digital representation comprises applying a query to the digital representation and each sub-structure is a part of the digital representation for which the query is satisfied.

3. The method of claim 2, wherein the query defines the sub-structure dynamically.

4. The method of claim 2 or 3, wherein the sub-structure is defined at the point of satisfying the query.

5. The method of any one of claims 2 to 4, wherein the query comprises a sequence of physical circuit element types.

6. The method of claim 5, wherein the physical circuit element types are purposive types.

7. The method of any one of claims 2 to 6, wherein the query comprises one or more parameters representing a number of the physical circuit elements and corresponding types of the physical circuit elements.

8. The method of claim 7, wherein the query comprises a threshold on the number of the physical circuit elements.

9. The method of claim 7 or 8, wherein the experiment is parameterised by parameter values of the parameters upon satisfying the query.

10. The method of any one of claims 2 to 9, wherein applying the query comprises executing a pattern-matching algorithm for recognizing calibration-relevant substructures.

11. The method of any one of claims 2 to 10, wherein applying the query is based on a rule-based engine that dynamically selects optimal calibration parameters based on circuit topology.

12. The method of any one of claims 2 to 11, wherein applying the query comprises optimizing calibration efficiency by prioritizing sub-structures with the highest expected error rates or selecting calibration sequences that minimize experimental overhead.

13. The method of any one of the preceding claims, wherein the substructures comprise one or more quantum mechanical systems and one or more classical circuit elements in line with the one or more quantum mechanical systems.

14. The method of any one of the preceding claims, wherein the query defines a qubit.

15. The method of claim 14, wherein searching the digital representation to find substructures comprises identifying qubits in the digital representation.

16. The method of claim 15, wherein identifying qubits comprises identifying logical qubits.

17. The method of any one of the preceding claims, wherein the digital representation comprises multi-qubit interactions for detection of entanglement errors or identification of qubit clusters exhibiting correlated noise.

18. The method of any one of the preceding claims, wherein the method further comprises creating a transformed digital representation by replacing the multiple physical circuit elements by the sub-structures identified in the representation.

19. The method of any one of the preceding claims, wherein the sub-structures are directly connectable to physical hardware to conduct the experiments.

20. The method of any one of the preceding claims, wherein determining the at least one experiment comprises retrieving the at least one experiment from a library of experiments.

21. The method of any one of the preceding claims, wherein the method comprises using historical calibration data to predict future deviations in qubit performance or suggest corrective actions before performance degradation occurs.

22. The method of any one of the preceding claims, wherein the multiple physical circuit elements comprise quantum mechanical systems and each experiment comprises control and read-out of the quantum mechanical systems.

23. The method of any one of the preceding claims, wherein calibrating the quantum device comprises adjusting control parameters or readout parameters or both of the quantum device.

24. The method of any one of the preceding claims, wherein the quantum mechanical systems comprise transmons.

25. A computer system comprising one or more processors configured to perform the method of any one of the preceding claims.

26. Software that, when executed by a computer, causes the computer to perform the method of any one of the preceding claims.

27. A quantum device comprising a classical controller configured to operate the quantum device according to operating parameters determined by the method of any one of the preceding claims.

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