Quantum bit leakage error reduction

Abstract

[0006] It is an object to provide a quantum computing system and arrangement. According to one embodiment, a qubit has a ground state and a plurality of excited states, the plurality of excited states including a lowest excited state, an energy difference between the ground state and the lowest excited state corresponds to a first frequency, an energy difference between the lowest excited state of the plurality of excited states and another excited state corresponds to a second frequency, an energy dissipation structure is configured to dissipate energy transferred to the energy dissipation structure, and a filter has a stopband and a passband, the filter is coupled to the qubit and the energy dissipation structure, the stopband includes the first frequency and the passband includes the second frequency. [0007] An arrangement, quantum computing system, and method are provided.

Description

[Technical Field]

[0001] The present disclosure relates to quantum computing, and more particularly to arrangements and quantum computing systems for reducing qubit leakage errors. [Background technology]

[0002] Quantum computing is based on the idea of ​​storing information in a two-order quantum system. However, many realizations of such qubits have more than two energy levels. In such cases, the qubit is formed by the two lowest energy levels, and excitation of higher levels must be prevented. The situation in which any of these higher energy levels risk being excited, i.e., their quantum state mixes with the quantum state of the computational base, is called a leakage error. This can occur, for example, due to applied gate operations or system-environment interactions. Leakage errors cannot be corrected by standard quantum error correction, which only deals with errors within the computational base. Summary of the Invention

[0003] This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential 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 object to provide an arrangement and a quantum computing system for reducing qubit leakage errors. These and other objects are achieved by the features of the independent claims. Further implementations are evident from the dependent claims, the description and the drawings.

[0005] According to a first aspect, an arrangement for reducing qubit leakage error includes at least one qubit having a ground state and a plurality of excited states, the plurality of excited states including a lowest excited state, wherein an energy difference between the ground state and the lowest excited state corresponds to a first frequency and an energy difference between the lowest excited state of the plurality of excited states and another excited state corresponds to a second frequency, an energy dissipation structure configured to dissipate energy transferred to the energy dissipation structure, and a filter having at least one stop band and at least one pass band, the filter coupled to the at least one qubit and the energy dissipation structure, the at least one stop band including the first frequency and the at least one pass band including the second frequency. The arrangement can reduce leakage error in the at least one qubit, for example, by not allowing transitions between the lowest excited state and the ground state while allowing transitions from at least another excited state to the lowest excited state.

[0006] In an implementation of the first aspect, the energy dissipation structure comprises at least one conventional metal-insulator-superconductor (NIS) junction, and the arrangement can, for example, efficiently dissipate photon energy from the qubit via the energy dissipation structure.

[0007] In a further implementation of the first aspect, the energy dissipation structure comprises a quantum circuit refrigerator, or QCR, which comprises a voltage-biased superconductor-insulator-normal metal-insulator-superconductor (SINIS) junction. The arrangement can, for example, efficiently dissipate photon energy from the qubit via the energy dissipation structure, and the dissipation can be controlled via the bias voltage.

[0008] In a further implementation of the first aspect, the energy dissipation structure is configured to dissipate photon energy transferred to the energy dissipation structure via photon-assisted electron tunneling in the NIS / SINIS junction.

[0009] In a further implementation of the first aspect, the filter comprises a bandstop filter or a lowpass filter. The configuration can, for example, block undesired state transitions of the qubit while allowing state transitions that reduce leakage errors.

[0010] In a further implementation of the first aspect, the at least one qubit comprises a superconducting qubit.

[0011] In a further implementation of the first aspect, the alternative excited state includes a second-lowest excited state of at least one qubit, and the arrangement can, for example, allow relaxation from the second-lowest excited state to the lowest excited state, eliminating leakage errors due to occupancy of the second-lowest excited state.

[0012] In a further implementation of the first aspect, at least one passband of the filter further includes a third frequency corresponding to an energy difference between two states in the plurality of excited states. The arrangement can, for example, enable relaxation between the two states, thereby reducing leakage errors.

[0013] In a further implementation of the first aspect, the at least one passband of the filter further includes a first plurality of frequencies, each frequency in the first plurality of frequencies corresponding to an energy difference between two consecutive excited states in the plurality of excited states of the at least one qubit. The arrangement can, for example, enable relaxation between consecutive excited states, thereby eliminating leakage errors by sequential relaxation between consecutive excited states.

[0014] In a further implementation of the first aspect, at least one stop band of the filter further includes a second plurality of frequencies, each frequency in the second plurality of frequencies corresponding to an energy difference between two non-contiguous states of the at least one qubit. The arrangement can, for example, restrict the at least one qubit to sequential relaxation, thus causing most of the leakage error to be extracted at the lowest excited state rather than the ground state.

[0015] According to a second aspect, a quantum computing device comprises an arrangement according to the first aspect. The quantum computing device may, for example, perform quantum computations using the arrangement with reduced leakage errors.

[0016] According to a third aspect, a quantum computing system comprises an arrangement according to the first aspect and a control unit coupled to the arrangement, the control unit configured to isolate a filter and / or an energy dissipation structure from at least one quantum bit responsive to a gate operation on the at least one quantum bit. The quantum computing system can, for example, mitigate any effects caused by the filter and / or the energy dissipation structure on the gate operation.

[0017] In an implementation of the third aspect, the quantum computing system further comprises a plurality of arrangements, each of the plurality of arrangements being implemented according to the first aspect, and a control unit coupled to each of the plurality of arrangements, the control unit being further configured to isolate a filter and / or energy dissipation structure of each of the plurality of arrangements from at least one qubit of the arrangement responsive to a gate operation on the qubit. The quantum computing system can, for example, mitigate any effect caused by the filter and / or energy dissipation structure on the gate operation at each of the arrangements.

[0018] According to a fourth aspect, a method for reducing qubit leakage error using at least one arrangement according to the first aspect includes decoupling a filter and / or energy dissipation structure from at least one qubit, performing at least one gate operation on the qubit, and recoupling the filter and / or energy dissipation structure to the at least one qubit. The method can, for example, mitigate any effects caused by the energy dissipation structure on the filter and / or gate operation.

[0019] In an implementation of the fourth aspect, the at least one arrangement comprises a plurality of arrangements, and the method further includes decoupling a filter and / or energy dissipation structure from at least one qubit in each arrangement in the plurality of arrangements, performing at least one multi-qubit gate operation using the at least one qubit in each arrangement in the plurality of arrangements, and recoupling the filter and / or energy dissipation structure to the at least one qubit in each arrangement in the plurality of arrangements. The method can, for example, mitigate any effect caused by the filter and / or energy dissipation structure on the gate operation at each arrangement.

[0020] Many of the attendant advantages will become more readily appreciated as the same becomes better understood by reference to the following detailed description, when considered in conjunction with the accompanying drawings.

[0021] In the following, exemplary embodiments will be explained in more detail with reference to the accompanying figures and drawings. [Brief explanation of the drawings]

[0022] [Figure 1] FIG. 1 shows a schematic diagram of an arrangement for reducing qubit leakage errors according to one embodiment. [Figure 2] FIG. 1 shows a schematic diagram of qubit energy levels according to one embodiment. [Figure 3] 1 shows a schematic diagram of a frequency response of a bandstop filter according to an embodiment. [Figure 4] 1 shows a schematic diagram of a frequency response of a low pass filter according to one embodiment. [Figure 5] 1 shows a schematic diagram of an energy dissipation structure according to one embodiment. [Figure 6] 1 shows an effective circuit model diagram of an arrangement according to one embodiment. [Figure 7] 10 shows a table of circuit parameters according to one embodiment. [Figure 8] FIG. 10 illustrates a plot of qubit eigenstate occupation during a gate operation according to one embodiment. [Figure 9]FIG. 1 shows a schematic diagram of a quantum computing system according to one embodiment. [Figure 10] 1 shows a schematic diagram of a control unit according to one embodiment. [Figure 11] FIG. 1 shows a flowchart diagram of a method for reducing qubit leakage error using at least one arrangement according to one embodiment.

[0023] In the following, like reference numerals will be used to denote like parts in the accompanying drawings. DETAILED DESCRIPTION OF THE INVENTION

[0024] In the following description, reference is made to the accompanying drawings that form a part of this disclosure, and which show, by way of illustration, specific aspects in which the present disclosure may be implemented. It is understood that other aspects may be utilized and structural or logical changes may be made without departing from the scope of the present disclosure. Therefore, the following detailed description is not to be taken in a limiting sense, as the scope of the present disclosure is defined by the appended claims.

[0025] For example, it is understood that disclosure related to a described method can also apply to a corresponding device or system configured to perform that method, and vice versa. For example, where particular method steps are described, a corresponding device may include units for performing the described method steps, although such units may not be explicitly described or shown in the figures. Conversely, for example, where a particular apparatus is described in terms of functional units, a corresponding method may include steps that perform the described functions, although such steps may not be explicitly described or shown in the figures. Furthermore, it should be understood that features of various exemplary aspects described herein can be combined with each other, unless otherwise specified.

[0026] FIG. 1 shows a schematic diagram of an arrangement 100 for reducing qubit leakage errors according to one embodiment.

[0027] According to one embodiment, configuration 100 includes at least one qubit 101 having a ground state and a plurality of excited states. The plurality of excited states includes a lowest excited state. The energy difference between the ground state and the lowest excited state may correspond to a first frequency. The energy difference between the lowest excited state and another excited state in the plurality of excited states may correspond to a second frequency.

[0028] As used herein, when phrases such as "lowest," "second-lowest," and "consecutive" are used to refer to the ordering of states of at least one qubit 101, these terms may refer to the ordering of states with respect to energy. For example, the ground state of at least one qubit 101 may refer to the lowest state of at least one qubit 101, meaning the state of at least one qubit 101 having the lowest energy. Similarly, the lowest excited state of at least one qubit 101 may refer to the excited state of at least one qubit 101 having the lowest energy, etc.

[0029] The first frequency may also be referred to as the resonant frequency of at least one qubit 101.

[0030] As used herein, any energy, such as the energy difference between states of a qubit,

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[0031] The other excited state may include, for example, the second lowest excited state of at least one quantum bit 101, the third lowest excited state of at least one quantum bit 101, or any other excited state in the plurality of excited states of at least one quantum bit 101.

[0032] According to one embodiment, at least one qubit 101 comprises a superconducting qubit. According to one embodiment, at least one qubit 101 comprises at least one Josephson junction.

[0033] According to one embodiment, at least one qubit 101 comprises a trasmon qubit, or may comprise any other type of qubit, such as a superconducting quantum interference device (SQUID) qubit, a flux qubit, a charge qubit, or a phase qubit.

[0034] Although some embodiments may be disclosed herein with reference to particular types of at least one qubit 101, these qubit types are merely exemplary. In any embodiment disclosed herein, at least one qubit 101 may be implemented in a variety of ways and using a variety of techniques.

[0035] The arrangement 100 may further comprise an energy dissipation structure 103 configured to dissipate energy transferred thereto.

[0036] In one embodiment, the energy dissipation structure 103 comprises at least one conventional metal-insulator-superconductor (NIS) junction. The energy dissipation structure 103 may be configured to dissipate photon energy transferred to the energy dissipation structure 103 via photon-assisted tunneling in the NIS junction.

[0037] According to one embodiment, the energy dissipation structure 103 comprises a quantum circuit refrigerator (QCR).

[0038] The configuration 100 may further include a filter 102 having at least one stopband and at least one passband. The filter 102 may be coupled to the at least one qubit 101 and the energy dissipation structure 103. The at least one stopband may include a first frequency, and the at least one passband may include a second frequency. The energy dissipation structure 103 coupled to the filter 102 provides a filtered energy dissipation structure. The filtered energy dissipation structure may include a noise spectrum that includes at least a band or passband of allowed frequencies, such that the noise spectrum does not disappear, or a gap or stopband of at least disallowed frequencies, such that the noise spectrum substantially disappears. When a quantum system, such as the at least one qubit 101, is coupled to the filtered energy dissipation structure, decay of system energy levels separated by frequencies within the stopband may be suppressed, while decay of system energy levels separated by frequencies within the allowed band may occur.

[0039] Filter 102 may be, for example, electrically, capacitively, inductively, and / or electromagnetically coupled to at least one qubit 101 and / or energy dissipation structure 103 .

[0040] The filter 102 may also be referred to as an electronic filter or the like. The filter 102 may include discrete elements, such as, for example, capacitors, inductors, and resistors, and / or distributed elements embodied, for example, in a transmission line. Although some embodiments disclosed herein may depict the filter 102 as including certain components, these are merely examples and the filter 102 may be implemented in a variety of other ways.

[0041] The filter 102 may transfer energy from the at least one qubit 101 to the energy dissipation structure 103. The energy transfer may be selective based on the frequency response of the filter 102.

[0042] Although several examples of the filter 102 are disclosed in several embodiments herein, the filter 102 may also be implemented in various other ways and using various other components / elements. In any embodiment disclosed herein, the filter 102 may be implemented using, for example, any type of bandstop filter. For example, the filter 102 may be implemented using more complex geometries corresponding to higher-order bandstop filters. Such higher-order bandstop filters may approximate the rectangular frequency response of an ideal bandstop filter.

[0043] Arrangement 100 may be embodied in, for example, a quantum computing device. Such a quantum computing device may include multiple qubits for performing quantum computations. Each such qubit may be implemented using arrangement 100.

[0044] The arrangement 100 can be implemented, for example, in a superconducting circuit architecture.

[0045] The arrangement 100 may be able to reduce leakage errors of the at least one qubit 101. Leakage errors can occur when the at least one qubit 101 is excited to the second-lowest excited state or a higher excited state. Thus, the state of the at least one qubit 101 leaks out of the computational base formed by the ground state and the lowest excited state. Typical error correction protocols, such as surface codes, can only correct bit and phase reversal errors in the computational base. Thus, leakage errors may need to be reduced in other ways.

[0046] Arrangement 100 can mitigate unwanted higher excited states of at least one qubit 101 through energy dissipation to energy dissipation structure 103 while leaving the lowest excited state intact. This may be referred to as targeted dissipation. The transition from the lowest excited state to the ground state may be protected by at least one stop band of filter 102.

[0047] Herein, the second lowest excited state to the lowest excited state (

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[0048] FIG. 2 shows a schematic diagram of qubit energy levels according to one embodiment.

[0049] At least one qubit 101 is in the ground state

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[0050] At least one qubit 101 may further have multiple excited states 204. The multiple excited states 204 include the lowest excited state 202.

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[0051] The ground state 201 and the lowest excited state 202 of the at least one qubit 101 may correspond to the computational basis of the at least one qubit 101. For example, the ground state 201 state may correspond to the computational basis of the at least one qubit 101.

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[0052] The energy difference 211 between the ground state 201 and the lowest excited state 202 is given by the first frequency

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[0053] The plurality of excited states 204 includes the second lowest excited state

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[0054] As used herein, any excited state above the second lowest excited state

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[0055] The plurality of excited states 204 may include any number of excited states. In the embodiment of Figure 2, four excited states are shown. However, as shown in Figure 2,

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[0056] According to one embodiment, the energy difference 212 between the lowest excited state 202 and the second lowest excited state 203 is a second frequency

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[0057] At least one passband of the filter 102 may include a second frequency. The energy difference between the lowest excited state 202 and another excited state in the plurality of excited states 204 may correspond to the second frequency.

[0058] According to one embodiment, the another excited state comprises the second-lowest excited state 203 of the at least one qubit 101. Thus, the filter 102 may allow the at least one qubit 101 to relax from the second-lowest excited state 203 to the lowest excited state 202 by transferring corresponding energy to the energy dissipation structure 103.

[0059] According to a first implementation, at least one passband of the filter 102 further includes a third frequency corresponding to an energy difference between two states in the plurality of excited states 204. The third frequency may be different from the second frequency. Thus, the filter 102 may enable relaxation between two states in the plurality of excited states 204 by transferring the corresponding energy to the energy dissipation structure 103.

[0060] According to one embodiment, the at least one passband of the filter 102 further includes a first plurality of frequencies. Each frequency in the first plurality of frequencies may correspond to an energy difference between two consecutive or non-consecutive excited states in the plurality of excited states 204 of the at least one qubit 101. Thus, the filter 102 may enable transitions between two consecutive states in the plurality of excited states 204. Thus, the at least one qubit 101 may computationally relax from an excited state in the plurality of excited states 204 via multiple transitions between consecutive excited states.

[0061] At least one stop band of the filter 102 is a first frequency

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[0062] On the other hand, at least one passband of filter 102 can include a second frequency, so that when at least one qubit 101 is in another excited state, such as the second-lowest excited state 203, energy can be transferred from at least one qubit 101 to energy dissipation structure 103 through filter 102. Thus, at least one qubit 101 can relax from another excited state to the lowest excited state 202, thus returning to the computational basis and reducing leakage errors.

[0063] 3 shows a schematic diagram of the frequency response of a bandstop filter according to one embodiment. The frequency response shown in the embodiment of FIG. 3 is merely exemplary and may not represent a physically realizable frequency response.

[0064] According to one embodiment, the filter 102 comprises a bandstop filter.

[0065] In the embodiment of FIG. 3, at least one stop band 301 of the filter 102 is a first frequency

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[0066] On the other hand, at least one passband 302 of filter 102 may include frequencies corresponding to various other transitions between states of at least one qubit 101. In the embodiment of FIG. 3, at least one passband 302 includes frequencies corresponding to energy differences between excited states of at least one qubit 101.

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[0067] At least one passband 302 of the filter 102 is

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[0068] 4 shows a schematic diagram of the frequency response of a low pass filter according to one embodiment. The frequency response shown in the embodiment of FIG. 4 is merely exemplary and may not represent a physically realizable frequency response.

[0069] According to one embodiment, the filter 102 comprises a low pass filter.

[0070] The anharmonicity of at least one qubit 101 widens the gap between successive excited states at a first frequency

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[0071] Similar to the bandstop filter of the embodiment of FIG. 3, the lowpass filter

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[0072] On the other hand, by restricting at least one qubit 101 to sequential transitions, the low-pass filter ensures that all leakage errors

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[0073] According to one embodiment, at least one stop band of the filter 102 further includes a second plurality of frequencies, each frequency in the second plurality of frequencies corresponding to an energy difference between two non-contiguous states of at least one quantum bit 101.

[0074] FIG. 5 shows a schematic diagram of an energy dissipation structure 103 according to one embodiment.

[0075] In one embodiment, the energy dissipation structure 103 comprises at least one conventional metal 501-insulator 502-superconductor 503 (NIS) junction, which may be voltage biased.

[0076] For example, in the embodiment of Figure 5, the energy dissipation structure 103 comprises two NIS junctions. These two NIS junctions form a superconductor-insulator-normal metal-insulator-superconductor (SINIS) junction. The SINIS junctions are connected by a bias voltage

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[0077] The filter 102 may be coupled to the normal metal 501 of the NIS / SINIS junction. Thus, the energy dissipation structure 103 may absorb photon energy from the at least one qubit 101 through the filter 102.

[0078] According to one embodiment, the energy dissipation structure 103 comprises a QCR, which comprises a SINIS junction.

[0079] In one embodiment, the energy dissipation structure 103 is configured to dissipate photon energy transferred to the energy dissipation structure via photon-assisted electron tunneling in the NIS / SINIS junction.

[0080] Figure 6 shows an effective circuit model diagram of arrangement 100 according to one embodiment. It should be understood that arrangement 100 need not include the circuit elements shown in the embodiment of Figure 6. Rather, the circuit elements shown in the embodiment of Figure 6 may represent electrical characteristics of at least one qubit 101, filter 102, and / or energy dissipation structure 103, and may be used to analyze the behavior of arrangement 100.

[0081] In the embodiment of Figure 6, the energy dissipation structure 103 comprises a QCR.

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[0082] According to the embodiment of Figure 6, the filter 102 comprises an LC bandstop filter.

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[0083] According to the embodiment of Figure 6, at least one qubit 101 comprises a transverse qubit. At least one qubit 101 comprises a capacitance

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[0084] The nodal fluxes of the two nodes on the normal metal island of the QCR, the filter 102, and at least one qubit 101 are determined by their conjugate nodal charges

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[0085] To a first approximation, a bandstop filter can be modeled by a first-order lumped-element LC filter. The arrangement 100 comprises a QCR connected to an LC bandstop filter that is capacitively connected to at least one qubit 101. The bandstop filter and QCR thus form a bandstop-filtered QCR. A bandstop-filtered QCR is an example of a filtered energy-dissipating structure. In the following, following a canonical formalism approach, we describe a Lagrangian system from which we derive a Hamiltonian expressed in terms of nodal fluxes and charges promoted to quantum operators.

[0086]

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[0087] Lagrange

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[0088] Using Fermi's golden rule, we can calculate the environmental decay rate of a three-level transmon.

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[0089] charge transfer operator

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[0090] The voltage noise spectrum of the bandstop filtered QCR is shown in Figure 102.

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[0091] 7 shows a table of circuit parameters according to one embodiment. The circuit parameters are merely exemplary.

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[0092]

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[0093] The above decay rates show that the QCR quickly depletes the second-lowest excited state, while the band-stop filter can efficiently protect the computational base from decay.

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[0094] In the following, we investigate the effect of the bandstop filtered QCR on the time evolution of a driven three-level truncated transmon. The Hamiltonian system includes a transmon term and a drive term, ordered as a matrix:

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[0095] The dissipative time evolution is modeled using the Lindblad master equation, where the amplitude of the dissipative term is

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[0096] Being a hyperoperator itself, the propagator of the hyperoperator equation above is the vectorized initial state

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[0097] The troublesome Dyson series of the hyperoperator equations can be approximated by the product of matrix exponentials (each of which is short

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[0098] Figure 8 shows a plot of qubit eigenstate occupancy during a gate operation according to one embodiment. In addition to environmentally induced excitation, leakage due to the driving field can be a major source of leakage error. Figure 8 shows the effect of bandstop filtered QCR on a qubit undergoing an X gate operation, i.e., a π pulse.

[0099] The plot in Figure 8

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[0100] Plots 810 in the left column show the situation with bandstop filtered QCR, while plots 820 in the right column show the evolution without bandstop filtered QCR.

[0101] If we consider maximum fidelity, i.e., a π-pulse applied to a qubit initially in the ground state, as in the upper panel of Fig. 8, or in the first excited state, as in the lower panel of Fig. 8, the qubit flips to the excited and ground states, respectively. Comparing the plots with and without dissipation, we see that dissipation increases the gate infidelity by an order of magnitude. However, once the pulse is terminated, the gate infidelity is reversed, especially when the initial state is in the excited state.

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[0102] FIG. 9 shows a schematic diagram of a quantum computing system 1000 according to one embodiment.

[0103] According to one embodiment, quantum computing system 1000 comprises arrangement 100 and a control unit 1001 coupled to arrangement 100. Control unit 1001 may be configured to decouple filter 102 and / or energy dissipation structure 103 from at least one qubit 101 in response to a gate operation on at least one qubit 101.

[0104] The gate operations may be performed by the control unit 1001 or by some other device within the quantum computing system 1000.

[0105] The filter 102 and / or the energy dissipation structure 103 may be coupled to the at least one qubit 101 by a controllable coupling. A control unit 1001 may be coupled to the controllable coupling, and the control unit 1001 may be configured to decouple the filter 102 and / or the energy dissipation structure 103 from the at least one qubit 101 by the controllable coupling in response to a gate operation on the at least one qubit 101. For example, in an embodiment in which the energy dissipation structure 103 comprises an NIS / SINIS junction, the control unit 1001 may be configured to control a bias voltage

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[0106] A gate operation may refer to a quantum logic gate operation, such as an X-gate, Y-gate, Z-gate, Hadamard gate, or phase gate, performed on at least one qubit 101.

[0107] Isolating the filter 102 and / or the energy dissipation structure 103 from the at least one qubit 101 may prevent the filter 102 and / or the energy dissipation structure 103 from affecting the computational base of the at least one qubit 101. According to the above analysis, this may not be necessary in some cases, such as when the decay rate is slow, but may be beneficial in some other situations.

[0108] When system 1000 is in operation, arrangement 100 may be physically located in a cryostat or the like. The cryostat may cool at least one qubit 101 and other components of arrangement 100, such as energy dissipation structure 103, to extremely low temperatures. This may be necessary if at least one qubit 101 includes, for example, a superconducting qubit. Control unit 1001 may be located outside of the cryostat.

[0109] 10, the connection between the arrangement 100 and the control unit 1001 is shown schematically as a single connection, the connection may include any number of connections. For example, the control unit 1001 may be coupled to at least one qubit 101, a filter 102, and / or an energy dissipation structure 103.

[0110] FIG. 10 shows a schematic diagram of a control unit 1001 according to one embodiment.

[0111] The control unit 1001 may comprise at least one processor 1101. The at least one processor 1101 may comprise one or more of various processing devices, such as, for example, a coprocessor, a microprocessor, the control unit 1001, a digital signal processor (DSP), a processing circuit with or without an associated DSP, or a variety of other processing devices including integrated circuits such as an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), a microprocessor unit (MCU), a hardware accelerator, a dedicated computer chip, or the like.

[0112] The control unit 1001 may further include a memory 1102. The memory 1102 may be configured to store, for example, computer programs. The memory 1102 may include one or more volatile memory devices, one or more non-volatile memory devices, and / or a combination of one or more volatile and non-volatile memory devices. For example, the memory 1102 may be embodied as a magnetic storage device (such as a hard disk drive, a floppy disk, or a magnetic tape), a magneto-optical storage device, or a semiconductor memory (such as a mask ROM, a PROM (programmable ROM), an EPROM (erasable PROM), a flash ROM, or a RAM (random access memory)).

[0113] The control unit 1001 may further comprise other components not shown in the embodiment of Figure 10. The control unit 1001 may, for example, comprise an input / output bus for connecting the control unit 1001 to the arrangement 100. Furthermore, a user may control the control unit 1001 via the input / output bus. A user may, for example, control the quantum computing operations performed by the arrangement 100 via the control unit 1001 and the input / output bus.

[0114] If the control unit 1001 is configured to implement several functions, several components and / or elements of the control unit 1001, such as the at least one processor 1102 and / or the memory 1102, may be configured to implement the functions. Furthermore, if the at least one processor 1101 is configured to implement several functions, the functions may be implemented using program code contained in the memory 1102, for example.

[0115] The control unit 1001 may be implemented using, for example, a computer, some other computing device, or the like.

[0116] FIG. 11 shows a flowchart diagram of a method 1200 for qubit leakage error reduction using at least one constellation according to one embodiment.

[0117] Method 1200 can include isolating 1201 a filter and / or energy dissipation structure from a qubit.

[0118] The method 1200 may further include performing 1202 at least one gate operation on the qubit.

[0119] Method 1200 may further include recoupling 1203 the filter and / or energy dissipation structure to the qubit.

[0120] The at least one qubit 101 may be isolated from the filter and / or energy dissipation structure at all times, except for certain "leakage removal times" during which the coupling to the energy dissipation structure is on for a time sufficient to remove the leakage. After the leakage removal, the at least one qubit 101 may be isolated again. The frequency at which these "leakage removal times" occur may depend on the amount of leakage accumulated in the at least one qubit 101 during the quantum computation. Thus, leakage removal may be performed, for example, after every gate, after every two gates, after every three gates, etc.

[0121] The at least one constellation may include multiple constellation, which may be the case, for example, in a quantum computing system including multiple qubits, where each qubit may be implemented using constellation 100. In such a case, method 1200 may be performed for each such constellation to remove leakage error from each qubit in the multiple qubits.

[0122] Method 1200 may include isolating 1201 a filter and / or energy dissipation structure from qubits in each location in the plurality of locations.

[0123] Method 1200 may further include performing 1202 at least one of a single-qubit gate operation or a multi-qubit gate operation using a qubit in each configuration in the plurality of configurations.

[0124] Method 1200 may further include recoupling 1203 the filter and / or energy dissipation structure in each location in the plurality of locations to the qubit.

[0125] The method 1200 may be performed, for example, by the control unit 1001 or any other device capable of controlling at least one arrangement.

[0126] In different embodiments, only one or more qubits in the plurality of qubits are coupled to their filter and / or dissipative structure for leakage error removal, while other qubits in the plurality of qubits remain isolated. In yet different embodiments, multiple qubits can be coupled or isolated to a common filter and / or dissipative structure.

[0127] Any range or device value given herein can be expanded or modified without losing the desired effect, and any embodiment can be combined with another embodiment unless expressly prohibited.

[0128] Although the present subject matter has been described in language specific to structural features and / or acts, it is to be understood that the present 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 example forms of implementing the claims, and other equivalent features and acts are intended to be within the scope of the claims.

[0129] It will be understood that the benefits and advantages described above may relate to one embodiment or to several embodiments. Embodiments are not limited to those that solve any or all of the described problems or that have any or all of the described benefits and advantages. It will be further understood that references to "an" item can refer to one or more of those items.

[0130] The steps of the methods described herein may be performed in any suitable order, or simultaneously as appropriate. Additionally, individual blocks may be deleted from any of the methods without departing from the spirit and scope of the subject matter described herein. Aspects of any of the above-described embodiments may be combined with aspects of any of the other embodiments described to form further embodiments without losing the desired effect.

[0131] The term "comprising" is used herein to mean including identified methods, blocks, or elements, but such blocks or elements do not include an exclusive list and a method or apparatus may include additional blocks or elements.

[0132] It will be understood that the above description is provided 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 the exemplary embodiments. Although various embodiments have been described above in a certain degree of detail, or with reference to one or more specific embodiments, those skilled in the art may make numerous modifications to the disclosed embodiments without departing from the spirit or scope of the specification.

Claims

1. 1. An arrangement (100) for reducing qubit leakage errors, comprising: at least one qubit (101) having a ground state (201) and a plurality of excited states (204), the plurality of excited states (204) including a lowest excited state (202), an energy difference (211) between the ground state and the lowest excited state corresponding to a first frequency, and an energy difference (212, 213, 214) between the lowest excited state and another excited state of the plurality of excited states corresponding to a second frequency; an energy dissipation structure (103) configured to dissipate the transferred energy; a filter (102) having at least one stop band (301) and at least one pass band (302), the filter (102) being coupled to the at least one qubit (101) and the energy dissipation structure (103), the at least one stop band (301) including the first frequency and the at least one pass band (302) including the second frequency; The arrangement (100), wherein the filter (102) comprises a bandstop filter or a lowpass filter.

2. The arrangement (100) of claim 1, wherein the energy dissipation structure (103) comprises at least one conventional metal-insulator-superconductor (NIS) junction.

3. 3. The arrangement (100) of claim 1 or 2, wherein the energy dissipation structure (103) comprises a quantum circuit refrigerator (QCR), the QCR comprising a voltage-biased superconductor-insulator-normal metal-insulator-superconductor (SINIS) junction.

4. The arrangement (100) of any one of claims 1 to 3, wherein the at least one qubit (101) comprises a superconducting qubit.

5. The arrangement (100) of any one of claims 1 to 4, wherein the other excited state comprises a second lowest excited state (203) of the at least one qubit (101).

6. 6. The arrangement (100) of claim 1, wherein the at least one passband (302) of the filter (102) further comprises a third frequency corresponding to an energy difference between two states in the plurality of excited states (204).

7. 7. The arrangement (100) of claim 1, wherein the at least one passband (302) of the filter (102) further comprises a first plurality of frequencies, each frequency in the first plurality of frequencies corresponding to an energy difference between two consecutive excited states in the plurality of excited states (204) of the at least one quantum bit (101).

8. 8. The arrangement (100) of any one of claims 1 to 7, wherein the at least one stop band (301) of the filter (102) further comprises a second plurality of frequencies, each frequency in the second plurality of frequencies corresponding to an energy difference between two non-contiguous states of the at least one quantum bit (101).

9. A quantum computing device comprising the arrangement according to any one of claims 1 to 8.

10. 9. A quantum computing system (1000) comprising the arrangement (100) of any one of claims 1 to 8 and a control unit (1001) coupled to the arrangement (100), wherein the control unit (1001) is configured to isolate the filter (102) and / or the energy dissipation structure (103) from the at least one quantum bit (101) in response to a gate operation on the at least one quantum bit (101).

11. 11. The quantum computing system (1000) of claim 10, further comprising a plurality of arrangements, each arrangement in the plurality of arrangements being implemented according to any one of claims 1 to 8, the control unit (1001) being coupled to each arrangement in the plurality of arrangements, and the control unit (1001) being further configured to isolate the filter (102) and / or the energy dissipation structure (103) of each arrangement in the plurality of arrangements from the at least one quantum bit (101) of the arrangement responsive to a gate operation on the quantum bit (101).

12. A method for reducing qubit leakage errors using at least one arrangement according to any one of claims 1 to 8, comprising the steps of: separating the filter and / or the energy dissipation structure from the at least one qubit; performing at least one gate operation on the qubit; and recoupling the filter and / or the energy dissipation structure to the at least one qubit.

13. the at least one arrangement comprises a plurality of arrangements, the method further comprising: isolating the filter and / or the energy dissipation structure from the at least one qubit in each location in the plurality of locations; performing at least one multi-qubit gate operation using the at least one qubit in each constellation in the plurality of constellations; and recoupling the filter and / or the energy dissipation structure to the at least one qubit in each location in the plurality of locations.

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