Method for transporting one or more charge carriers through a one-dimensional quantum channel, and apparatus and quantum-computing architecture

Abstract

The disclosure relates to a method of transporting of one or more charge carriers through a one- dimensional quantum channel defined in a semiconductor by an array of consecutive control gates The invention further relates to an apparatus and in particular a quantum-computing architecture configured to perform the method. The method comprises applying k time-varying control signals to the array of consecutive control gates, to generate a moving potential configured to transport the one or more charge carriers through the quantum channel, k being an integer greater than or equal to 8, wherein a respective same control signal is applied to every k'th consecutive control gate of the array of consecutive control gates, wherein the k time-varying control signals are configured to mitigate potential-disorder in the one-dimensional quantum channel, to coherently transport quantum information carried by the one or more charge carriers, such as a spin, through the one-dimensional quantum channel.

Description

[0001]Method for transporting one or more charge carriers through a one-dimensional quantum channel, and apparatus and quantum-computing architecture Field of the invention The invention relates to a method of transporting one or more charge carriers through a one- dimensional quantum channel defined in a semiconductor by an array of consecutive control gates. The invention further relates to an apparatus and in particular a quantum-computing architecture configured to perform the method. Background art Transporting a charge carrier, such as an electron or a hole, through a one-dimensional quantum channel in a semiconductor is a promising building block in realizing a scalable quantum-computing architecture. The charge carrier can carry quantum information such as a spin used as a qubit and the transporting of the charge carrier enables to establish a quantum link between distant qubits. The ability to establish such quantum links provides design flexibility for realizing a scalable quantum-computing architecture, for instance based on semiconductor spin qubits. For example, different quantum registers and / or different parts within a quantum register can be connected via quantum links, thereby allowing to physically isolate single qubits to avoid undesired local interactions while also allowing to couple different qubits by transporting a qubit via the quantum link. Known methods of transporting charge carriers through a one-dimensional quantum channel, defined in a semiconductor by an array of consecutive control gates, include bucket- brigade shuttling and conveyer-mode shuttling. These known methods are based on applying suitable time-varying control signals to the array of consecutive control gates, which cause the charge carrier to controllably move through the one-dimensional quantum channel along the array of consecutive control gates [e.g., Langrock et al; Seidler et al; Struck et al; and references therein]. The transport-methods attempt to coherently transport the charge carrier and its quantum information with sufficiently high speed and with sufficiently high fidelity so as to be useful in performing quantum-computing tasks. In this technical context, the term shuttling also refers to this attempt physically displacing the charge carrier while preserving its quantum information such as its spin state. However, efficiently transporting charge carriers to reach a sufficiently high shuttling speed and fidelity remains a challenging task. Summary of the invention A general object of the invention is to efficiently transport charge carriers through a one-dimensional quantum channel defined in a semiconductor by an array of consecutive control gates. Therefore, according to a first aspect of the invention, a method as defined in appended claim 1 is provided. According to further aspects of the invention, an apparatus and a quantum-computing architecture, as defined in appended claims 12 and 14, are provided. The above-referenced aspects of the invention enable ultra-fast and high-fidelity shuttling of the charge carrier and in a more power-efficient manner, as compared to known methods. Furthermore, the aspects enable relatively long-range spin shuttling in the order of micrometers, useful for developing sparse spin-qubit registers. The invention has applications in quantum computing and may be implemented in quantum-computing architectures. Further advantages are discussed further below in the detailed description. Brief description of the drawings The present invention is discussed in more detail below, with reference to the attached drawings, in which: Fig.1a shows a quantum-computing architecture comprising two quantum registers that are connected via a one-dimensional quantum channel. Fig.1b shows a quantum register comprising a one-dimensional quantum channel. Fig. 2 shows a one-dimensional quantum channel in a semiconductor defined by an array of consecutive control gates. Fig.3 shows a one-dimensional quantum channel controlled according to conventional conveyer-mode shuttling. Fig. 4 shows a one-dimensional quantum channel controlled according to an example of the method of the present disclosure. Figs.5a-5c show experimental results of an illustrative example. Fig.6 shows an aspect of the method of the present disclosure in a flow chart. Fig.7 shows an apparatus according to the present disclosure. Detailed description Embodiments of the present disclosure will be described herein below with reference to the accompanying drawings. However, the embodiments of the present disclosure are not limited to the specific embodiments and should be construed as including all modifications, changes, equivalent devices and methods, and / or alternative embodiments of the present disclosure. The terms “have,” “may have,” “include,” and “may include” as used herein indicate the presence of corresponding features (for example, elements such as numerical values, functions, operations, or parts), and do not preclude the presence of additional features. The terms “A or B,” “at least one of A or / and B,” or “one or more of A or / and B” as used herein include all possible combinations of items enumerated with them. For example, “A or B,” “at least one of A and B,” or “at least one of A or B” means (1) including at least one A, (2) including at least one B, or (3) including both at least one A and at least one B. The terms such as “first” and “second” as used herein may modify various elements regardless of an order and / or importance of the corresponding elements, and do not limit the corresponding elements. These terms may be used for the purpose of distinguishing one element from another element. For example, a first element may be referred to as a second element without departing from the scope the present invention, and similarly, a second element may be referred to as a first element. It will be understood that, when an element (for example, a first element) is “(operatively or communicatively) coupled with / to” or “connected to” another element (for example, a second element), the element may be directly coupled with / to another element, and there may be an intervening element (for example, a third element) between the element and another element. To the contrary, it will be understood that, when an element (for example, a first element) is “directly coupled with / to” or “directly connected to” another element (for example, a second element), there is no intervening element (for example, a third element) between the element and another element. The expression “configured to (or set to)” as used herein may be used interchangeably with “suitable for” “having the capacity to” “designed to” “adapted to” “made to,” or “capable of” according to a context. The term “configured to (set to)” does not necessarily mean “specifically designed to” in a hardware level. Instead, the expression “apparatus configured to…” may mean that the apparatus is “capable of…” along with other devices or parts in a certain context. The terms used in describing the various embodiments of the present disclosure are for the purpose of describing particular embodiments and are not intended to limit the present disclosure. As used herein, the singular forms are intended to include the plural forms as well, unless the context clearly indicates otherwise. All of the terms used herein including technical or scientific terms have the same meanings as those generally understood by an ordinary skilled person in the related art unless they are defined otherwise. The terms defined in a generally used dictionary should be interpreted as having the same or similar meanings as the contextual meanings of the relevant technology and should not be interpreted as having ideal or exaggerated meanings unless they are clearly defined herein. According to circumstances, even the terms defined in this disclosure should not be interpreted as excluding the embodiments of the present disclosure. The person skilled in the art will understand that the features described above and / or below may be combined in any way deemed useful. The drawings of the present disclosure show examples / embodiments of the invention, which will be described in detail hereinafter. It is to be understood that one or more of elements / components shown and / or described in one or more of these examples / embodiments and not in others may be used in those others too unless mechanical or other limitations prevent such an implementation. Moreover, describing features of different examples / embodiments in a single passage does not automatically mean that those features are inextricably linked. They may be applied separately from one another. The inventors have identified a particularly advantageous method of transporting one or more charge carriers 1, such as an electron or a hole, through a one-dimensional quantum channel 2 defined in a semiconductor 3 by an array of consecutive control gates 4. Before describing the method, such a one-dimensional quantum channel 2 is illustrated in the context of Figs.1-2. Fig. 1a shows a quantum-computing architecture 9 comprising two quantum-registers 10 and 11 that are connected via a one-dimensional quantum channel 2. Fig. 1a shows a first quantum-register 10 and a second quantum-register 11 each comprising respective qubits 10(1), 10(3), 10(5), 10(7), 11(1), 11(3), 11(5), and shows a one-dimensional quantum-channel 2, an apparatus 12 and a plurality of control lines 5. The one-dimensional quantum-channel 2 can provide a quantum link between the quantum-registers 10 and 11. The provided quantum link can be used to couple qubits of the first quantum-register 10 with qubits of the second quantum-register 11. For example, a first qubit starting from a point A in the first quantum-register 10 may be physically transported through the one-dimensional quantum channel 2 to a second point B in the second quantum- register 11. The transporting of the first qubit may be combined with coupling of the first qubit to a second qubit in the second quantum-register 11. For example, after the transporting, the first and second qubits may be coupled or may be manipulated with qubit gates such as a 2- qubit gate so as to perform an operation on the qubits. Furthermore, after the transporting and the coupling, the first qubit may again be transported back through the one-dimensional quantum channel 2. In semiconductor-based spin qubits, each qubit 10(i) may correspond to a spin state of a respective charge carrier such as an electron or hole (also referred to as Loss-DiVincenzo qubits). A qubit is however not necessarily defined by a spin state of a single charge carrier, as for example also a combined spin state of two charge carriers can form a qubit (e.g., singlet- triplet qubit) Fig.1b shows a quantum-register 10 comprising respective qubits 10(1), 10(3), 10(5), 10(7), 10(9) and a one-dimensional quantum channel 2 that can provide a connection between two points A and B in the quantum-register 10. For example, a first qubit 10(5) can be transported through the one-dimensional quantum channel 2 from A to B and can be coupled to a second qubit 10(9). In general, a quantum-computing architecture 9 is not limited to the number of qubit- registers, qubits in each qubit-register, and one-dimensional quantum channels as shown in the illustrations of Figs.1a and 1b, but a quantum-computing architecture 9 may include a plurality of qubit-registers, each with a respective plurality of qubits, and may further include a plurality of one-dimensional quantum channels each defined by a respective array of control gates. Furthermore, each qubit may correspond for example to a charge carrier that is physically transported through the one-dimensional quantum channel 2. Each qubit may also correspond to quantum information that may be transferred to a charge carrier which in turn is transported through the one-dimensional quantum channel 2. Furthermore, more than a single charge carrier 1 can be shuttled. For example, two charge carriers 1 (e.g., electrons) can be shuttled in two neighbouring minima, the two charge carriers 1 together forming a singlet-triplet qubit. Fig.2 shows a one-dimensional quantum channel 2 defined in a semiconductor 3 by an array of consecutive control gates 4, with control gates 4(1), 4(2), …, 4(17), a number of quantum dots 8 labelled as 8(1), 8(2), …, 8(8), a charge carrier 1, and two points A and B. Each control gate 4(i), i=1, 2,…, 17, can be implemented as a gate electrode, for instance a metal gate or metal gate electrode. By applying suitable control signals to the control gates, quantum dots 8(i) can be defined in the semiconductor 3. A quantum dot 8(i) can correspond to a potential-well in which the charge carrier 1 such as an electron or a hole can be localized. That is, by applying voltages / control signals to the control gates, charge carriers such as electrons or holes can be trapped in a potential-well region of the semiconductor 3, the potential well being generated by the applied voltages / control signals. The number of the involved elements, such as control gates and quantum dots, is merely for illustration but is not for limiting the concept of the one-dimensional quantum channel 2. The one-dimensional quantum channel 2 may also comprise further gates such as a single- electron transistor (not shown in Fig.2) for initializing the charge carrier 1 such as an electron to a starting point A related to a first control gate 4(1), a detecting gate for detecting charges, etc., but such further gates are not illustrated as they are not essential for the present invention. The one-dimensional quantum channel 2 provides a quantum link over which quantum information can be transported. For example, the charge carrier 1 can carry quantum information such as a spin state, and by physically transporting the charge carrier 1 through the one-dimensional quantum channel 2, the quantum information is also transferred. However, for efficiently transferring the quantum information, the transporting of the charge carrier 1 should effectively preserve coherence so as to avoid loss of information. The one-dimensional quantum channel 2 may be subjected to an external magnetic field generated by one or more magnetic-field generators. The external magnetic field may induce for instance Zeeman splitting in energy levels of the quantum dots. The induced Zeeman splittings may be used for providing an energetic path for the charge carrier 1 through the quantum channel 2. The charge carrier 1 may correspond to an electron which carries a spin-1 / 2 degree of freedom. The electron-spin may be used as a qubit in semiconductor-based qubit systems. For example, in silicon-based semiconductor platforms, electron-spin qubits are already used in small-scale quantum computing and are a promising candidate to large-scale quantum computing [e.g., Philips et al and references therein]. The charge carrier 1 may also correspond to a hole as for example in semiconductors such as Germanium. In general, more than a single charge carrier 1 can be shuttled. For example, two charge carriers 1 can be shuttled in two neighbouring minima of a generated moving potential, together forming a singlet-triplet qubit. In general, one or more charge carriers 1 may carry quantum information corresponding to a qubit (e.g., singlet-triplet qubit), and the one or more charge carriers 1 may my shuttled in for example two neighbouring minima of the moving potential. The one-dimensional quantum channel 2 is defined in the semiconductor 3 by the array of consecutive control gates 4(1)-4(17). By applying suitable time-varying control signals to the control gates 4(1)-4(17), the charge carrier 1 can be transported along the array. In the figures, the one-dimensional quantum channel 2 is illustrated as a straight line, but the one- dimensional quantum channel 2 may in general also be implemented differently, for example as a curved line, and is not limited to the illustrated straight line. The one-dimensionality refers to the ability to control a directionality of the transport of the charge carrier 1 through the quantum channel 2. For example, the charge carrier 1 can be transported from A to B and also from B to A. For example, in bucket-brigade shuttling [e.g. Langrock et al, Mills et al, and references therein], electric potentials are successively adapted so as to transport the charge carrier 1 via tunnelling through potential barriers in between quantum dots so as to consecutively tunnel from one quantum dot to the next one, e.g. from 8(1) to 8(2), then from 8(2) to 8(3), etc. In a conveyer-mode shuttling method, four specific time-varying control signals ^^(^), ⋯ , ^^(^) are applied to the array of consecutive control gates 4, to generate a moving potential configured to transport the charge carrier 1 through the quantum channel 2. Conventional conveyer-mode shuttling is discussed next with reference to Fig.3. Fig. 3 shows part of the one-dimensional quantum channel 2 of Fig. 2 and in addition control lines 5 with individual control lines labelled as 5(1), 5(2), 5(3), 5(4). For intelligibility, only a sub-set of control gates 4(1), 4(2), 4(5), 4(6), 4(9), 4(10), 4(13) is illustrated in Fig.3. Each control line 5(i) is configured to apply a respective same control signal ^^(^)to every fourth consecutive control gate. For example, a first control line 5(1) is configured to apply the same control signal ^^(^)to control gates 4(1), 4(5), 4(9), 4(13), etc. A second control line 5(2) is configured to apply the same control signal ^^(^)to control gates 4(2), 4(6), 4(10), etc. Similarly for the third 5(3) and fourth 5(4) control lines. In conventional conveyer-mode shuttling, the four control signals are, modulo off-sets, specifically as follows: ^^,^(^)= ^ ^^^(^^), with a certain amplitude ^, a certain frequency ω, and a time parameter ^. In combination, the control signals ^^(^)corresponding to phase-shifted sine waves can together generate a moving potential that transports the charge carrier 1 with a certain shuttle velocity v through the quantum channel 2. The shuttle velocity v is related to the frequency ω with which the control signals ^^(^)vary in time. The method devised by the inventors provides a more efficient way of transporting. In general, the method is for transporting one or more charge carriers 1, such as an electron or a hole, through a one-dimensional quantum channel 2 defined in a semiconductor 3 by an array of consecutive control gates 4. The method comprises applying k time-varying control signals ^^(^), ⋯ , ^^(^)to the array of consecutive control gates 4, to generate a moving potential configured to transport the one or more charge carriers 1 through the quantum channel 2, k being an integer greater than or equal to 8, wherein a respective same control signal is applied to every k’th consecutive control gate of the array of consecutive control gates 4 (e.g., ^^(^)to 4(1), 4(1+k), 4(1+2k),… ; ^^(^)to 4(2), 4(2+k), 4(2+2k), …; etc.), wherein the k time-varying control signals are configured to mitigate potential-disorder in the one-dimensional quantum channel 2, to coherently transport quantum information carried by the one or more charge carriers 1, such as a spin, through the one-dimensional quantum channel 2. The combination of specifically applying k time-varying control signals with ^ ≥ 8 that generate a moving potential and that at the same time mitigate potential-disorder in the one- dimensional quantum channel 2 has the synergetic technical effect of enabling ultra-fast and high-fidelity shuttling of the one or more charge carriers 1. The inventors have identified that potential-disorder in the semiconductor 3 is a dominant factor for limiting effective transport of the charge carrier 1, and that by specifically introducing an increased number (^ ≥ 8) of time-varying control signals that are adapted to mitigate the potential-disorder, a surprisingly ultra-fast and high-fidelity shuttling is obtained. By achieving an effective high-speed and high-fidelity shuttling, the method enables among other things long-range spin shuttling that is useful for developing sparse spin-qubit registers and for creating space between quantum registers and qubit-groups within quantum registers, so as to alleviate crosstalk between qubits. An example of potential-disorder is inhomogeneity in the semiconductor 3 due to material imperfection. For example, an externally applied magnetic field may induce Zeeman splittings in energy levels across the quantum channel 2. The induced Zeeman splittings can vary over the quantum channel 2 due to for example variations in g-factors, a natural consequence of material properties. Furthermore, a magnetic field may vary along the one- dimensional quantum channel 2 due to the use of micro-magnets that may be equipped for qubit operations. Furthermore, potential-disorder can contribute to inter-dot leakage during transport of the one or more charge carriers 1. For example, a quantum-mechanical wave function of a charge carrier, such as an electron wave function, may split into neighbouring quantum-dot regions during transport of the charge carrier 1, thereby de-synchronizing with control signals. As a consequence, the charge carrier 1 de-localizes and transport can be prohibited and / or quantum information carried by the one or more charge carriers 1 may be destroyed---for example, a spin may diphase and / or pick up an unexpected phase. An example of the method according to the present disclosure is discussed next with reference to Fig.4. Fig.4 shows a charge carrier 1---in this example an electron carrying a negative electric charge and a spin---with a velocity v pointing from a first point A to a second point B in the one-dimensional quantum channel 2 defined in a semiconductor 3 by an array of control gates 4 with some individual control gates being labelled as 4(1), 4(2), 4(3), …, 4(9), 4(10), 4(11), …, 4(17), 4(18), 4(19), …, control lines 5 with individual control lines being labelled as 5(1), 5(2), 5(3), 5(4), 5(5), 5(6), 5(7), 5(8), time-varying control signals V1(t), V2(t), V3(t), V4(t), V5(t), V6(t), V7(t), V8(t), and an apparatus 12 comprising a processor 12(1) and a memory 12(3). Control gates 4 may be implemented for example as metal gate electrodes (or metal gates), on each of which a respective time-varying control signal corresponding to a time- varying voltage can be applied. Control gates 4 may also be referred to according to their functionality, and may thus include one or more of potential-barrier gates configured to control potential-barriers between quantum dots, plunger gates configured to control on-site chemical potentials related to on-site energies, tunnel-barrier gates configured to control tunnelling amplitudes on the boundary of the one-dimensional quantum channel 2, etc. According to the method of the present disclosure, a respective same control signal is applied to every k’th consecutive control gate of the array of consecutive control gates 4 (e.g., ^^(^)to 4(1), 4(1+k), 4(1+2k),… ; ^^(^)to 4(2), 4(2+k), 4(2+2k), …; etc.). In general, each respective set of every k’th consecutive control gate thus corresponds to a periodic sub-set of the array of consecutive control gates 4. In the illustration of Fig. 4, k=8, and the following voltages V1(t)-V8(t) are applied to respective every 8’th consecutive control gates: Control line Control gates Control signal 5(1) 4(1), 4(9), 4(17) V1(t) 5(2) 4(2), 4(10), 4(18) V2(t) 5(3) 4(3), 4(11), 4(19) V3(t) 5(4) 4(4) ,4(12) V4(t) 5(5) 4(5) ,4(13) V5(t) 5(6) 4(6) ,4(14) V6(t) 5(7) 4(7) ,4(15) V7(t) 5(8) 4(8) ,4(16) V8(t) [In rows 5(1)-5(8), possible further control gates are not illustrated in Fig.4.] That means, in Fig.4, a first time-varying control signal V1(t) is applied to gates 4(1), 4(9), 4(17); a second time-varying control signal V2(t) is applied to gates 4(2), 4(10), 4(18); a third time-varying control signal V3(t) is applied to gates 4(3), 4(10), 4(17); etc. By applying the respective same control signals to every k’th consecutive control gate, a control-potential landscape that is periodic in space along the one-dimensional quantum channel 2 can be generated. That provides an efficient way of generating the in-time moving potential by varying the set of k applied time-varying control signals accordingly. In Fig.4, a particularly advantageous way of applying the k time-varying control signals to their respective set of every k’th consecutive control gate is illustrated. In Fig.4, each control line is configured to control a respective set of every eighth control gate. For example, a first control line 5(1) is configured to control the control gates 4(1), 4(9), 4(17); a second control line 5(2) is configured to control the control gates 4(2), 4(10), 4(18); etc. Each respective control line of the control lines 5 can be established by electrically connecting the to-be-controlled gates to the respective control line. Preferably, in the method according to the present disclosure, the applying of the k time- varying control signals (^^(^), ⋯ , ^^(^)) comprises: controlling k control lines (5) to output the k time-varying control signals (^^(^), ⋯ , ^^(^)) to the array of consecutive control gates (4), wherein each one (5(1); 5(2)) of the k control lines (5) is configured to output the respective same control signal (^^ to the respective every k’th consecutive control gate (4(1), 4(1+k),4(1+2k); 4(2), 4(2+k), 4(2+2k))). The number of control lines may advantageously correspond to the number of time- varying control signals. Thereby, the number of parameters that have to be varied and controlled can be limited while scaling up. For example, for a one-dimensional quantum channel 2 with for example a total of 160 control gates, instead of individual controlling the 160 different control gates via 160 inputs, using control lines allows to reduce the number of inputs to 8 while still generating a moving potential that can transport the one or more charge carriers 1. That is, in general, by repeating the set of k time-varying control signals over the array of consecutive control gates 4, via for instance employing control lines 5, the method of the present disclosure is particularly suitable for scaling up. The number of control gates 4 is not limited to the illustrations, but may depend on various choices such as in which context the quantum channel 2 is to be implemented, which quantum registers are to be connected, which parts within a quantum register are to be connected, etc. A feasible maximum number of control gates 4 may depend on parameters such as a decoherence time, shuttling velocity, etc. Preferably, in the method according to the present disclosure, for the configuring of the k time-varying control signals (^^(^), ⋯ , ^^(^)) to mitigate the potential-disorder: each one of the k applied time-varying control signals (^^(^), ⋯ , ^^(^)) comprises a respective sum of two or more sinusoidal waves involving respective controllable amplitudes (Ai,1, Ai,2) and controllable phases (φi,1, φi,2), a first frequency (ω) of a first sinusoidal wave being larger than a second frequency (ω / 2) of a second sinusoidal wave of the two or more sinusoidal waves, in particular being substantially twice as large. The inventors found that specifically considering for each time-varying control signal a superposition of at least two sinusoidal waves is particularly advantageous, as it can effectively mitigate the potential-disorder and reduce inter-dot leakage. For example, an amount of inter- dot leakage depends on the proximity of neighbouring minima, and a technical advantage of including more sinusoidal waves to a time-varying control signal is that a distance between neighbouring potential minima becomes larger. At the example of considering two sinusoidal waves with a first frequency ω being substantially twice as large as a second frequency ω / 2, the distance between the neighbouring potential minima increases by a factor of two. Thereby, interdot tunnel coupling is effectively suppressed, and interdot leakage is significantly reduced. Preferably, the method of the present disclosure comprises controlling the respective amplitudes (Ai,1, Ai,2) involved in the respective sum of two or more sinusoidal waves to control detuning between nearest-neighbour minima. A technical advantage thereof is that by including two or more sinusoidal waves, the involved controllable amplitudes allow to control a ratio between a first amplitude of a first sinusoidal wave and a second amplitude of a second sinusoidal wave, which yields control over detuning between nearest-neighbour minima. Preferably, the method of the present disclosure yet further comprises controlling the respective phases (φi,1, φi,2) involved in the respective sum of two or more sinusoidal waves to control a tunnel coupling. A technical advantage thereof is that the involved controllable phases can be tuned to adjust tunnel coupling amplitudes. For example, in a quantum channel 2 with inherent disorder, detuning may be adjusted via adjusting the controllable phases. A particularly advantageous example is discussed next. As shown in Fig.4, the i’th time-varying signal Vi(t) may be specifically considered as wherein Ai,1 and Ai,2 correspond to controllable amplitudes, wherein φi,1 and φi,2 correspond to controllable phases, wherein Bi(t) correspond to controllable voltage off-sets, and wherein ω corresponds to an angular frequency related to a frequency f of the time-varying control signal by ω = 2π^. By for instance varying the controllable amplitudes Ai,1and Ai,2, one can effectively control a shape of the generated moving potential and a coupling between nearest-neighbour moving potential and isolate the moving potential from environmental noise. As a consequence, voltage amplitudes become much lower, as compared to using only a single sinusoidal wave with a single amplitude. That advantage is particularly prominent for higher frequencies ω corresponding to higher shuttle velocities v. The inventors found that in conventional conveyer-mode shuttling, potential-disorder is a significant factor such that reaching higher frequencies becomes unfeasible and potential- disorder can no longer be effectively mitigated by increasing an applied amplitude of the time- varying control signals. For frequencies in the MHz regime, a required amplitude is even growing exponentially, meaning a significant increase in required power and limited effectiveness. Furthermore, even when attempting to suppress potential-disorder in conventional conveyer-mode shuttling via increasing the amplitude, the transport of the charge carrier is no longer coherent so that quantum information is lost. By using the two or more sinusoidal waves as discussed above, the potential-disorder is mitigated in an effective manner and much higher frequencies corresponding to higher shuttling velocities can be obtained. For example, at a frequency range of about 50 to 100 Mega-Hz (MHz), an amplitude range of about 30-40 milli-Volt (mV) can be applied. As another example, at an even higher frequency range of about 100 to 200 MHz, an amplitude range of about 40- 50 mV can be applied. As yet another example, at a yet higher frequency range of about 200 to 300 MHz, an amplitude range of about 50-90 mV can be applied. More examples are also discussed in the context of Figs.5a-5c. Preferably, in the method according to the present invention, two respective sinusoidal waves are used for each time-varying control signal, respectively, and for any integer i between one and k, the phases involved in the two respective sinusoidal waves are: φ^,^= 2π(^ − 1) / ^ and φ^,^= φ^,^ / 2. Considering for illustration the example k=8, then with this specific choice of the phases, the time-varying control signals Vi(t) for i =1, ..., 8 become: φ^= π(^ − 1) / 4. The off-sets Bi(t) can be chosen depending on for example a distance of a control gate relative to a path of the charge carrier 1 through the one-dimensional quantum channel 2. In this example, relatively high frequencies ω in the MHz range corresponding to relatively high shuttle velocities v can be achieved. The method is not limited to k=8 and is not limited to including merely two sinusoidal waves in each respective time-varying control signal. Preferably, in the method of the present disclosure, each one of the k applied time-varying control signals (^^(^), ⋯ , ^^(^)) is substantially given by: wherein Ai,jcorrespond to the controllable amplitudes, wherein φi,jcorrespond to the controllable phases, wherein Bi(t) correspond to controllable voltage off-sets, wherein N is an integer larger than one. The case of N=1 corresponds to adding one more harmonic with half a frequency. Larger values of N means including additional harmonics, resembling the implementation of a Fourier series, but for practical purposes and for scalability, including one additional harmonic is in general preferred. Preferably, in the method of the present disclosure, for any integer i between one and k, and for any integer j between 1 and N, the respective controllable phase φi,j is substantially given by: In general, considering time-varying control signals that include two or more harmonics such as illustrated above is preferred. The semiconductor 3 may be based on for example Silicon, Germanium, or other semiconductor-platforms for implementing semiconductor-based spin qubits. Preferably, the semiconductor 3 is based on Silicon / Silicon-Germanium (Si / SiGe), Gallium Arsenide (GaAs), Germanium / Silicon-Germanium (Ge / SiGe), and / or Silicon metal-oxide-semiconductor (SiMOS). Preferably, each of the applied k time-varying control signals ⋯ , ^^(^)) is periodic and the generated moving potential is periodic. Preferably, the one-dimensional quantum channel 2 comprises a quantum-dot array 8 controllably defined via the array of consecutive control gates 4. For example, a moving potential minimum of the generated moving potential may be regarded as a quantum dot controllably moving along the one-dimensional quantum channel 2. Figs. 5a-5c show experimental results comparing conventional conveyer-mode shuttling referred to as “4 phase CV” and an illustrative example of the method of the present disclosure referred to as “8 phase CV”. In the illustrative example, 8 control signals were applied to an array of consecutive control gates, and for i = 1, …, 8: φ^= π(^ − 1) / 4. The parameter A corresponds to the “Amplitude” in Fig.5a. The parameter ^ is related to the parameter “CV frequency” in Figs.5a-5c by ^ = 2^^. In the experiments, an electron was shuttled that had an initial spin being in a superposition state between up and down and having a certain phase. By the shuttling, one can investigate if the phase is coherent during transport. The phase may not only be affected by shuttling, but also by natural dephasing because of noise for example. In Fig. 5a, the value of “Amplitude” corresponds to a minimal amplitude required for successful transporting of the electron. The minimal amplitude relates only to the transporting of the electron and does not take into consideration spin coherence. Indeed, for the 4 phase CV, one could barely transport the electron at 230 MHz, and moreover the spin coherence at such a frequency value was already completely destroyed, thus coherent transport / shuttling was not observed. The coherence could only be maintained up to about 100MHz, as also shown in Figs. 5b-5c. In contrast, the “8 phase CV” example shows a lower required Amplitude and furthermore shows transport up to a frequency value of even 370 MHz. Figs. 5b and 5c show “Ramset CV 4 phase” / ”Ramset CV 8 phase” and “Echo CV 4 phase” / “Echo CV 8 phase”, respectively. In the “Ramset CV 4 phase” / Ramset CV 8 phase” experiments, it was detected what happened to the phase without distinguishing between the origin of dephasing. This scenario is relevant for practical reasons since natural dephasing can be present and can be taken into account when executing algorithms such as the method according to the present disclosure. In the “Echo CV 4 phase” / “Echo CV 8 phase” experiments, additionally a microwave pulse was applied to the spin to refocus the phase and thus to boost a coherence value. Fig.5b shows only frequency ranges of “CV frequency” up to 100 MHz, because above said value, coherence could not be maintained. Fig. 5c shows that coherence could be maintained even up to 370 MHz for the “CV 8 phase” example, for which shuttling-speeds of up to about 60m / s were obtained. Fig. 6 shows the method of the present disclosure in a flow chart. The method is of transporting one or more charge carriers, such as an electron or a hole, through a one- dimensional quantum channel defined in a semiconductor by an array of consecutive control gates. The method comprises: applying (20) k time-varying control signals to the array of consecutive control gates, to generate a moving potential configured to transport the charge carrier through the quantum channel, k being an integer greater than or equal to 8, wherein (21) a respective same control signal is applied to every k’th consecutive control gate of the array of consecutive control gates and wherein the k time-varying control signals are configured to mitigate potential-disorder in the one-dimensional quantum channel, to coherently transport quantum information carried by the charge carrier, such as a spin, through the one-dimensional quantum channel. Fig. 7 shows an apparatus 12 according to the present disclosure. The apparatus 12 is configured to transport one or more charge carriers 1, such as an electron or a hole, through a one-dimensional quantum channel 2 in a semiconductor 3 using an array of consecutive control gates 4. The apparatus 12 comprises: a processor (12(1)), and a memory (12(3)) comprising instructions, which, when executed by the processor (12(1)), cause the apparatus (12) to execute the method of the present disclosure, preferably the method including preferred aspects of the method. Preferably, the apparatus of the present disclosure further comprises k control lines 5 configured to control the array of consecutive control gates 4. A quantum-computing architecture 9 can be configured to carry out the method of any one of the preceding method claims. For example, the present disclosure can be implemented in a quantum-computing architecture 9 comprising an apparatus 12 according to the present disclosure. For example, a quantum-computing architecture 9 may comprise a memory storing instructions, the instructions causing the apparatus 12 to output time-varying control signals so as to execute the method of the present disclosure. The following list of references is referred to in the present document and is incorporated herein by way of reference. List of references [B] Authors. Title. Publisher. Date. [Langrock et al] Veit Langrock, Jan A. Krzywda, Niels Focke, Inga Seidler, Lars R. Schreiber, and Łukasz Cywiński. Blueprint of a Scalable Spin Qubit Shuttle Device for Coherent Mid- Range Qubit Transfer in Disordered Si / SiGe / SiO_2. PRX Quantum 4, 020305.11 April 2023. [Mills et al] A. R. Mills, D. M. Zajac, M. J. Gullans, F. J. Schupp, T. M. Hazard & J. R. Petta. Shuttling a single charge across a one-dimensional array of silicon quantum dots. Nature Communications volume 10, Article number: 1063 (2019).5 March 2019. [Philips et al] Stephan G. J. Philips, Mateusz T. Mądzik, Sergey V. Amitonov, Sander L. de Snoo, Maximilian Russ, Nima Kalhor, Christian Volk, William I. L. Lawrie, Delphine Brousse, Larysa Tryputen, Brian Paquelet Wuetz, Amir Sammak, Menno Veldhorst, Giordano Scappucci & Lieven M. K. Vandersypen. Universal control of a six-qubit quantum processor in silicon. Nature volume 609, pages 919–924 (2022).28 September 2022. [Seidler et al] Inga Seidler, Tom Struck, Ran Xue, Niels Focke, Stefan Trellenkamp, Hendrik Bluhm & Lars R. Schreiber. Conveyor-mode single-electron shuttling in Si / SiGe for a scalable quantum computing architecture. npj Quantum Information volume 8, Article number: 100 (2022).30 August 2022. [Struck et al] Tom Struck, Mats Volmer, Lino Visser, Tobias Offermann, Ran Xue, Jhih-Sian Tu, Stefan Trellenkamp, Łukasz Cywiński, Hendrik Bluhm, Lars R. Schreiber. Spin-EPR-pair separation by conveyor-mode single electron shuttling in Si / SiGe, arXiv:2307.04897, 10 July 2023.

Claims

What is claimed is:

1. Method of transporting one or more charge carriers (1), such as an electron or a hole, through a one-dimensional quantum channel (2) defined in a semiconductor (3) by an array of consecutive control gates (4), the method comprising: applying k time-varying control signals (^^(^), ⋯ , ^^(^)) to the array of consecutive control gates (4), to generate a moving potential configured to transport the one or more charge carriers (1) through the quantum channel (2), k being an integer greater than or equal to 8, wherein a respective same control signal (^^(^); ^^(^)) is applied to every k’th consecutive control gate (4(1),4(1+k),4(1+2k); 4(2),4(2+k),4(2+2k)) of the array of consecutive control gates (4), wherein the k time-varying control signals are configured to mitigate potential-disorder in the one-dimensional quantum channel (2), to coherently transport quantum information carried by the one or more charge carriers (1), such as a spin, through the one-dimensional quantum channel (2).

2. The method of claim 1, wherein, for the configuring of the k time-varying control signals (^^(^), ⋯ , ^^(^)) to mitigate the potential-disorder: each oneof the k applied time-varying control signals (^^(^), ⋯ , ^^(^)) comprises a respective sum of two or more sinusoidal waves involving respective controllable amplitudes (Ai,1, Ai,2) and controllable phases (φi,1, φi,2), a first frequency (ω) of a first sinusoidal wave being larger than a second frequency (ω / 2) of a second sinusoidal wave of the two or more sinusoidal waves, in particular being substantially twice as large.

3. The method of any one of the preceding claims, wherein the applying of the k time-varying control signals (^^(^), ⋯ , ^^(^)) comprises: controlling k control lines (5) to output the k time-varying control signals (^^(^), ⋯ , ^^(^)) to the array of consecutive control gates (4), wherein each one (5(1); 5(2)) of the k control lines (5) is configured to output the respective same control signal (^^(^); ^^(^)) to the respective every k’th consecutive control gate (4(1), 4(1+k),4(1+2k); 4(2), 4(2+k), 4(2+2k))).

4. The method of any one of the preceding claims, further comprising:controlling the respective amplitudes (Ai,1, Ai,2) involved in the respective sum of two or more sinusoidal waves to control detuning between nearest-neighbour minima.

5. The method of any one of the preceding claims, further comprising: controlling the respective phases (φi,1, φi,2) involved in the respective sum of two or more sinusoidal waves to control a tunnel coupling.

6. The method of any one of the preceding claims, wherein each one (^^(^)) of the k applied time-varying control signals⋯ , ^^(^)) is substantially given by:wherein Ai,j correspond to the controllable amplitudes, wherein φi,j correspond to the controllable phases, wherein Bi(t) correspond to controllable voltage off-sets, wherein N is an integer larger than one.

7. The method of the preceding claim, wherein, for any integer i between one and k, and for any integer j between 1 and N, the respective controllable phase φi,j is substantially given by:

8. The method of any one of the preceding claims, wherein each one (^^(^)) of the k applied time-varying control signals⋯ , ^^(^)) is substantially given by:wherein Ai,1 and Ai,2 correspond to controllable amplitudes, wherein φi,1 and φi,2 correspond to controllable phases, wherein Bi(t) correspond to controllable voltage off-sets.

9. The method of the preceding claim, wherein for any integer i between one and k: φ^,^= 2π(^ − 1) / ^ and φ^,^= φ^,^ / 2.

10. The method of any one of the preceding claims, wherein each of the applied k time-varying control signals (^^(^), ⋯ , ^^(^)) is periodic and the generated moving potential is periodic.

11. The method of claim 1, wherein the one-dimensional quantum channel (2) comprises a quantum-dot array (8) controllably defined via the array of consecutive control gates (4).

12. Apparatus (12) configured to transport one or more charge carriers (1), such as an electron or a hole, through a one-dimensional quantum channel (2) in a semiconductor (3) using an array of consecutive control gates (4), the apparatus (12) comprising: a processor (12(1)), and a memory (12(3)) comprising instructions, which, when executed by the processor (12(1)), cause the apparatus (12) to execute the method of any one of the preceding method claims.

13. The apparatus (12) of claim 12, further comprising k control lines (5) configured to control the array of consecutive control gates (4).

14. Quantum-computing architecture (9) configured to carry out the method of any one of the preceding method claims.

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