Efficient approximation of a 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] The subject disclosure relates to waveform generation, and more particularly, 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 use frequency sweeps, including areas such as Rabi spectroscopy, testing of RF filters, attenuators and transmission cables, and the operation of quantum computers. To generate a frequency sweep, existing waveform generation techniques generate a series of waveforms that are identical except for the output frequency. Summary of the Invention

[0003] The following presents a summary in order to provide a basic understanding of one or more embodiments of the invention. This summary is not intended to identify key or critical elements or to limit the scope of the particular embodiments or claims. Its sole purpose is to present ideas in a simplified form as a prelude to the more detailed description that is presented later. One or more embodiments described herein describe a system, computer-implemented method, or computer program product, or combination thereof, that facilitates efficiently approximating a range of sideband frequencies.

[0004] According to one embodiment, a system may include a processor that executes computer-executable components stored in a memory. The computer-executable components may include a wave splitting component that generates a plurality of waveform snippets using a definition of an intended waveform, where the plurality of waveform snippets may be phase shifted. The computer-executable components may further include a rotation component that assigns a phase rotation to apply to at least one waveform snippet of the plurality of waveform snippets, where the phase rotation is out of phase with a previous waveform snippet of the plurality of waveform snippets. An advantage of such a system is that by splitting the intended waveform into a plurality of waveform snippets, an approximation of the intended waveform may 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 the plurality of waveform segments using a phase rotation factor 2π(ω+ε)t, where t is the time that at least one of the plurality of waveform segments is played by the waveform generator and ω+ε is the frequency of the intended waveform. An advantage of such a system is that at least one of the plurality of waveform segments can be used to approximate the intended waveform.

[0006] According to another embodiment, a computer-implemented method may include generating, by a system operatively coupled to a processor, a plurality of waveform segments using a definition of an intended waveform, where the plurality of waveform segments may be phase shifted. The computer-implemented method may further include assigning, by the system, a phase rotation to apply to at least one waveform segment of the plurality of waveform segments, where the phase rotation is out of phase with a previous waveform segment of the plurality of waveform segments. An advantage of such a computer-implemented method is that by dividing the intended waveform into a plurality of waveform segments, an approximation of the intended waveform may be efficiently stored in memory.

[0007] In some embodiments, the computer-implemented method may further include the system assigning a phase rotation applied by the waveform generator to at least one waveform segment of the plurality of waveform segments using a phase rotation factor 2π(ω+ε)t, where t is the time at which at least one waveform segment of the plurality of waveform segments is played by the waveform generator and ω+ε is the frequency of the intended waveform. An advantage of such a computer-implemented method is that at least one waveform segment of the plurality of waveform segments may be used to approximate the intended waveform.

[0008] According to another embodiment, a computer program product includes a computer readable storage medium having program instructions embodied therein that are executable by the processor to cause the processor to generate a plurality of waveform segments using a definition of an intended waveform, the plurality of waveform segments being phase shifted. The program instructions are further executable by the processor to cause the processor to assign 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. An advantage of such a computer program product is that by dividing the intended waveform into a plurality of waveform segments, an approximation of the intended waveform may be efficiently stored in memory.

[0009] In some embodiments, the program instructions are further executable by the processor to cause the processor to assign a phase rotation applied to at least one waveform segment of the plurality of waveform segments using a phase rotation factor 2π(ω+ε)t, where t is a time that at least one waveform segment of the plurality of waveform segments is played by the waveform generator and ω+ε is a frequency of the intended waveform. An advantage of such a computer program product is that at least one waveform segment of the plurality of waveform segments can be used to approximate an intended waveform.

[0010] According to one embodiment, a system may include a processor executing computer-executable components stored in a memory, the computer-executable components including a wave splitting component for generating a plurality of waveform segments using a definition of a resource waveform, where a phase slip may be inserted between each of the plurality of waveform segments, the computer-executable components further including a phase slip component for assigning a phase slip to insert between at least two of the plurality of waveform segments. An advantage of such a computer program product is that by splitting a resource wave into a plurality of waveform segments, an approximation of an intended waveform may be efficiently stored. [Brief description of the drawings]

[0011] [Figure 1A] FIG. 1 is a block diagram of an example, non-limiting system that can facilitate operation of quantum hardware in accordance with one or more embodiments described herein. [Figure 1B] FIG. 1 is a block diagram of an exemplary, non-limiting system capable of completing the execution of a quantum job in accordance with one or more embodiments described herein. [Diagram 2] FIG. 1 is a block diagram of an example, non-limiting system that can facilitate efficiently approximating a range of sideband frequencies in accordance with one or more embodiments described herein. [Diagram 3] FIG. 1 is a block diagram of an example, non-limiting system that can facilitate efficiently approximating a range of sideband frequencies in accordance with one or more embodiments described herein. [Figure 4] FIG. 1 is a block diagram of an example, non-limiting system associated with dividing an intended waveform into waveform segments and determining phase rotation, according to one or more embodiments described herein. [Diagram 5]FIG. 2 is a block diagram of an example non-limiting system related to dividing a waveform into waveform segments and determining a phase slip, according to one or more embodiments described herein. [Figure 6] 1 is a graph illustrating a carrier wave of an approximated waveform according to one or more embodiments described herein. [Figure 7] FIG. 1 is a flow diagram of an example, non-limiting computer-implemented method that can facilitate efficiently approximating a range of sideband frequencies in accordance with one or more embodiments described herein. [Figure 8] FIG. 1 is a flow diagram of an example, non-limiting computer-implemented method that can facilitate efficiently approximating a range of sideband frequencies in accordance with one or more embodiments described herein. [Figure 9] FIG. 1 is a flow diagram of an example, non-limiting computer-implemented method that can facilitate efficiently approximating a range of sideband frequencies in accordance with one or more embodiments described herein. [Figure 10] FIG. 1 is a block diagram of an exemplary non-limiting operating environment capable of facilitating one or more embodiments described herein. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0012] The following detailed description is for illustrative purposes only, and is not intended to limit the embodiments or the application or uses of the embodiments, or both, nor is it intended to be bound by any express or implied information presented in the Background or Summary or Detailed Description above.

[0013] One or more embodiments will now be described with reference to the drawings. The same reference numerals are used to refer to the same elements throughout. In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a more thorough understanding of one or more embodiments. However, it will be apparent that in various cases one or more embodiments may be practiced without these specific details.

[0014] Quantum computing is generally the use of quantum-mechanical phenomena to perform computing and information processing functions. Quantum computing can be seen in contrast to classical computing, which generally uses transistors to perform operations on binary values. That is, while classical computers can perform operations on bit values ​​that are either 0 or 1, quantum computers perform operations on quantum bits (qubits) that contain superpositions of both 0 and 1, and superpositions allow large numbers of qubits to be entangled and use interference. This quantum superposition allows quantum systems to store and represent large data sets that are difficult to represent using 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 their computational complexity. In many forms of quantum computers, the qubits in the quantum computer are operated by using radio frequency waves. Thus, the quantum computer can receive instructions from classical inputs and then execute the instructions by using waveforms to operate the qubits in the quantum computer. Therefore, efficient waveform generation is important for the efficient operation of quantum computers.

[0015] A problem with existing waveform generation is that generating a series of waveforms that are identical except for their output frequency, such as a series of waveforms used for a frequency sweep, is very memory intensive because each waveform is represented as a series of points, or samples are taken independently and stored in classical memory. The waveform generator can then use those samples as a set of instructions on how to play the waveform. The taking or generation of these samples can have a large impact on the time it takes to play the series of waveforms. This is because generating the samples for an entire waveform takes time and requires a large amount of classical memory and computation to accomplish.

[0016] Given the above-mentioned problems of existing waveform generation techniques, the present disclosure may be implemented to produce a solution to these problems in the form of a system, computer-implemented method, or computer program product, or combination thereof, that may generate a plurality of waveform segments using a definition of an intended waveform, the plurality of waveform segments being phase shifted, or assigning a phase rotation to be applied to at least one of the plurality of waveform segments, the phase rotation being out of phase with a previous waveform segment of the plurality of waveform segments, or both, to facilitate efficiently approximating a range of sideband frequencies. An advantage of such a system, computer-implemented method, or computer program product, or combination thereof, is that the memory workload used to generate the waveform may be reduced. For example, the plurality of waveform segments may include identical waveform segments. As such, samples representing a single waveform may be generated and reused to represent the plurality of waveform segments, as opposed to generating samples representing the entire intended waveform.

[0017] In some embodiments, the present disclosure may be implemented to produce a solution to the above-mentioned problem in the form of a system, computer-implemented method, or computer program product, or combination thereof, which may further facilitate efficiently approximating a range of sideband frequencies by assigning a phase rotation applied to at least one of the plurality of waveform fragments using a phase rotation coefficient 2π(ω+ε)t, where t is the time that at least one of the plurality of waveform fragments is played by the waveform generator, and ω+ε is the frequency of the intended waveform, or by playing one or more waveform fragments with a phase rotation by the waveform generator, or both. An advantage of such a system, computer-implemented method, or computer program product, or combination thereof, is that at least one of the plurality of waveform fragments may be used to approximate an intended waveform without the need to generate and store in memory samples representative of the entire intended waveform. For example, the waveform generator may repeatedly play the waveform fragment with a different phase rotation each time to approximate the intended waveform. In this way, the waveform generator can reproduce an approximation of the intended waveform without samples that represent the entire intended waveform.

[0018]

[0023] Referring initially generally to Figure 1A, one or more embodiments described herein may include one or more devices, systems and / or apparatuses that may facilitate the performance of one or more quantum operations to facilitate the output of one or more quantum results. For example, Figure 1A illustrates a block diagram of an exemplary, non-limiting system 100 that may facilitate the operation of quantum hardware.

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

[0020] 1B, one or more embodiments described herein may include one or more devices, systems and / or apparatuses that may facilitate the execution of one or more quantum operations to facilitate the output of one or more quantum results. For example, FIG. 1B illustrates a block diagram of an exemplary, non-limiting system 150 that may 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 like system, or combinations thereof) can perform quantum operations or functions or both on input data using quantum algorithms and / or quantum circuits including computing components and / or devices to produce a result that can be output to an entity. A quantum circuit can include quantum bits (qubits), such as multi-bit qubits, physical circuit level components, higher level components or functions, or combinations thereof. A quantum circuit can include physical pulses that can be constructed (e.g., arranged or designed, or arranged and designed) to perform a desired quantum function or calculation or both on data (e.g., input data, or intermediate data derived from the input data, or both) to produce one or more quantum results as output. The quantum results (e.g., quantum measurements 113) can be in response to a quantum job request 106 and associated input data and can be based, at least in part, on the input data, quantum functions, or quantum calculations, or combinations thereof.

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

[0023] Quantum computing component 107 may obtain (e.g., download, receive, search, or the like, or a combination thereof) quantum job request 106 that requests execution of one or more quantum programs. In one example, quantum job request 106 may be a digital signal. Quantum computing component 107 may determine one or more quantum logic circuits, such as quantum logic circuit 111, for executing the quantum programs. Request 106 may be provided in any suitable format, such as a text format, a binary format, or another suitable format, or a combination thereof. In one or more embodiments, request 106 may be received by a component other than a component of quantum system 110, such as a component of a classical system coupled to quantum system 110 and / or a component of a classical system in communication with quantum system 110.

[0024] 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, quantum computing component 107 can operate one or more qubit effectors, such as waveform generator 108, qubit oscillator, harmonic oscillator, pulse generator, or the like, or combinations thereof, such 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, that quantum system 110 includes. That is, quantum computing component 107 can be combined, for example, with quantum processor 109 to perform the operations of a quantum logic circuit on one or more qubits (e.g., qubits 112A, 112B, or 112C, or combinations thereof) of that circuit. Quantum computing component 107 can output one or more quantum job results, such as one or more quantum measurements 113, in response to quantum job requests 106.

[0025] It will be appreciated that the following description relates to the operation of a single quantum program from a single quantum job request, however, it will also be appreciated that one or more of the processes described herein may be scalable, such as the execution of one or more quantum programs and / or quantum job requests in parallel with one another.

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

[0027] In such cases, one or more communications between one or more components of the non-limiting system 150 and one or more components of the classical system may be facilitated by wired or wireless means, or both, including, but not limited to, 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 for facilitating 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), high speed packet access (HSPA), high speed packet radio (HPA), high speed packet radio (HSP), high speed packet radio (HSP), high speed packet access (HSP ... These may include High Speed ​​Passive Access (HSPA), Zigbee and other 802.XX wireless technologies and / or traditional telecommunications technologies, BLUETOOTH®, Session Initiation Protocol (SIP), ZIGBEE®, RF4CE protocol, WirelessHART protocol, 6LoWPAN (IPv6 over Low power Wireless Area Networks), Z-Wave, ANT, ultra-wideband (UWB) standard protocols, and / or other proprietary and non-proprietary communication protocols.

[0028] 2 and 3 each illustrate a block diagram of exemplary, non-limiting systems 200 and 300, each of which can facilitate efficiently approximating a range of sideband frequencies to aid in 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. Quantum computing component 107 can include a waveform approximation system 201. In one embodiment, quantum computing component 107 can receive a quantum job request 106. Based on the quantum job request 106, quantum computing component 107 can define a waveform that a waveform generator uses to compute, simulate, or manipulate, or compute, simulate and manipulate, the state of one or more qubits, such as qubits 112A, 112B, or 112C, or a combination thereof, to facilitate the execution of quantum job request 106. For example, quantum computing component 107 can provide as an input to waveform approximation system 201 a definition of an intended waveform. The waveform approximation system 201 can generate one or more samples and / or instructions that, when provided to the waveform generator 108, cause the waveform generator 108 to reproduce an approximation of a defined waveform for operating the qubits 112A, 112B, or 112C, or combinations thereof. The waveform approximation system 201 can include a memory 202, a processor 203, a wave splitting component 204, a rotation component 205, or a bus 206, or combinations thereof. The waveform approximation system 201 of the system 300 shown in FIG. 3 can further include a phase slip component 308.

[0029] It should be appreciated that the embodiments of the subject disclosure illustrated in the various figures disclosed herein are for illustrative purposes only, and thus the architecture of such embodiments is not limited to the systems, devices, or components, or combinations thereof, illustrated in those figures. For example, in some embodiments, the system 100, the system 150, the system 200, the system 300, or the waveform approximation system 201, or combinations thereof, may further include various computer elements and / or computing-based elements described herein with respect to the operating environment 1000 of FIG. 10. In some embodiments, such computer elements and / or computing-based elements may be used in connection with the implementation of one or more of the systems, devices, components, or computer-implemented operations or combinations thereof illustrated and described in connection with FIG. 1A, FIG. 1B, FIG. 2, FIG. 3, or other figures or combinations thereof disclosed herein.

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

[0031] The memory 202 can include volatile memory (e.g., random access memory (RAM), static RAM (SRAM), dynamic RAM (DRAM) or another type 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 ROM (EEPROM) or another type of non-volatile memory or a combination thereof), or both, which can use one or more memory architectures. Additional examples of memory 202 are described below with respect to system memory 1016 of FIG. 10. Any embodiment of the subject disclosure can be implemented using such examples of memory 202.

[0032] The processor 203 may include one or more types of processors and / or electronic circuitry (e.g., classical processors and / or other types of processors and / or electronic circuitry) capable of implementing one or more components and / or instructions that a computer and / or machine can read, write and / or execute and / or a combination thereof, which may be stored in the memory 202. For example, the processor 203 may perform various operations that may be specified by such components and / or instructions that a computer and / or machine can read, write and / or execute and / or a combination thereof, including, but not limited to, logic, control, input / output (I / O), arithmetic or other operations or combinations thereof. In some embodiments, the processor 203 may include one or more central processing units, multi-core 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 of FIG. 10. Any such example of the processor 203 may be used to implement any embodiment of the subject disclosure.

[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 splitting component 204, rotation component 205, waveform generator 108, phase slip component 308, or other components of waveform approximation system 201 described herein, or combinations thereof, may be communicatively, electrically, operatively, or optically coupled to one another, or combinations thereof, via bus 206. 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 of FIG. 10. Any embodiment of the subject disclosure may be implemented using such examples of bus 206.

[0034] The waveform approximation system 201 may include any type of component, machine, device, facility, apparatus, and / or equipment that includes a processor and / or that can be in effective and / or operative communication with a wired network and / or a wireless network. All such embodiments are contemplated. For example, the waveform approximation system 201 may include a server device, a computing device, a general purpose computer, a special purpose computer, a tablet computing device, a handheld device, a server class computing machine and / or database, a laptop computer, a notebook computer, a desktop computer, a mobile phone, a smart phone, a consumer device and / or appliance, an industrial and / or commercial device, a digital assistant, an Internet-enabled multimedia telephone, a multimedia player, and / or other types of devices.

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

[0036] In some embodiments, the waveform approximation system 201 may be coupled (e.g., communicatively, electrically, operatively, optically, or by another type of coupling, or combinations thereof) 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) via a network. For example, such a network may include a wired network or a wireless network, or both, including, but not limited to, a cellular network, a wide area network (WAN) (e.g., the Internet), or a local area network (LAN), or combinations thereof. The waveform approximation system 201 may communicate with one or more external systems, sources or devices, such as computing devices, or combinations thereof, using substantially any desired wired and / or wireless technology, including, but 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 (LOEV), and the like.Mobile Broadband (UMB), high speed packet access (HSPA), Zigbee and other 802.XX wireless technologies and / or traditional telecommunications technologies, BLUETOOTH®, Session Initiation Protocol (SIP), ZIGBEE®, RF4CE protocol, WirelessHART protocol, 6LoWPAN (IPv6 over Low power Wireless Area Networks), Z-Wave, ANT, ultra-wideband (UWB) standard protocols, and / or other proprietary and non-proprietary communications protocols. Thus, in some embodiments, the waveform approximation system 201 may include hardware (e.g., a central processing unit (CPU), a transceiver, a decoder, quantum hardware, a quantum processor or other hardware or a combination 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 a combination thereof), or a combination of hardware and software that can facilitate information transfer between the waveform approximation system 201 and an external system, source or device or a combination thereof (e.g., a computing device, a communications device and / or another type of external system, source and / or device).

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

[0038] The waveform approximation system 201 may facilitate the execution (e.g., by the processor 203) of operations performed by the wave splitting component 204, the rotation component 205, the waveform generator 108, the phase slip component 308, and / or any components disclosed herein associated with the waveform approximation system 201, and / or operations associated with the wave splitting component 204, the rotation component 205, the waveform generator 108, the phase slip component 308, and / or any components disclosed herein associated with the waveform approximation system 201. For example, as described in more detail below, the waveform approximation system 201 can facilitate generating a plurality of waveform segments, which may be phase shifted; assigning a phase rotation to be applied to at least one waveform segment of the plurality of waveform segments upon playback using a phase rotation coefficient 2π(ω+ε)t, where t is the time at which the at least one waveform segment is played and ω+ε is the frequency of the intended waveform, where the phase rotation is out of phase with a previous waveform segment of the plurality of waveform segments; or playing at least one waveform segment of the plurality of waveform segments with a phase rotation by a waveform generator, or combinations thereof.

[0039] Wave division component 204 can generate multiple waveform segments, which can be phase shifted. As referred to herein, an "intended waveform" is a waveform for which waveform generator 108 reproduces an approximation of the waveform, and a "waveform segment" is a small portion of the waveform. Additionally, as referred to herein, a "sample" is a numerical data point that can be used to represent a waveform. In one embodiment, wave division component 204 can receive a definition of an intended waveform. For example, as described above, quantum operations component 107 can receive quantum job request 106. Based on quantum job request 106, quantum operations component 107 can define an intended waveform to reproduce to manipulate or operate or to manipulate and operate qubits 112A, 112B, or 112C, or a combination thereof, to perform quantum job request 106. Quantum operations component 107 can generate the intended waveform by converting the intended waveform into a waveform that is generated by the quantum operations component.

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

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[0041] In one embodiment, the wave division component 204 can determine the length τ of the waveform snippets based on the accuracy of the approximation. For example, the smaller the length τ of the waveform snippets, the more accurate the approximation. Thus, if a high level of accuracy of the waveform approximation is required to perform the quantum job request 106, the wave division component can generate waveform snippets of small length τ. If a lower level of accuracy of the waveform approximation is acceptable to perform the quantum job request 106, the wave division component 204 can generate waveform snippets of large length τ. In one embodiment, the wave division component 204 can receive as input the intended level of accuracy of the approximation or the length τ, or both, from the quantum operation component 107.

[0042] In another embodiment, the wave splitting component 204 can determine the length of the 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 played for 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 play the waveform fragment, in this case two times. It should be appreciated that the wave splitting component 204 can generate waveform fragments of any length τ. For example, τ can be shorter than the wavelength of the intended waveform or longer than the wavelength of the intended waveform.

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

[0044] The rotation component 205 can assign a phase rotation to apply to at least one of the waveform fragments, which is out of phase with a previous one of the 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 the 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 factor 2πωt, where t is the time at which the waveform fragment is played back to assign a phase rotation to be used by the waveform generator 108 upon playback. In this example, the rotation component 205 can assign a phase rotation to apply to at least one of the waveform fragments upon playback. For example, given an intended waveform defined by the quantum computing component 107 in which the wave splitting component 204 has generated a plurality of waveform fragments including four identical waveform fragments, the rotation component 205 may 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 plurality of waveform fragments and the corresponding sequence of phase rotations may then be passed to the waveform generator 108. For example, the waveform generator 108 may use samples representing the waveform fragments stored in memory to play the first waveform fragment with a phase rotation of 0. The waveform generator 108 may then use samples representing the waveform fragments in memory to play the second waveform fragment with a phase rotation of π / 2. The waveform generator 108 may then play the third and fourth waveform segments with corresponding third and fourth phase rotations.By playing these four waveform fragments in sequence with corresponding phase rotations, the waveform generator 108 can reproduce an approximation of the intended waveform for operating or manipulating qubits 112A, 112B, or 112C, or combinations thereof, to execute quantum job request 106. As discussed above, when the wave splitting component 204 generates the waveform fragments based on a definition of the intended waveform, the wave splitting component 204 can store samples of a single waveform fragment and use that single waveform fragment to represent each of those multiple waveform fragments that are used by the waveform generator 108 to generate the approximation of the intended waveform. Thus, the rotation component 205 can enable the waveform generator 108 to indefinitely extend the approximation of the intended waveform to approximate a continuous waveform by allowing the waveform generator 108 to play the stored single waveform fragment with a new phase rotation assigned by the rotation component 205 each time a waveform fragment is played.

[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 segments of the plurality of waveform segments, which, when played back with phase rotation by the waveform generator 108, approximates a frequency sweep. As discussed above, a frequency sweep can be described as a series of identical waveforms, except that the output frequencies differ. 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 factor 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), ε is the change in frequency, and t is the time at which the waveform segment is played back by the waveform generator 108. If the wave splitting component 204 generates a plurality of waveform fragments including four identical waveform fragments, the rotation component 205 may assign a phase rotation to the first waveform fragment using a first ε value in the rotation coefficient, may assign a phase rotation to the second waveform fragment using a second ε value in the rotation coefficient, may assign a phase rotation to the third waveform fragment using a third ε value, and may assign a phase rotation to the fourth waveform fragment using a fourth ε value. The rotation component 205 may then pass the plurality of waveform fragments and the corresponding phase rotations to the waveform generator 108.

[0046] In one embodiment, the ε value may be determined based on the difference in frequency between the first waveform and the current waveform in the series of waveforms representing the frequency sweep. For example, a contemplated frequency sweep including two waveforms may be determined by the quantum computing component 107 as follows:

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[0047] In this example, by varying the ε value when assigning the phase rotation, the rotation component 205 can assign a phase rotation that allows the waveform generator 108 to play the waveform segments at different frequencies. In one embodiment, the rotation component 205 can utilize different ε values ​​to assign different phase rotations to be applied by the waveform generator 108 each time it plays a waveform segment. In another embodiment, the rotation component 205 can utilize the same ε value to assign phase rotations for multiple waveform segments of the plurality of waveform segments when the multiple waveform segments are played by the waveform generator 108 at the same output frequency.

[0048] In one embodiment, the rotation component 205 can assign a phase rotation to at least one of the waveform segments to be applied by the waveform generator 108 prior to playback. For example, if the wave split component generates a plurality of waveform segments including four identical waveform segments, the rotation component 205 can assign a corresponding phase rotation to the plurality of waveform segments and pass the plurality of waveform segments and the corresponding phase rotation to the waveform generator 108. In another embodiment, the rotation component 205 can assign a phase rotation to be applied to the waveform segments upon playback by the waveform generator. For example, the wave split component 204 can pass the plurality of waveform segments to the waveform generator 108. The waveform generator 108 can then request a phase rotation to be played along with a first waveform segment of the plurality of waveform segments. The rotation component 205 can assign a phase rotation as described above and pass the phase rotation to the waveform generator 108. The waveform generator 108 can then play the first waveform segment with the phase rotation. The waveform generator 108 may then request a phase rotation to play with a second waveform segment of the plurality of waveform segments. This process may continue until the waveform generator 108 has played all of the waveform segments in the plurality of waveform segments.

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

[0050] It should be appreciated that by assigning phase rotations to the waveform snippets as described above, the rotation component 205 can improve efficiency in approximating the waveform. For example, by assigning phase rotations having different frequencies to each identical waveform snippet, the waveform generator 108 can recreate an approximation of a frequency sweep using a single waveform snippet and a series of phase rotations rather than using samples that represent the entire frequency sweep. In this example, the rotation component 205 can reduce storage used to recreate an approximation of the frequency sweep because the frequency sweep can be stored as a single waveform snippet and a series of phase rotations rather than as samples of the entire frequency sweep. By reducing storage usage (e.g., memory usage), the rotation component 205 can improve efficiency in approximating the waveform.

[0051] The waveform generator 108 can play at least one waveform segment of the plurality of waveform segments with a phase rotation. For example, the waveform generator 108 can receive the plurality of waveform segments from the wave splitting component 204 and can receive one or more phase rotations from the rotation component 205. As explained above, the plurality of waveform segments can include identical waveform segments. Thus, the plurality of waveform segments can be represented as a single waveform segment and a number of times to play the single waveform segment. In this example, if the waveform generator 108 receives a plurality of waveform segments including four waveform segments and receives four corresponding phase rotation factors, the waveform generator can play a first waveform segment of the plurality of waveform segments with a first phase rotation, a second waveform segment with a second phase rotation, a third waveform segment with a third phase rotation, and a fourth waveform segment with a fourth phase slip. By playing four identical waveform snippets in sequence with corresponding phase rotations, waveform generator 108 can reproduce an approximation of the intended waveform defined by quantum computation component 107 and thus operate or manipulate qubits 112A, 112B or 112C or any combination thereof to execute quantum job request 106.

[0052] In another embodiment, the waveform generator 108 may receive multiple waveform segments and may request a phase rotation from the rotation component 205. For example, if the waveform generator 108 receives a plurality of waveform segments including four waveform segments, the waveform generator may request a phase rotation for a first waveform segment from the rotation component 205. After the waveform generator 108 receives the phase rotation from the rotation component 205, the waveform generator 108 may play the first waveform segment with this phase rotation. The waveform generator 108 may then request a second phase rotation for the second waveform segment. After the waveform generator 108 receives the second phase rotation, the waveform generator 108 may play the second waveform segment with the second phase rotation. This process may be repeated until the waveform generator 108 has played all of the waveform segments of the plurality of waveform segments. The waveform generator 108 may be a signal generator, a function generator, a radio frequency generator, a microwave signal generator, a digital pattern generator, a frequency generator, a pitch generator, an 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 disclosure can be implemented to produce a solution to the above-mentioned problems in the form of a system, computer-implemented method, or computer program product, or combination thereof, which generates a plurality of waveform segments, where a phase slip may be inserted before each waveform segment of the plurality of waveform segments, which can further facilitate efficiently approximating a range of sideband frequencies by generating, allocating a phase slip for insertion before at least one waveform segment of the plurality of waveform segments, or by regenerating a phase slip and at least one waveform segment of the plurality of waveform segments, or combinations thereof.

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

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[0055] In these examples, by assigning a phase slip along with a phase jump to insert before each waveform snippet is played, the phase slip component 308 can enable the waveform generator 108 to play an approximation of the intended waveform using the waveform snippet of the resource waveform and one or more phase slips.

[0056] Using the definitions of phase slip and phase jump, we can write the approximated signal as

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[0057] It should be appreciated that by allocating a phase slip to be inserted by the waveform generator 108 prior to reproducing a waveform snippet, the phase slip component 308 can improve waveform generation through the use of a sawtooth phase jump function. Because sawtooth functions are relatively easy to compute, the phase slip component 308 can enable the waveform generator 108 to efficiently reproduce an approximation of an intended waveform without having to generate and store in memory samples of the entire intended waveform. As noted above, existing waveform generation techniques are very memory intensive, and by enabling the waveform generator 108 to reproduce an approximation of an intended waveform using a waveform snippet of a resource waveform, the phase slip component 308 can enable the waveform approximation system 201 to improve waveform generation and reproduction by reducing the storage operations associated with waveform generation and reproduction.

[0058] 4 illustrates a block diagram of an exemplary, non-limiting system associated with generating waveform snippets and assigning phase rotations in accordance with one or more embodiments described herein. For the sake of brevity, repeated descriptions of identical elements used in other embodiments described herein have been omitted.

[0059] The system 400 includes a wave splitting component 204 of a waveform approximation system 201. The wave splitting component 204 may receive a definition of an intended waveform 401 from the quantum computing component 107. The wave splitting component 204 may generate multiple waveform fragments by generating samples of a single waveform fragment and the number of times to play the waveform fragment. Because the multiple waveform fragments include the same waveform fragment that is used repeatedly, the wave splitting component 204 may store a single waveform fragment 402 to be repeated for each waveform fragment of the multiple waveform fragments. The rotation component 205 may assign a set of phase rotations to be applied to the waveform fragment by the waveform generator 108 each time the waveform fragment is played. The samples representing the waveform fragment 402, the number of times to play the waveform fragment, and the set of phase rotations 403 may then be passed to the waveform generator 108. The waveform generator 108 may then use the waveform snippet and a series of phase rotations as described with reference to Figure 2 to reproduce an approximation of the intended waveform, to operate or manipulate qubits 112A, 112B or 112C, or a combination thereof, to execute the quantum job request 106. It should be appreciated that by performing these operations, the efficiency of frequency sweep generation may be improved by generating a single waveform snippet and assigning a series of phase rotations, rather than generating samples that represent the entire intended waveform.

[0060] 5 illustrates a block diagram of an exemplary, non-limiting system associated with generating waveform snippets and assigning phase slips in accordance with one or more embodiments described herein. For the sake of brevity, repeated descriptions of identical elements used in other embodiments described herein have been omitted.

[0061] The system 500 includes a wave division component 204 of a 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 plays the waveform fragment. Since the single waveform fragment 502 is reused to represent the multiple waveform fragments, the wave division component 204 can store samples representing the waveform fragment 502 to be repeated for each waveform fragment of the multiple waveform fragments. The phase slip component 308 can receive a definition of an intended waveform 504 to be approximated from the quantum operation component 107. The phase slip component 308 can assign a set of phase slips and phase jumps to be inserted between the waveform fragments of the multiple waveform fragments by the waveform generator 108. The samples representing the waveform fragment 502, the number of times to play the waveform fragment, and the set 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 snippet 502 and a series of phase slips and phase jumps as described with reference to Figure 3 to recreate an approximation of the intended waveform, to operate or manipulate qubits 112A, 112B or 112C, or a combination thereof, to execute the quantum job request 106. It should be appreciated that by performing these operations, the efficiency of frequency sweep generation can be improved by generating a single waveform snippet and assigning a series of phase slips, rather than generating samples that represent the entire intended waveform.

[0062] 6 illustrates a graph 600 associated with a carrier of an approximated waveform, according to one or more embodiments described herein. For the sake of brevity, repeated descriptions of the same elements and / or processes used in each corresponding embodiment are omitted. As explained above, the phase slip component 308 adjusts the phase of the approximated signal.

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[0063] 7 illustrates a flow diagram of an exemplary non-limiting computer-implemented method 700 that can facilitate efficiently approximating a range of sideband frequencies in accordance with one or more embodiments described herein. For the sake of brevity, repeated descriptions of the same elements and / or processes used in each corresponding embodiment have been omitted.

[0064] At 701, the computer-implemented method 700 may include generating, by a system operatively coupled to a processor (e.g., processor 203) (e.g., via the waveform approximation system 201 or the wave splitting component 204, or both), a plurality of waveform fragments by generating a single waveform fragment using a definition of an intended waveform and a number of times to play the single waveform fragment.

[0065] At 702, the computer-implemented method 700 may include assigning, by the system (e.g., via the waveform approximation system 201 or the rotation component 205 or both), a phase rotation applied by a waveform generator (e.g., the waveform generator 108) 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.

[0066] At 703, the computer-implemented method 700 may include playing, by a waveform generator (e.g., waveform generator 108), at least one waveform segment of the plurality of waveform segments with the assigned phase rotation.

[0067] 8 illustrates a flow diagram of an exemplary non-limiting computer-implemented method 800 that can facilitate efficiently approximating a range of sideband frequencies in accordance with one or more embodiments described herein. For the sake of brevity, repeated descriptions of the same elements and / or processes used in each corresponding embodiment have been omitted.

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

[0069] At 802, the computer-implemented method 800 may include assigning by the system (e.g., via the waveform approximation system 201 and / or the rotation component 205) a different phase rotation applied by a waveform generator (e.g., the waveform generator 108) to each waveform segment of the plurality of waveform segments using a phase rotation factor 2π(ω+ε)t, with a different ε value being used for each waveform segment of the plurality of waveform segments. In this example, the approximated waveform may be stored as a single waveform segment that is repeatedly used to represent each waveform segment of the plurality of waveform segments, and a corresponding phase rotation to apply to each waveform segment of the two or more waveform segments, as described above with reference to Figures 1 and 2.

[0070] At 803, the computer-implemented method 800 may include playing, by a waveform generator (e.g., waveform generator 108), at least one waveform segment of the plurality of waveform segments with an assigned phase rotation. For example, as described above with reference to Figures 2 and 3, by playing the plurality of waveform segments with different phase rotations for various waveform segments of the plurality of waveform segments, the waveform generator 108 may play an approximation of a frequency sweep because the various waveform segments of the plurality of waveform segments have different output frequencies due to the different phase rotations applied by the waveform generator 108 to the various waveform segments as the waveform generator 108 plays each waveform segment.

[0071] 9 illustrates a flow diagram of an exemplary non-limiting computer-implemented method 900 that can facilitate efficiently approximating a range of sideband frequencies in accordance with one or more embodiments described herein. For the sake of brevity, repeated descriptions of the same elements and / or processes used in each corresponding embodiment have been omitted.

[0072] At 901, the computer-implemented method 900 may include generating, by a system operatively coupled to a processor (e.g., processor 203) (e.g., via the waveform approximation system 201 or wave splitting component 204, or both), a plurality of waveform snippets by generating a single waveform snippet using a definition of a resource waveform and a number of times to play the single waveform snippet. For example, as described above with reference to FIG. 3, by generating waveform snippets of a resource signal that may have a phase slip inserted by a waveform generator (e.g., waveform generator 108) before the waveform snippet, the waveform approximation system 201 may manipulate the waveform snippets to approximate an intended signal.

[0073] At 902, the computer-implemented method 900 can include assigning, by the system (e.g., via the waveform approximation system 201 and / or the phase slip component 308), a phase slip to be inserted by a waveform generator before at least one of the plurality of waveform segments. For example, as described in detail above with reference to FIG. 3, the phase slip component 308 can assign a phase slip to be inserted by a waveform generator (e.g., the waveform generator 108) according to a phase slip definition:

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[0074] At 903, the computer-implemented method 900 may include reproducing, by a waveform generator (eg, waveform generator 108), the phase slip and at least one waveform segment of the plurality of waveform segments.

[0075] The waveform approximation system 201 may be associated with various technologies, for example, the waveform approximation system 201 may be associated with quantum technology, RF technology, microwave technology, spectroscopic technology, or other technology, or a combination thereof.

[0076] The waveform approximation system 201 may provide technical improvements to systems, devices, components, operational or processing steps, or combinations thereof associated with the various techniques identified above. For example, the waveform approximation system 201 may use waveform snippets of a resource waveform to generate an approximation of an intended waveform. In this example, the waveform approximation system 201 may generate multiple waveform snippets using a single waveform snippet generated using a definition of the resource waveform. The waveform approximation system 201 may further assign a phase slip to be inserted by a waveform generator (e.g., waveform generator 108) before each waveform snippet as the waveform snippet is played by the waveform generator (e.g., waveform generator 108). In this example, the waveform approximation system 201 may play an approximation of an intended waveform via a waveform generator. In another example, the waveform approximation system 201 may generate the waveform snippets using a definition of the intended waveform. The waveform approximation system 201 may assign a phase rotation to be applied by the waveform generator (e.g., waveform generator 108) to the waveform snippet each time the waveform generator plays the waveform snippet. In one embodiment, the phase rotation applied by the waveform generator can be different each time a waveform segment is played, so that the output waveform approximates the intended waveform.

[0077] The waveform approximation system 201 may provide technical improvements to memory units associated with the waveform approximation system 201. For example, by generating a single waveform snippet for repeated use, a waveform generator (e.g., waveform generator 108) may use phase rotation or phase slip to regenerate an approximation of a frequency sweep without having to generate samples in memory that represent the entire frequency sweep, 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 may thereby facilitate improved performance, improved efficiency, or reduced computational costs, or a combination thereof, associated with such memory units.

[0078] Furthermore, by reducing the use of memory units, the waveform approximation system 201 may provide a technical improvement to the operation of a quantum system. For example, by reducing the use of memory units and the number of memory operations used in generating a waveform to operate a quantum system, the generation of the waveform may be performed faster, thereby enabling faster operation of the quantum system. Furthermore, by reducing the use of memory units, the waveform approximation system 201 may enable the use of smaller or less expensive to manufacture memory units, or smaller and less expensive to manufacture memory units, in generating the waveform.

[0079] It should be appreciated that the various operations that may be performed by the waveform approximation system and / or components thereof described herein are operations beyond the capabilities of human intelligence, and therefore the waveform approximation system 201 may utilize various combinations of electrical components, mechanical components, and circuitry that cannot be replicated or performed by the human intelligence. For example, the amount of data processed by the waveform approximation system 201 in a given period of time, the rate at which such data is processed, or the type of data may be greater than, faster than, or a different type of data than the human intelligence can process in the same period of time.

[0080] According to some embodiments, the waveform approximation system 201 may further be fully operable to perform one or more other functions (e.g., fully power on, fully run, or other functions, or combinations thereof) while performing the various operations described herein. It should be appreciated that such simultaneous multi-operation execution is beyond the human intellect. It should also be appreciated that the waveform approximation system 201 may include information that is not manually obtainable by an entity such as a human user. For example, the type, amount, or variety of information included in the waveform approximation system 201, the wave splitting component 204, the rotation component 205, the waveform generator 108, or the phase slip component 308, or combinations thereof, may be more complex than information manually obtained by an entity such as a human user.

[0081] The waveform approximation system 201 may use hardware or software to solve problems that are highly technical in nature, not abstract, and cannot be performed as a set of mental acts by a human being. In some embodiments, one or more of the processes described herein may be performed by one or more special-purpose computers (e.g., a special-purpose processing unit, a special-purpose classical computer, a special-purpose quantum computer, or another type of special-purpose computer) to perform the stated tasks related to the various technologies identified above. The waveform approximation system 201 or components thereof, or both, may be used to solve new problems that arise due to the use of the above-mentioned technological advances, quantum computing systems, cloud computing systems, computer architectures, or other technologies, or combinations thereof.

[0082] For simplicity of explanation, these computer-implemented methodologies are depicted and described as a series of operations. It should be understood and appreciated that the subject innovation is not limited by the operations depicted and / or by the order of operations, e.g., operations can be performed in various orders or simultaneously, or both, and can be performed with other operations not depicted and described herein. Moreover, not all depicted operations are required to implement a computer-implemented methodology in accordance with the disclosed subject matter. Moreover, those skilled in the art will understand and appreciate that a computer-implemented methodology can alternatively be represented as a series of interrelated states, such as by a state diagram or events. It should also be appreciated that the computer-implemented methodologies disclosed below and throughout this specification can be stored on an article of manufacture to facilitate transporting and transferring such computer-implemented methodologies to a computer. As used herein, the term article of manufacture is intended to encompass a computer program accessible from a computer-readable device or storage medium.

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

[0084] 10, a suitable operating environment 1000 for implementing various aspects of the present disclosure may further include a computer 1012. The computer 1012 may further include a processing unit 1014, a system memory 1016, and a system bus 1018. The system bus 1018 couples system components including, but not limited to, the system memory 1016 to the processing unit 1014. The processing unit 1014 may be any of a variety of processors available. Dual microprocessors and other multi-processor architectures may also be used as the processing unit 1014. The system bus 1018 may be any of several types of bus structures including a memory bus or memory controller, a peripheral or external bus, and / or a local bus using any of a variety of 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), Card Bus, Universal Serial Bus (USB), Advanced Graphics Port (AGP), Firewire (IEEE 1394), and Small Computer Systems Interface (SCSI).

[0085] The system memory 1016 may further include a volatile memory 2020 and a non-volatile memory 2022. The non-volatile memory 2022 stores a basic input / output system (BIOS), which includes the basic routines for transferring information between elements within the computer 1012, such as during start-up. The computer 1012 may further include removable / non-removable volatile / non-volatile computer storage media. FIG. 10 illustrates, for example, a disk storage 1024. The disk storage 1024 may further include devices such as, but not limited to, a magnetic disk drive, a floppy disk drive, a tape drive, a Jaz drive, a Zip drive, an LS-100 drive, a flash memory card, or a memory stick. The disk storage 1024 may further include storage media separate from or in combination with other storage media. To facilitate connection of the disk storage 1024 to the system bus 1018, a removable or non-removable interface, such as an interface 1026, is typically used. 10 further illustrates software that acts as an intermediary between users and the basic computer resources described within suitable operating environment 1000. Such software may further include, for example, an operating system 1028. The operating system 1028, which may be stored on disk storage 1024, functions to control and allocate resources of the computer 1012.

[0086] System applications 1030 take advantage of the management of resources by 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 appreciated that the present disclosure may be implemented with various operating systems or combinations of operating systems. A user enters commands or information into computer 1012 through input devices 1036. Input devices 1036 include, but are not limited to, a pointing device such as a mouse, a trackball, a stylus, a touch pad, a keyboard, a microphone, a joystick, a game pad, a satellite dish, a scanner, a TV tuner card, a digital camera, a digital video camera, a web camera, and the like. These and other input devices connect to processing unit 1014 through system bus 1018 via interface ports 1038. Interface ports 1038 include, for example, serial ports, parallel ports, game ports, and a universal serial bus (USB). The output device 1040 uses some of the same types of ports as the input device 1036. Thus, for example, a USB port may be used to provide input to the computer 1012 and to output information from the computer 1012 to the output device 1040. An output adapter 1042 is provided to illustrate that there are some output devices 1040 that require dedicated adapters, such as monitors, speakers, and printers, among others. By way of example, output adapters 1042 include, but are not limited to, video cards and sound cards that provide a means of connection between the output device 1040 and the system bus 1018. It should be noted that other devices and / or device systems, such as a remote computer 1044, provide both input and output capabilities.

[0087] The computer 1012 can operate in a networked environment using logical connections to one or more remote computers, such as a remote computer 1044. The remote computer 1044 can be a computer, a server, a router, a network PC, a workstation, a microprocessor-based device, a peer device or other common network node, and typically further includes many or all of the elements described with respect to the computer 1012. For simplicity, only a memory storage device 1046 is shown in the remote computer 1044. The remote computer 1044 is logically connected to the computer 1012 through a network interface 1048, and then physically connected through a communication connection 1050. The network interface 1048 encompasses a wired and / or wireless communication network, such as a local area network (LAN), a wide area network (WAN), a cellular network, and / or another wired and / or wireless communication network. LAN technologies include Fiber Distributed Data Interface (FDDI), Copper Distributed Data Interface (CDDI), Ethernet, Token Ring, and the like. WAN technologies include, but are not limited to, point-to-point links, circuit-switched networks such as Integrated Services Digital Networks (ISDN) and variations thereon, packet-switched networks, and Digital Subscriber Lines (DSL). The communications connection 1050 refers to the hardware / software used to connect the network interface 1048 to the system bus 1018. For ease of illustration, the communications connection 1050 is shown internal to the computer 1012, however, the communications connection 1050 can also be external to the computer 1012. For purposes of illustration only, the hardware / software for connecting to the network interface 1048 can further include internal and external technologies such as modems, including regular telephone grade modems, cable modems and DSL modems, ISDN adapters, and Ethernet cards.

[0088] The present invention can be a system, a method, an apparatus, or a computer program product, or a combination thereof, at any level of technical detail capable of integration. The computer program product can include a computer readable storage medium having computer readable program instructions thereon for causing a processor to execute aspects of the present invention. The computer readable storage medium can be a tangible device capable of holding and storing instructions for use by an instruction execution device. The computer readable storage medium can be, for example, but not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination thereof. A non-exhaustive 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 disk (DVD), memory stick, floppy disk, mechanically encoded devices such as punch cards or raised structures in grooves on which instructions are recorded, and suitable combinations thereof. As used herein, computer readable storage media should not be construed as being, in itself, a transitory signal, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating in a wave guide or other transmission body (e.g., light pulses traveling in a fiber optic cable), or electrical signals transmitted through electrical wires.

[0089] The computer readable program instructions described herein may be downloaded from a computer readable storage medium into the respective computing / processing device or may be downloaded to an external computer or storage device over a network, such as the Internet, a local area network, a wide area network, or a wireless network, or a combination thereof. The network may include copper transmission cables, optical transmission fiber, wireless transmission, routers, firewalls, switches, gateway computers, or edge servers, or a combination thereof. A network adapter card or network interface in each computing / processing device receives the computer readable program instructions from the network and transfers the computer readable program instructions to a computer readable storage medium in the respective computing / processing device for storage. The computer readable program instructions for carrying out the operations 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 may be source or object code written in any combination of one or more programming languages, including object oriented programming languages ​​such as Smalltalk®, C++, and procedural programming languages ​​such as the “C” programming language or the like. The computer readable program instructions may be executed entirely on the user's computer, partially on the user's computer, as a stand-alone 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 above, the remote computer may be connected to the user's computer via any type of network, including a local area network (LAN) or wide area network (WAN), or the connection may be made to an external computer (e.g., via the Internet using an Internet Service Provider). In some embodiments, electronic circuitry, including, for example, programmable logic circuits, field programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), may execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry to carry out aspects of the invention.

[0090] Aspects of the present invention are described herein with reference to flowchart and / or block diagram illustrations of methods, apparatus (systems) and computer program products according to embodiments of the present invention. It will be understood that each block of the flowchart and / or block diagram illustrations, and combinations of blocks in the flowchart and / or block diagram illustrations, can be implemented by computer readable program instructions. These computer readable program instructions can be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing device forming a machine such that the instructions, executed by the processor of the computer or other programmable data processing device, generate means for implementing the functions / operations specified in the blocks of the flowchart and / or block diagram illustrations. These computer readable program instructions can further be stored on a computer readable storage medium capable of directing a computer, programmable data processing device, or other device, or combination thereof, to function in a particular manner, such that the computer readable storage medium having instructions stored therein comprises a product including instructions for implementing aspects of the functions / operations specified in the blocks of the flowchart and / or block diagram illustrations. These computer readable program instructions can further be loaded onto a computer, other programmable apparatus or other device to cause the computer, other programmable apparatus or other device to perform a series of operational steps to generate a computer-implemented process in a manner such that the instructions executed on the computer, other programmable apparatus or other device perform the functions / operations specified in the blocks of these flowcharts and / or block diagrams.

[0091] The flowcharts and block diagrams in the accompanying figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in the flowcharts or block diagrams may represent a module, segment, or portion of instructions, including one or more executable instructions for implementing a specified logical function. In some alternative implementations, the functions shown in the blocks may be implemented in an order different from that shown in the figures. For example, two blocks shown in succession may in fact be executed substantially simultaneously, or the blocks may be executed in the reverse order depending on the functionality involved. It should also be noted that each block of the block diagrams and / or flowcharts, as well as combinations of blocks in the block diagrams and / or flowcharts, may be implemented by a hardware-based dedicated system that executes the specified functions or operations or implements a combination of dedicated hardware and computer instructions.

[0092] Although the subject matter has been described above in the general context of computer-executable instructions for a computer program product executing on one computer or multiple computers, or both, those skilled in the art will recognize that the disclosure may 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 particular tasks or implement particular abstract data types, or both. Furthermore, those skilled in the art will recognize that the computer-implemented methods of the present invention may also be implemented with other computer system configurations, including single-processor or multi-processor computer systems, minicomputing devices, mainframe computers, computers, handheld computing devices (e.g., PDAs, telephones), microprocessor-based or programmable home or industrial electronic devices, and the like. The illustrated aspects may also be implemented in distributed computing environments in which tasks are performed by remote processing devices linked through a communications network. However, some, if not all, aspects of the disclosure may also be implemented on stand-alone computers. In a distributed computing environment, program modules may be located in both local and remote memory storage devices. For example, in one or more embodiments, the computer-executable components may be executed from a memory that may include or 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 may execute code of the computer-executable components in a distributed manner, e.g., across multiple processors coupled or acting in cooperation to execute code 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 multiple memories or memory units in one or more locations.

[0093] As used in this application, the terms "component," "system," "platform," "interface," and the like, may refer to or include a computer-related or operational machine-related entity having one or more specific functions, or both. The entities disclosed herein may be hardware, a combination of hardware and software, software, or software in execution. For example, a component may be, but is not limited to, a process running on a processor, a processor, an object, an executable, a thread of execution, a program, or a computer, or combinations thereof. As an example, both an application running on a server and the server may be a component. Within a process or thread of execution, or both, one or more components may be localized on one computer or distributed between two or more computers, or both. In another example, corresponding respective components may be executed from various computer-readable media having various data structures stored thereon. A component may communicate via local or remote processes or both, e.g., according to a signal having one or more data packets (e.g., data from one component interacting with another component via a signal, either within a local system, within a distributed system, or across a network such as the Internet, or with other systems, or a combination thereof. As another example, a component may be a device having a particular function provided by mechanical parts operated by electrical or electronic circuits, which are operated by a software or firmware application executed by a processor.In such cases, the processor may be located within the device or external to the device and may execute at least a portion of the software or firmware application. As another example, a component may be a device that provides a particular functionality through electronic components that do not include mechanical parts, and those electronic components may include a processor or other means for executing software or firmware that at least partially provides the functionality of the electronic component. In one aspect, a component may emulate an electronic component through a virtual machine, for example in a cloud computing system.

[0094] Furthermore, the term "or" is intended to mean an inclusive "or" rather than an exclusive "or". That is, unless otherwise stated or clear 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 clear from the context to indicate the singular form, the articles "a" and "an" used in this specification and the accompanying drawings should generally be construed to mean "one or more". As used herein, the terms "example" and / or "exemplary" are utilized to mean serving as an example, instance, or illustration. For the avoidance of doubt, the subject matter disclosed herein is not limited by such examples. Moreover, any aspect or design described herein as "example" and / or "exemplary" is not necessarily to be construed as preferred or advantageous over other aspects or designs, or to be meant to exclude equivalent exemplary structures and techniques known to those skilled in the art.

[0095] As used herein, the term "processor" may refer to virtually any computing processing unit or device, including, but not limited to, a single-core processor, a single-core processor with software multithreaded execution capabilities, a multi-core processor, a multi-core processor with software multithreaded execution capabilities, a multi-core processor with hardware multithreading techniques, a parallel platform, and a parallel platform with distributed shared memory. Additionally, a processor may refer to an integrated circuit designed to perform the functions described herein, an application specific integrated circuit (ASIC), a digital signal processor (DSP), a field programmable gate array (FPGA), a programmable logic controller (PLC), a complex programmable logic device (CPLD), discrete gate or transistor logic, discrete hardware components, or any combination thereof. Additionally, a processor may utilize nanoscale architectures, such as, but not limited to, molecular-based and quantum dot-based transistors, switches, and gates, to optimize space usage or enhance the performance of a user device. A processor may also be implemented as a combination of computing processing units. In this disclosure, terms such as "store," "storage," "data store," "data storage," "database," and substantially any other information storage component associated with the operation and functionality of the component are utilized to refer to a "memory component" that is an entity embodied as a "memory" or a component that includes memory. It should be appreciated that the memory and / or memory components described herein can be volatile or non-volatile memory, or can include both volatile and non-volatile memory.By way of 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. Many forms of RAM may be used, including, by way of example, but 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). Additionally, the disclosed memory components of the systems or computer-implemented methods herein are intended to include, but are not limited to, these and other suitable types of memory.

[0096] What has been described above includes merely examples of systems and computer-implemented methods. Of course, it is not possible to describe every conceivable combination of components or computer-implemented methods in order to describe the present disclosure, but one of ordinary skill in the art can appreciate that many other combinations and permutations of the present disclosure are possible. Moreover, to the extent that the terms "includes," "has," "possesses," and the like are used in the detailed description, claims, appendices, and drawings, such terms are intended to be inclusive in the same manner as the term "comprising" is interpreted when used as a transitional word in the claims.

[0097] The above description of various embodiments is provided for illustrative purposes, and is not intended to be exhaustive or to be limited to only the disclosed embodiments. Many modifications and variations that do not depart from the scope and spirit of the described embodiments will be apparent to those skilled in the art. The terms used in this specification have been selected to best explain the principles of the embodiments, practical applications, or technical improvements over commercially available technology, or to enable those skilled in the art to understand the embodiments disclosed herein.

Claims

1. 1. A system comprising: a memory for storing an executable component; a processor for executing computer-executable components stored in memory; the computer executable components comprising: a wave splitting component that generates a plurality of waveform segments using a definition of an intended waveform, the plurality of waveform segments being capable of being phase shifted; and 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; Including, the system.

2. a waveform generator for regenerating the at least one waveform segment of the plurality of waveform segments with the phase rotation. The system of claim 1 .

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

4. The system of claim 3 , wherein a starting phase rotation of the waveform segments of the plurality of waveform segments is zero.

5. 5. The system of claim 4, wherein the rotation component assigns the phase rotation applied by the waveform generator to the at least one waveform segment of the plurality of waveform segments using a phase rotation factor 2π(ω+ε)t, where t is the time that the at least one waveform segment of the plurality of waveform segments is played by the waveform generator and ω+ε is a frequency of the intended waveform.

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

7. 7. The system of claim 6, wherein playing the plurality of waveform segments by the waveform generator with the different phase rotations for each waveform segment of the plurality of waveform segments approximates a frequency sweep.

8. 8. The system of claim 5, wherein the phase rotation applied to the at least one waveform segment of the plurality of waveform segments is assigned upon playback of the at least one waveform segment of the plurality of waveform segments.

9. 1. A computer-implemented method comprising: generating, by a system operatively coupled to a processor, a plurality of waveform segments using a definition of an intended waveform, the plurality of waveform segments being capable of being phase shifted; and assigning, by the system, 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.

23. A computer-implemented method comprising:

10. reproducing, by the system via a waveform generator, the at least one waveform segment of the plurality of waveform segments with the phase rotation. The computer-implemented method of claim 9 , further comprising:

11. 11. The computer-implemented method of claim 10, wherein the at least one waveform snippet of the plurality of waveform snippets reproduced with the phase rotation by the waveform generator approximates a continuous waveform.

12. The computer-implemented method of claim 11 , wherein a starting phase rotation of the plurality of waveform snippets is zero.

13. 13. The computer-implemented method of claim 12, wherein the system assigns the phase rotation applied by the waveform generator to the at least one waveform segment of the plurality of waveform segments using a phase rotation coefficient 2π(ω+ε)t, where t is the time that the at least one waveform segment of the plurality of waveform segments is played by the waveform generator and ω+ε is the frequency of the intended waveform.

14. 14. The computer-implemented method of claim 13, wherein the system assigns different phase rotations applied by the waveform generator to each waveform segment of the plurality of waveform segments by using different ε values ​​for each waveform segment of the plurality of waveform segments.

15. 15. The computer-implemented method of claim 14, wherein playing, by the waveform generator, the plurality of waveform segments with the different phase rotations for each waveform segment of the plurality of waveform segments approximates a frequency sweep.

16. 16. The computer-implemented method of claim 13, wherein the phase rotation applied to the at least one waveform segment of the plurality of waveform segments is determined upon playback of the at least one waveform segment of the plurality of waveform segments.

17. A computer program product, the computer program product including one or more computer readable storage media having program instructions embodied therein, the program instructions comprising: generating, by a processor, a plurality of waveform segments using a definition of an intended waveform, the plurality of waveform segments being capable of being phase shifted; and assigning, by the processor, 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. a computer program product executable by the processor to cause the processor to execute the

18. The program instructions further include: regenerating the at least one waveform segment of the plurality of waveform segments with the phase rotation via a waveform generator.

20. The computer program product of claim 17, executable by the processor to cause the processor to execute:

19. 20. The computer program product of claim 18, wherein the at least one waveform segment of the plurality of waveform segments reproduced with the phase rotation by the waveform generator approximates a continuous waveform.

20. 20. The computer program product of claim 19, wherein a starting phase rotation of the plurality of waveform snippets is zero.

21. 21. The computer program product of claim 20, wherein the phase rotation applied to the at least one waveform segment of the plurality of waveform segments is assigned using a phase rotation factor 2π(ω+ε)t, where t is a time at which the at least one waveform segment of the plurality of waveform segments is played by the waveform generator and ω+ε is a frequency of the intended waveform.

22. 22. The computer program product of claim 21, wherein the processor assigns different phase rotations applied by the waveform generator to each waveform segment of the plurality of waveform segments by using different ε values ​​for each waveform segment of the plurality of waveform segments.

23. 23. The computer program product of claim 22, wherein playing, by the waveform generator, the plurality of waveform segments with the different phase rotations for each waveform segment of the plurality of waveform segments approximates a frequency sweep.

24. 24. A computer program product as claimed in any one of claims 21 to 23, wherein the phase rotation applied to at least one waveform segment of the plurality of waveform segments is assigned during playback of the at least one waveform segment of the plurality of waveform segments.

25. 1. A system comprising: a memory for storing an executable component; a processor for executing computer-executable components stored in memory; the computer executable components comprising: a wave splitting component that generates a plurality of waveform segments using a resource waveform definition, the wave splitting component being capable of inserting a phase slip between each of the plurality of waveform segments; and a phase slip component that assigns the phase slip to be inserted between at least two waveform segments of the plurality of waveform segments; Including, the system.

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