Scalable architecture for coupling andreev spin qubits, and methods of manufacturing and operating such

Abstract

The disclosure relates to scalable architectures for coupling Andreev spin qubits (ASQs), and methods of manufacturing and operating such. Disclosed are an ASQ circuit, a method of manufacturing the ASQ circuit and a method of operating the ASQ circuit to couple two or more ASQs. The provided ASQ circuit enables selective connectivity between any pair of ASQs while maintaining other ASQs uncoupled. Thereby, a scalable architecture for coupling multiple ASQs is provided. Furthermore, an all-to-all connectivity is achieved, which means a largely increased qubit connectivity opening the possibility of using quantum error correction codes with a lower number of physical qubits per logical qubit than existent approaches, thus giving more flexibility in using number-efficient correction codes. Furthermore, the all-to-all connectivity increases the range of computational or physical problems that can be simulated without the need for sacrificial qubits.

Description

[0001] Scalable architecture for coupling Andreev spin qubits, and methods of manufacturing and operating such

[0002] Field of the invention

[0003] The invention relates to Andreev spin qubits, and methods of manufacturing and operating such.

[0004] Background art

[0005] Andreev spin qubits (ASQs) are a promising hybrid-qubit platform that combines concepts of superconducting qubits and spin qubits. ASQs are therefore also referred to as superconducting spin qubits. An ASQ’s quantum state involves a spin state localized within a semiconducting quantum dot, similar as a spin qubit. However, for creating the ASQ, the semiconducting quantum dot is placed in a Josephson junction and is tunnel -coupled to two superconducting leads, which enables coupling of the spin state to a supercurrent between the two superconducting leads. Background on ASQs can be found in [Chtchelkatchev et al; Hays et al; Padurariu et al; Park et al; Pita- Vidal et al, a; Pita- Vidal et al, b; Spethmann et al].

[0006] Recent experimental realizations of ASQs explore systems with a single ASQ [Hays et al; Pita- Vidal et al, a] as well as supercurrent-mediated coupling between two ASQs [Pita- Vidal et al, b]. However, existing architectures only enable coupling between nearest-neighbour qubits, which makes up-scaling the architecture to a quantum-computer based on ASQs inefficient and difficult. Furthermore, the only existing proposal for scaling up ASQs [Spethmann et al.] is limited to coupling ASQs that are physically located relatively close to each other, but such a close-distance requirement is detrimental for scaling up ASQs.

[0007] There is thus a need to provide a scalable architecture for coupling ASQs.

[0008] Summary of the invention

[0009] A general object of the invention is to provide a scalable architecture for coupling ASQs.

[0010] Therefore, according to a first aspect of the invention, an ASQ circuit as defined in appended claim 1, is provided. According to further aspects of the invention, a method of manufacturing the ASQ circuit and a method of operating the ASQ circuit to couple two or more ASQs are provided.

[0011] The provided ASQ circuit enables selective connectivity between any pair of ASQs while maintaining other ASQs uncoupled. Thereby, a scalable architecture for coupling multiple ASQs is provided. Furthermore, an all-to-all connectivity is achieved, which means a largely increased qubit connectivity opening the possibility of using quantum error correction codes with a lower number of physical qubits per logical qubit than existent approaches, thus giving more flexibility in using number-efficient correction codes. Furthermore, the all-to-all connectivity increases the range of computational or physical problems that can be simulated without the need for sacrificial qubits. Further advantages are discussed further below in the detailed description.

[0012] Brief description of the drawings

[0013] The present invention is discussed in more detail below, with reference to the attached drawings, in which:

[0014] Fig- 1 shows an ASQ circuit of the present invention.

[0015] Fig- 2 shows an abstract circuit diagram of the ASQ circuit.

[0016] Fig- 3 shows four possible phase setpoints for an ASQ.

[0017] Figs. 4A-4C show global configurations of the ASQ circuit.

[0018] Figs. 5 A and 5B show a transmon circuit and a fluxonium circuit, respectively.

[0019] Detailed description

[0020] 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.

[0021] 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.

[0022] 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.

[0023] 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.

[0024] 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.

[0025] 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.

[0026] 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.

[0027] 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.

[0028] Fig- 1 shows an ASQ circuit 1 of the present invention. The ASQ circuit 1 comprises a coupling Josephson junction element 2 and an array of a plurality of twisted-loop devices 3-1, 3-2, 3-3. The number of illustrated twisted-loop devices 3-1, 3-2, 3-3 and elements of Fig. 1 is not limited to the illustrated number, as further reference signs are not indicated for reasons of intelligibility only.

[0029] The plurality of twisted-loop devices 3-1, 3-2, 3-3 is coupled in parallel to the coupling Josephson junction element 2. Each twisted-loop device 3-1, 3-2, 3-3 comprises a respective loop 4-1, 4-2, 4-3. At the example of loop 4-1 : each loop (e.g. 4-1) comprises a first subloop (e.g. 4-1-1) and a second subloop (e.g. 4-1-2). Within the loop (e.g. 4-1), the first and second subloops are interconnected by a twisted connection (e.g. 4-1-3). A first inductive element (e.g.

[0030] 5-1-1) is arranged within the first subloop (e.g. 4-1-1) and a second inductive element (e.g. 5- 1-2) is arranged within the respective second subloop (e.g. 4-1-2). Similarly for other loops 4- 2, 4-3, etc., for which a repetitive description is avoided.

[0031] The ASQ circuit 1 further comprises a plurality of conductive flux bias lines 6-1, 6-2,

[0032] 6-3. At the example of flux bias line 6-1 : each flux bias line (e.g. 6-1) is adjacent to a corresponding loop (e.g. 4-1) and extends along the respective first (e.g. 4-1-1) and the second (e.g. 4-1-2) subloop of the corresponding loop (e.g. 4-1). Similarly for other flux bias lines 6- 2, 6-3, etc., for which a repetitive description is avoided.

[0033] In each pair of neighbouring twisted-loop devices in the array (e.g. the pair (3-1, 3-2)), the second subloop (e.g. 4-1-2) of one (e.g. 3-1) of the pair of neighbouring twisted-loop devices connects to the first subloop (e.g. 4-2-1) of the other (e.g. 3-2) of the pair of neighbouring twisted-loop devices, such that at a connection of the pair (3-1, 3-2), the second inductive element (e.g. 5-1-2) of the one (e.g. 3-1) twisted-loop device and the first inductive element (e.g. 5-2-1) of the other (e.g. 3-2) twisted-loop device form an ASQ device (e.g. ASQ1) for hosting an ASQ.

[0034] The ASQ circuit 1 arranges a plurality of ASQ devices (ASQ1, ASQ2, ASQ3, ASQ4, . . . ) in a specific way so as to enable selectively coupling any pair of ASQs hosted in a respective pair of ASQ devices and thereby provides a scalable architecture for coupling ASQs. Furthermore, multiple ASQs can be selectively coupled to each other. Examples and preferred aspects thereof are described next.

[0035] Fig- 1 further shows magnetic fluxes through loop i (for i=l,2,3,4, .. .). By arranging the plurality of conductive flux bias lines adjacent to the corresponding loops and extending along the respective first and second subloops, the magnetic fluxes can be efficiently controlled. For example, magnetic flux ! can be efficiently controlled by current Ii flowing through the flux bias line 6-1. Similarly for the other magnetic fluxes illustrated in Fig. 1. In other words, the conductive flux bias lines inductively couple to their respective loop to provide control of a magnetic flux through the respective loop.

[0036] The inventors have found that by the flux bias lines 6-1, 6-2, 6-3 etc., one can control phase drops related to the individual ASQs (ASQ1, ASQ2, ASQ3, etc.) given by = .kl(pk, k running from 1 to i, wherein / 40with magnetic flux quantum 40= h / 2e, wherein h is the Planck constant and e is the absolute value of the electron charge.

[0037] Thereby, individual ASQs can be controllably manipulated between two states, OFF and ON. For example, when <pi = ± a spin-dependent component Is,i of a supercurrent vanishes and the corresponding ASQ is labelled as OFF. When <pt= TT, 0, then the spindependent component of the supercurrent is maximal and the corresponding ASQ is labelled as ON. By controlling currents through the flux bias lines, ASQs can be controllably switched between the states OFF and ON. The values are but examples.

[0038] The configuration of the ASQ circuit 1 involving the flux bias lines and loops with respective subloops and inductive elements forming the ASQ devices enables to tune the fluxes in adjacent loops independently from one another. That is, in practice, fluxes through adjacent loops can be tuned independently and with maximal addressability using the geometry illustrated in Fig. 1.

[0039] The twisted connections (e.g. 4-1-3) mean that each loop is implemented with a twisted gradiometric loop geometry. I.e., the twisted-loop devices implement the twisted gradiometric loop geometry.

[0040] The ASQ circuit 1, including elements of the ASQ circuit 1, is typically provided on an insulating substrate (not illustrated in Fig. 1).

[0041] Preferably, each of the first (4-1-1) and second (4-1-2) subloops is extended by a respective line pair portion (4-1 -1-1; 4- 1-2-1) on which at a distal end thereof the respective first (5-1-1) and second (5-1-2) inductive element is located, the respective line pair portion consisting of a pair of parallel lines adjacent to each other.

[0042] By providing such line pair portions as illustrated in Fig. 1, the magnetic flux through the line pair portions is substantially zero, which means that the coupling between ASQs can be controlled more accurately. With a substantially zero gap between the lines in the portion, the line pair portions are thus configured to exhibit substantially zero magnetic flux therethrough, while still providing a connection between the Andreev spin-qubit devices. Preferably, the pair of parallel lines in each of the line pair portions is insulated from each other to provide a substantially zero gap so as to exhibit the substantially zero magnetic flux therethrough.

[0043] ASQs typically exhibit a spin-dependent Josephson energy. So, preferably, each ASQ device (ASQ1) is configured to have a controllable Josephson energy (Eso.i) dependent on a spin of a qubit localized in the ASQ device (ASQ1).

[0044] Preferably, each flux bias line (6-1) is configured with a symmetric design and comprises a first part (6-1 -la) extending along the first subloop (4-1-1) and a second part (6-1- 2a) extending along the second subloop (4-1-2) in an opposite direction relative to the first part.

[0045] Thereby, each loop is inductively coupled to a respective flux bias line with a respective current. The combination of the loop and flux bias line designs maximizes their coupling while minimizing unwanted cross-coupling to other loops, for various reasons. First, the two opposite currents on the flux line induce contributions to the flux through the loop that add up due to its twisted geometry. Second, the generated magnetic field decreases with distance faster than for monopole flux line configurations, resulting in reduced magnetic fields at the locations of other loops. Third, the gradiometric loop design reduces the sensitivity to homogeneous fields, again reducing the unwanted cross-coupling, as well as the sensitivity to global magnetic noise.

[0046] Preferably, the flux bias line (6-1) comprises a first (6-1-1), second (6-1-2) and third (6- 1-3) terminal of which the first and second terminals (6-1-1, 6-1-2) are arranged at a respective end of the flux bias line (6-1) and the third terminal (6-1-3) is connected to substantially halfway the flux bias line (6-1).

[0047] Preferably, the ASQ circuit 1 further comprises at each ASQ device (ASQ1) an electrostatic gate and / or a conductive drive line coupled to the respective electrostatic gate.

[0048] That is, the ASQ circuit 1 allows for at least two possible driving mechanisms: using the same flux bias lines for driving the ASQs via supercurrent, or connecting drive lines to the electrostatic gates to address each ASQ via a electric dipole spin resonance (EDSR) mechanism.

[0049] Preferably, in each loop, the first and second subloops are configured to surround an area of the same size on the insulating substrate. Thereby, external magnetic noise can be efficiently cancelled.

[0050] Preferably, each loop (e.g., 4-1) has a symmetrical layout, such as a rectangular layout, formed by interconnected line elements. Preferably, the first (e.g., 4-1-1) and second (e.g., 4-1- 2) subloops each have a symmetrical layout, such as a rectangular layout, formed by interconnected line elements. Preferably, from a top view on the ASQ circuit (1), in the array the twisted-loop devices 3-1, 3-2, 3-3, etc., are arranged in line with each other.

[0051] Preferably, from a top view on the ASQ circuit (1), in the array the one (3-1) of the pair (3-1, 3-2) of neighbouring twisted-loop devices and the other (3-2) of the pair (3-1, 3-2) of neighbouring twisted-loop devices are arranged diagonally to each other, and the ASQ device (ASQ1) is located at an adjacent comer between the one (3-1) and the other (3-2) of the pair (3- 1, 3-2).

[0052] Such a configuration of diagonally arranging twisted-loop devices is illustrated in Fig. 1, in which for example twisted-loop devices 3-1, 3-2, 3-3 are shown to be arranged diagonally to each other in the array. The inventors have identified that the specific design of the ASQ circuit 1 involving the diagonally arranged twisted-loop devices minimizes flux cross-coupling between different loops, and is therefore particularly advantageous. However, various other configurations may be considered as well and the invention is not limited to the illustration.

[0053] ASQs typically involve superconducting currents. So, preferably, each loop (4-1) is a superconducting loop comprising a superconductor material such as Aluminium. Preferably, each inductive element of the ASQ circuit (1) is implemented as a superconducting inductive element comprising a superconductor material. Preferably, each line forming part of the ASQ circuit (1) is a superconducting line comprising a superconductor material.

[0054] Fig. 2 is an abstract circuit diagram of the ASQ circuit 1 of the present invention. Fig. 2 shows N ASQs (ASQ1, ASQ2, ..., ASQN) connected in parallel to a coupling Josephson junction 2 with Josephson energy Ej. The circuit diagram thus shows a configuration defining N loops. Furthermore shown are that each ASQ (e.g., ASQi, i=l,...,N) has spin-independent and spin-dependent Josephson energies Ej,i and Eso., (SO for “spin-orbit”), respectively. The magnetic flux through loop i is denoted as and the phase drop across ASQi is denoted as <p . The phase drop across the Josephson coupling junction is denoted as <p.

[0055] Preferably, the ASQ circuit 1 is operated in the regime £} »Ej.,, Eso.i for all i, which results in <p « 0.

[0056] Fig. 3 shows four possible phase setpoints for an ASQ. When <pi = ± a spindependent component Is,i of a supercurrent vanishes and the corresponding ASQ (ASQi in Fig. 3) is labelled as OFF. When <pt= TT, 0, then the spin-dependent component of the supercurrent is maximal and the corresponding ASQ is labelled as ON. Thereby, individual ASQs can be controllably manipulated between two states, OFF and ON. Thus, by controlling currents through the flux bias lines, ASQs can be controllably switched between the states OFF and ON.

[0057] Figs. 4A-4C show global configurations of the ASQ circuit 1 and illustrate that a global configuration can be adjusted by varying the flux setpoints of all qubits (ASQs).

[0058] Fig. 4A shows an idling configuration in which all qubits are OFF. In this example, by setting / controlling = 40 / 4, ASQ1 is set to its OFF state with ! = TT / 2. In turn, d = <b0 / 2 for all i>l results in alternating phase drops of TT / 2 and —Till, for all other qubits, rendering the other qubits OFF as well. Consequently, in this idling configuration, all qubits are uncoupled.

[0059] Figs. 4B and 4C show two examples of selective two-qubit coupling that deviate from the illustrated idling configuration of Fig. 4A.

[0060] In Fig. 4B, ASQ5 and ASQ8 are controlled as ON by modifying their associated phase drops accordingly to be either 0 or TT, thereby thus maximizing their respective spin-dependent supercurrent. Similarly, in Fig. 4C, ASQ1 and ASQ9 and coupled. In both configurations illustrated in Figs. 4B and 4C, the respective two selected qubits are longitudinally coupled to each other while the rest of the qubits remains uncoupled.

[0061] Thus, Figs. 4A-4C show all-to-all selective coupling between ASQs, enabled by the ASQ circuit 1. In addition to the illustrated configurations involving coupling of two qubits, further configurations involving coupling of three of more, even all, qubits are enabled by the ASQ circuit 1. Coupling of three or more qubits may be useful for example for a quantum simulation of a highly-connected system, such as a highly-connected Ising system.

[0062] Preferably, the ASQ circuit 1 further comprises a transmon circuit comprising a capacitor device connected in parallel to the coupling Josephson junction and to the ASQ devices. The transmon circuit may be used for example for reading out a state of the ASQ circuit.

[0063] Fig. 5A schematically illustrates such a transmon circuit.

[0064] Preferably, the ASQ circuit 1 further comprises a fluxonium circuit comprising a capacitor and an inductor in parallel to each other, the fluxonium circuit connected in parallel to the coupling Josephson junction (2) and to the ASQ devices.

[0065] Fig. 5B schematically illustrates such a fluxonium circuit. Furthermore, a method of manufacturing the ASQ circuit 1 is provided. The method of manufacturing comprises:

[0066] - providing an insulating substrate;

[0067] - creating, on the insulating substrate, a thin film patterned structure of a coupling Josephson junction element (2) and an array of a plurality of twisted-loop devices (3-1, 3-2, 3- 3) coupled in parallel to the coupling Josephson junction element (2), wherein each twisted- loop device (3-1) comprises a loop (4-1) on the substrate, the loop (4-1) comprising a first subloop (4-1-1) and a second subloop (4-1-2), within the loop (4-1) the first and second subloops being interconnected by a twisted connection (4-1-3), a first inductive element (5-1- 1) being arranged within the first subloop (4-1-1) and a second inductive element (5-1-2) being arranged within the second subloop (4-1-2);

[0068] - creating, on the insulating substrate, a plurality of conductive flux bias lines (6-1, 6-2, 6-3), each flux bias line (6-1) adjacent to a corresponding loop (4-1) and extending along the first (4-1-1) and the second (4-1-2) subloop of the corresponding loop (4-1); and creating, in each pair (3-1; 3-2) of neighbouring twisted-loop devices in the array, the second subloop (4-1-2) of one (3-1) of the pair of neighbouring twisted-loop devices to connect to the first subloop (4-2-1) of the other (3-2) of the pair of neighbouring twisted-loop devices, such that at a connection of the pair (3-1; 3-2), the second inductive element (5-1-2) of the one (3-1) twisted-loop device and the first inductive element (5-2-1) of the other (3-2) twisted-loop device form an ASQ device (ASQ1) for hosting an ASQ..

[0069] Furthermore, a method of operating the ASQ circuit 1 is provided, to couple two or more of ASQ devices (e.g., ASQ1, ASQ2) in the ASQ circuit 1. The method comprises: controlling, for each twisted-loop device (e.g. 3-1, 3-2), a respective magnetic flux (<!>!, <t>2) therethrough by tuning currents of the plurality of conductive flux bias lines (6-1, 6- 2, 6-3); controlling phase drops (1( 2) associated with the two or more of the ASQ devices (ASQ1, ASQ2) so as to tune on (ON) a spin-dependent component of a supercurrent, and controlling remaining phase drops of the remaining ASQ devices so that their corresponding spin-dependent components of the supercurrent vanish (OFF).

[0070] By the operating method, all-to-all connectivity between multiple ASQs can be established. Examples of the method of operating are illustrated in Figs. 4A-4C. The invention has been described with reference to the preferred embodiment. Obvious modifications and alterations will occur to others upon reading and understanding the preceding detailed description. It is intended that the invention be construed as including all such modifications and alterations insofar as they come within the scope of the appended claims.

[0071] Aspects of the present document are disclosed in the following clauses.

[0072] 1. Andreev spin-qubit, ASQ, circuit (1) comprising: a coupling Josephson junction element (2) and an array of a plurality of twisted-loop devices (3-1, 3-2, 3-3) coupled in parallel to the coupling Josephson junction element (2), wherein each twisted-loop device (3-1) comprises a loop (4-1) on the substrate, the loop (4-1) comprising a first subloop (4-1-1) and a second subloop (4-1-2), within the loop (4-1) the first and second subloops being interconnected by a twisted connection (4-1-3), a first inductive element (5-1-1) being arranged within the first subloop (4-1-1) and a second inductive element (5-1-2) being arranged within the second subloop (4-1-2); and a plurality of conductive flux bias lines (6-1, 6-2, 6-3), each flux bias line (6-1) adjacent to a corresponding loop (4-1) and extending along the first (4-1-1) and the second (4-1-2) subloop of the corresponding loop (4-1); wherein in each pair (3-1; 3-2) of neighbouring twisted-loop devices in the array, the second subloop (4-1-2) of one (3-1) of the pair of neighbouring twisted-loop devices connects to the first subloop (4-2-1) of the other (3-2) of the pair of neighbouring twisted-loop devices, such that at a connection of the pair (3-1; 3-2), the second inductive element (5-1-2) of the one (3-1) twisted-loop device and the first inductive element (5-2-1) of the other (3-2) twisted-loop device form an ASQ device (ASQ1) for hosting an ASQ.

[0073] 2. The ASQ circuit (1) according to clause 1, wherein each of the first (4-1-1) and second (4-1-2) subloops is extended by a respective line pair portion (4-1 -1 -1 ; 4-1 -2-1) on which at a distal end thereof the respective first (5-1-1) and second (5-1-2) inductive element is located; the respective line pair portion consisting of a pair of parallel lines adjacent to each other.

[0074] 3. The ASQ circuit (1) according to clause 1 or 2, wherein the ASQ device (ASQ1) is configured to have a Josephson energy (Eso.i) dependent on a spin of a qubit localized in the ASQ device (ASQ1).

[0075] 4. The ASQ circuit (1) according to any one of clauses 1 - 3, wherein each flux bias line (6-1) is configured with a symmetric design and comprises a first part (6-1 -la) extending along the first subloop (4-1-1) and a second part (6-1 -2a) extending along the second subloop (4-1-2) in an opposite direction relative to the first part. 5. The ASQ circuit (1) according to clause 4, wherein the flux bias line (6-1) comprises a first (6-1-1), second (6-1-2) and third (6-1-3) terminal of which the first and second terminals (6-1-1, 6-1-2) are arranged at a respective end of the flux bias line (6-1) and the third terminal (6-1-3) is connected to substantially halfway the flux bias line (6-1).

[0076] 6. The ASQ circuit (1) according to any one of clauses 1 - 5, further comprising at each ASQ device (ASQ1) an electrostatic gate and / or a conductive drive line coupled to the respective electrostatic gate.

[0077] 7. The ASQ circuit (1) according to any one of preceding clauses 1 - 6, wherein the loop (4-1) has a symmetrical layout, such as a rectangular layout, formed by interconnected line elements.

[0078] 8. The ASQ circuit (1) according to any one of clauses 1 - 6, wherein the first (4-1-1) and second (4-1-2) subloops each have a symmetrical layout, such as a rectangular layout, formed by interconnected line elements.

[0079] 9. The ASQ circuit (1) according to clause 8, wherein, from a top view on the ASQ circuit (1), in the array the twisted-loop devices are arranged in line with each other.

[0080] 10. The ASQ circuit (1) according to clause 8 or 9, wherein, from a top view on the ASQ circuit (1), in the array the one (3-1) of the pair (3-1, 3-2) of neighbouring twisted-loop devices and the other (3-2) of the pair (3-1, 3-2) of neighbouring twisted-loop devices are arranged diagonally to each other, and the ASQ device (ASQ1) is located at an adjacent corner between the one (3-1) and the other (3-2) of the pair (3-1, 3-2).

[0081] 11. The ASQ circuit (1) according to any one of the preceding clauses, wherein each loop (4-1) is a superconducting loop comprising a superconductor material.

[0082] 12. The ASQ circuit (1) according to any one of the preceding clauses, further comprising a transmon circuit comprising a capacitor device connected in parallel to the coupling Josephson junction and to the ASQ devices.

[0083] 13. The ASQ circuit (1) according to any one of the preceding clauses, further comprising a fluxonium circuit comprising a capacitor and an inductor in parallel to each other, the fluxonium circuit connected in parallel to the coupling Josephson junction (2) and to the ASQ devices.

[0084] 14. Method of manufacturing an Andreev spin-qubit, ASQ, circuit (1) according to any one of the preceding clauses, comprising:

[0085] - providing an insulating substrate;

[0086] - creating, on the insulating substrate, a thin film patterned structure of a coupling Josephson junction element (2) and an array of a plurality of twisted-loop devices (3-1, 3-2, 3- 3) coupled in parallel to the coupling Josephson junction element (2), wherein each twisted-loop device (3-1) comprises a loop (4-1) on the substrate, the loop (4-1) comprising a first subloop (4-1-1) and a second subloop (4-1-2), within the loop (4-1) the first and second subloops being interconnected by a twisted connection (4-1-3), a first inductive element (5-1- 1) being arranged within the first subloop (4-1-1) and a second inductive element (5-1-2) being arranged within the second subloop (4-1-2);

[0087] - creating, on the insulating substrate, a plurality of conductive flux bias lines (6-1, 6-2, 6-3), each flux bias line (6-1) adjacent to a corresponding loop (4-1) and extending along the first (4-1-1) and the second (4-1-2) subloop of the corresponding loop (4-1);

[0088] - creating, in each pair (3-1; 3-2) of neighbouring twisted-loop devices in the array, the second subloop (4-1-2) of one (3-1) of the pair of neighbouring twisted-loop devices to connect to the first subloop (4-2-1) of the other (3-2) of the pair of neighbouring twisted-loop devices, such that at a connection of the pair (3-1; 3-2), the second inductive element (5-1-2) of the one (3-1) twisted-loop device and the first inductive element (5-2-1) of the other (3-2) twisted-loop device form an ASQ device (ASQ1) for hosting an ASQ.

[0089] 15. The method according to clause 14, further comprising creating one or more of

[0090] - each of the first (4-1-1) and second (4-1-2) subloops is extended by a respective line pair portion (4-1 -1 -1 ; 4-1 -2-1) on which at a distal end thereof the respective first (5-1-1) and second (5-1-2) inductive element is located; the respective line pair portion consisting of a pair of parallel lines adjacent to each other;

[0091] - each flux bias line (6-1) is configured with a symmetric design and comprises a first part (6-1 -la) extending along the first subloop (4-1-1) and a second part (6-1 -2a) extending along the second subloop (4-1-2) in an opposite direction relative to the first part;

[0092] - the flux bias line (6-1) comprises a first (6-1-1), second (6-1-2) and third (6-1-3) terminal of which the first and second terminals (6-1-1, 6-1-2) are arranged at a respective end of the flux bias line (6-1) and the third terminal (6-1-3) is connected to substantially halfway the flux bias line (6-1).

[0093] 16. Method of operating an ASQ circuit (1) according to any one of the preceding clauses 1-13, to couple two or more of ASQ devices (ASQ1, ASQ2) in the ASQ circuit (1), the method comprising: controlling, for each twisted-loop device (3-1, 3-2), a respective magnetic flux (<!>!,<J>2) therethrough by tuning currents of the plurality of conductive flux bias lines (6-1, 6-2, 6-3); controlling phase drops (1( 2) associated with the two or more of the ASQ devices (ASQ1, ASQ2) so as to tune on (ON) a spin-dependent component of a supercurrent, and controlling remaining phase drops of the remaining ASQ devices so that their corresponding spin-dependent components of the supercurrent vanish (OFF).

[0094] The following list of references is referred to in the present document and is incorporated herein by way of reference.

[0095] List of references

[0096] [A] Authors. Title. Publisher. Date.

[0097] [Chtchelkatchev et al] Nikolai M. Chtchelkatchev and Yu. V. Nazarov. Andreev Quantum Dots for Spin Manipulation. Phys. Rev. Lett. 90, 226806. 4 June 2003.

[0098] [Hays et al] Hays et al. Coherent manipulation of an Andreev spin qubit. Science Vol 373, 430- 433. 23 July 2021.

[0099] [Padurariu et al] C. Padurariu and Yu. V. Nazarov. Theoretical proposal for superconducting spin qubits. Phys. Rev. B 81, 144519. 29 April 2010.

[0100] [Park et al] Sunghun Park and A. Levy Yeyati. Andreev spin qubits in multichannel Rashba nanowires. Phys. Rev. B 96, 125416. 12 September 2017.

[0101] [Pita- Vidal et al, a] Marta Pita- Vidal et al. Direct manipulation of a superconducting spin qubit strongly coupled to a transmon qubit. Nature Physics volume 19, pages 1110-1115. 22 May 2023.

[0102] [Pita- Vidal et al, b] Marta Pita- Vidal et al. Strong tunable coupling between two distant superconducting spin qubits. arXiv:2307.15654. 28 July 2023.

[0103] [Spethmann et al] Maria Spethmann, Xian-Peng Zhang, Jelena Klinovaja, and Daniel Loss. Coupled superconducting spin qubits with spin-orbit interaction. Phys. Rev. B 106, 115411. 12 September 2022.

Claims

What is claimed is:

1. Andreev spin-qubit, ASQ, circuit (1) comprising: a coupling Josephson junction element (2) and an array of a plurality of twisted-loop devices (3-1, 3-2, 3-3) coupled in parallel to the coupling Josephson junction element (2), wherein each twisted-loop device (3-1) comprises a loop (4-1) on an insulating substrate, the loop (4-1) comprising a first subloop (4-1-1) and a second subloop (4-1-2), within the loop (4-1) the first and second subloops being interconnected by a twisted connection (4-1- 3), a first inductive element (5-1-1) being arranged within the first subloop (4-1-1) and a second inductive element (5-1-2) being arranged within the second subloop (4-1-2); and a plurality of conductive flux bias lines (6-1, 6-2, 6-3), each flux bias line (6-1) adjacent to a corresponding loop (4-1) and extending along the first (4-1-1) and the second (4-1-2) subloop of the corresponding loop (4-1), wherein each loop is implemented with a twisted gradiometric loop geometry; wherein in each pair (3-1; 3-2) of neighbouring twisted-loop devices in the array, the second subloop (4-1-2) of one (3-1) of the pair of neighbouring twisted-loop devices connects to the first subloop (4-2-1) of the other (3-2) of the pair of neighbouring twisted-loop devices, such that at a connection of the pair (3-1; 3-2), the second inductive element (5-1-2) of the one (3-1) twisted-loop device and the first inductive element (5-2-1) of the other (3-2) twisted-loop device form an ASQ device (ASQ1) for hosting an ASQ.

2. The ASQ circuit (1) according to claim 1, wherein each of the first (4-1-1) and second (4-1- 2) subloops is extended by a respective line pair portion (4-1 -1 -1 ; 4-1 -2-1) on which at a distal end thereof the respective first (5-1-1) and second (5-1-2) inductive element is located; the respective line pair portion consisting of a pair of parallel lines adjacent to each other.

3. The ASQ circuit (1) according to claim 1 or 2, wherein the ASQ device (ASQ1) is configured to have a Josephson energy (Eso.i) dependent on a spin of a qubit localized in the ASQ device (ASQ1).

4. The ASQ circuit (1) according to any one of claims 1 - 3, wherein each flux bias line (6-1) is configured with a symmetric design and comprises a first part (6-1-la) extending along the first subloop (4-1-1) and a second part (6-1 -2a) extending along the second subloop (4-1-2) in an opposite direction relative to the first part.

5. The ASQ circuit (1) according to claim 4, wherein the flux bias line (6-1) comprises a first (6-1-1), second (6-1-2) and third (6-1-3) terminal of which the first and second terminals (6-1- 1, 6-1-2) are arranged at a respective end of the flux bias line (6-1) and the third terminal (6-1- 3) is connected to substantially halfway the flux bias line (6-1).

6. The ASQ circuit (1) according to any one of claims 1 - 5, further comprising at each ASQ device (ASQ1) an electrostatic gate and / or a conductive drive line coupled to the respective electrostatic gate.

7. The ASQ circuit (1) according to any one of preceding claims 1 - 6, wherein the loop (4-1) has a symmetrical layout, such as a rectangular layout, formed by interconnected line elements.

8. The ASQ circuit (1) according to any one of claims 1 - 6, wherein the first (4-1-1) and second (4-1-2) subloops each have a symmetrical layout, such as a rectangular layout, formed by interconnected line elements.

9. The ASQ circuit (1) according to claim 8, wherein, from a top view on the ASQ circuit (1), in the array the twisted-loop devices are arranged in line with each other.

10. The ASQ circuit (1) according to claim 8 or 9, wherein, from a top view on the ASQ circuit (1), in the array the one (3-1) of the pair (3-1, 3-2) of neighbouring twisted-loop devices and the other (3-2) of the pair (3-1, 3-2) of neighbouring twisted-loop devices are arranged diagonally to each other, and the ASQ device (ASQ1) is located at an adjacent corner between the one (3-1) and the other (3-2) of the pair (3-1, 3-2).

11. The ASQ circuit (1) according to any one of the preceding claims, wherein each loop (4-1) is a superconducting loop comprising a superconductor material.

12. The ASQ circuit (1) according to any one of the preceding claims, further comprising a transmon circuit comprising a capacitor device connected in parallel to the coupling Josephson junction and to the ASQ devices.

13. The ASQ circuit (1) according to any one of the preceding claims, further comprising a fluxonium circuit comprising a capacitor and an inductor in parallel to each other, the fluxonium circuit connected in parallel to the coupling Josephson junction (2) and to the ASQ devices.

14. Method of manufacturing an Andreev spin-qubit, ASQ, circuit (1) according to any one of the preceding claims, comprising:- providing the insulating substrate;- creating, on the insulating substrate, a thin film patterned structure of a coupling Josephson junction element (2) and an array of a plurality of twisted-loop devices (3-1, 3-2, 3- 3) coupled in parallel to the coupling Josephson junction element (2), wherein each twisted-loop device (3-1) comprises a loop (4-1) on the substrate, the loop (4-1) comprising a first subloop (4-1-1) and a second subloop (4-1-2), within the loop (4-1) the first and second subloops being interconnected by a twisted connection (4-1-3), a first inductive element (5-1- 1) being arranged within the first subloop (4-1-1) and a second inductive element (5-1-2) being arranged within the second subloop (4-1-2);- creating, on the insulating substrate, a plurality of conductive flux bias lines (6-1, 6-2, 6-3), each flux bias line (6-1) adjacent to a corresponding loop (4-1) and extending along the first (4-1-1) and the second (4-1-2) subloop of the corresponding loop (4-1);- creating, in each pair (3-1; 3-2) of neighbouring twisted-loop devices in the array, the second subloop (4-1-2) of one (3-1) of the pair of neighbouring twisted-loop devices to connect to the first subloop (4-2-1) of the other (3-2) of the pair of neighbouring twisted-loop devices, such that at a connection of the pair (3-1; 3-2), the second inductive element (5-1-2) of the one (3-1) twisted-loop device and the first inductive element (5-2-1) of the other (3-2) twisted-loop device form an ASQ device (ASQ1) for hosting an ASQ.

15. The method according to claim 14, further comprising creating one or more of:- each of the first (4-1-1) and second (4-1-2) subloops is extended by a respective line pair portion (4-1 -1 -1 ; 4-1 -2-1) on which at a distal end thereof the respective first (5-1-1) and second (5-1-2) inductive element is located; the respective line pair portion consisting of a pair of parallel lines adjacent to each other;- each flux bias line (6-1) is configured with a symmetric design and comprises a first part (6-1 -la) extending along the first subloop (4-1-1) and a second part (6-1 -2a) extending along the second subloop (4-1-2) in an opposite direction relative to the first part;- the flux bias line (6-1) comprises a first (6-1-1), second (6-1-2) and third (6-1-3) terminal of which the first and second terminals (6-1-1, 6-1-2) are arranged at a respective end of the flux bias line (6-1) and the third terminal (6-1-3) is connected to substantially halfway the flux bias line (6-1).

16. Method of operating an ASQ circuit (1) according to any one of the preceding claims 1-13, to couple two or more of the ASQs hosted in the ASQ devices (ASQ1, ASQ2) of the ASQ circuit (1), the method comprising: controlling, for each twisted-loop device (3-1, 3-2), a respective magnetic flux (<!>!,(b2) therethrough by tuning currents of the plurality of conductive flux bias lines (6-1, 6-2, 6-3); controlling phase drops (1( 2) associated with the two or more of the ASQ devices (ASQ1, ASQ2) so as to tune on (ON) a spin-dependent component of a supercurrent, and controlling remaining phase drops of the remaining ASQ devices so that their corresponding spin-dependent components of the supercurrent vanish (OFF).

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