Efficient approximation of a single range of sideband frequencies

Abstract

Systems, computer-implemented methods, and computer program products are provided that facilitate efficiently approximating a range of sideband frequencies. According to one embodiment, the system may include a processor executing computer-executable components stored in a memory. The computer-executable components may include a wave splitting component that generates a plurality of waveform segments using a definition of an intended waveform, the plurality of waveform segments being phase shifted. The computer-executable components may further include a rotation component that assigns a phase rotation to apply to at least one waveform segment of the plurality of waveform segments, the phase rotation being out of phase with a previous waveform segment of the plurality of waveform segments.

Description

[Technical Field]

[0001] This subject disclosure relates to waveform generation, and more specifically, to efficiently approximating a range of sideband frequencies. [Background technology]

[0002] Waveform generation has a wide range of applications in radio frequency (RF) technology. Many of these applications, including fields such as Rabi spectroscopy, testing of RF filters, attenuators, and transmission cables, and the operation of quantum computers, utilize frequency sweeps. To generate frequency sweeps, existing waveform generation techniques produce a set of waveforms that are identical except for the output frequency. [Overview of the project]

[0003] The following is an overview that provides a basic understanding of one or more embodiments of the present invention. This summary is not intended to identify key or critically important elements, nor to limit the scope of any particular embodiment or claim. Its sole purpose is to present the idea in a simplified form as a prelude to a more detailed description that follows. One or more embodiments described herein describe a system, computer implementation, or computer program product, or a combination thereof, that facilitates the efficient approximation of a range of sideband frequencies.

[0004] According to one embodiment, the system may include a processor that executes computer executable components stored in memory. These computer executable components include a wave splitting component that generates a plurality of waveform snippets using a definition of an intended waveform, and these plurality of waveform snippets may be phase-shifted. These computer executable components further include a rotation component that assigns a phase rotation to be applied to at least one of the plurality of waveform snippets, and this phase rotation is out of phase with respect to a previous waveform snippet among the plurality of waveform snippets. The advantage of such a system is that by dividing the intended waveform into a plurality of waveform snippets, an approximation of the intended waveform can be efficiently stored in memory.

[0005] In some embodiments, the rotation component assigns a phase rotation applied by the waveform generator to at least one of its multiple waveform fragments using a phase rotation factor 2π(ω+ε)t, where t is the time at least one of its multiple waveform fragments is reproduced by the waveform generator, and ω+ε is the frequency of the intended waveform. The advantage of such a system is that the intended waveform can be approximated using at least one of its multiple waveform fragments.

[0006] According to another embodiment, a computer implementation may include a system operably coupled to a processor generating a plurality of waveform fragments using a definition of an intended waveform, wherein the plurality of waveform fragments may be phase-shifted. The computer implementation may further include the system assigning a phase rotation to apply to at least one of the plurality of waveform fragments, wherein the phase rotation is out of phase with respect to a previous waveform fragment among the plurality of waveform fragments. The advantage of such a computer implementation is that by dividing the intended waveform into a plurality of waveform fragments, an approximation of the intended waveform can be efficiently stored in memory.

[0007] In some embodiments, the computer implementation described above may further include the system assigning a phase rotation applied by the waveform generator to at least one of the multiple waveform fragments using a phase rotation coefficient 2π(ω+ε)t, where t is the time at which at least one of the multiple waveform fragments is reproduced by the waveform generator, and ω+ε is the frequency of the intended waveform. The advantage of such a computer implementation is that the intended waveform can be approximated using at least one of the multiple waveform fragments.

[0008] According to another embodiment, a computer program product includes a computer-readable storage medium on which program instructions are implemented, the program instructions being executable by a processor to cause the processor to generate a plurality of waveform fragments using a definition of an intended waveform, the plurality of waveform fragments being phase-shifted. The program instructions are further executable by the processor to cause the processor to assign a phase rotation to be applied to at least one of the plurality of waveform fragments, the phase rotation being out of phase with respect to a previous waveform fragment among the plurality of waveform fragments. The advantage of such a computer program product is that by dividing the intended waveform into a plurality of waveform fragments, an approximation of the intended waveform can be efficiently stored in memory.

[0009] In some embodiments, the program instruction can be further made executable by the processor to assign a phase rotation to be applied to at least one of the multiple waveform segments using a phase rotation coefficient 2π(ω+ε)t, where t is the time at least one of the multiple waveform segments is reproduced by the waveform generator, and ω+ε is the frequency of the intended waveform. The advantage of such a computer program product is that the intended waveform can be approximated using at least one of the multiple waveform segments.

[0010] According to one embodiment, the system may include a processor that executes computer executable components stored in memory. These computer executable components include a wave division component that generates a plurality of waveform fragments using a definition of a resource waveform, and a phase slip may be inserted between each of these plurality of waveform fragments. These computer executable components further include a phase slip component that assigns a phase slip to be inserted between at least two of these plurality of waveform fragments. The advantage of such a computer program product is that by dividing the resource waveform into a plurality of waveform fragments, an approximation of the intended waveform can be efficiently stored. [Brief explanation of the drawing]

[0011] [Figure 1A] This is a block diagram of an exemplary and non-limiting system that facilitates the operation of quantum hardware according to one or more embodiments described herein. [Figure 1B] This is a block diagram of an exemplary, non-limiting system capable of completing the execution of a quantum job, according to one or more embodiments described herein. [Figure 2] This is a block diagram of an exemplary and non-limiting system, according to one or more embodiments described herein, which facilitates efficient approximation of a range of sideband frequencies. [Figure 3] This is a block diagram of an exemplary and non-limiting system, according to one or more embodiments described herein, which facilitates efficient approximation of a range of sideband frequencies. [Figure 4] This is a block diagram of an exemplary and non-limiting system relating to the division of an intended waveform into waveform fragments and the determination of phase rotation, according to one or more embodiments described herein. [Figure 5]This is a block diagram of an exemplary and non-limiting system relating to the division of a waveform into waveform fragments and the determination of phase slip, according to one or more embodiments described herein. [Figure 6] This is a graph showing an approximated carrier waveform according to one or more embodiments described herein. [Figure 7] This is a flowchart illustrating an exemplary and non-limiting computer-aided method that facilitates efficient approximation of a range of sideband frequencies according to one or more embodiments described herein. [Figure 8] This is a flowchart illustrating an exemplary and non-limiting computer-aided method that facilitates efficient approximation of a range of sideband frequencies according to one or more embodiments described herein. [Figure 9] This is a flowchart illustrating an exemplary and non-limiting computer-aided method that facilitates efficient approximation of a range of sideband frequencies according to one or more embodiments described herein. [Figure 10] This is an exemplary and non-limiting block diagram of an operating environment that can facilitate one or more embodiments described herein. [Modes for carrying out the invention]

[0012] The following detailed description is for illustrative purposes only and is not intended to limit the embodiments, or the uses or applications of the embodiments, or both. Furthermore, it is not intended to be constrained by the express or implied information provided in the above "Background Art," "Summary of the Invention," or "Modes for Carrying Out the Invention."

[0013] Next, one or more embodiments will be described with reference to the drawings. The same reference numerals are used throughout to refer to the same elements. In the following description, for the purpose of explanation, numerous specific details are set forth to provide a more complete understanding of one or more embodiments. However, it is apparent that in various cases, one or more embodiments can be implemented without these specific details.

[0014] Quantum computing generally refers to the use of quantum-mechanical phenomena to perform computing and information processing functions. Quantum computing can generally be viewed as contrasting with classical computing, which performs operations on binary values using transistors. That is, while a classical computer can perform operations on bit values that are either 0 or 1, a quantum computer performs operations on quantum bits (qubits), which include superposition of both 0 and 1. Superposition can entangle multiple qubits and enable the use of interference. This quantum superposition allows quantum systems to store and represent large data sets that are difficult to represent with classical methods. Quantum computing has the potential to solve problems that cannot be solved, or can only be solved slowly, on classical computers due to computational complexity. In many forms of quantum computers, qubits within a quantum computer operate by using high frequencies. Accordingly, a quantum computer can receive instructions from classical input by using waveforms to manipulate qubits within the quantum computer, and then execute those instructions. Therefore, efficient waveform generation is critical for the efficient operation of a quantum computer.

[0015] A problem with existing waveform generation is that generating a series of waveforms that are completely identical except for the output frequency, such as a series of waveforms used for frequency sweeping, is extremely memory-intensive, because each waveform is represented as a series of points, or samples are generated independently and stored in classical memory. A waveform generator can then use those samples as a set of instructions on how to reproduce the waveform. The generation or production of these samples can have a significant impact on the time it takes to reproduce a series of waveforms. This is because it takes time to generate samples for the entire waveform, which requires a large amount of classical memory and computation to achieve.

[0016] Given the aforementioned problems with existing waveform generation techniques, implementing the present disclosure can provide solutions in the form of a system, computer-implemented method, computer program product, or combination thereof that address these problems. Said system, computer-implemented method, computer program product, or combination thereof can facilitate efficient approximation of a range of sideband frequencies by: generating a plurality of waveform fragments using a definition of an intended waveform, wherein the plurality of waveform fragments can be phase-shifted; assigning a phase rotation applied to at least one of the plurality of waveform fragments, wherein the phase rotation has a different phase from the preceding waveform fragment among the plurality of waveform fragments; or both. An advantage of such a system, computer-implemented method, computer program product, or combination thereof is that it can reduce the memory workload used to generate waveforms. For example, the plurality of waveform fragments can comprise identical waveform fragments. Thus, in contrast to generating samples representing the entire intended waveform, samples representing a single waveform can be generated and reused to represent the plurality of waveform fragments.

[0017] In some embodiments, the present disclosure can be implemented to produce solutions to the above-described problems in the form of systems, computer implementations, computer program products, or combinations thereof, wherein a phase rotation applied to at least one of a plurality of waveform fragments is assigned using a phase rotation coefficient 2π(ω+ε)t, where t is the time it takes for at least one of the plurality of waveform fragments to be reproduced by a waveform generator, and ω+ε is the frequency of the intended waveform, thereby further facilitating the efficient approximation of a range of sideband frequencies by assigning a phase rotation to at least one waveform fragment applied to at least one of the plurality of waveform fragments, by the waveform generator, by reproducing one or more waveform fragments with phase rotation, or both. The advantage of such systems, computer implementations, computer program products, or combinations thereof is that the intended waveform can be approximated using at least one of the plurality of waveform fragments without the need to generate and store in memory a sample representing the entire intended waveform. For example, the waveform generator can repeatedly reproduce its waveform fragment with different phase rotations each time in order to approximate the intended waveform. In this way, the waveform generator can reproduce an approximation of the intended waveform without having a sample that represents the entire intended waveform.

[0018] Referring first to Figure 1A in its entirety, one or more embodiments described herein may include one or more devices, systems, or apparatus, or both, that can facilitate the execution of one or more quantum operations to facilitate the output of one or more quantum results. For example, Figure 1A shows a block diagram of an exemplary and non-limiting system 100 that can facilitate the operation of quantum hardware.

[0019] In one or more embodiments, system 100 may include a classical computer 101, a control system 102, quantum hardware 103, or a readout system 104, or a combination thereof. The classical computer 101 may output a quantum job request to the control system 102 as a digital signal 120. Based on the digital signal 120, the control system 102 may regenerate a microwave signal via a waveform generator to facilitate the completion of the quantum job. For example, the control system 102 may regenerate a microwave signal 130 via a waveform generator to operate or manipulate a qubit in the quantum hardware 103 to execute a quantum job request. In another example, the control system 102 may regenerate a microwave signal 131 to the readout system 104 via a waveform generator. The readout system 104 may repeat the microwave signal 131 to operate or manipulate a qubit in the quantum hardware 103 to output a microwave signal 132 of the quantum state of the qubit in the quantum hardware 103. The readout system 104 can then convert the microwave signal 132 into a digital signal 121 containing the quantum state of one or more qubits in the quantum hardware 103 and send it to the classical computer 101.

[0020] Next, referring to Figure 1B in general terms, one or more embodiments described herein may include one or more devices, systems, or apparatus, or both, that can facilitate the execution of one or more quantum operations to facilitate the output of one or more quantum results. For example, Figure 1B shows a block diagram of an exemplary and non-limiting system 150 that can complete the execution of a quantum job.

[0021] A quantum system 110 (e.g., a quantum computer system, a superconducting quantum computer system, or other similar systems or combinations thereof) can perform quantum operations or functions or both on input data using quantum algorithms or quantum circuits or both, which include computing components or devices or both, to produce results that can be output to an entity. A quantum circuit may include qubits (qubits) such as multibit qubits, physical circuit-level components, high-level components or functions or combinations thereof. A quantum circuit may include physical pulses that can be constructed (e.g., arranged or designed or arranged and designed) to perform desired quantum functions or computations or both on data (e.g., input data or intermediate data derived from input data or both) to produce one or more quantum results as an output. A quantum result (e.g., a quantum measurement 113) may respond to a quantum job request 106 and associated input data and may be at least in part based on the input data, quantum functions or quantum computations or combinations thereof.

[0022] In one or more embodiments, the quantum system 110 may include one or more quantum components, such as a quantum computing component 107, a quantum processor 109, and a quantum logic circuit 111, the quantum logic circuit 111 may include one or more qubits (e.g., qubits 112A, 112B, or 112C, or a combination thereof), also referred herein as qubit devices 112A, 112B, and 112C. The quantum processor 109 can be any suitable processor, such as a processor capable of controlling qubit coherence and other similar processors. The quantum processor 109 may generate one or more instructions for controlling one or more processes of the quantum computing component 107.

[0023] The quantum computing component 107 can receive (e.g., download, receive, search for, or do other similar things, or a combination thereof) a quantum job request 106 that requests the execution of one or more quantum programs. In one example, the quantum job request 106 may be a digital signal. The quantum computing component 107 can determine one or more quantum logic circuits, such as the quantum logic circuit 111, to execute the quantum program. The request 106 can be provided in any suitable format, such as text format, binary format, or another suitable format or a combination thereof. In one or more embodiments, components other than the components of the quantum system 110, such as components of a classical system coupled to the quantum system 110, or components of a classical system communicating with the quantum system 110, or both, can receive the request 106.

[0024] The quantum computing component 107 can perform one or more quantum processes, calculations, or measurements, or combinations thereof, to operate one or more quantum circuits on one or more qubits 112A, 112B, or 112C or combinations thereof. For example, the quantum computing component 107 can operate one or more qubit effectors, such as a waveform generator 108, a qubit oscillator, a harmonic oscillator, a pulse generator, or other similar devices or combinations thereof, so that one or more pulses simulate or manipulate, or simulate and manipulate, the state of one or more qubits 112A, 112B, or 112C or combinations thereof contained in the quantum system 110. That is, the quantum computing component 107 can be used, for example, in combination with a quantum processor 109 to perform the operation of a quantum logic circuit on one or more qubits of that circuit (e.g., qubits 112A, 112B, or 112C or combinations thereof). In response to a quantum job request 106, the quantum computing component 107 can output one or more quantum job results, such as one or more quantum measurements 113.

[0025] It will be noted that the following description pertains to the operation of a single quantum program from a single quantum job request. However, it will also be noted that one or more of the processes described herein can be scalable, such as the execution of one or more quantum programs or quantum job requests or both in parallel with each other.

[0026] In one or more embodiments, the non-limiting system 150 can be a hybrid system, and thus the non-limiting system 150 can include both one or more classical systems, such as a quantum program implementation system, and one or more quantum systems, such as the quantum system 110. In one or more other embodiments, the quantum system 110 can be a system that is separate from the classical system, but can function in combination with the classical system.

[0027] In such cases, but not limited to, one or more communications between one or more components of a non-limited system 150 and one or more components of a classical system can be facilitated by wired or wireless means, or both, including the use of a cellular network, a wide area network (WAN) (e.g., the Internet), or a local area network (LAN), or a combination thereof.Suitable wired or wireless technologies to facilitate communication include, but are not limited to, Wireless Fidelity (Wi-Fi), Global System for Mobile Communications (GSM), Universal Mobile Telecommunications System (UMTS), Worldwide Interoperability for Microwave Access (WiMAX), Enhanced General Packet Radio Service (Enhanced GPRS), Third Generation Partnership Project (3GPP) Long Term Evolution (LTE), Third Generation Partnership Project 2 (3GPP2) Ultra Mobile Broadband (UMB), and High Speed ​​Packet Access. This may include HSPA (802.XX Wireless Access), Zigbee and other 802.XX wireless technologies and / or conventional telecommunications technologies, BLUETOOTH(R), Session Initiation Protocol (SIP), ZIGBEE(R), RF4CE protocol, WirelessHART protocol, 6LoWPAN (IPv6 over Low power Wireless Area Networks), Z-Wave, ANT, ultra-wideband (UWB) standard protocols, and / or other dedicated and non-dedicated communication protocols.

[0028] Figures 2 and 3 show exemplary and non-limiting block diagrams of systems 200 and 300, respectively, which can facilitate the efficient approximation of a range of sideband frequencies to support the operation of quantum system 110 according to one or more embodiments described herein. Systems 200 and 300 can each include a quantum computing component 107 of quantum system 110. The quantum computing component 107 can include a waveform approximation system 201. In one embodiment, the quantum computing component 107 can receive a quantum job request 106. Based on the quantum job request 106, the quantum computing component 107 can compute, simulate or manipulate the state of one or more qubits, such as qubits 112A, 112B, or 112C or a combination thereof, or define a waveform to be used by a waveform generator to compute, simulate and manipulate, in order to facilitate the execution of the quantum job request 106. For example, the quantum computing component 107 can provide the waveform approximation system 201, as input, with a definition of an intended waveform. The waveform approximation system 201 can generate one or more samples or instructions, or both, which, when provided to the waveform generator 108, cause the waveform generator 108 to reproduce an approximation of a defined waveform in order to operate the qubits 112A, 112B, or 112C, or a combination thereof. The waveform approximation system 201 may include a memory 202, a processor 203, a wave division component 204, a rotation component 205, or a bus 206, or a combination thereof. The waveform approximation system 201 of system 300 shown in Figure 3 may further include a phase slip component 308.

[0029] The embodiments of the subject disclosure shown in the various figures disclosed herein are for illustrative purposes only, and it should be recognized that the architecture of such embodiments is not limited to the systems, devices, or components or combinations thereof shown in those figures. For example, in some embodiments, System 100, System 150, System 200, System 300, or Waveform Approximation System 201 or a combination thereof may further include various computer elements or computing-based elements or both described herein in relation to the operating environment 1000 of Figure 10. In some embodiments, such computer elements or computing-based elements or both may be used in relation to one or more implementations of the systems, devices, components, or computer operations or combinations thereof illustrated and described in relation to Figure 1A, Figure 1B, Figure 2, Figure 3, or other figures disclosed herein or a combination thereof.

[0030] Memory 202 can store one or more components or instructions or both that can be read, written to, or executed by a computer or a machine or both, or a combination thereof, and which, when executed by a processor 203 (e.g., a classical processor, a quantum processor or another type of processor or a combination thereof), facilitate the execution of operations defined by the executable components or instructions or both. For example, memory 202 can store one or more components or instructions or both that can be read, written to, or executed by a computer or a machine or both, or a combination thereof, and which, when executed by a processor 203, facilitate the execution of various functions described herein relating to the waveform approximation system 201, the wave division component 204, the rotation component 205, the waveform generator 108, the phase slip component 308, or another component related to the waveform approximation system 201, or a combination thereof, described herein with or without reference to various figures of the subject disclosure.

[0031] Memory 202 may include volatile memory (e.g., random-access memory (RAM), static RAM (SRAM), dynamic RAM (DRAM), or other types of volatile memory, or a combination thereof) or non-volatile memory (e.g., read-only memory (ROM), programmable ROM (PROM), erasable programmable ROM (EPROM), electrically erasable programmable OM (EEPROM), or other types of non-volatile memory, or a combination thereof), or both, and such volatile memory or non-volatile memory, or both, may use one or more memory architectures. Additional examples of memory 202 are described below with respect to system memory 1016 in Figure 10. Any embodiment of the subject disclosure can be carried out using such examples of memory 202.

[0032] The processor 203 may include one or more types of processors or electronic circuits (e.g., classical processors and / or other types of processors and / or electronic circuits) that can implement one or more components or instructions or both that can be read, written to, or executed by a computer or machine or both, or a combination thereof, and which can be stored in memory 202. For example, the processor 203 may perform a variety of operations that can be specified by such components or instructions or both that can be read, written to, or executed by a computer or machine or both, or a combination thereof, and such operations may include, but are not limited to, logic, control, input / output (I / O), arithmetic operations, or other operations or combinations thereof. In some embodiments, the processor 203 may include one or more central processing units, multicore processors, microprocessors, dual microprocessors, microcontrollers, systems on a chip (SOC), array processors, vector processors, quantum processors, or other types of processors, or combinations thereof. Additional examples of the processor 203 are described below with respect to the processing unit 1014 in Figure 10. Any embodiment of the subject disclosure can be carried out using such an example of processor 203.

[0033] To perform the functions of System 100, System 150, System 200, System 300, Waveform Approximation System 201, or components coupled thereto, or combinations thereof, Waveform Approximation System 201, Memory 202, Processor 203, Wave Division Component 204, Rotation Component 205, Waveform Generator 108, Phase Slip Component 308, or other components of Waveform Approximation System 201 as described herein, or combinations thereof, may be coupled to one another via Bus 206, in a communicative, electrically, operably, or optically, or in combination thereof. Bus 206 may include one or more memory buses, memory controllers, peripheral buses, external buses, local buses, quantum buses, or other types of buses, or combinations thereof, and these buses may use a variety of bus architectures. Additional examples of Bus 206 are described below with respect to System Bus 1018 in Figure 10. Any embodiment of the subject disclosure can be carried out using such examples of Bus 206.

[0034] The waveform approximation system 201 may include any type of component, machine, device, equipment, apparatus and / or instrument, including a processor, and / or be able to communicate effectively and / or operably with wired and / or wireless networks. All such embodiments are envisioned. For example, the waveform approximation system 201 may include server devices, computing devices, general-purpose computers, dedicated computers, tablet computing devices, handheld devices, server-class computing machines and / or databases, laptop computers, notebook computers, desktop computers, mobile phones, smartphones, consumer equipment and / or instruments, industrial and / or commercial devices, digital assistants, internet-enabled multimedia telephones, multimedia players and / or other types of devices.

[0035] The waveform approximation system 201 can be coupled to one or more external systems, sources, or devices or combinations thereof (e.g., classical and / or quantum computing devices, communication devices, and / or other types of external systems, sources, and / or devices) using wires, cables, or both (e.g., communicatively, electrically, operationally, optically, or by other types of coupling, or in combination thereof). For example, the waveform approximation system 201 can be coupled to one or more external systems, sources, or devices or combinations thereof (e.g., classical and / or quantum computing devices, communication devices, and / or other types of external systems, sources, and / or devices) using data cables including, but not limited to, High-Definition Multimedia Interface (HDMI(R)) cables, recommended standard (RS)232 cables, Ethernet(R) cables, or other data cables, or combinations thereof (e.g., communicatively, electrically, operationally, optically, or by other types of coupling, or in combination thereof) using wires, cables, or both.

[0036] In some embodiments, the waveform approximation system 201 can be coupled via a network to one or more external systems, sources, or devices or combinations thereof (e.g., classical and / or quantum computing devices, communication devices, and / or other types of external systems, sources, and / or devices) (e.g., by communication, electrical, operational, optical, or other types of coupling, or by combinations thereof). For example, such a network may include, but is not limited to, a wired network or a wireless network including a cellular network, a wide area network (WAN) (e.g., the Internet), or a local area network (LAN), or a combination thereof, or both. The waveform approximation system 201 can communicate with one or more external systems, sources, or devices, such as computing devices, or a combination thereof, using substantially any desired wired or wireless technology or both, and this substantially any desired wired and wireless technology includes, but is not limited to, Wireless Fidelity (Wi-Fi), Global System for Mobile Communications (GSM), Universal Mobile Telecommunications System (UMTS), Worldwide Interoperability for Microwave Access (WiMAX), Enhanced General Packet Radio Service (Enhanced GPRS), Third Generation Partnership Project (3GPP), and Long Term Evolution.This includes LTE (LTE evolution), Third Generation Partnership Project 2 (3GPP2) Ultra Mobile Broadband (UMB), High Speed ​​Packet Access (HSPA), Zigbee and other 802.XX radio technologies and / or conventional telecommunications technologies, BLUETOOTH(R), Session Initiation Protocol (SIP), ZIGBEE(R), RF4CE protocol, WirelessHART protocol, 6LoWPAN (IPv6 over Low Power Wireless Area Networks), Z-Wave, ANT, Ultra-Wideband (UWB) standard protocols, and / or other dedicated and non-dedicated communication protocols. Therefore, in some embodiments, the waveform approximation system 201 may include hardware (e.g., a central processing unit (CPU), transceivers, decoders, quantum hardware, quantum processors, or other hardware or combinations thereof), software (e.g., a set of threads, a set of processes, running software, quantum pulse schedules, quantum circuits, quantum gates, or other software or combinations thereof), or a combination of hardware and software, which can facilitate information transfer between the waveform approximation system 201 and external systems, sources, or devices or combinations thereof (e.g., computing devices, communication devices, and / or other types of external systems, sources, and / or devices).

[0037] The waveform approximation system 201 may include one or more components or instructions or both that can be read, written to, or executed by a computer or a machine or both, or a combination thereof, and which, when executed by a processor 203 (e.g., a classical processor or another type of processor or a combination thereof), facilitate the execution of operations defined by such components or instructions or both. Furthermore, in many embodiments, any components related to the waveform approximation system 201 described herein with or without reference to various figures of the subject disclosure may include one or more components or instructions or both that can be read, written to, or executed by a computer or a machine or both, or a combination thereof, and which, when executed by a processor 203, facilitate the execution of operations defined by such components or instructions or both. For example, a wave splitting component 204, a rotation component 205, a waveform generator 108, a phase slip component 308, or other components disclosed herein relating to the waveform approximation system 201, or combinations thereof, (e.g., coupled communicatively, electronically, operably and / or optically to the waveform approximation system 201, and / or used communicatively, electronically, operably and / or optically by the waveform approximation system 201) may include multiple such components or instructions, or both, that can be read, written to, or executed, or a combination thereof, by a computer or a machine or both.As a result, according to many embodiments, the waveform approximation system 201 or any component disclosed herein related to the waveform approximation system 201, or both, can use the processor 203 to execute such components or instructions, or both, that a computer or machine or both can read, write to, or execute, or a combination thereof, in order to facilitate the execution of one or more operations described herein with respect to the waveform approximation system 201 or any component related to the waveform approximation system 201, or both.

[0038] The waveform approximation system 201 can facilitate the execution (e.g., by the processor 203) of operations performed by the wave division component 204, the rotation component 205, the waveform generator 108, the phase slip component 308, and / or any other components disclosed herein related to the waveform approximation system 201, as well as operations related to the wave division component 204, the rotation component 205, the waveform generator 108, the phase slip component 308, and / or any other components disclosed herein related to the waveform approximation system 201. For example, as will be explained in detail later, the waveform approximation system 201 generates multiple waveform fragments, which may be phase-shifted; assigns a phase rotation to be applied to at least one of the multiple waveform fragments during playback using a phase rotation coefficient 2π(ω+ε)t, where t is the time during which at least one waveform fragment is played back, and ω+ε is the frequency of the intended waveform, such that the phase rotation is out of phase with a previous waveform fragment among the multiple waveform fragments; or facilitates playback of at least one of the multiple waveform fragments with a phase rotation by a waveform generator; or facilitates a combination of these.

[0039] The wave splitting component 204 can generate multiple waveform fragments, and these waveform fragments may be phase-shifted. As used herein, “intended waveform” is the waveform that the waveform generator 108 reproduces as an approximation of that waveform, and “waveform fragment” is a small portion of the waveform. Furthermore, as used herein, “sample” is a numerical data point that can be used to represent a waveform. In one embodiment, the wave splitting component 204 may receive a definition of the intended waveform. For example, as described above, the quantum computing component 107 may receive a quantum job request 106. Based on the quantum job request 106, the quantum computing component 107 may define an intended waveform to be reproduced to operate or activate or manipulate qubits 112A, 112B, or 112C or a combination thereof in order to execute the quantum job request 106. The quantum computing component 107 then uses the intended waveform to

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[0040] In one embodiment, the intended waveform can be a frequency sweep. As described herein, a frequency sweep is a series of waveforms that are identical except for having different output frequencies. For example, the quantum computing component 107 can define a frequency sweep as a series of definitions of the intended waveform. Therefore, given an intended frequency sweep containing two intended waveforms, the quantum computing component 107 can define the first waveform as

number

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[0041] In one embodiment, the wave splitting component 204 can determine the length τ of a waveform fragment based on the accuracy of the approximation. For example, the smaller the length τ of the waveform fragment, the more accurate the approximation. Therefore, if a high level of accuracy of the waveform approximation is required for the execution of the quantum job request 106, the wave splitting component can generate a waveform fragment of small length τ. If a lower level of accuracy of the waveform approximation is required for the execution of the quantum job request 106, the wave splitting component 204 can generate a waveform fragment of long length τ. In one embodiment, the wave splitting component 204 can receive, as input, the intended level of accuracy of the approximation, the length τ, or both, from the quantum computing component 107.

[0042] In another embodiment, the wave splitting component 204 can determine the length of a waveform fragment based on the wavelength of the intended waveform. For example, if the quantum computing component 107 defines an intended waveform that is intended to be replayed over two wavelengths, the wave splitting component 204 can generate a waveform fragment of length τ equal to one wavelength, and thus the wave splitting component 204 can generate multiple waveform fragments by defining the number of times to replay that waveform fragment, which in this case is defined as two times. It should be noted that the wave splitting component 204 can generate waveform fragments of any length τ. For example, τ may be shorter or longer than the wavelength of the intended waveform.

[0043] It should be recognized that the wave splitting component 204 can improve waveform generation by generating samples of waveform fragments that can be phase-shifted. For example, instead of generating a sample that represents the entire series of waveforms in a frequency sweep, the wave splitting component 204 can generate multiple waveform fragments using a sample of a single waveform fragment generated from the definition of the first waveform in the series of waveforms in the frequency sweep, and the number of times that waveform fragment is reused. In this example, by performing the generation operation described above, the wave splitting component 204 can reduce the memory usage and / or time associated with the generation of the frequency sweep by allowing a single waveform fragment to represent multiple waveform fragments in memory, rather than generating a sample of the entire series of waveforms exactly the same. In this example, the wave splitting component 204 can improve such a waveform approximation process by reducing the memory usage and / or time associated with waveform approximation.

[0044] The rotation component 205 can assign a phase rotation to be applied to at least one of its multiple waveform fragments, such that this phase rotation is out of phase with respect to previous waveform fragments among those multiple waveform fragments. For example, the rotation component 205 can assign a phase rotation using a constant complex multiplier that allows the waveform generator 108 to phase rotate the waveform fragment to an appropriate starting phase. For example, if the intended wave envelope is a sidebanded square pulse at a normalized frequency ω = 1 / 64 (i.e., 64 samples are used to represent the wavelength), the rotation component 205 can use a phase rotation coefficient 2πωt, where t is the time at which the waveform fragment is regenerated to assign a phase rotation to be used by the waveform generator 108 during regeneration. In this example, the rotation component 205 can assign a phase rotation to be applied to at least one of its multiple waveform fragments during regeneration. For example, given an intended waveform defined by the quantum computation component 107, where the wave splitting component 204 has generated multiple waveform fragments containing four identical waveform fragments, the rotation component 205 can assign a phase rotation of 0 (complex multiplier 1+0j) to the first waveform fragment, a phase rotation of π / 2 (complex multiplier 0+1) to the second waveform fragment, a phase rotation of π (complex multiplier -1+0j) to the third waveform fragment, and a phase rotation of 3π / 2 (complex multiplier 0-1j) to the fourth waveform fragment. These multiple waveform fragments and the corresponding sequence of phase rotations can then be passed to the waveform generator 108. For example, the waveform generator 108 can use samples representing the waveform fragments stored in memory to regenerate the first waveform fragment with a phase rotation of 0. The waveform generator 108 can then use samples representing the waveform fragments in memory to regenerate the second waveform fragment with a phase rotation of π / 2. The waveform generator 108 can then reproduce the third and fourth waveform fragments with corresponding third and fourth phase rotations.By sequentially reproducing these four waveform fragments with corresponding phase rotations, the waveform generator 108 can reproduce an approximation of the intended waveform to operate or manipulate qubits 112A, 112B, or 112C or any combination thereof to execute the quantum job request 106. As described above, when the wave division component 204 generates waveform fragments based on the definition of the intended waveform, the wave division component 204 can store a sample of a single waveform fragment, and that single waveform fragment can be used to represent each of the waveforms among those multiple waveform fragments used by the waveform generator 108 to generate an approximation of the intended waveform. Thus, the rotation component 205 allows the waveform generator 108 to extend the approximation of the intended waveform indefinitely and approximate a continuous waveform by enabling the waveform generator 108 to reproduce the stored single waveform fragment with a new phase rotation assigned by the rotation component 205 each time a waveform fragment is reproduced.

[0045] In another embodiment, the rotation component 205 can assign a phase rotation applied by the waveform generator 108 to at least one of the waveform fragments of its plurality of waveform fragments, so that when those waveform fragments are reproduced with the phase rotation by the waveform generator 108, they approximate a frequency sweep. As mentioned above, a frequency sweep can be described as a series of waveforms that are exactly the same except for having different output frequencies. For example, if the intended waveform defined by the quantum computing component 107 is a frequency sweep, the frequency of the intended waveform can be defined as ω+ε, where ω is the initial frequency of the frequency sweep and ε is the change in frequency. If the intended waveform is a frequency sweep, the rotation component 205 can assign a phase rotation using a phase rotation coefficient 2π(ω+ε)t, where ω is the initial frequency of the frequency sweep (e.g., the frequency of the first waveform in the series of waveforms), ε is the change in frequency, and t is the time over which the waveform fragments are reproduced by the waveform generator 108. If the wave splitting component 204 generates multiple waveform fragments, each containing four identical waveform fragments, the rotation component 205 can assign a phase rotation to the first waveform fragment using a first ε value in the rotation coefficient, to the second waveform fragment using a second ε value in the rotation coefficient, to the third waveform fragment using a third ε value, and to the fourth waveform fragment using a fourth ε value. The rotation component 205 can then pass these multiple waveform fragments and their corresponding phase rotations to the waveform generator 108.

[0046] In one embodiment, the ε value can be determined based on the frequency difference between the first waveform and the current waveform in a series of waveforms representing a frequency sweep. For example, an intended frequency sweep involving two waveforms is performed by the quantum computing component 107.

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[0047] In this example, by changing the ε value when assigning a phase rotation, the rotation component 205 can assign a phase rotation that allows the waveform generator 108 to reproduce waveform fragments at different frequencies. In one embodiment, the rotation component 205 can use different ε values ​​to assign different phase rotations that the waveform generator 108 applies each time the waveform generator 108 reproduces a waveform fragment. In another embodiment, if a large number of waveform fragments among those multiple waveform fragments are reproduced by the waveform generator 108 at the same output frequency, the rotation component 205 can use the same ε value to assign a phase rotation to those multiple waveform fragments.

[0048] In one embodiment, the rotation component 205 can assign a phase rotation to at least one of its multiple waveform fragments that is applied by the waveform generator 108 before playback. For example, if the wave splitting component generates multiple waveform fragments, each containing four identical waveform fragments, the rotation component 205 can assign the corresponding phase rotation to those multiple waveform fragments and pass those multiple waveform fragments and their corresponding phase rotations to the waveform generator 108. In another embodiment, the rotation component 205 can assign a phase rotation to be applied to the waveform fragments by the waveform generator during playback. For example, the wave splitting component 204 can pass its multiple waveform fragments to the waveform generator 108. The waveform generator 108 can then request a phase rotation to be played back along with a first waveform fragment of those multiple waveform fragments. The rotation component 205 can assign the phase rotation as described above and pass that phase rotation to the waveform generator 108. The waveform generator 108 can then play back the first waveform fragment with the phase rotation. The waveform generator 108 can then request a phase rotation to be played back along with the second waveform fragment of those multiple waveform fragments. This process can continue until the waveform generator 108 has finished playing back all the waveform fragments within those multiple waveform fragments.

[0049] For example, if the waveform segment is reproduced four times by the waveform generator 108, the rotation component 205 can provide the waveform generator 108 with a phase rotation to apply before each reproduction of the waveform segment.

[0050] It should be recognized that by assigning phase rotations to waveform fragments as described above, the rotation component 205 can improve its efficiency in approximating waveforms. For example, by assigning phase rotations with different frequencies to each identical waveform fragment, the waveform generator 108 can reconstruct an approximation of the frequency sweep using a single waveform fragment and a series of phase rotations, rather than using a sample representing the entire frequency sweep. In this example, since the frequency sweep can be stored as a single waveform fragment and a series of phase rotations rather than as a sample of the entire frequency sweep, the rotation component 205 can reduce the storage used to reconstruct the frequency sweep approximation. By reducing storage usage (e.g., memory usage), the rotation component 205 can improve its efficiency in waveform approximation.

[0051] The waveform generator 108 can reproduce at least one of the multiple waveform fragments with a phase rotation. For example, the waveform generator 108 can receive multiple waveform fragments from the wave division component 204 and one or more phase rotations from the rotation component 205. As described above, these multiple waveform fragments can contain exactly the same waveform fragment. Therefore, these multiple waveform fragments can be represented as a single waveform fragment and the number of times that single waveform fragment is reproduced. In this example, if the waveform generator 108 receives multiple waveform fragments containing four waveform fragments and four corresponding phase rotation coefficients, the waveform generator can reproduce the first waveform fragment with a first phase rotation, the second waveform fragment with a second phase rotation, the third waveform fragment with a third phase rotation, and the fourth waveform fragment with a fourth phase slip. By sequentially reproducing four identical waveform fragments with corresponding phase rotations, the waveform generator 108 can reproduce an approximation of the intended waveform defined by the quantum computing component 107, and thus can operate or manipulate qubits 112A, 112B, or 112C or any combination thereof to execute the quantum job request 106.

[0052] In another embodiment, the waveform generator 108 can receive multiple waveform fragments and request phase rotations from the rotation component 205. For example, if the waveform generator 108 receives multiple waveform fragments, including four waveform fragments, the waveform generator can request a phase rotation for the first waveform fragment from the rotation component 205. After the waveform generator 108 receives the phase rotation from the rotation component 205, the waveform generator 108 can regenerate the first waveform fragment with this phase rotation. The waveform generator 108 can then request a second phase rotation for the second waveform fragment. After the waveform generator 108 receives the second phase rotation, the waveform generator 108 can regenerate the second waveform fragment with the second phase rotation. This process can be repeated until the waveform generator 108 has finished regenerating all of those multiple waveform fragments. The waveform generator 108 may be a signal generator, function generator, high-frequency generator, microwave signal generator, digital pattern generator, frequency generator, pitch generator, arbitrary waveform generator, or any other form of electronic test equipment capable of outputting a waveform, or a combination thereof.

[0053] In some embodiments, the present disclosure can be implemented to produce solutions to the above-mentioned problems in the form of a system, a computer implementation, a computer program product, or a combination thereof, which generate a plurality of waveform fragments, in which a phase slip may be inserted before each of the plurality of waveform fragments, which can further facilitate the efficient approximation of a range of sideband frequencies by generating, assigning a phase slip to be inserted before at least one of the plurality of waveform fragments, or by reproducing a phase slip and at least one of the plurality of waveform fragments, or a combination thereof.

[0054] In one embodiment, the wave division component 204 can generate waveform fragments of a resource waveform. For example, the wave division component 204 may receive a definition of an intended waveform from the quantum computing component 107 as

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[0055] In these examples, by assigning phase slips along with phase jumps to be inserted before each waveform segment each time it is played back, the phase slip component 308 can enable the waveform generator 108 to play back an approximation of the intended waveform using the waveform segments of the resource waveform and one or more phase slips.

[0056] Using the definitions of phase slip and phase jump, approximate the signal.

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[0057] It should be recognized that the phase slip component 308 can improve waveform generation by using a sawtooth phase jump function by allocating a phase slip to be inserted by the waveform generator 108 before reproducing waveform fragments. Since the sawtooth function is relatively easy to compute, the phase slip component 308 can enable the waveform generator 108 to efficiently reproduce an approximation of the intended waveform without the need to generate and store samples of the entire intended waveform in memory. As mentioned above, existing waveform generation techniques are highly memory-intensive, and by enabling the waveform generator 108 to reproduce an approximation of the intended waveform using waveform fragments of a resource waveform, the phase slip component 308 can improve waveform generation and reproduction by reducing the storage operation associated with waveform generation and reproduction.

[0058] Figure 4 shows a block diagram of an exemplary, non-limiting system related to waveform segment generation and phase rotation assignment according to one or more embodiments described herein. For brevity, repeated descriptions of the same elements used in other embodiments described herein have been omitted.

[0059] System 400 includes a wave division component 204 of the waveform approximation system 201. The wave division component 204 can receive the definition of the intended waveform 401 from the quantum computing component 107. The wave division component 204 can generate multiple waveform fragments by generating a sample of a single waveform fragment and the number of times to replay that waveform fragment. Since these multiple waveform fragments include the same waveform fragment that is used repeatedly, the wave division component 204 can store a single waveform fragment 402 that is used repeatedly for each of these multiple waveform fragments. The rotation component 205 can assign a series of phase rotations that the waveform generator 108 applies to the waveform fragment each time the waveform fragment is replayed. The sample representing the waveform fragment 402, the number of times to replay the waveform fragment, and the series of phase rotations 403 can then be passed to the waveform generator 108. The waveform generator 108 can then use waveform fragments and a series of phase rotations, as described with reference to Figure 2, to operate or manipulate or operate qubits 112A, 112B, or 112C or a combination thereof to execute the quantum job request 106, thereby reproducing an approximation of the intended waveform. It should be noted that by performing these operations, frequency sweep generation efficiency can be improved by generating a single waveform fragment and assigning a series of phase rotations, rather than generating a sample that represents the entire intended waveform.

[0060] Figure 5 shows a block diagram of an exemplary, non-limiting system related to waveform fragment generation and phase slip assignment according to one or more embodiments described herein. For brevity, repeated descriptions of the same elements used in other embodiments described herein have been omitted.

[0061] System 500 includes a wave division component 204 of the waveform approximation system 201. The wave division component 204 can receive a definition of a resource waveform 501. The wave division component 204 can generate multiple waveform fragments by generating samples of a single waveform fragment 502 and the number of times the waveform generator 108 will replay that waveform fragment. Since the single waveform fragment 502 is reused to represent these multiple waveform fragments, the wave division component 204 can store samples representing the waveform fragment 502 to be used repeatedly for each of these multiple waveform fragments. The phase slip component 308 can receive a definition of the intended waveform 504 to be approximated from the quantum computation component 107. The phase slip component 308 can assign a series of phase slips and phase jumps to be inserted between the waveform fragments of these multiple waveform fragments by the waveform generator 108. The samples representing the waveform fragment 502, the number of times the waveform fragment is replayed, and the series of phase slips and phase jumps 503 can then be passed to the waveform generator 108. The waveform generator 108 can then use the waveform fragment 502 and a series of phase slips and phase jumps, as described with reference to Figure 3, to operate or manipulate or operate the qubits 112A, 112B, or 112C or a combination thereof to execute the quantum job request 106, thereby reproducing an approximation of the intended waveform. It should be noted that by performing these operations, the frequency sweep generation efficiency can be improved by generating a single waveform fragment and assigning a series of phase slips, rather than generating a sample that represents the entire intended waveform.

[0062] Figure 6 shows graph 600 relating to the carrier of the approximated waveform according to one or more embodiments described herein. For brevity, descriptions of the repetition of the same elements or processes, or both, used in each corresponding embodiment have been omitted. As described above, the phase slip component 308 approximates the signal

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[0063] Figure 7 shows a flowchart of an exemplary, non-limiting computer implementation 700 that facilitates efficient approximation of a range of sideband frequencies according to one or more embodiments described herein. For brevity, descriptions of repeated elements or processes, or both, used in the corresponding embodiments have been omitted.

[0064] In 701, the computer implementation method 700 may include generating multiple waveform fragments by generating single waveform fragments using an intended waveform definition and the number of times to regenerate a single waveform fragment, via a system operably coupled to a processor (e.g., processor 203) (e.g., via a waveform approximation system 201 or a wave division component 204 or both).

[0065] In 702, the computer implementation method 700 may include, by its system (e.g., via a waveform approximation system 201 or a rotation component 205 or both), assigning a phase rotation applied by a waveform generator (e.g., waveform generator 108) to at least one of the plurality of waveform fragments, wherein the phase rotation is out of phase with respect to a previous waveform fragment of the plurality of waveform fragments.

[0066] In 703, the computer implementation method 700 may include using a waveform generator (e.g., waveform generator 108) to reproduce at least one of the plurality of waveform fragments with an assigned phase rotation.

[0067] Figure 8 shows a flowchart of an exemplary, non-limiting computer implementation 800 that facilitates efficient approximation of a range of sideband frequencies according to one or more embodiments described herein. For brevity, descriptions of repeated elements or processes, or both, used in the corresponding embodiments have been omitted.

[0068] In 801, the computer implementation method 800 may include generating multiple waveform fragments by generating single waveform fragments using a definition of an intended waveform and the number of times to regenerate a single waveform fragment, via a system operably coupled to a processor (e.g., processor 203) (e.g., via a waveform approximation system 201 or a wave division component 204 or both).

[0069] In 802, the computer implementation method 800 may include assigning different phase rotations to each of the multiple waveform fragments applied by a waveform generator (e.g., waveform generator 108) using a phase rotation coefficient 2π(ω+ε)t, by its system (e.g., via the waveform approximation system 201 or the rotation component 205 or both), where a different ε value is used for each of the multiple waveform fragments. In this example, as described above with reference to Figures 1 and 2, the approximated waveforms can be stored as a single waveform fragment used repeatedly to represent each of the multiple waveform fragments, and as corresponding phase rotations applied to each of the two or more waveform fragments.

[0070] In 803, the computer implementation method 800 may include having a waveform generator (e.g., waveform generator 108) reproduce at least one of the plurality of waveform fragments with an assigned phase rotation. For example, as described above with reference to Figures 2 and 3, the waveform generator 108 can reproduce an approximation of a frequency sweep by reproducing the plurality of waveform fragments with different phase rotations for different waveform fragments among the plurality of waveform fragments. This is because different waveform fragments among the plurality of waveform fragments have different output frequencies, as different phase rotations are applied to different waveform fragments by the waveform generator 108 when it reproduces each waveform fragment.

[0071] Figure 9 shows a flowchart of an exemplary, non-limiting computer implementation 900 that facilitates efficient approximation of a range of sideband frequencies according to one or more embodiments described herein. For brevity, descriptions of repeated elements or processes, or both, used in the corresponding embodiments have been omitted.

[0072] In 901, the computer implementation method 900 may include generating multiple waveform fragments by a system operably coupled to a processor (e.g., processor 203) (e.g., via a waveform approximation system 201 or a wave division component 204 or both) by generating a single waveform fragment using a definition of a resource waveform and a number of times to regenerate a single waveform fragment. For example, as described above with reference to Figure 3, the waveform approximation system 201 can manipulate the waveform fragments to approximate an intended signal by generating a waveform fragment of a resource signal which may have a phase slip inserted before the waveform fragment by a waveform generator (e.g., waveform generator 108).

[0073] In 902, the computer implementation method 900 may include assigning a phase slip to be inserted by the waveform generator before at least one of the multiple waveform fragments by its system (e.g., via the waveform approximation system 201 or the phase slip component 308 or both). For example, as described in detail above with reference to Figure 3, the phase slip component 308 defines the phase slip to be inserted by the waveform generator (e.g., waveform generator 108).

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[0074] In 903, the computer implementation method 900 may include reproducing a phase slip and at least one waveform fragment from among a plurality of waveform fragments using a waveform generator (e.g., waveform generator 108).

[0075] The waveform approximation system 201 can be associated with various technologies. For example, the waveform approximation system 201 can be associated with quantum technology, RF technology, microwave technology, spectroscopic technology, or other technologies or combinations thereof.

[0076] The waveform approximation system 201 can provide technical improvements to systems, devices, components, operation steps or processing steps, or combinations thereof, related to the various technologies identified above. For example, the waveform approximation system 201 can use waveform fragments of a resource waveform to generate an approximation of an intended waveform. In this example, the waveform approximation system 201 can generate multiple waveform fragments using a single waveform fragment generated using the definition of the resource waveform. The waveform approximation system 201 can further assign a phase slip to be inserted by the waveform generator (e.g., waveform generator 108) before each waveform fragment when the waveform fragment is reproduced by the waveform generator. In this example, the waveform approximation system 201 can reproduce an approximation of an intended waveform via the waveform generator. In another example, the waveform approximation system 201 can generate waveform fragments using the definition of an intended waveform. The waveform approximation system 201 can assign a phase rotation to be applied to the waveform fragment by the waveform generator (e.g., waveform generator 108) each time the waveform generator reproduces a waveform fragment. In one embodiment, the phase rotation applied by the waveform generator can differ each time a waveform fragment is regenerated so that the output waveform approximates the intended waveform.

[0077] The waveform approximation system 201 can provide technical improvements to the memory units associated with the waveform approximation system 201. For example, by generating a single waveform segment for repeated use, a waveform generator (e.g., waveform generator 108) can reconstruct an approximation of the frequency sweep using phase rotation or phase slip without needing to generate a sample representing the entire frequency sweep in memory, thereby reducing the use of a memory unit (e.g., memory 202). In these examples, by reducing the use of such memory units (e.g., memory 202), the waveform approximation system 201 can thereby facilitate improvements in performance, efficiency, or computational costs associated with such memory units, or a combination thereof.

[0078] Furthermore, by reducing the use of memory units, the waveform approximation system 201 can provide technical improvements to the operation of the quantum system. For example, by reducing the use of memory units and the number of memory operations performed when generating waveforms to operate the quantum system, waveform generation can be performed more quickly, thereby enabling faster operation of the quantum system. In addition, by reducing the use of memory units, the waveform approximation system 201 can enable the use of smaller memory units or memory units with lower manufacturing costs when generating waveforms.

[0079] Since the various operations that can be performed by the waveform approximation system, its components, or both described herein are operations beyond human intelligence, it should be recognized that the waveform approximation system 201 can utilize various combinations of electrical components, mechanical components, and circuits that cannot be replicated by human intelligence or performed by humans. For example, the amount of data processed by the waveform approximation system 201 over a period of time, the rate at which such data is processed, or the type of data may be greater than the amount, faster than the rate at which human intelligence can process it, or different from the type of data that human intelligence can process, over the same period of time.

[0080] According to some embodiments, the waveform approximation system 201 may also be fully operable to perform one or more other functions (e.g., a fully powered-on function, a fully executed function, or other functions or a combination thereof) while performing the various operations described herein. It should be recognized that such simultaneous multi-operation execution exceeds human intelligence. It should also be recognized that the waveform approximation system 201 may contain information that is impossible for entities such as human users to obtain manually. For example, the type, quantity, or variety of information contained in the waveform approximation system 201, the wave division component 204, the rotation component 205, the waveform generator 108, or the phase slip component 308, or a combination thereof, may be more complex than information obtained manually by an entity such as a human user.

[0081] The waveform approximation system 201 can use hardware or software to solve problems that are, in their nature, highly technical, not abstract, and cannot be performed as a set of human mental actions. In some embodiments, one or more processes among those described herein can be performed by one or more dedicated computers (e.g., dedicated processing units, dedicated classical computers, dedicated quantum computers, or other types of dedicated computers) to perform defined tasks relating to the various technologies identified above. The waveform approximation system 201 or its components or both can be used to solve new problems arising from the use of the aforementioned technological advancements, quantum computing systems, cloud computing systems, computer architectures, or other technologies or combinations thereof.

[0082] For the sake of simplicity, these computer implementation methodologies are presented and described as a series of operations. It should be understood and recognized that the innovations of the subject matter are not limited by the operations presented, or by the order of the operations, or both. For example, the operations can be performed in various orders, simultaneously, or both, and in conjunction with other operations not presented herein and not described herein. Furthermore, not all of the operations presented are necessary to implement a computer implementation methodology in accordance with the disclosed subject matter. Additionally, those skilled in the art will understand and recognize that, as an alternative, a computer implementation methodology can be represented as a series of interconnected states, such as by a state diagram or events. Furthermore, it should be recognized that the computer implementation methodologies disclosed below and throughout this specification can be stored on a product to facilitate the transfer and transmission of such computer implementation methodologies to a computer. As used herein, the term "product" is intended to encompass computer programs accessible from a computer-readable device or storage medium.

[0083] To provide background to various aspects of the disclosed subject matter, Figure 10 and the following discussion are intended to provide a general description of suitable environments in which various aspects of the disclosed subject matter can be carried out. Figure 10 shows a block diagram of an exemplary, non-limiting operating environment that may facilitate one or more embodiments described herein. For brevity, repeated descriptions of the same elements used in other embodiments described herein have been omitted.

[0084] Referring to Figure 10, a suitable operating environment 1000 for carrying out various aspects of the present disclosure may further include a computer 1012. The computer 1012 may further include a processing unit 1014, system memory 1016, and a system bus 1018. The system bus 1018 connects system components, including, but not limited to, system memory 1016, to the processing unit 1014. The processing unit 1014 can be any processor from a variety of available processors. Dual microprocessors and other multiprocessor architectures may also be used as the processing unit 1014. System Bus 1018 can be any bus structure among several types of bus structures, including a memory bus or memory controller, a peripheral bus or external bus, or a local bus, or a combination thereof, using any bus architecture from among the various available bus architectures, including but not limited to Industrial Standard Architecture (ISA), Microchannel Architecture (MCA), Enhanced ISA (EISA), Intelligent Drive Electronics (IDE), VESA Local Bus (VLB), Peripheral Component Interconnect (PCI), CardBus, Universal Serial Bus (USB), Advanced Graphics Port (AGP), Firewire (IEEE 1394), and Small Computer Systems Interface (SCSI).

[0085] System memory 1016 may further include volatile memory 2020 and non-volatile memory 2022. Non-volatile memory 2022 stores the Basic Input / Output System (BIOS), which includes basic routines for transferring information between elements within computer 1012, such as during startup. Computer 1012 may further include removable / non-removable volatile / non-volatile computer storage media. Figure 10 shows, for example, disk storage 1024. Disk storage 1024 may further include, but is not limited to, devices such as magnetic disk drives, floppy disk drives, tape drives, Jaz drives, Zip drives, LS-100 drives, flash memory cards, or memory sticks. Disk storage 1024 may further include storage media separate from other storage media, or combined with other storage media. To facilitate connection of disk storage 1024 to system bus 1018, removable or non-removable interfaces, such as interface 1026, are typically used. Figure 10 further illustrates software that acts as an intermediary between the basic computer resources described in a suitable operating environment 1000 and the user. Such software may further include, for example, an operating system 1028. The operating system 1028, which can be stored in disk storage 1024, functions to control and allocate the resources of computer 1012.

[0086] The system application 1030 utilizes resource management by the operating system 1028 via program modules 1032 and program data 1034 stored, for example, in system memory 1016 or disk storage 1024. It should be recognized that this disclosure can be implemented using various operating systems or combinations of operating systems. The user inputs commands or information to the computer 1012 via an input device 1036. The input device 1036 includes, but is not limited to, pointing devices such as a mouse, trackballs, styluses, touchpads, keyboards, microphones, joysticks, gamepads, satellite antennas, scanners, TV tuner cards, digital cameras, digital video cameras, and webcams. These and other input devices connect to the processing unit 1014 via an interface port 1038 and through the system bus 1018. The interface port 1038 includes, for example, a serial port, a parallel port, a game port, and a Universal Serial Bus (USB). Output device 1040 uses several ports of the same type as input device 1036. Therefore, for example, a USB port can be used to provide input to computer 1012, and information can be output from computer 1012 to output device 1040. An output adapter 1042 is provided to indicate that some output devices 1040 require dedicated adapters, such as monitors, speakers, and printers. For example, output adapter 1042 includes, but is not limited to, video cards and sound cards that provide means of connection between output device 1040 and system bus 1018. It should be noted that other devices or device systems, or both, such as remote computer 1044, provide both input and output capabilities.

[0087] Computer 1012 can operate in a networked environment using logical connections to one or more remote computers, such as remote computer 1044. Remote computer 1044 can be a computer, server, router, network PC, workstation, microprocessor-based device, peer device, or other common network node, and typically also include many or all of the elements described for computer 1012. For brevity, only a memory storage device 1046 is shown for remote computer 1044. Remote computer 1044 is logically connected to computer 1012 via network interface 1048, and then physically connected via communication connection 1050. Network interface 1048 includes wired and / or wireless communication networks such as local area networks (LANs), wide area networks (WANs), cellular networks, and / or other wired and / or wireless communication networks. LAN technologies include fiber optic distributed data interfaces (FDDI), copper distributed data interfaces (CDDI), Ethernet, Token Ring, and others. WAN technologies include, but are not limited to, point-to-point links, circuit-switched networks, such as Integrated Services Digital Network (ISDN) and its variations, packet-switched networks, and digital subscriber lines (DSL). Communication connection 1050 refers to the hardware / software used to connect network interface 1048 to system bus 1018. For clarity in the diagram, communication connection 1050 is shown inside computer 1012, but communication connection 1050 could also be placed outside computer 1012. For illustrative purposes only, the hardware / software for connecting to network interface 1048 could further include internal and external technologies such as modems including standard telephone-grade modems, cable modems and DSL modems, ISDN adapters, and Ethernet cards.

[0088] The present invention may be a system, method, apparatus, or computer program product, or a combination thereof, at any level of technical detail on which integration is possible. The computer program product may include a computer-readable storage medium having computer-readable program instructions thereon for causing a processor to execute aspects of the present invention. This computer-readable storage medium may be a tangible device capable of holding and storing instructions for use by an instruction execution device. This computer-readable storage medium may be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or a suitable combination thereof. A non-exclusive list of more specific examples of computer-readable storage media may further include portable computer diskettes, hard disks, random-access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random-access memory (SRAM), portable compact disk read-only memory (CD-ROM), digital versatile disks (DVDs), memory sticks, floppy disks, mechanically coded devices such as punch cards or raised structures in grooves on which instructions are recorded, and appropriate combinations thereof. When used herein, computer-readable storage media should not be construed as transient signals, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating within waveguides or other transmission bodies (e.g., light pulses passing through optical fiber cables), or electrical signals transmitted through wires.

[0089] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to the corresponding computing / processing device, or downloaded to an external computer or external storage device via a network, such as the Internet, a local area network, a wide area network, or a wireless network, or a combination thereof. This network may include copper transmission cables, optical transmission fibers, wireless transmissions, routers, firewalls, switches, gateway computers or edge servers, or a combination thereof. A network adapter card or network interface within each computing / processing device receives the computer-readable program instructions from the network and transfers those computer-readable program instructions for storage in the corresponding computer-readable storage medium within the respective computing / processing device. The computer-readable program instructions for performing the operation of the present invention may be assembler instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state setting data, or configuration data for an integrated circuit, or they may be source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk(R) and C++, and procedural programming languages ​​such as the C programming language or similar programming languages. These computer-readable program instructions may be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or remote server.In the last scenario described above, the remote computer may be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or this connection may be made to an external computer (for example, via the Internet using an Internet service provider). In some embodiments, to carry out aspects of the present invention, an electronic circuit, for example, including a programmable logic circuit, a field-programmable gate array (FPGA), or a programmable logic array (PLA), may execute the computer-readable program instruction by personalizing the electronic circuit using state information of the computer-readable program instruction.

[0090] In this specification, aspects of the present invention will be described with reference to flowcharts, block diagrams, or both, of methods, apparatus (systems), and computer program products according to embodiments of the present invention. It will be understood that each block in those flowcharts, block diagrams, or both, and combinations of blocks in those flowcharts, block diagrams, or both, can be implemented by computer-readable program instructions. These computer-readable program instructions can be provided to the processor of a general-purpose computer, a dedicated computer, or other programmable data processing device forming a machine, such that the instructions executed by the processor of that computer or other programmable data processing device generate means to perform the functions / operations specified in the blocks of those flowcharts, block diagrams, or both. These computer-readable program instructions can further be stored in a computer-readable storage medium that can instruct a computer, a programmable data processing device, or other device or a combination thereof to function in a particular manner, such that the computer-readable storage medium in which the instructions are stored contains a product containing instructions that perform the functions / operations specified in the blocks of those flowcharts, block diagrams, or both. These computer-readable program instructions can further be loaded onto a computer, other programmable device, or other device in such a manner that these instructions, executed on the computer, other programmable device, or other device, perform the functions / operations specified in the blocks of these flowcharts or block diagrams or both, in order to cause a series of operational steps on the computer, other programmable device, or other device to generate a process to be performed by the computer.

[0091] The flowcharts and block diagrams in the attached figures illustrate the architecture, functions, and operation of possible embodiments of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in those flowcharts or block diagrams may represent a module, segment, or portion of instructions containing one or more executable instructions for performing a specified logical function. In some alternative embodiments, the functions shown in these blocks may be performed in an order different from the order shown in the figures. For example, two consecutively shown blocks may actually be executed substantially simultaneously, or depending on the functions they contain, they may be executed in reverse order. It should also be noted that each block in those block diagrams or flowcharts or both, and combinations of blocks in those block diagrams or flowcharts or both, may be implemented by a hardware-based dedicated system that performs a specified function or operation or implements a combination of dedicated hardware and computer instructions.

[0092] While the subject matter has been described above in the general context of computer execution instructions for a computer program product running on one computer, multiple computers, or both, those skilled in the art will recognize that the disclosure can also be implemented in combination with other program modules. Generally, a program module includes routines, programs, components, data structures, or other program modules, or combinations thereof, that perform a specific task, implement a specific abstract data type, or both. Furthermore, those skilled in the art will recognize that the computer implementation of the present invention can also be implemented using other computer system configurations, including single-processor or multi-processor computer systems, minicomputing devices, mainframe computers, computers, handheld computing devices (e.g., PDAs, telephones), and microprocessor-based or programmable consumer or industrial electronic devices. The embodiments shown can also be implemented in a distributed computing environment where tasks are performed by remote processing devices linked through a communication network. However, some, if not all, embodiments of the disclosure can also be implemented on a standalone computer. In a distributed computing environment, program modules can reside on both local and remote memory storage devices. For example, in one or more embodiments, a computer executable component can be executed from memory that may include one or more distributed memory units, or from memory that may consist of one or more distributed memory units. As used herein, the terms “memory” and “memory unit” are interchangeable. Furthermore, one or more embodiments described herein can execute the code of a computer executable component in a distributed manner on a number of processors that are coupled or work together to execute the code, for example, from one or more distributed memory units.As used herein, the term “memory” may encompass a single memory or memory unit in one location, or a number of memories or memory units in one or more locations.

[0093] As used in this application, the terms “component,” “system,” “platform,” and “interface” may refer to, or include, one or more entities having specific functions, and may be entities relating to a computer or an operational machine, or both. Entities disclosed herein may be hardware, a combination of hardware and software, software, or running software. For example, a component may be, but is not limited to, a process running on a processor, a processor, an object, an executable file, an execution thread, a program or computer, or a combination thereof. For example, both an application running on a server and the server may be components. One or more components may reside in a process or an execution thread or both, and a component may be localized on one computer, distributed across two or more computers, or both. In another example, corresponding components may be executed from various computer-readable media on which various data structures are stored. A component can communicate via a local process, a remote process, or both, according to a signal consisting of, for example, one or more data packets (e.g., data from one component interacting with another component via a signal, together with other systems, within a local system, within a distributed system, across a network such as the Internet, or a combination thereof). Another example is a device having a specific function provided by a mechanical part operated by an electrical or electronic circuit, which is operated by a software or firmware application run by a processor.In such cases, the processor can be located inside or outside the device and can run at least part of a software application or firmware application. As another example, a component may be a device that provides a specific function through electronic components that do not include mechanical parts, and these electronic components may include a processor or other means for running software or firmware that gives at least part of the functionality of the electronic components. In one embodiment, a component may emulate an electronic component via a virtual machine, for example, within a cloud computing system.

[0094] Furthermore, the term “or” is intended to mean inclusive, not exclusive. That is, unless otherwise stated or evident from the context, “X uses A or B” is intended to mean any of the natural inclusive permutations. That is, if X uses A, if X uses B, or if X uses both A and B, “X uses A or B” is satisfied under any of the above cases. Furthermore, unless otherwise stated or evident from the context that it refers to a singular form, the articles “a” and “an” used herein and in accompanying drawings should generally be interpreted as meaning “one or plural.” When used herein, the terms “example” or “exemplary” or both are used to mean something that serves as an example, case, or illustration. To avoid misunderstanding, the subject matter disclosed herein is not limited by such examples. Furthermore, any embodiment or design described herein as an “example” or “exemplary” or both should not necessarily be interpreted as being preferable or advantageous to other embodiments or designs, nor should such embodiment or design be interpreted as excluding equivalent exemplary structures and techniques known to those skilled in the art.

[0095] As used herein, the term “processor” can refer to substantially any computing processing unit or device, including, but not limited to, single-core processors, single-core processors with software multithreading capabilities, multi-core processors, multi-core processors with software multithreading capabilities, multi-core processors with hardware multithreading technology, parallel platforms, and parallel platforms with distributed shared memory. Furthermore, a processor can refer to an integrated circuit, application-specific integrated circuit (ASIC), digital signal processing processor (DSP), field-programmable gate array (FPGA), programmable logic controller (PLC), complex-programmable logic device (CPLD), discrete gate or transistor logic, discrete hardware component, or any combination thereof, designed to perform the functions described herein. Additionally, a processor may utilize nanoscale architectures, such as molecular-based and quantum dot-based transistors, switches, and gates, to optimize space use or enhance the performance of user equipment, but is not limited to these. A processor can also be implemented as a combination of computing processing units. In this disclosure, terms such as “store,” “storage,” “data store,” “data storage,” and “database,” as well as substantially any other information storage component relating to the operation and function of the component, are used to refer to “memory” or “memory component,” which is an entity implemented as a component containing memory. It should be recognized that the memory or memory component or both described herein may be volatile memory or non-volatile memory, or may contain both volatile and non-volatile memory.For example, non-volatile memory may include, but is not limited to, read-only memory (ROM), programmable ROM (PROM), erasable programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), flash memory, or non-volatile random-access memory (RAM) (e.g., ferroelectric RAM (FeRAM)). Volatile memory may include RAM, which may function, for example, as external cache memory. For example, but is not limited to, static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data-rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), direct Rambus RAM (DRRAM), direct Rambus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM). Furthermore, the memory components disclosed in the systems or computer implementations herein are intended to include, but are not limited to, these types of memory and other appropriate types of memory.

[0096] The above description includes only examples of systems and computer implementations. Naturally, it is impossible to describe every conceivable combination of components or computer implementations in order to illustrate this disclosure, but those skilled in the art will understand that many other combinations and substitutions are possible. Furthermore, to the extent that terms such as “includes,” “has,” and “possesses” are used in the detailed description, claims, appendices, and drawings, such terms are intended to be inclusive, just as the term “comprising” is interpreted when used as a transitional word in a claim.

[0097] The above description of various embodiments is for illustrative purposes only and is not intended to be exhaustive or to limit the description to the disclosed embodiments. Those skilled in the art will see many changes and modifications that do not depart from the scope and spirit of the described embodiments. The terminology used herein has been chosen to best describe the principles, practical applications, or technical improvements not found in commercially available art, or to enable those skilled in the art to understand the embodiments disclosed herein.

Claims

1. It is a system, Memory for storing executable components, A processor that executes computer executable components stored in memory. The computer executable component includes, A wave splitting component that generates multiple waveform fragments using the definition of an intended waveform, wherein the multiple waveform fragments may be phase-shifted, and A rotation component that assigns a phase rotation to be applied to at least one waveform segment among the plurality of waveform segments, wherein the phase rotation is in a different phase from the previous waveform segment among the plurality of waveform segments. A system that includes this.

2. The waveform generator further includes a waveform generator that reproduces at least one of the plurality of waveform fragments with the phase rotation applied. The system according to claim 1.

3. The system according to claim 2, wherein at least one of the plurality of waveform fragments reproduced by the waveform generator with the phase rotation applied approximates a continuous waveform.

4. The system according to claim 3, wherein the starting phase rotation of one of the plurality of waveform fragments is zero.

5. The system according to claim 4, wherein the rotating component assigns the phase rotation applied by the waveform generator to at least one of the plurality of waveform fragments using a phase rotation coefficient 2π(ω+ε)t, where t is the time for which at least one of the plurality of waveform fragments is reproduced by the waveform generator, and ω+ε is the frequency of the intended waveform.

6. The system according to claim 5, wherein the rotation component assigns different phase rotations applied by the waveform generator to each of the plurality of waveform fragments by using different ε values ​​for each of the plurality of waveform fragments.

7. The system according to claim 6, wherein the waveform generator approximates a frequency sweep by regenerating the plurality of waveform fragments with the different phase rotations for each of the plurality of waveform fragments.

8. The system according to claim 5, wherein the phase rotation applied to at least one waveform fragment among the plurality of waveform fragments is assigned when the at least one waveform fragment among the plurality of waveform fragments is played back.

9. A computer implementation method, The process involves a system operably coupled to a processor to generate multiple waveform fragments using the definition of an intended waveform, wherein the multiple waveform fragments may be phase-shifted, and The system assigns a phase rotation to be applied to at least one of the plurality of waveform fragments, wherein the phase rotation is in a different phase from the previous waveform fragment among the plurality of waveform fragments. A computer implementation method including

10. In the processor, The process involves generating multiple waveform fragments using the definition of an intended waveform, wherein the multiple waveform fragments may be phase-shifted, and The processor assigns a phase rotation to be applied to at least one of the plurality of waveform fragments, wherein the phase rotation is in a different phase from that of a previous waveform fragment among the plurality of waveform fragments. A computer program designed to execute something.

11. It is a system, Memory for storing executable components, A processor that executes computer executable components stored in memory. The computer executable component includes, A wave splitting component that generates multiple waveform fragments using a definition of a resource waveform, wherein a phase slip may be inserted between each of the multiple waveform fragments, and A phase slip component that assigns the phase slip to be inserted between at least two of the plurality of waveform fragments. A system that includes this.

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