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Title:
QUBIT RESET
Document Type and Number:
WIPO Patent Application WO/2023/275426
Kind Code:
A1
Abstract:
It is an objective to provide an arrangement for resetting at least one qubit. According to an embodiment, an arrangement for resetting at least one qubit comprises at least one qubit; an energy dissipation structure selectively couplable to the at least one qubit; and a control unit, configured to reset the at least one qubit by performing: couple the at least one qubit to the energy dissipation structure for a reset period using a control signal, wherein the control signal controls a coupling strength between the at least one qubit and the energy dissipation structure; and after the reset period, decouple the at least one qubit from the energy dissipation structure during a decoupling period using the control signal, wherein the coupling strength comprises, during the decoupling period, at least a temporally linearly decreasing component and at least one temporally sinusoidal component.

Inventors:
MÖTTÖNEN MIKKO (FI)
TUORILA JANI (FI)
Application Number:
PCT/FI2021/050500
Publication Date:
January 05, 2023
Filing Date:
June 28, 2021
Export Citation:
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Assignee:
IQM FINLAND OY (FI)
International Classes:
G06N10/40
Foreign References:
CN213024477U2021-04-20
Other References:
BASILEWITSCH DANIEL ET AL: "Reservoir engineering using quantum optimal control for qubit reset", NEW JOURNAL OF PHYSICS, vol. 21, no. 9, 1 September 2019 (2019-09-01), pages 093054, XP055897892, Retrieved from the Internet DOI: 10.1088/1367-2630/ab41ad
SEVRIUK V. A. ET AL: "Fast control of dissipation in a superconducting resonator", APPLIED PHYSICS LETTERS, vol. 115, no. 8, 19 August 2019 (2019-08-19), 2 Huntington Quadrangle, Melville, NY 11747, pages 082601, XP055802521, ISSN: 0003-6951, Retrieved from the Internet DOI: 10.1063/1.5116659
Attorney, Agent or Firm:
PAPULA OY (FI)
Download PDF:
Claims:
CLAIMS: 1. An arrangement (100) for resetting at least one qubit, comprising: at least one qubit (101); an energy dissipation structure (102) selectively couplable to the at least one qubit (101), wherein the energy dissipation structure (102) is configured to dis- sipate energy transferred to the energy dissipation structure from the at least one qubit (101); and a control unit (103), configured to reset the at least one qubit (101) by performing: couple the at least one qubit (101) to the energy dissipation structure for a reset period using a control signal, wherein the control signal controls a coupling strength between the at least one qubit (101) and the energy dissipation structure (102); and after the reset period, decouple the at least one qubit (101) from the energy dissipation structure (102) during a decoupling period using the control sig- nal, wherein the coupling strength between the at least one qubit (101) and the energy dissipation structure (102) comprises, during the decoupling period, at least a temporally linearly decreasing component and at least one temporally sinusoidal component. 2. The arrangement (100) according to claim 1, wherein the coupling strength between the at least one qubit (101) and the energy dissipation structure (102) further comprises, during the decoupling period, a plu- rality of temporally sinusoidal components, wherein a period of each temporally sinusoidal component is less than or equal to a temporal length of the decoupling period. 3. The arrangement (100) according to claim 2, wherein the period of an ^th sinusoidal component in the plurality of temporally sinusoidal components is τ/l, wherein τ is the temporal length of the decoupling pe- riod. 4. The arrangement (100) according to any preceding claim, wherein the temporally linearly decreasing com- ponent decreases from a maximum value to substantially zero during the decoupling period. 5. The arrangement (100) according to any preceding claim, wherein each sinusoidal component in the plural- ity of temporally sinusoidal components is substantially zero at a start of the decoupling period and substan- tially zero at an end of the decoupling period. 6. The arrangement (100) according to any preceding claim wherein a time derivative of the coupling strength between the at least one qubit (101) and the energy dissipation structure (102) is substantially zero at a start of the decoupling period and at an end of the decoupling period.

7. The arrangement (100) according to any preceding claim, wherein the coupling strength between the at least one qubit (101) and the energy dissipation struc- ture (102) is temporally strictly decreasing during the decoupling period. 8. The arrangement (100) according to any preceding claim, wherein the energy dissipation structure comprise at least one normal metal – insulator – superconductor, NIS, junction. 9. The arrangement (100) according to any preceding claim, wherein the energy dissipation structure com- prises a quantum circuit refrigerator, QCR, wherein the QCR comprises a voltage-biased superconductor – insula- tor – normal metal – insulator – superconductor, SINIS, junction, and wherein the at least one qubit is elec- trically coupled to the normal metal of the SINIS junc- tion of the energy dissipation structure. 10. The arrangement (100) according to claim 8, wherein the control unit is configured to control the coupling strength between the at least one qubit and the energy dissipation structure by tuning a bias voltage of the SINIS junction of the energy dissipation struc- ture based on the control signal. 11. The arrangement (100) according to any of claims 8 – 10, wherein the energy dissipation structure is configured to dissipate photon energy transferred to the energy dissipation structure via photon-assisted electron tunnelling in the NIS/SINIS junction. 12. The arrangement (100) according to any preced- ing claim, wherein the at least one qubit comprises at least one superconductive qubit. 13. The arrangement (100) according to any preced- ing claim, wherein the control unit (103) is further configured, after the reset period and before the de- coupling period, perform a pre-decoupling using the con- trol signal, wherein a magnitude of a time derivative of the coupling strength between the at least one qubit (101) and the energy dissipation structure (102) during the pre-decoupling is less than a magnitude of a time derivative of the coupling strength between the at least one qubit (101) and the energy dissipation structure (102) during the decoupling period. 14. A quantum computing system comprising a plural- ity of arrangements according to any preceding claim. 15. A method (500) for resetting at least one qubit using an energy dissipation structure selectively cou- plable to the at least one qubit, wherein the energy dissipation structure is configured to dissipate energy transferred to the energy dissipation structure from the at least one qubit, the method comprising: coupling (501) the at least one qubit to the energy dissipation structure for a reset period using a control signal, wherein the control signal controls a coupling strength between the at least one qubit and the energy dissipation structure; and after the reset period, decoupling (502) the at least one qubit from the energy dissipation structure during a decoupling period using the control signal, wherein the coupling strength between the at least one qubit and the energy dissipation structure comprises, during the decoupling period, at least a temporally lin- early decreasing component and at least one temporally sinusoidal component.

Description:
QUBIT RESET TECHNICAL FIELD [0001] The present disclosure relates to quantum com- puting, and more particularly to an arrangement for re- setting at least one qubit, to a method for resetting at least one qubit, and to a quantum computing system. BACKGROUND [0002] The ability to reset qubits fast and with high fidelity is one of the prerequisites for coherent quan- tum computations. In superconducting realizations, for example, experimental developments have been obtained recently with approaches based on Purcell-filtered cav- ities, feedback-based schemes, and unconditional all- microwave protocols. However, reset fidelities above 99% required by quantum-err→r correction schemes remain a technological challenge in the 10 nanosecond time scales required by the coherent operation of the qubits. SUMMARY [0003] This summary is provided to introduce a selec- tion of concepts in a simplified form that are further described below in the detailed description. This sum- mary is not intended to identify key features or essen- tial features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter. [0004] It is an objective to provide an arrangement for resetting at least one qubit, a method for resetting at least one qubit, and a quantum computing system. The foregoing and other objectives are achieved by the fea- tures of the independent claims. Further implementation forms are apparent from the dependent claims, the de- scription and the figures. [0005] According to a first aspect, an arrangement for resetting at least one qubit comprises: at least one qubit; an energy dissipation structure selectively cou- plable to the at least one qubit, wherein the energy dissipation structure is configured to dissipate energy transferred to the energy dissipation structure from the at least one qubit; and a control unit, configured to reset the at least one qubit by performing: couple the at least one qubit to the energy dissipation structure for a reset period using a control signal, wherein the control signal controls a coupling strength between the at least one qubit and the energy dissipation structure; and after the reset period, decouple the at least one qubit from the energy dissipation structure during a decoupling period using the control signal, wherein the coupling strength between the at least one qubit and the energy dissipation structure comprises, during the de- coupling period, at least a temporally linearly decreas- ing component and at least one temporally sinusoidal component. The arrangement can, for example, reset the at least one qubit with reduced initialization errors. [0006] In an implementation form of the first aspect, the coupling strength between the at least one qubit and the energy dissipation structure further comprises, dur- ing the decoupling period, a plurality of temporally sinusoidal components, wherein a period of each tempo- rally sinusoidal component is less than or equal to a temporal length of the decoupling period. The arrange- ment can, for example, with such a coupling strength, smoothly decouple the at least one qubit and the energy dissipation structure. [0007] In another implementation form of the first aspect, the period of an ^th sinusoidal component in the plurality of temporally sinusoidal components is ^/^, wherein ^ is the temporal length of the decoupling pe- riod. The arrangement can, for example, with such a coupling strength, ensure that the sinusoidal components are such that initialization errors are reduced. [0008] In another implementation form of the first aspect, the temporally linearly decreasing component decreases from a maximum value to substantially zero during the decoupling period. The arrangement can, for example, with such a coupling strength, make the cou- pling go to substantially zero at the end of the decou- pling period. [0009] In another implementation form of the first aspect, each sinusoidal component in the plurality of temporally sinusoidal components is substantially zero at a start of the decoupling period and substantially zero at an end of the decoupling period. The arrangement can, for example, with such a coupling strength, ensure that the sinusoidal components are such that initiali- zation errors are reduced. [0010] In another implementation form of the first aspect, a time derivative of the coupling strength be- tween the at least one qubit and the energy dissipation structure is substantially zero at a start of the de- coupling period and at an end of the decoupling period. The arrangement can, for example, with such a coupling strength, ensure that the decoupling is smooth at the start and at the end of the decoupling period, which can reduce initialization errors. [0011] In another implementation form of the first aspect, the coupling strength between the at least one qubit and the energy dissipation structure is temporally strictly decreasing during the decoupling period. The arrangement can, for example, with such a coupling strength, reduce the temporal length of the decoupling period, and thus make the resetting of the at least one qubit faster. [0012] In another implementation form of the first aspect, the energy dissipation structure comprises at least one normal metal – insulator – superconductor, NIS, junction. The arrangement can, for example, utilise the NIS junction for efficient and controllable energy dissipation. [0013] In another implementation form of the first aspect, the energy dissipation structure comprises a quantum circuit refrigerator, QCR, wherein the QCR com- prises a voltage-biased superconductor – insulator – normal metal – insulator – superconductor, SINIS, junc- tion, and wherein the at least one qubit is electrically coupled to the normal metal of the SINIS junction of the energy dissipation structure. The arrangement can, for example, utilise the SINIS junction for efficient and controllable energy dissipation. [0014] In another implementation form of the first aspect, the control unit is configured to control the coupling strength between the at least one qubit and the energy dissipation structure by tuning a bias voltage of the SINIS junction of the energy dissipation struc- ture based on the control signal. The arrangement can, for example, efficiently control the coupling via the bias voltage. [0015] In another implementation form of the first aspect, the energy dissipation structure is configured to dissipate photon energy transferred to the energy dissipation structure via photon-assisted electron tun- nelling in the NIS/SINIS junction. The arrangement can, for example, efficiently dissipate the transferred en- ergy via the photon-assisted electron tunnelling. [0016] In another implementation form of the first aspect, the at least one qubit comprises at least one superconductive qubit. [0017] In another implementation form of the first aspect, the control unit is further configured, after the reset period and before the decoupling period, per- form a pre-decoupling using the control signal, wherein a magnitude of a time derivative of the coupling strength between the at least one qubit and the energy dissipation structure during the pre-decoupling is less than a magnitude of a time derivative of the coupling strength between the at least one qubit and the energy dissipation structure during the decoupling period. The arrangement can, for example, further reduce initiali- zation errors via the pre-decoupling. [0018] According to a second aspect, a quantum compu- ting system comprises a plurality of arrangements ac- cording to the first aspect. [0019] According to a third aspect, a method for re- setting at least one qubit using an energy dissipation structure selectively couplable to the at least one qubit, wherein the energy dissipation structure is con- figured to dissipate energy transferred to the energy dissipation structure from the at least one qubit, the method comprises: coupling the at least one qubit to the energy dissipation structure for a reset period using a control signal, wherein the control signal controls a coupling strength between the at least one qubit and the energy dissipation structure; and after the reset pe- riod, decoupling the at least one qubit from the energy dissipation structure during a decoupling period using the control signal, wherein the coupling strength be- tween the at least one qubit and the energy dissipation structure comprises, during the decoupling period, at least a temporally linearly decreasing component and at least one temporally sinusoidal component. [0020] Many of the attendant features will be more readily appreciated as they become better understood by reference to the following detailed description consid- ered in connection with the accompanying drawings. DESCRIPTION OF THE DRAWINGS [0021] In the following, example embodiments are de- scribed in more detail with reference to the attached figures and drawings, in which: [0022] Fig. 1 illustrates a schematic representation of an arrangement for resetting at least one qubit ac- cording to an embodiment; [0023] Fig. 2 illustrates a schematic representation of a coupling strength between at least one qubit and an energy dissipation structure according to an embod- iment; [0024] Fig. 3 illustrates a schematic representation an energy dissipation structure comprising a supercon- ductor – insulator – normal metal – insulator – super- conductor junction according to an embodiment; [0025] Fig. 4 illustrates a schematic representation of a control unit according to an embodiment; and [0026] Fig. 5 illustrates a flow chart representation of a method for resetting at least one qubit according to an embodiment. [0027] In the following, like reference numerals are used to designate like parts in the accompanying draw- ings. DETAILED DESCRIPTION [0028] In the following description, reference is made to the accompanying drawings, which form part of the disclosure, and in which are shown, by way of illustra- tion, specific aspects in which the present disclosure may be placed. It is understood that other aspects may be utilised, and structural or logical changes may be made without departing from the scope of the present disclosure. The following detailed description, there- fore, is not to be taken in a limiting sense, as the scope of the present disclosure is defined be the ap- pended claims. [0029] For instance, it is understood that a disclo- sure in connection with a described method may also hold true for a corresponding device or system configured to perform the method and vice versa. For example, if a specific method step is described, a corresponding de- vice may include a unit to perform the described method step, even if such unit is not explicitly described or illustrated in the figures. On the other hand, for ex- ample, if a specific apparatus is described based on functional units, a corresponding method may include a step performing the described functionality, even if such step is not explicitly described or illustrated in the figures. Further, it is understood that the features of the various example aspects described herein may be combined with each other, unless specifically noted oth- erwise. [0030] Fig. 1 illustrates a schematic representation of an arrangement for resetting at least one qubit ac- cording to an embodiment. [0031] According to an embodiment, the arrangement 100 comprises at least one qubit 101. [0032] The at least one qubit 101 may have a ground state . Herein, the ground state may refer to a quan- tum state of the qubit with the lowest energy. [0033] The at least one qubit 101 may further have at least one excited state. The at least one excited state may comprise a lowest excited state . Herein, the low- est excited state may refer to a quantum state of the qubit with the second lowest energy. [0034] The ground state and the lowest excited state of a qubit may correspond to the computational basis of the qubit. For example, the ground state may corre- spond to the state of the qubit and the lowest ex- cited state may correspond to the state of the qubit or vice versa. Other quantum states of a qubit may be referred to as non-computational states. [0035] The energy gap between the ground state and the lowest excited state may correspond to a resonance fre- quency of the qubit. The energy gap may also be referred to as the qubit energy, and the corresponding frequency as the qubit frequency. [0036] Herein, resetting a qubit may refer to the act of transitioning a qubit to a pure quantum state, typ- ically the ground state, after, for example, a quantum computation. Resetting a qubit may also be referred to as initializing the qubit. [0037] The arrangement 100 may further comprise an energy dissipation structure 102 selectively couplable to the at least one qubit 101. The energy dissipation structure 102 may be configured to dissipate energy transferred to the energy dissipation structure from the at least one qubit. [0038] The energy dissipation structure 102 may also be referred to as an energy relaxation structure, a controllable an environment, a controllable energy dis- sipation structure, an engineered environment, a bath, a dissipation source, or similar. [0039] The arrangement 100 may further comprise a con- trol unit 103 configured to reset the at least one qubit by performing: couple the at least one qubit to the energy dissipation structure for a reset period using a control signal, wherein the control signal controls a coupling strength between the at least one qubit and the energy dissipation structure, and after the reset pe- riod, decouple the at least one qubit from the energy dissipation structure during a decoupling period using the control signal, wherein the coupling strength be- tween the at least one qubit and the energy dissipation structure comprises, during the decoupling period, at least a temporally linearly decreasing component and at least one temporally sinusoidal component. [0040] The control signal may also be referred to as a control voltage, a control pulse, a bias voltage, junction bias voltage, or similar. [0041] The coupling strength between the at least one qubit and the energy dissipation structure may also be referred to as coupling strength, decoupling protocol, relaxation rate, or similar. [0042] In some embodiments, the control signal may directly control the coupling strength between the at least one qubit and the energy dissipation structure. For example, the coupling strength between the at least one qubit and the energy dissipation structure may be linearly dependent on the control signal. In other em- bodiments, the control signal may control the coupling strength between the at least one qubit and the energy dissipation structure indirectly. For example, the con- trol signal may be a radio frequency (RF) signal and the coupling strength between the at least one qubit and the energy dissipation structure may depend on the control signal in some non-linear fashion. [0043] Although some embodiments and analysis dis- closed herein may refer to specific implementations of the energy dissipation structure 102, it should be ap- preciated that the energy dissipation structure 102 may be implemented using, for example, any energy dissipa- tion structure with a coupling to the at least one qubit 101. [0044] The energy dissipation structure 102 may be electromagnetically coupled to the at least one qubit 101. [0045] Herein, when two elements are electromagneti- cally coupled, the elements may have an electromagnetic connection between each other. The electromagnetic con- nection may comprise any number of electrical compo- nents/elements, such as capacitors, inductors, mutual inductances, transmission lines etc. [0046] It should be appreciated that although the at least one qubit 101 and the energy dissipation structure 102 may be electromagnetically coupled continuously, the relaxation rate of the qubit 101 as inflicted by the energy dissipation structure 102 may still be selective, if the properties of the relaxation structure 102 can be controlled. The effect of the control signal can, for example, be such that when the control signal is applied photon-assisted tunnelling in the energy dissipation structure 102 becomes energetically favourable with pho- ton energies corresponding to the difference of the en- ergies of the excited and ground states of the qubit 101. In some embodiments, when the control signal is not applied, the photon assisted tunnelling is highly un- likely irrespective of the state of the at least one qubit 101. [0047] Herein, when the properties of the energy dis- sipation structure 102 are controllable, the strength of interaction between the energy dissipation structure 102 and other objects may be controlled and/or turned on or off. It should be appreciated that even if there is a continuous connection, such as an electrical/ca- pacitive/inductive connection, between two elements, the interaction between the elements can be tuned. [0048] According to an embodiment, the at least one qubit 101 comprises at least one superconductive qubit. [0049] According to an embodiment, the at least one qubit 101 comprises at least one Josephson junction. [0050] According to an embodiment, the at least one qubit 101 comprises a transmon qubit. Alternatively, the at least one qubit 101 may comprise any other type of qubit, such as, a flux qubit, a charge qubit, a phase qubit, or a fluxonium qubit. [0051] Although some embodiments may be disclosed herein with reference to a certain type of qubit, these qubit types are only exemplarily. In any embodiment dis- closed herein, the at least one qubit 101 may be imple- mented in various ways and using various technologies. [0052] The arrangement 100 may be embodied in, for example, a quantum computing device. Such a quantum com- puting device may comprise a plurality of qubits for performing quantum computation. Each such qubit may be implemented using the arrangement 100. [0053] The arrangement 100 may be realized, for exam- ple, in a superconducting circuit architecture. [0054] When the arrangement 100 is operational, the at least one qubit 101 and the energy dissipation struc- ture 102 may be physically located in a cryostat or similar. The cryostat may cool the at least one qubit 101 and other components of the arrangement 100, such as the energy dissipation structure 102, to cryogenic temperatures. This may be required if the at least one qubit 101 correspond to, for example, a superconductive qubit. [0055] The following analysis searches for an opti- mized protocol for decoupling the at least one qubit 101 from initially strongly-coupled energy dissipation structure 102, which can be considered a low-temperature bath. The energy dissipation structure 102 may be real- ized with, for example, a quantum-circuit refrigerator (QCR). [0056] The fidelity of the protocol can be quantified as the leakage to the excited qubit states, i.e. l(t) = 1 − ρ g (t), where ρ g is the ground-state occupation of the at least one qubit 101. Due to the strong coupling, the steady state of the at least one qubit 101 is determined by entanglement with the energy dissipation structure 102, and can be expressed as where κ is the zero-temperature qubit relaxation rate in the Born-Markov approximation, ω q is the qubit angu- lar frequency, γ = 0.577 … is the Euler constant, ω c ≫ ω q is the cut-off frequency of the bath, and A = [−1 − γ + ln ( ω c / ω q )]/(2π ω q ). If one neglects the direct in influence of the changing κ(t) to the system, the dynamics of the at least one qubit 101 can be solved from the equation of motion which describes relaxation of the at least one qubit 101 towards the entangled steady state under time-dependent coupling strength κ(t). [0057] The relaxation process determined by the equa- tion above can be optimized by maximizing the relaxation rate at each instant in time with respect to κ. Thus, by setting , one obtains Replacing this into the equation of motion above, one obtains One can then separate the variables, and obtain After integration, one obtains the solution where ρ e (0) is the initial condition for the density op- erator. Using the aforementioned equation κ = ρ e /(2A), one obtains the protocol for the relaxation rate to be where κ max is the initial (strong) relaxation rate. In- dependent on the realization of the energy dissipation structure 102, there exists a minimum value of the dis- sipation rate, denoted with κ min . This sets the lower limit for the achievable initialization error for the above protocol. It may be beneficial to minimize excited state occupation of the at least one qubit 101 by tuning the relaxation rate κ to as low value as possible with the energy dissipation structure 102, denoted with κ min ≪ κ max . Such value can be reached with the above protocol in time given by Consequently, the minimal initialization error is given as which is twice the limiting value set by the qubit-bath correlations. Since the above re- sult is obtained by maximizing the relaxation rate at all times, one can conclude that, in order to reach the correlation limited initialization error, the protocol duration should be longer than τ 1 . [0058] One can extract the minimum total dissipa- tion/relaxation rate by measuring the relaxation time of the at least one qubit 101. However, the relaxation rate depends on the coupling to the energy dissipation structure 102 and also on internal sources of relaxation that may not be controllable. It may not be possible to separate these sources in the measurement. In the ideal case, the relaxation rate caused by the energy dissipa- tion structure 102 is the only source of relaxation. [0059] However, since should be of the order of, or preferably smaller than, the intrinsic decoherence time of the at least one qubit 101, even the above value τ 1 for the protocol duration τ may be too large for use in fast, high-fidelity initialization. Moreover, a sweep to κ min that is faster than that given by κ(t) above can lead to a larger initialization error than given above since, for such sweep protocols, the relaxation rate from the excited states is not maximized and the dura- tion of the sweep is shorter than in the optimized case. This is referred to as the decoupling error, which re- sults into a trade-off between the reset speed and fi- delity. Such error can still be below the error-correc- tion threshold if the value of κ min is low enough. This suggests that the protocol for κ(t) above should be mod- ified with a fast decoupling starting at time t ≪ τ 1 . Herein, this is referred to as forced decoupling. [0060] For analysis, let us assume that initially the system of the at least one qubit 101 and the energy dissipation structure 102 is in an initial state . This may be the result of a pre-initialization pro- cess realized with the decoupling scheme given by the relaxation rate κ(t) above. Such a process can be slow and, thus, one can apply forced decoupling for a fixed time interval . Here, the zero of time has been shifted to the instant at which the forced decou- pling starts. Within this interval, one can search for such a protocol κ(t): κ max → κ min that minimizes the ex- cited-state occupation ρ e (τ) at the end of the protocol. [0061] The full model for the qubit dissipation con- sists of the Hamiltonian Here, the system of the at least one qubit 101 and the energy dissipation structure 102 is modelled as a qubit with angular frequency ω q coupled to a bath of oscilla- tors with angular frequencies ω k . The coupling angular frequencies between the qubit and the oscillators are given by g k . The ground state can be found analytically by neglecting the co-rotating terms from the Hamilto- nian. If the couplings are weak, one can diagonalize the system approximatively in second order in g k with the transformation where Here, the coupling coefficients g k are time-dependent and, as a consequence, the transformation is time-de- pendent. Thus, the transformed Hamiltonian can be writ- ten as where and . In the third equality, it has been assumed that the system starts from the adiabatic ground state and, thus, the dominating term inducing transitions between the adia- batic states is the latter one. Thus, we have neglected the terms that induce transitions between the oscilla- tors. [0062] The protocol may be such that, in the first phase, the decoupling κ(t) disclosed above is used to relax the at least one qubit 101 quickly near to the steady state. Thus, after the fast relaxation phase, the qubit-bath system should be close to its adiabatic ground state. Then, one can apply a rotation that de- couples the at least one qubit 101 from the energy dis- sipation structure 102. It may be beneficial to have such a decoupling that transitions from the adiabatic ground state are minimized. This can be obtained with a protocol during which the system is diagonal in the so- called first super-adiabatic eigenbasis. This is equiv- alent to the requirement that ̇ are constant, i.e., that the couplings g k depend linearly on time. [0063] Based on the above, it is assumed here that the system starts in the adiabatic ground state . Here, the notation is such that the first index gives the state of the qubit and the second index rep- resents the total occupation number of the oscillators. Hamiltonian in disclose above shows that the adiabatic ground state is coupled to the two-excitation states of the form , where k labels the oscillator with a single excitation with all other oscillators in their ground states. Moreover, the oscillators are mutually decoupled. [0064] One can consider the case with a single oscil- lator. The full model for the qubit decay consists of the Hamiltonian where a qubit with angular frequency ω q is coupled to a bath of oscillators with angular frequencies ω k . The coupling frequencies between the qubit and the oscilla- tors are given by g k . Here, one can consider the inter- action between the qubit and one of the oscillators. Consequently, the Hamiltonian operator can be written as One can consider a situation in which the system starts from the ground state of the above Hamiltonian. This corresponds to the thermal state of the qubit-bath sys- tem at zero temperature. If g k / ω q ≪ 1 the ground state is effectively a superposition of the states and . One can, therefore, truncate the above Hamilto- nian into the subspace spanned by these two states. As a consequence, the Hamiltonian operator can be written as and and . One can make a transfor- mation into the adiabatic basis using the time-dependent unitary operator , where As a consequence, the effective Hamiltonian can be writ- ten as where , and are the instantaneous eigenstates of the Hamiltonian H k (t) above. [0065] If the state vector points along the Hamilto- nian vector during the whole dynamics, the process is called adiabatic. However, one may wish to minimize the non-adiabatic occupation at the end of the dynamics. Therefore, one can consider the state vector represented in the adiabatic basis. One can try to min- imize the error defined at t = τ as where τ is the duration of the sweep. The time-dependent Schrödinger equation for the Hamiltonian H eff (t) above can be written as Since |α| 2 − |β| 2 = 1 − 4|α∗β| 2 , one obtains , where the sign of the last term should be changed if |α| 2 > |β| 2 . On the Bloch sphere, one can write β = cos ( θ/2) and α = sin ( θ/2)exp (iφ). Consequently, one obtains One can define φ = φ' − ∫dt ω(t). Assuming that initially the system is in the adiabatic ground state with α(0) = 0 and β(0) = 1, one obtains through time integration from 0 to τ that Here, one can make some simplifying approximations. One can assume that the coupling with the oscillators is weak such that ω(t) ≈ ω q + ω k . In addition, one can look for a solution that causes small deviations from the adiabatic solution. This means that we make an approx- imation that sin θ ≈ θ and cos θ ≈ 1. As a consequence, one can obtain that This implies that the error, i.e. the occupation in the excited adiabatic state, can be written as This means that the error of the qubit-oscillator system is given by the power spectrum of the coupling strength evaluated at the resonance frequency ω q + ω k . One can try to minimize the total error . However, since the oscillators are assumed independent, it is enough to minimize the errors from each individual oscillator. The solution is the so-called Slepian function. However, the Slepian function does not go to zero in the beginning and in the end of the pulse, which is may be desirable in the current case. Functions with such boundary con- ditions can be quite generally approximated to a good accuracy by couple of first terms from the ansatz The values λ l are constrained by which is obtained by integration of the ansatz. [0066] Plugging this into the equation for above, one obtains For typical experimental parameters, ω q /(2π) = 5 GHz and τ ≈ 10 ns. Consequently, if l ≲ 5, one obtains that 4π 2 l 2 ≪ ( ω q + ω k )τ. Thus, , where l max ≤ 5. For an arbitrary τ and ω k , is zero if One can recall here the constraint Thus, these two equations can determine the situation if l max = 2. For larger truncations with l max > 2, one has l max − 2 free parameters that can be used to optimize the drive signal. [0067] The coupling frequency to oscillator k can be, thus, written as For simplicity, one can assume here that the coupling g k (τ) = 0. Therefore, one obtains the constraint Thus, with the change of parameters , one can obtain with the constraints and One can define the decoupling protocol for a single oscillator as In principle, the decoupling protocol could be different for each bath oscillator. However, here it is assumed that each oscillator is decoupled with the same protocol f(t). [0068] One can make the connection between the decou- pling rate f(t) for the oscillators, and the effective decay rate of the qubit. Consequently, one can derive the Lindblad equation for time-dependent coupling frequencies between a qubit and the bath oscillators. Once can model the situation with the Hamiltonian where ω q and ω k are the angular frequencies of the qubit and the bath oscillators, respectively, g k (t) are the time-dependent coupling frequencies, and are the Pauli spin operators, and and are the annihilation operators of the qubit and the bath oscillators, respectively. [0069] In the interaction picture, the von Neumann equation for the density operator of the combined sys- tem can be written as One can show the above equation iteratively. After one iteration step, one obtains where and . In the following, the Markovian approximation is made, and it is assumed that throughout the whole integration. This can be justified by the fact that the two-time correlation function of the bath is non-zero only in the vicinity of t' = t, and decays very rapidly to zero for other times t'. Similarly, one can assume in the following that g k (t') ≈ g k (t). This means that the decoupling protocol is slow in the time scale given by the lifetime of the bath correlations. After these approximations, the deriva- tion of the Lindblad equation is equivalent to the con- ventional case in which the coupling frequencies are constant. [0070] After a secular approximation, one can obtain the Lindblad equation in the Schrödinger picture as where . Above, the time-dependent decay rate of the qubit is defined as κ(t) = f(t) 2 κ(0), where f(t) is defined above, and κ(0) is the value of the relaxation rate at the initial time of the protocol. [0071] Fig. 2 illustrates a schematic representation of a coupling strength between the at least one qubit and the energy dissipation structure according to an embodiment. [0072] One can recall that the decoupling f(t) proto- col defined above where τ is the duration of the decoupling protocol, and the following constraints should be fulfilled in order to obtain optimized decoupling: [0073] For the case l max = 2, one obtains Thus, the corresponding protocol can be written as [0074] In the embodiment of Fig. 2 a coupling strength 201 corresponding to the equation above and a linear coupling strength 202 are illustrated. [0075] According to an embodiment, the coupling strength between the at least one qubit 101 and the energy dissipation structure 102 further comprises, dur- ing the decoupling period, a plurality of temporally sinusoidal components, wherein a period of each tempo- rally sinusoidal component is less than or equal to a temporal length of the decoupling period. [0076] For example, the sinusoidal components may be of the form , where τ is the temporal length of the decoupling period. [0077] According to an embodiment, the period of an lth sinusoidal component in the plurality of temporally sinusoidal components is τ/l, wherein τ is the temporal length of the decoupling period. [0078] For example, the lth sinusoidal components may be of the form , where τ is the temporal length of the decoupling period. [0079] According to an embodiment, the temporally lin- early decreasing component decreases from a maximum value to substantially zero during the decoupling pe- riod. [0080] For example, the linearly decreasing component can be of the form if the maximum value of the linearly decreasing component is normalized to unity. [0081] According to an embodiment, each sinusoidal component in the plurality of temporally sinusoidal com- ponents is substantially zero at a start of the decou- pling period and substantially zero at an end of the decoupling period. [0082] According to an embodiment, a time derivative of the coupling strength between the at least one qubit 101 and the energy dissipation structure 102 is sub- stantially zero at a start of the decoupling period and at an end of the decoupling period. [0083] The time derivative may refer to the first time derivative. [0084] Thus, the coupling strength and the time de- rivative of the coupling strength may be continuous at the start and at the end of the decoupling period. This can minimize non-adiabatic error caused by the decou- pling. [0085] According to an embodiment, the coupling strength between the at least one qubit 101 and the energy dissipation structure 102 is temporally strictly decreasing during the decoupling period. [0086] “Temporally strictly decreasing” means that the coupling strength is a temporally strictly decreas- ing function. Thus, f(t 2 ) < f(t 1 ) for all t 2 > t 1 , where t 1 and t 2 are within the decoupling period. [0087] According to an embodiment, the control unit 103 is further configured, after the reset period and before the decoupling period, perform a pre-decoupling using the control signal, wherein a magnitude of a time derivative of the coupling strength between the at least one qubit 101 and the energy dissipation structure 102 during the pre-decoupling is less than a magnitude of a time derivative of the coupling strength between the at least one qubit 101 and the energy dissipation structure 102 during the decoupling period. [0088] For example, an average magnitude of a time derivative of the coupling strength during the pre-de- coupling may be less than an average magnitude of a time derivative of the coupling strength the decoupling pe- riod. Alternatively or additionally, a maximum magnitude of a time derivative of the coupling strength during the pre-decoupling may be less than a maximum magnitude of a time derivative of the coupling strength the decou- pling period. Alternatively or additionally, a maximum magnitude of a time derivative of the coupling strength during the pre-decoupling may be less than a minimum magnitude of a time derivative of the coupling strength the decoupling period. [0089] The pre-decoupling can result in an improved fidelity (smaller initialization error). However, the speed (time derivative) of the pre-decoupling protocol may be small. Thus, the speed can be greater during the decoupling period, which can result in a greater ini- tialization error. One can find an appropriate trade- off between the speed and accuracy of the reset by op- timizing the durations of the different phases (reset, pre-decoupling, and decoupling). [0090] Fig. 3 illustrates a schematic representation an energy dissipation structure comprising a supercon- ductor – insulator – normal metal – insulator – super- conductor junction according to an embodiment. [0091] According to an embodiment, the energy dissi- pation structure 102 comprises at least one normal metal – insulator – superconductor (NIS) junction. [0092] According to an embodiment, the energy dissi- pation structure 102 comprises a quantum circuit re- frigerator, QCR, wherein the QCR comprises a voltage- biased superconductor 303 – insulator 302 – normal metal 301 – insulator 302 – superconductor 303 (SINIS) junc- tion, and wherein the at least one qubit is electrically coupled to the normal metal 301 of the SINIS junction of the energy dissipation structure. [0093] The control signal may correspond to a bias voltage over the NIS/SINIS junction. [0094] According to an embodiment, the control unit 103 is configured to control the coupling strength be- tween the at least one qubit and the energy dissipation structure by tuning a bias voltage of the SINIS junction of the energy dissipation structure based on the control signal. [0095] According to an embodiment, the energy dissi- pation structure 102 is configured to dissipate photon energy transferred to the energy dissipation structure 102 via photon-assisted electron tunnelling in the NIS/SINIS junction. [0096] Photon-assisted tunnelling involves a tunnel- ling process where the qubit excitation energy enables a tunnelling process which otherwise is not favourable due to an energy barrier of the NIS/SINIS junction. The barrier may be the superconducting energy gap of the NIS/SINIS junction, possibly accompanied by Coulomb gap depending on the charging energies. [0097] In the embodiment of Fig. 7, the energy dissi- pation structure 102 comprises two NIS junctions. These two NIS junctions form a superconductor 303 – insulator 302 – normal metal 301 – insulator 302 – superconductor 303 (SINIS) junction. The SINIS junction may be biased by a bias voltage V B 304. [0098] In this scheme, the at least one qubit 101 may be capacitively coupled to the QCR which can be seen as a thermal bath whose effective temperature and coupling strength to the at least one qubit 101 can be controlled with a bias voltage across the SINIS junction. The ef- fective dissipation rate can be changed over several orders of magnitude which can allow for on-demand source of dissipation for rapid and accurate qubit reset. Strong dissipation results in fast decay to thermal equilibrium, where ideally the at least one qubit 101 is close to its ground state at low temperatures. [0099] The energy relaxation properties of the SINIS junction can be controlled by the bias voltage V B 304. The SINIS junction may be referred to as a quantum cir- cuit refrigerator (QCR). In some embodiments, the bias voltage V B 304 is time-dependent. [0100] The at least one qubit 101 may be electromag- netically coupled to the SINIS junction of the energy dissipation structure 102. Thus, the energy relaxation structure 102 may absorb photon energy from the at least one qubit 101. [0101] The energy dissipation structure 102 may absorb photons from the at least one qubit 101 at bias voltages where an electron needs to receive an additional energy quantum from the at least one qubit 101 to overcome the Bardeen-Cooper-Schrieffer (BCS) energy gap in the su- perconductor 303. For example, if eV B <2Δ, there is ide- ally only a small probability of electron tunnelling through the SINIS junction spontaneously. Moreover, if eV B + hf>2Δ , an electron can tunnel via photon-assisted tunnelling with the absorption of a photon of energy hf. Here ^ is the BCS gap or superconducting gap of the superconducting electrode material, V B is the bias volt- age, e the electron charge, h the Planck constant, and f the frequency of the photon. If, furthermore, the energy hf corresponds to the energy difference of the excited and ground states of the qubit, the qubit is in its excited state, and if the SINIS junction is electromag- netically coupled to the qubit, the qubit can relax from the excited state to the ground state through the re- laxation channel provided by the photon-assisted tun- nelling in the SINIS junction. However, if eV B + ℎf<2Δ ,the photon-assisted tunnelling is ideally forbid- den. Thus, a time-dependent control signal V B can be used to control resetting of the at least one qubit 101. [0102] Fig. 4 illustrates a schematic representation of a control unit 103 according to an embodiment. [0103] The control unit 103 may comprise at least one processor 401. The at least one processor 401 may com- prise, for example, one or more of various processing devices, such as a co-processor, a microprocessor, a digital signal processor (DSP), a processing circuitry with or without an accompanying DSP, or various other processing devices including integrated circuits such as, for example, an application specific integrated cir- cuit (ASIC), a field programmable gate array (FPGA), a microprocessor unit (MCU), a hardware accelerator, a special-purpose computer chip, or the like. [0104] The control unit 103 may further comprise a memory 402. The memory 402 may be configured to store, for example, computer programs and the like. The memory 402 may comprise one or more volatile memory devices, one or more non-volatile memory devices, and/or a com- bination of one or more volatile memory devices and non- volatile memory devices. For example, the memory 402 may be embodied as magnetic storage devices (such as hard disk drives, floppy disks, magnetic tapes, etc.), opti- cal magnetic storage devices, and semiconductor memories (such as mask ROM, PROM (programmable ROM), EPROM (eras- able PROM), flash ROM, RAM (random access memory), etc.). [0105] The control unit 103 may further comprise other components not illustrated in the embodiment of Fig. 4. The control unit 103 may comprise, for example, an in- put/output bus for connecting the control unit 103 to other devices. Further, a user may control the control unit 103 via the input/output bus. The user may, for example, control quantum computation operations per- formed by the arrangement 100 via the control unit 103 and the input/output bus. [0106] When the control unit 103 is configured to im- plement some functionality, some component and/or com- ponents of the control unit 103, such as the at least one processor 401 and/or the memory 402, may be config- ured to implement this functionality. Furthermore, when the at least one processor 401 is configured to imple- ment some functionality, this functionality may be im- plemented using program code comprised, for example, in the memory. [0107] The control unit 103 may be implemented using, for example, a computer, some other computing device, or similar. [0108] Fig. 5 illustrates a flow chart representation of a method 1100 for resetting at least one qubit using an energy dissipation structure selectively couplable to the at least one qubit according an embodiment. [0109] The method 500 may comprise coupling 501 the at least one qubit to the energy dissipation structure for a reset period using a control signal, wherein the control signal controls a coupling strength between the at least one qubit and the energy dissipation structure. [0110] The method 500 may further comprise, after the reset period, decoupling 502 the at least one qubit from the energy dissipation structure during a decoupling period using the control signal, wherein the coupling strength between the at least one qubit and the energy dissipation structure comprises, during the decoupling period, at least a temporally linearly decreasing com- ponent and at least one temporally sinusoidal component. [0111] The method 500 may be performed by, for exam- ple, the control unit 103. [0112] Any range or device value given herein may be extended or altered without losing the effect sought. Also any embodiment may be combined with another embod- iment unless explicitly disallowed. [0113] Although the subject matter has been described in language specific to structural features and/or acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the specific features and acts described above are disclosed as examples of implementing the claims and other equiv- alent features and acts are intended to be within the scope of the claims. [0114] It will be understood that the benefits and advantages described above may relate to one embodiment or may relate to several embodiments. The embodiments are not limited to those that solve any or all of the stated problems or those that have any or all of the stated benefits and advantages. It will further be un- derstood that reference to 'an' item may refer to one or more of those items. [0115] The steps of the methods described herein may be carried out in any suitable order, or simultaneously where appropriate. Additionally, individual blocks may be deleted from any of the methods without departing from the spirit and scope of the subject matter de- scribed herein. Aspects of any of the embodiments de- scribed above may be combined with aspects of any of the other embodiments described to form further embodiments without losing the effect sought. [0116] The term 'comprising' is used herein to mean including the method, blocks or elements identified, but that such blocks or elements do not comprise an exclu- sive list and a method or apparatus may contain addi- tional blocks or elements. [0117] It will be understood that the above descrip- tion is given by way of example only and that various modifications may be made by those skilled in the art. The above specification, examples and data provide a complete description of the structure and use of exem- plary embodiments. Although various embodiments have been described above with a certain degree of particu- larity, or with reference to one or more individual embodiments, those skilled in the art could make numer- ous alterations to the disclosed embodiments without departing from the spirit or scope of this specifica- tion.