Qubit frequency control

Abstract

Provided is a qubit frequency control method, comprising applying (S110) an AC Stark pulse to at least one qubit (110, 120) during an application of a quantum gate, wherein the AC Stark pulse is generated using a waveform envelope comprising a rising edge and / or of a falling edge that reduces non-adiabatic error of the AC Stark pulse.

Description

[0001] Qubit Frequency Control

[0002] Technical Field

[0003] The present disclosure relates to a qubit frequency control method for applying one or more AC Stark pulses to tune qubit state ( s ) on resonance , in particular to tune two qubit states on resonance , during a coupler flux pulse . The present disclosure is also related to a corresponding qubit frequency control apparatus and a quantum system .

[0004] Quantum computing processors execute quantum circuits defined by gates which may be considered as fundamental building blocks for manipulating quantum information . The power of quantum computing lies in its ability to exploit quantum superposition and entanglement to perform parallel computations , exponentially increasing its computational capacity compared to classical computers . The success ful technical implementation and precise control of single-qubit and two- qubit gates are crucial for building scalable and fault- tolerant quantum processors , advancing the field towards solving complex problems that are intractable for classical computers .

[0005] Single-qubit gates act on individual physical qubits which are the basic units of quantum information di f ferent from binary digital technologies . These gates perform operations like rotations and flips , altering the state of a qubit , for example Pauli gates , the Hadamard gate , phase gates and the like .

[0006] Two-qubit gates , on the other hand, interact between pairs of physical qubits , allowing for the creation of entangled states and enabling more complex quantum computations . Examples are the controlled NOT ( CNOT ) gate , controlled Z ( CZ ) gates , SWAP gates , controlled Hadamard gates , controlled phase gates and the like .

[0007] There are di f ferent technical reali zations of physical qubits . Qubits can be reali zed as fixed frequency qubits or tunable frequency qubits . In the case of superconducting qubits , a fixed frequency qubit can comprise a single Josephson j unction, while a tunable frequency qubit can be a flux-tunable qubit based on a superconducting quantum interference device ( SQUID) loop for which the frequency may be controlled by changing the magnetic flux passing though the SQUID loop . One example of a technical reali zation is a flux-tunable transmon qubits for which gates may be implemented using capacitively coupled lines . Pulse forms for the qubit drives may be generated by arbitrary-waveform generators . A read out may be performed using a readout structure having a readout resonator and a Purcell filter, being coupled to a transmission line .

[0008] Fidelity in quantum computing refers to the accuracy and reliability with which quantum gates perform their intended operations on qubits . Fidelity is a measure of how closely the output of a quantum gate aligns with the desired quantum state . High fidelity is crucial in quantum computing because it ensures that quantum operations are executed precisely, minimi zing errors and deviations from the expected results . In the context of single-qubit gates , high fidelity ensures the accurate manipulation of individual qubits , preserving the integrity of quantum information encoded in their states . For two-qubit gates , fidelity becomes even more critical as it influences the creation and maintenance of entangled states , which are essential for quantum parallelism and the potential computational advantages of quantum algorithms . Achieving higher fidelities in both single-qubit and two-qubit gates is a key challenge in the development of quantum processors , as it directly impacts the reliability and ef ficiency of quantum computations . In the context of pursuing higher fidelities , shorter gate times in quantum computing are highly desirable due to their impact on the overall performance and ef ficiency of quantum processors . Gate time refers to the duration it takes for a quantum gate operation to be executed on qubits . Minimi zing gate times is crucial for several reasons . Firstly, shorter gate times reduce the vulnerability to environmental noise and decoherence , which can negatively af fect the stability of quantum states . Additionally, faster gate operations enable the implementation of quantum algorithms with improved speed and computational power . Shorter gate times also contribute to the mitigation of errors during quantum computations , enhancing the reliability of quantum processors . As quantum technologies rapidly advance towards practical applications , achieving shorter gate times becomes a central focus in the development of scalable and f ault-tolerant quantum computers , paving the way for the reali zation of quantum advantage in solving complex problems that classical computers find challenging .

[0009] Technical Problem

[0010] Tunable couplers have been introduced to control the qubitqubit interactions in real time and support the technical implementation of high- fidelity two-qubit gates on the nanosecond time scale . Tunable couplers may also be used for isolated gate operations in scalable quantum processor architectures , see for example , Marxer et al . , PRX Quantum 4 , 010314 , 2023 . For example , two-qubit gates implemented with flux pulses on a tunable coupler can achieve shorter gate times compared to other techniques , including cross resonance gates or parametric gates , or other QPU architectures which do not employ couplers . In the case of a qubit-coupler-qubit system, the qubit and the coupler frequencies are tuned by creating a magnetic field threading through the SQUID loops , see also Sung et al . , Phys . Rev . X 11 , 021058 , 2021 . The purpose of the frequency tuning of the qubit ( s ) is to relax the requirements of the idling configuration, in particular of a larger quantum processor unit ( QPU) having a larger number of qubits . That is , the respective states do not initially have to be close to resonance . Instead, flux pulses are used to bring the respective states into resonance to achieve a high- fidelity two-qubit gate , in particular during a coupler pulse . However, the skilled person understands that such a configuration increases the hardware costs as additional fast flux lines are required, and lead to increased complexity of the tune-up procedure ( including (pre- ) compensation procedures ) . Here , fast flux lines refer to control lines where fast DC pulses , preferably less than 60ns long, can be applied .

[0011] Gate errors remain a maj or bottleneck in such a configuration . Pursuing high fidelity gates across a large range of frequencies is important , for example to have better flexibility of the idling configuration ( i . e . a state in which a quantum processor is not actively engaged in performing computational tasks but is instead maintaining the coherence of its qubits ) .

[0012] As such, there is a need for achieving higher fidelities across a large range of frequencies without additional hardware requirements .

[0013] Solution

[0014] The present inventors have reali zed that high fidelity gates and reduced error and reduced hardware requirements can be achieved by applying an AC Stark pulse to a qubit for frequency tuning of a qubit , in particular during a coupler flux pulse . According to an aspect of the present disclosure , a qubit frequency control method, comprises applying an AC Stark pulse to at least one qubit during an application of a quantum gate , wherein the AC Stark pulse is generated using a waveform envelope comprising a rising edge and / or of a falling edge that reduces non-adiabatic error of the AC Stark pulse .

[0015] According to another aspect of the present disclosure , the waveform envelope may be modulated with a selected AC Stark frequency to generate the AC Stark pulse .

[0016] According to another aspect of the present disclosure , the waveform envelope may be one of a plurality of waveform envelopes having di f ferent rising edges and / or falling edges , the one waveform envelope being selected to minimi ze the non- adiabatic error of the AC Stark pulse .

[0017] According to another aspect of the present disclosure , a shape of the rising edge and / or a fall ing edge may be a Slepian- based pulse shape or a Cosine-based pulse shape .

[0018] According to another aspect of the present disclosure , the AC Stark pulse may have a total duration of less than 60 nanoseconds , in particular less than 40 nanoseconds .

[0019] According to another aspect of the present disclosure , the quantum gate may be a two-qubit gate or a single-qubit gate .

[0020] According to another aspect of the present disclosure , the quantum gate may be a CZ gate or an iSWAP gate .

[0021] According to another aspect of the present disclosure , the method may further comprise applying, during the application of the AC Stark pulse to the at least one qubit , a control pulse to a tunable coupler . According to another aspect of the present disclosure , the control pulse may be a flux pulse .

[0022] According to another aspect of the present disclosure , the method may further comprise applying another AC Stark pulse to another qubit during the application of the quantum gate .

[0023] According to another aspect of the present disclosure , a qubit frequency control apparatus may comprise a pulse generator configured to apply an AC Stark pulse to at least one qubit during an application of a quantum gate , wherein the AC Stark pulse is generated using a waveform envelope comprising a shape and duration of a rising edge and / or of a falling edge that reduces non-adiabatic error of the AC Stark pulse .

[0024] According to another aspect of the present disclosure , a quantum system comprises a plurality of qubits ; and a qubit frequency control apparatus having a pulse generator configured to apply an AC Stark pulse to at least one qubit during an application of a quantum gate , wherein the AC Stark pulse is generated using a waveform envelope comprising a shape and duration of a rising edge and / or of a falling edge that reduces non-adiabatic error of the AC Stark pulse .

[0025] According to another aspect of the present disclosure , the qubit frequency control apparatus of the quantum system may be configured to apply the AC Stark pulse to one or more of the plurality of qubits .

[0026] According to another aspect of the present disclosure , the quantum system may further comprise at least one tunable coupler configured to couple to a first qubit and to a second qubit of the plurality of qubits .

[0027] According to another aspect of the present disclosure , the pulse generator of the quantum system may be configured to apply, during the application of the AC Stark pulse to the first qubit and / or the second qubit, a control pulse to the tunable coupler.

[0028] According to another aspect of the present disclosure, the pulse generator of the quantum system may be configured to apply, during the application of a first AC Stark pulse to the first qubit and the application of a second AC Stark pulse to the second qubit, a control pulse to the tunable coupler.

[0029] According to another aspect of the present disclosure, the control pulse of the pulse generator of the quantum system may be a flux pulse.

[0030] According to another aspect of the present disclosure, the qubits of the plurality of qubits may be fixed-frequency qubits .

[0031] According to another aspect of the present disclosure, qubit drive lines may be used for the application of the one or more AC Stark pulses.

[0032] As the AC Stark pulses can use already present qubit drive lines, this decreases hardware requirements as less control lines are required compared to flux- tunable qubits. Therefore, flux-tunable qubits are not required, simplifying the setup and control of QPU architectures.

[0033] Brief Description of the Drawings

[0034] Fig. 1 shows a quantum energy state diagram of a quantum system comprising a first qubit (QI) , a second qubit (Q2) , and a coupler (C) according to a qubit frequency control method using AC Stark pulse (s) .

[0035] Fig. 2 illustrates a quantum system according to an embodiment. Fig . 3 illustrates a flowchart of a qubit frequency control method according to an embodiment .

[0036] Fig . 4A shows an example of two waveform envelopes selectable for an AC Stark pulse of 40 nanoseconds according to an embodiment .

[0037] Fig . 4B illustrates the non-adiabatic error ( on a logarithmic scale ) as a function of the rise time for a Slepian rising and falling edge and a cosine rising and falling edge .

[0038] Figs . 5A and 5B show a comparison of a conventional application of a quantum gate ( e . g . a CZ gate ) with the application of the quantum gate according to the present disclosure , respectively .

[0039] Detailed Description

[0040] Embodiments of the present disclosure will now be described in reference to the enclosed figures . In the following detailed description, numerous speci fic details are set forth . These speci fic details are only to provide a thorough understanding of the various described embodiments . Further, although the terms first , second, etc . may be used to describe various elements , these elements should not be limited by these terms . These terms are only used to distinguish one element from another .

[0041] Where technical features in the drawings , detailed description or any claim are followed by reference signs , the reference signs have been included for the sole purpose of increasing the intelligibility of the drawings , detailed description, and claims . Accordingly, neither the reference signs nor their absence have any limiting ef fect on the scope of any claim elements . Fig. 1 shows a quantum energy state diagram of a qubit-coupler- qubit system with regard to a first qubit (QI) , a second qubit (Q2) , and a coupler (C) . Here, the states |Q1, C, Q2> denote the uncoupled energy states of the qubit-coupler-qubit system. In this illustrative example, both qubits are fixed frequency qubits, i.e. qubits without a specific hardware flux line for the application of a flux pulse. Alternatively, at least one of the qubits can be a frequency-tunable qubit having a specific hardware flux line for the application of a flux pulse. Furthermore, as will be further discussed in conjunction with Fig. 5B, the frequency of the coupler may be tuned by a flux pulse, and the frequency of (at least) the second qubit (Q2) is tuned by the application of an AC Stark pulse. A purpose of the frequency tuning of the qubit (s) is to relax the requirements of the idling configuration, in particular of a larger quantum processor unit (QPU) having a larger number of qubits. That is, the respective states (in this example | 200> and | 101>) do not initially have to be close to resonance. According to the present disclosure, one or more AC Stark pulses can be used to bring the respective states into resonance to achieve a high-fidelity two-qubit gate, in particular during a coupler pulse. By using AC Stark pulses, the hardware costs can be reduced because additional fast flux lines are not required for frequency tuning (as in the conventional systems) .

[0042] Fig. 2 illustrates a quantum system according to an embodiment. As shown, the quantum system includes a quantum processor component 100 and a qubit frequency control apparatus 200. The quantum processor component 100 has a plurality of qubits; Fig. 2 illustrates a first qubit 110 and a second qubit 120 of the plurality of qubits, but the quantum processor component 100 may have more than two qubits. At least one of the first qubit 110 and the second qubit 120 is a qubit tunable with an AC Stark pulse (in other words, a fixed-frequency qubit without a specific hardware flux line for the application of a flux pulse) . The quantum processor component 100 may also have a coupler 130 . The coupler 130 is preferably configured to couple to the first qubit 110 and to the second qubit 120 of the plurality of qubits . The coupler 130 is preferably a tunable coupler ; the tunable coupler 130 can be tuned to turn the interaction between neighbouring qubits on and of f and thus provides a tunable ef fective qubit-qubit coupling . Alternatively, the tunable coupler may also provide a frequency tunability .

[0043] The coupler may be a transmon coupler, as described in Marxer et al . , PRX Quantum 4 , 010314 , 2023 , to implement a system in which two grounded transmon qubits ( implemented by the first and second qubit 110 and 120 , respectively) interact through a floating transmon coupler . In such an architecture , the transmon qubits ( first and second qubit ) may be connected to the tunable coupler with two waveguide structures mediating ef fective capacitances between the qubits and the coupler . The two waveguide structures may be implemented of coplanar waveguides having resonance frequencies being an order of magnitude higher than those of the qubits and coupler frequencies . This allows flexibility in independently adj usting capacitance values so that the quantum system can ef fectively dimensioned by coupling strengths between the first qubit and the coupler, between the second qubit and the coupler, and between the first and second qubit . The skilled person understands that this a non-limiting technical example of a quantum system having tunable coupling . For example , also direct capacitive couplings may also be implemented, see Sete et al . , Phys . Rev . Appl . 15 , 064063 , 2021 . The skilled person also understands that the quantum system is scalable in that identical couplings may simultaneously implemented for more than the two qubits illustrated, such as , for example , four neighbouring qubits in a qubit lattice .

[0044] The qubit frequency control apparatus 200 in Fig . 2 includes a pulse generator 210 configured to generate control pulses to the first qubit 110, the second qubit 120, and / or the coupler 130. In particular, the pulse generator may be an arbitrary- waveform generator that can be programmed (based on software instructions and including waveform data) to generate arbitrary waveforms, in particular to determine, adjust, shape AC Stark pulses (as will be further described below) . The pulse generator 210 may generate different pulse shapes for the first qubit 110, the second qubit 120, and / or the coupler 130; preferably, the pulse generator 210 may represent individual pulse generators for the first qubit 110, the second qubit 120, and / or the coupler 130. The pulse generator (s) may apply the pulses at the qubit drive lines of the respective qubits and may apply the flux pulse at the flux line of the coupler.

[0045] Fig. 3 illustrates a flowchart of a qubit frequency control method according to an embodiment. As shown, in step Slid, an AC Stark pulse, as generated by the pulse generator 210, is applied to the first qubit 110 and / or the second qubit 120 during an application of a quantum gate. The existing drive lines of the qubit can be used for the application of the AC Stark pulse (s) so that addition flux lines are not required (thus eliminating the need for flux tunable qubits) .

[0046] The AC Stark pulse may be generated using a waveform envelope comprising a rising edge and / or falling edge that reduces a non-adiabatic error of the AC Stark pulse. In other words, by selecting parameters of the rising edge and / or the falling edge, such as a shape and / or duration of the rising edge and / or the falling edge, the overall non-adiabatic error resulting from the application of the AC Stark pulse can be reduced or minimized. As such, a reduction in hardware costs (avoidance of flux lines) can advantageously combined with higher fidelity values .

[0047] The AC Stark pulse is an off-resonant drive pulse and is used to provide a frequency tuning to bring certain states (of another qubit and / or the coupler) on resonance. In other words, the AC Stark pulse causes a (temporary) frequency shift of the qubit due to the AC Stark effect and this is performed for frequency alignment, not for frequency collision mitigation, as described in US 11,789, 812 B2. In general, the qubit frequency shift is found to scale quadratically with the amplitude of the AC Stark pulse.

[0048] The AC Stark pulse has, in general, an oscillating electromagnetic field or oscillating microwave field component, with an oscillating frequency between, for example, 4 GHz and 6 GHz. For example, if the qubit frequency is at a frequency of 4 GHz, the selected AC Stark frequency may be in a range between 4.1 GHz and 4.4 GHz. The skilled person understands that the oscillation frequency is selected or adapted with regard to the qubit's frequency. The AC Stark pulse may have a waveform envelope comprising a rising edge, a flat part, and a falling edge. The rising edge may be defined for a time duration (rise time) from a start of the AC Stark pulse until the start of the flat part, and the falling edge may be defined for a time duration (fall time) from the end of the flat part until the end of the AC Stark pulse. Further, the duration of the flat part of the AC Stark pulse envelope may be defined by (or set according to) the duration of a quantum gate that is applied at the same time. A total duration of the waveform envelope (which corresponds to a total duration of the AC Stark pulse) may be considered as a sum of the time duration (rise time) of the rising edge, the time duration of the flat part and the time duration (fall time) of the falling edge. A total duration of the waveform envelope and therefore the AC Stark pulse may be less than 60 nanoseconds, in particular less than 40 nanoseconds.

[0049] In addition, the AC Stark pulse may be defined by a shape of the rising edge and / or a shape of the falling edge being optimized to reduce non-adiabatic error. In other words, given a certain non-adiabatic error that may be predefined (e.g. with regard to a tolerable non-adiabatic error) and may be determined with regard to di f ferent shapes of the rising and / or falling edge , the duration of the rise and / or fall times may be minimi zed .

[0050] Fig . 4A shows an example of two waveform envelopes selectable for an AC Stark pulse of 40 nanoseconds according to an embodiment . In particular, Fig . 4A shows a first waveform envelope ( straight line ) having a Slepian shape for the rising edge with a rise time between 0 ns to about 10 ns and having a Slepian shape for the falling edge with a fall time between about 30 ns to 40 ns defining the shape of the rising edge and falling edge as a Slepian rising edge and a Slepian falling edge , respectively, as well as a second waveform envelope ( dashed line ) having a Cosine shape for the rising edge and a Cosine shape for the falling edge as a Cosine rising edge and a Cosine falling edge , respectively . The skilled person understands that the Cosine rising edge and the Cosine falling edge may be defined by hal f a period of a Cosine function, and that a Slepian rising edge and a Slepian falling edge may be defined using a Fourier basis function in an accelerated time frame . The skilled person also understands that the duration of the rise time and / or the fall time can be more or less than 10 ns . Further, the duration of the rise time and / or the fall time may depend on a desired coupling strength between the electromagnetic field ( s ) created by the AC Stark pulse ( s ) and the qubit ( s ) .

[0051] Preferably, the AC Stark pulse is generated by modulating the waveform envelope ( as , for example , shown in Fig . 4A) with a selected AC Stark frequency, for example selected in the range between 4 GHz and 6 GHz .

[0052] According to a preferred embodiment , the used waveform envelope is selected from a plurality of di f ferent waveform envelopes having di f ferent shapes of the rising and / or falling edge . For example , while the flat part remains unadj usted, the shape of the rising edge and / or the falling edge may be di f ferent , and may have , for example , a Slepian pulse shape or a Cosine-based pulse shape . The di f ferent waveform envelopes may cause di f ferent non-adiabatic errors ; preferably the waveform envelope is selected which minimi zes the non-adiabatic error of the AC Stark pulse . Thus , a Slepian rising and / or falling edge or a Cosine rising and / or falling edge may be selected, depending, for example on the selected rise time and / or fall time .

[0053] The selection of the waveform envelope may thus be based on the non-adiabatic error associated with the waveform envelope for a particular shape and / or duration of the rising and / or falling edge .

[0054] Fig . 4B illustrates the non-adiabatic error ( on a logarithmic scale ) as a function of the rise time , where it is assumed that the fall time is equal to the rise time . The rising edge and the falling edge may have the same time duration . The skilled person understands that the non-adiabatic error is signi ficantly reduced at longer rise times and that the Slepian-based pulse shape generally results in a smaller non- adiabatic error compared to the Cosine-based pulse shape for a given rise / fall time .

[0055] In other words , while the overall AC Stark pulse should be made shorter to improve overall fidelity and have an amplitude suf ficient enough to induce the required frequency shi ft , there is the opposite tendency to have a suf ficiently long rise and / or fall time so that the non-adiabatic error is less than a predefined threshold . In the example , illustrated in Fig . 4B, the rise time of the rising edge and / or the fall time of the falling edge of at least 10ns is associated with a non- adiabatic error being less than about 10-6for the Slepian rising / falling edge .

[0056] As explained, the thus generated one or more AC Stark pulse ( s ) is ( are ) applied to at least one qubit during an operation of a quantum gate; that is, the (respective) AC Stark pulse is used to shift the qubit frequency to allow a fast single / two- qubit gate to be executed. Preferably the quantum gate is a two two-qubit gate or a single-qubit gate, for example a controlled-Z (CZ) gate or an iSWAP gate. Here, the above rise time and shape of the rising edge and / or fall time and shape of the falling edge and the associated non-adiabatic error can also be gate specific. In other words, while the duration of the flat part of the waveform envelope (as shown in Fig. 4A between 10 ns and 30 ns) may be gate specific, different non- adiabatic error (s) may be acceptable for different gates, and therefore also the rise time and shape of the rising edge and / or the fall time and shape of the falling edge can be gate specific .

[0057] According to a preferred embodiment, illustrated by step S130 in Fig. 3, during the application of the AC Stark pulse to the first qubit 110 and / or the second qubit 120, the pulse generator 210 may simultaneously apply a control pulse to the tunable coupler 130. The control pulse to the tunable coupler 130 may be a control pulse to tune the frequency of the coupler to turn on the interaction between the qubits.

[0058] Such a control pulse to the tunable coupler may be a flux pulse, for example a Slepian-shaped flux pulse, for example when executing a high-fidelity controlled-Z gate, to minimize dominant leakage processed during the gate from a (second) qubit to the coupler. The skilled person understands that distortions (e.g. introduced by the electrical operations of the hardware components) on the flux pulse shape may be mitigated, for example by using infinite-impulse-response filters to correct for the flux pulse shape in real time, by adding idle times before and / or after the flux pulse, and the like. The control pulse to the tunable coupler may also be an AC Stark pulse, as described in the present disclosure. According to a preferred embodiment , also distortions on the pulse shape of the AC Stark pulse due to the electrical operations of the hardware components are pre-compensated or compensated in real time . Advantageously, such distortions are less relevant and thus signi ficantly less compensation of distortions is required for AC Stark pulses (because the oscillating nature of the AC Stark pulses lead to cancellation ef fects between the respective oscillating phases ) . For a precompensation, the influence of the electrical operations of the hardware components may be simulated or measured in advance , so that the actual AC Stark pulse shape is generated in a way that the distortions of the electrical operations of the hardware components lead to the intended AC Stark pulse shape . The compensation in real time also can be implemented by applying an appropriate filter, for example a finite impulse response ( FIR) filter .

[0059] According to another preferred embodiment , during the application of the AC Stark pulse to the first qubit 110 , another ( a second) AC Stark pulse may simultaneously be applied to another qubit ( the second qubit 120 or another qubit ) during the application of the quantum gate . This may be useful for a two-qubit gate but may also be applied for a single-qubit gate , for example by tuning the neighbouring qubits away to apply simultaneous single-qubit gates . The second AC Stark pulse may generally be generated as described above ; in addition, it may preferable that the first and second AC Stark pulse are di f ferent in terms of at least one of selected Stark frequency, waveform envelope , rising edge ( including rise time and / or shape ) and / or falling edge ( including fall time and / or shape ) . As such, a flexible frequency control mechanism is provided to adj ust the qubit frequencies with less control lines ( since the AC Stark pulse can use the existing qubit drive lines and additional flux lines are not required for this frequency control ) . Figs. 5A and 5B show a comparison of an execution of a quantum gate, for example a CZ gate, using conventional flux pulses vis-a-vis using AC Stark pulses according to the present disclosure. As shown in Fig. 5A, a flux pulse (e.g. a pulse having a Cosine-based raise and fall pulse shape) may be applied via a flux line to the first qubit while a control pulse (e.g. a Slepian-based control pulse) is simultaneously applied via a flux line to the tunable coupler to bring respective frequencies into resonance. As further indicated, a second flux pulse may simultaneously be applied via another flux line to the second qubit. As shown in Fig. 5B, while the control pulse may also be applied via a flux line to the tunable coupler, according to the present disclosure, a specifically shaped AC Stark pulse is applied via an already existing drive line to the first qubit. Fig. 5B illustrates the modulated waveform envelope (the frequency component used in Fig. 5B is merely for illustrative purposes) , i.e. the form of an AC Stark pulse to be applied at the drive line(s) of the qubit (s) . The specifically shaped AC Stark pulse is provided with a particular pulse shape for the rising and / or falling edge to minimize non-adiabatic error, as described above. By comparison, while the gate time / duration for the AC pulse shape in Fig. 5B may be somewhat longer (to have a sufficiently low non-adiabatic error) , this is an acceptable compromise in terms of short gate times and high fidelity vis-a-vis reduced hardware requirements (no extra flux lines are required to the qubits) .

[0060] The qubit frequency control apparatus 200 shown in Fig. 2 comprises the pulse generator 210 which is configured (by hardware and software) to generate and apply one or multiple (simultaneously or in sequence) AC Stark pulses, as described above, to at least the qubit 110 and / or the qubit 120, during an application of one or more quantum gates. As described, the AC Stark pulse is generated using a waveform envelope having a specific shape and / or time duration for the rising edge and / or for the falling edge that reduces non-adiabatic error of the AC Stark pulse .

[0061] While the quantum system in Fig . 2 shows the first qubit 110 and the second qubit 120 , the quantum system may also comprise more than two qubits , for example tens of qubits . The quantum system also comprises the qubit frequency control apparatus 200 that is configured to apply the one or more AC Stark pulses to each of the plurality of qubits . Respective AC Stark pulses may be applied to each of the plurality of qubits , for example , for implementing simultaneous single-gate qubits (while tuning away neighbouring qubits ) . As described above , at least one tunable coupler 130 may also be to couple to couple respective qubits of the plurality of qubits .

[0062] The quantum processor component 100 can work in conj unction with the qubit frequency control apparatus 200 ( including the pulse generator ( s ) 210 ) to facilitate performing the various functions described above . The quantum processor component 100 and the qubit frequency control apparatus 200 can employ one or more processors , microprocessors , or controllers that can process data, such as information relating to qubits , quantum circuits , quantum operations , gates , AC Stark pulses , stark shi fting, coupler pulses , and functions as described above ,

[0063] The qubit frequency control apparatus 200 may also include data memory (not shown) to store data related to qubits , circuits , quantum operations , gates , AC Stark pulses , Stark shi fting, coupler pulses , and functions described above . In an aspect , a processor component can be functionally coupled to the data memory in order to store and retrieve information desired to operate and / or control functionality of the pulse generator .

[0064] The systems and / or devices are described herein with respect to interaction between several components . It should be appreciated that such systems and components can include those components or sub-components speci fied therein, some of the speci fied components or sub-components , and / or additional components . Sub-components could also be implemented as components communicatively coupled to other components rather than included within parent components . Further yet , one or more components and / or sub-components may be combined into a single component providing aggregate functionality . The components may also interact with one or more other components not speci fically described herein for the sake of brevity, but known by those of skill in the art .

[0065] It will be apparent to those skilled in the art that various modi fications and variations can be made in the entities and methods of this disclosure as well as in the construction of this disclosure without departing from the scope or spirit of the disclosure .

[0066] The disclosure has been described in relation to particular embodiments which are intended in all aspects to be illustrative rather than restrictive . Those skilled in the art will appreciate that many di f ferent combinations of hardware , software and / or firmware will be suitable for practicing the present disclosure .

[0067] Moreover, other implementations of the disclosure will be apparent to those skilled in the art from consideration of the speci fication and practice of the disclosure disclosed herein . It is intended that the speci fication and the examples be considered as exemplary only . To this end, it is to be understood that inventive aspects lie in less than all features of a single foregoing disclosed implementation or configuration . Thus , the true scope and spirit of the disclosure is indicated by the following claims .

Claims

Claims1. A qubit frequency control method, comprising: applying (S110) an AC Stark pulse to at least one qubit (110, 120) during an application of a quantum gate, wherein the AC Stark pulse is generated using a waveform envelope comprising a rising edge and / or of a falling edge that reduces non-adiabatic error of the AC Stark pulse .

2. The method of claim 1, wherein the waveform envelope is modulated with a selected AC Stark frequency to generate the AC Stark pulse.

3. The method of any of claims 1 - 2, wherein the waveform envelope is one of a plurality of waveform envelopes having different rising edges and / or falling edges, the one waveform envelope being selected to minimize the non-adiabatic error of the AC Stark pulse.

4. The method of any of claims 1 - 3, wherein a shape of the rising edge and / or the falling edge is a Slepian- based pulse shape or a Cosine-based pulse shape.

5. The method of any of claims 1 - 4, wherein the AC Stark pulse has a total duration of less than 60 nanoseconds, in particular less than 40 nanoseconds.

6. The method of any of claims 1 - 5, wherein the quantum gate is a two-qubit gate, in particular a CZ gate or an iSWAP gate, or a single-qubit gate.

7. The method of any of claims 1 - 6, further comprising applying (S130) , during the application of the AC Stark pulse to the at least one qubit, a control pulse to a tunable coupler, in particular the control pulse being a flux pulse.

8. The method of any of claims 1 - 7, further comprising applying another AC Stark pulse to another qubit during the application of the quantum gate.

9. A qubit frequency control apparatus (200) , comprising a pulse generator (210) configured to apply an AC Stark pulse to at least one qubit (110, 120) during an application of a quantum gate, wherein the AC Stark pulse is generated using a waveform envelope comprising a shape and duration of a rising edge and / or of a falling edge that reduces non-adiabatic error of the AC Stark pulse.

10. A quantum system, comprising: a plurality of qubits (110, 120) ; and a qubit frequency control apparatus (200) according to claim 9, in particular the qubit frequency control apparatus (200) being configured to apply the AC Stark pulse to one or more of the plurality of qubits (110, 120) .

11. The quantum system of claim 10, further comprising at least one tunable coupler (130) configured to couple to a first qubit (110) and to a second qubit (120) of the plurality of qubits.

12. The quantum system of claim 11, wherein the pulse generator (210) is configured to apply, during the application of the AC Stark pulse to the first qubit and / or the second qubit, a control pulse to the tunable coupler, in particular the control pulse being a flux pulse .

13. The quantum system of claim 11, wherein the pulse generator (210) is configured to apply, during the application of a first AC Stark pulse to the first qubit and the application of a second AC Stark pulse to the second qubit, a control pulse to the tunable coupler, in particular the control pulse being a flux pulse.

14. The quantum system of any of claims 10 - 13, wherein the plurality of qubits are fixed- frequency qubits.

15. The quantum system of any of claims 10 - 14, wherein qubit drive lines are used for the application of the AC Stark pulse.

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