Reducing qubit leakage errors

Abstract

It is an object to provide an arrangement for reducing qubit leakage errors in a quantum computing system. According to an embodiment, the arrangement (100) for reducing qubit leakage errors comprises a first qubit (101) and a second qubit (102) selectively couplable to one another. The arrangement (100) may further comprise a first energy dissipation structure (103) selectively couplable to the first qubit (101), the first energy dissipation structure (103) configured to dissipate energy transferred to the first energy dissipation structure (103). The configuration (100) may further comprise a control unit (104) configured to perform a first quantum operation to transfer at least one characteristic of the quantum state from the first quantum bit (101) to the second quantum bit (102), couple the first quantum bit (101) to the first energy dissipation structure (103) for a time interval, and after the time interval, perform a second quantum operation to transfer at least one characteristic of the quantum state from the second quantum bit (102) to the first quantum bit (101).

Description

[Technical Field]

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

[0002] In quantum computing, binary information is typically stored in two-level quantum systems. However, many realizations or implementations of such qubits have more than two energy levels. In such cases, qubits are typically assigned to the two lowest energy levels, forming a computational basis. For a system to accurately implement a qubit, excitation to a higher energy level must be prevented. A situation in which one of these higher energy levels is excited is sometimes called a leakage error. This situation can arise, for example, due to gate operations applied to the qubit or system-environment interactions. Leakage errors cannot be corrected by conventional quantum error correction, which only handles errors within the computational basis. 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 important 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 for reducing qubit leakage errors in quantum computing systems. These and other objects are achieved by the features of the independent claims. Further embodiment forms are evident from the dependent claims, the description and the figures.

[0005] According to a first aspect, an arrangement for reducing qubit leakage errors includes a first qubit and a second qubit selectively couplable to each other, a first energy dissipation structure selectively couplable to the first qubit, the first energy dissipation structure configured to dissipate energy transferred to the first energy dissipation structure, and a control unit configured to perform a first quantum operation to transfer at least one characteristic of a quantum state from the first qubit to the second qubit, couple the first qubit to the first energy dissipation structure for a time interval, and, after the time interval, perform a second quantum operation to transfer at least one characteristic of the quantum state from the second qubit to the first qubit. This arrangement can, for example, reduce leakage errors in the first qubit.

[0006] In an embodiment of the first aspect, the arrangement further comprises a second energy dissipation structure selectively couplable to the second qubit, the second energy dissipation structure configured to dissipate energy transferred to the second energy dissipation structure, and the control unit is further configured to initialize the second qubit to a ground state by coupling the second qubit to the second energy dissipation structure before performing the first quantum operation and / or to initialize the second qubit to a ground state by coupling the second qubit to the second energy dissipation structure after performing the second quantum operation. This arrangement can efficiently initialize the second qubit, for example, to store at least one characteristic from the first qubit.

[0007] In a further embodiment of the first aspect, the first energy dissipation structure and / or the second energy dissipation structure comprises at least one normal-metal-insulator-superconductor NIS junction, which can, for example, efficiently transfer energy from the first qubit to the energy dissipation structure, thereby reducing the population of the non-computational state of the first qubit.

[0008] In a further embodiment of the first aspect, the first energy dissipation structure and / or the second energy dissipation structure comprise a quantum circuit refrigerator (QCR), the QCR comprising a voltage-biased superconductor-insulator-normal metal-insulator-superconductor SINIS junction, and the first qubit is electrically coupled to the normal metal of the SINIS junction of the first energy dissipation structure and / or the second qubit is electrically coupled to the normal metal of the SINIS junction of the second energy dissipation structure. This configuration can, for example, efficiently and controllably transfer energy from the first qubit to the energy dissipation structures, thereby reducing the population of the non-computational state of the first qubit.

[0009] In a further embodiment of the first aspect, the control unit is configured to couple the first qubit to the first energy dissipation structure for the time interval by adjusting a bias voltage of a SINIS junction of the first energy dissipation structure, which can, for example, efficiently control coupling between the energy dissipation structure and the first qubit.

[0010] In a further embodiment of the first aspect, the first energy dissipation structure and / or the second energy dissipation structure are configured to dissipate photon energy transferred to the energy dissipation structure via photon-assisted electron tunneling at the NIS / SINIS junction, e.g., this configuration can efficiently dissipate photon energy transferred to the first energy dissipation structure.

[0011] In a further embodiment of the first aspect, the first qubit and / or the second qubit comprise a superconducting qubit.

[0012] In a further embodiment of the first aspect, the first qubit and / or the second qubit comprise a transmon qubit.

[0013] In a further embodiment of the first aspect, the control unit is configured to perform the first quantum operation and / or the second quantum operation by performing a SWAP or iSWAP operation between the first qubit and the second qubit, which can, for example, efficiently transfer at least one property of the quantum state between the first qubit and the second qubit.

[0014] In a further embodiment of the first aspect, the control unit is configured to perform the first quantum operation and / or the second quantum operation by causing the first quantum bit and the second quantum bit to resonate via shifting the resonant frequencies of the first / second quantum bits, which can, for example, efficiently control the transfer of at least one property of the quantum state between the first quantum bit and the second quantum bit.

[0015] In a further embodiment of the first aspect, the control unit is configured to shift the resonant frequency of the first / second qubit via flux tuning, which can, for example, effectively shift the resonant frequency of the first qubit / second qubit.

[0016] In a further embodiment of the first aspect, the configuration includes a first plurality of qubits including a first qubit; a second plurality of qubits including a second qubit, wherein each qubit of the second plurality of qubits is selectively couplable to a corresponding qubit of the first qubit; and a plurality of energy dissipating structures including a first energy dissipating structure, wherein each energy dissipating structure of the plurality of energy dissipating structures is selectively couplable to a corresponding qubit of the first plurality of qubits, and wherein each energy dissipating structure of the plurality of energy dissipating structures dissipates energy transferred to it. and a plurality of energy dissipation structures configured to couple each qubit of the first plurality of qubits to a corresponding qubit of the second plurality of qubits, wherein the control unit is further configured to: perform a first quantum operation to transfer at least one characteristic of the quantum state from each qubit of the first plurality of qubits to a corresponding qubit of the second plurality of qubits for a time interval; couple each qubit of the first plurality of qubits to a corresponding energy dissipation structure of the plurality of energy dissipation structures for a time interval; and perform a second quantum operation to transfer at least one characteristic of the quantum state from each qubit of the second plurality of qubits to a corresponding qubit of the first plurality of qubits. This configuration can reduce leakage errors, for example, when a quantum state is formed by the first plurality of qubits collectively.

[0017] According to a second aspect, a quantum computing system comprises an arrangement according to the first aspect.

[0018] According to a third aspect, a method of reducing qubit leakage error includes performing a first quantum operation to transfer at least one characteristic of a quantum state from a first qubit to a second qubit, coupling the first qubit to an energy dissipation structure for a time interval, and after the time interval, performing a second quantum operation to transfer at least one characteristic of the quantum state from the second qubit to the first qubit.

[0019] According to a fourth aspect, a computer program product comprises program code configured to perform the method according to the third aspect when the computer program product is run on a computer.

[0020] Many of the attendant features will be more readily appreciated as the same becomes better understood by reference to the following detailed description considered in connection with the accompanying drawings.

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

[0022] [Figure 1] 1 shows a schematic diagram of an arrangement for reducing qubit leakage errors according to an embodiment. [Figure 2] FIG. 1 shows a schematic diagram of an arrangement for reducing qubit leakage errors according to another embodiment. [Figure 3] 1 shows a schematic diagram of an energy dissipation structure according to an embodiment. [Figure 4] 1 illustrates a graphical representation of a single gate error according to an embodiment. [Figure 5] 1 shows a table of circuit parameters according to an embodiment. [Figure 6] 1 illustrates a graphical representation of coordination between a first qubit and a second qubit, coordination between a first qubit and a first energy dissipation structure, and state occupancy, according to an embodiment. [Figure 7] 1 shows a schematic diagram of a control unit according to an embodiment. [Figure 8] 1 shows a flowchart representation of a method for reducing qubit leakage errors according to an embodiment. DETAILED DESCRIPTION OF THE INVENTION

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

[0024] In the following detailed description of the present disclosure, reference is made to the accompanying drawings that form a part hereof, and in which is shown by way of illustration specific embodiments in which the present disclosure may be arranged. It is understood that other embodiments 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 should not be taken in a limiting sense, as the scope of the present disclosure is defined by the appended claims.

[0025] For example, it will be understood that disclosure related to a described method also applies 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, even if such units are not 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 for performing the described functions, even if such steps are not explicitly described or shown. Furthermore, it will be understood that features of the various exemplary aspects described herein can be combined with each other, unless otherwise specified.

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

[0027] According to an embodiment, configuration 100 includes a first qubit 101 and a second qubit 102 that are selectively couplable to one another. First qubit 101 and second qubit 102 may, for example, be electrically coupled to one another. First qubit 101 may also be referred to as a computation qubit, and second qubit 102 may also be referred to as an ancillary qubit.

[0028] As used herein, when two elements are electrically coupled, the elements may have an electrical connection with each other. The electrical connection may include any number of electrical components / elements, such as capacitors, inductors, transmission lines, etc.

[0029] The first / second qubit 101, 102 may have a ground state |g〉. In this specification, ground state refers to the quantum state of the qubit that has the lowest energy.

[0030] The first / second qubit 101, 102 may further have multiple excited states. The multiple excited states may include the lowest excited state |e〉. As used herein, the lowest excited state refers to the quantum state of the qubit with the second lowest energy.

[0031] The ground state and lowest excited state of a qubit may correspond to the computational basis of the qubit. For example, the ground state |g〉 corresponds to the |0〉 state of the qubit, and the lowest excited state |e〉 corresponds to the |1〉 state of the qubit, or vice versa. Other quantum states of the qubit are sometimes called non-computational states.

[0032] The energy gap between the ground state and the lowest excited state may correspond to the resonant frequency of the qubit.

[0033] The plurality of excited states can further include a second-lowest excited state |f〉, which has a higher energy than the ground state |g〉 and the lowest excited state |e〉.

[0034] Configuration 100 may further include a first energy dissipation structure 103 selectively couplable to first qubit 101. First energy dissipation structure 103 may be configured to dissipate energy transferred to first energy dissipation structure 103.

[0035] The first energy dissipation structure 103 may be considered an environment, an engineered environment, a vessel, a dissipative source, or the like.

[0036] Although some embodiments and analyses disclosed herein may refer to particular implementations of first energy dissipation structure 103, it should be understood that first energy dissipation structure 103 may be implemented using, for example, any dissipation structure having controllable coupling to first quantum bit 101.

[0037] The first energy dissipation structure 103 may be electrically coupled to the first qubit 101. The first energy dissipation structure 103 may be selectively couplable to the first qubit 101, for example, by adjusting the coupling strength between the first energy dissipation structure 103 and the first qubit 101.

[0038] It should be understood that while the first quantum bit 101 and the first energy dissipation structure 103 may be electrically coupled in series, the coupling between the first quantum bit 101 and the first energy dissipation structure 103 may still be selective if the coupling strength between the first quantum bit 101 and the first energy dissipation structure 103 is controllable.

[0039] As used herein, when two objects are selectively coupleable, the strength of the interaction between the objects can be controlled and / or switched on and off. For example, two selectively coupleable objects may be tuned to resonance or detuned from resonance, and / or the magnitude of coupling can be controlled. It should be understood that even if there is a continuous connection between two elements, such as an electrical / capacitive / inductive connection, the elements can still be selectively coupleable if the interaction between the elements can be adjusted. For example, a first qubit 101 and a second qubit 102 may be capacitively coupled, but the interaction between the qubits can be adjusted, for example, by shifting the qubits to resonate and de-resonate, so that the coupling between the qubits can be selective.

[0040] Configuration 100 may further comprise a control unit 104. Control unit 104 may be configured to perform a first quantum operation to transfer at least one characteristic of the quantum state from first qubit 101 to second qubit 102.

[0041] Control unit 104 may be coupled to first qubit 101 , second qubit 102 , first energy dissipation structure 103 and / or other elements / components of configuration 100 .

[0042] The first quantum operation may include, for example, a first SWAP operation.

[0043] The at least one property of the quantum state may include, for example, any single property of the quantum state, multiple properties of the quantum state, or the entire quantum state.

[0044] A quantum state can have at least one of local properties or nonlocal properties. For a general many-body quantum state, i.e., a quantum state encoded with multiple qubits, local properties can refer to properties that can be obtained through local measurements of individual qubits. These include, for example, the population or coherence of the qubits. Similarly, nonlocal properties can refer to properties that are encoded in two or more qubits and can only be obtained through nonlocal measurements across the two or more qubits, including, for example, entanglement.

[0045] The control unit 104 may, for example, cause the first qubit 101 and the second qubit 102 to resonate to perform a first quantum operation. When the first qubit 101 and the second qubit 102 are in a resonant state, they may be referred to as being coupled. When the first qubit 101 and the second qubit 102 are resonant / coupled, a quantum logic gate operation may be performed on the qubits.

[0046] According to an embodiment, the control unit 104 is configured to perform the first quantum operation and / or the second quantum operation by causing the first quantum bit 101 and the second quantum bit 102 to resonate via shifting the resonant frequencies of the first / second quantum bits.

[0047] According to an embodiment, the control unit 104 is configured to shift the resonant frequency of the first / second qubit via magnetic flux tuning, in which the control unit 104 can tune the resonant frequency of the first / second qubit 101, 102 by inducing a magnetic flux through the first / second qubit 101, 102.

[0048] The first quantum operation may include, for example, a SWAP gate operation or an iSWAP gate operation. An iSWAP gate can be converted to a SWAP gate by a single qubit operation. Thus, the terms SWAP and iSWAP may be used interchangeably herein.

[0049] The first qubit 101 and the second qubit 102 may be initially separated. The first qubit 101 may initially be in some unknown quantum state, and the second qubit 102 may initially be in a ground state. A quantum operation may transfer computational information from the first qubit 101 to the second qubit 102. For ideal gate operations, the transfer of non-computational populations between qubits during a quantum operation may be negligible.

[0050] The control unit 104 may be further configured to couple the first qubit 101 to the energy dissipation structure 103 at intervals of time. The control unit 104 may couple the first qubit 101 to the energy dissipation structure 103, for example, by adjusting a coupling strength between the first qubit 101 and the energy dissipation structure 103.

[0051] The time interval may be long enough to ensure that the non-computing state of the first qubit 101 is depleted.

[0052] After a time interval, the control unit 104 can turn off the coupling between the first qubit 101 and the first energy dissipation structure 103 .

[0053] The coupling between the first qubit 101 and the first energy dissipation structure 103 may rapidly reduce the occupancy of the non-computational state of the first qubit 101. The coupling may increase the occupancy of the computational state of the first qubit 101. Thus, the leakage error of the first qubit 101 may be reduced.

[0054] The control unit 104 may be further configured to perform a second quantum operation to transfer at least one characteristic of the quantum state from the second qubit 102 to the first qubit 101 after a time interval.

[0055] A first / second quantum operation may also be referred to as a first / second quantum gate, a first / second quantum gate operation, etc.

[0056] During the first quantum operation, computational information can be transferred from the first qubit 101 to the second qubit 102. The occupancy of the non-computational state of the first qubit 101 can be reduced during coupling between the first qubit 101 and the first energy dissipation structure 103. Then, computational information can be transferred from the second qubit 102 back to the first qubit 101 via the second quantum operation. Although the non-computational information is removed from the first qubit 101 during coupling to the energy dissipation structure 103, there is always a non-zero occupancy in the lowest excited state after coupling. This is a bit-flip error. Furthermore, for any initial state, the off-diagonal elements will also be non-zero in the computational basis, which includes a phase-flip error. There are also some unavoidable bit-flip and phase-flip errors that occur in the SWAP operation. Therefore, the leakage error of the first qubit 101 can be converted into a bit-flip and phase error. The bit-flip and phase error can be corrected using, for example, a quantum error-correcting code.

[0057] According to an embodiment, first qubit 101 and / or second qubit 102 comprise a superconducting qubit.

[0058] According to an embodiment, the first qubit 101 and / or the second qubit 102 comprise a transmon qubit. Alternatively, the first / second qubit 101, 102 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.

[0059] Although some embodiments may be disclosed herein with reference to particular types of qubits, these qubit types are exemplary only. In any embodiment disclosed herein, the first / second qubits may be implemented in a variety of ways and using a variety of technologies.

[0060] Configuration 100 may be embodied, for example, in a quantum computing system. Such a quantum computing system may include multiple qubits for performing quantum computations. Each such qubit may be implemented using configuration 100.

[0061] Configuration 100 can be implemented, for example, in a superconducting circuit architecture.

[0062] According to an embodiment, the control unit 104 is configured to perform the first quantum operation and / or the second quantum operation by causing the first quantum bit 101 and the second quantum bit 102 to resonate via shifting the resonant frequencies of the first / second quantum bits 101, 102.

[0063] When configuration 100 is operational, first qubit 101, second qubit 102, and energy dissipation structure 103 may be physically located, such as in a cryostat. The cryostat can cryogenically cool qubits 101, 102 and other components of configuration 100, such as energy dissipation structure 103. This may be necessary if qubits 101, 102 correspond to superconducting qubits, for example. Control unit 104 may be located outside of the cryostat.

[0064] According to an embodiment, configuration 100 further comprises a first plurality of qubits including first qubit 101 and a second plurality of qubits including second qubit 102. Each qubit in the second plurality of qubits may be selectively couplable to a corresponding qubit in the first plurality of qubits. Configuration 100 may further comprise a plurality of energy dissipation structures including first energy dissipation structure 103, each energy dissipation structure of the plurality of energy dissipation structures selectively couplable to a corresponding qubit of the first plurality of qubits, and each energy dissipation structure of the plurality of energy dissipation structures configured to dissipate energy transferred to that energy dissipation structure.

[0065] The control unit 104 may be further configured to perform a first quantum operation to transfer at least one characteristic of the quantum state from each qubit of the first plurality of qubits to a corresponding qubit of the second plurality of qubits, couple each qubit of the first plurality of qubits to a corresponding energy dissipation structure of the plurality of energy dissipation structures for a time interval, and perform a second quantum operation to transfer at least one characteristic of the quantum state from each qubit of the second plurality of qubits to a corresponding qubit of the first plurality of qubits.

[0066] FIG. 2 shows a schematic diagram of an arrangement according to another embodiment.

[0067] Configuration 100 may further comprise a second energy dissipation structure 201 selectively couplable to second qubit 102. Second energy dissipation structure 201 may be configured to dissipate energy transferred to second energy dissipation structure 201.

[0068] The control unit 104 may be further configured to initialize the second qubit 102 to a ground state by coupling the second qubit 102 to the second energy dissipation structure 201 prior to the first quantum operation.

[0069] Alternatively or additionally, the control unit 104 may be further configured to initialize the second quantum bit 102 to a ground state by coupling the second quantum bit 102 to the second energy dissipation structure 201 after the second quantum operation.

[0070] The control unit 104 may be further configured to couple the second qubit 102 to the second energy dissipation structure 201 for a second time interval. The control unit 104 may couple the second qubit 102 to the second energy dissipation structure 201, for example, by adjusting a coupling strength between the second qubit 102 and the second energy dissipation structure 201.

[0071] The second time interval may be long enough to ensure that non-computational states and / or states other than the ground state of second qubit 102 are depleted.

[0072] 3 shows a schematic diagram of an energy dissipation structure according to an embodiment. The first energy dissipation structure 103 and / or the second energy dissipation structure 201 can be implemented, for example, as in the embodiment of FIG.

[0073] According to an embodiment, the first energy dissipation structure 103 and / or the second energy dissipation structure 201 comprises at least one normal metal-insulator-superconductor NIS junction.

[0074] For example, in the embodiment of Figure 3, the energy dissipation structure 103 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 junctions are connected by a bias voltage V B can be biased by

[0075] The metal island 301 is connected to the bias voltage V B The SINIS junction can be charged and discharged by controlling the junction temperature. Such tunneling transitions can also involve the absorption or emission of photons. A SINIS junction is sometimes called a quantum circuit refrigerator (QCR).

[0076] The first qubit 101 may be electrically coupled to the normal metal 301 of the NIS / SINIS junction of the first energy dissipation structure 103. Thus, the first energy dissipation structure 103 may absorb photon energy from the first qubit 101.

[0077] The second qubit 102 may be electrically coupled to the normal metal 301 of the NIS / SINIS junction of the second energy dissipation structure 201. Thus, the second energy dissipation structure 201 may absorb photon energy from the second qubit 102.

[0078] According to an embodiment, the first energy dissipation structure 103 and / or the second energy dissipation structure 201 comprise a quantum circuit refrigerator (QCR), which comprises a voltage-biased SINIS junction. The first qubit 101 may be electrically coupled to the normal metal of the SINIS junction of the first energy dissipation structure 103, and / or the second qubit 102 may be electrically coupled to the normal metal of the SINIS junction of the second energy dissipation structure 201.

[0079] The control unit 104 may be configured to couple the first qubit 101 to the first energy dissipation structure 103 for a time interval by adjusting a bias voltage of a SINIS junction of the first energy dissipation structure 103.

[0080] According to an embodiment, the first energy dissipation structure 103 and / or the second energy dissipation structure 201 are configured to dissipate photon energy transferred to the energy dissipation structure via photon-assisted electron tunneling at the NIS / SINIS junction.

[0081] The first energy dissipation structure 103 can absorb a photon from the first qubit 101 at a bias voltage at which the electron needs to receive an additional quantum of energy from the first qubit 101 to overcome the Bardeen-Cooper-Schrieffer energy gap of the superconductor 303. Therefore, the control unit 104 controls the bias voltage V B The coupling strength between the first energy dissipation structure 103 and the first quantum bit 101 can be adjusted via

[0082] In the following, the behavior of an embodiment of the configuration 100 is analyzed.

[0083] The configuration 100 can be modeled by a system Hamiltonian.

number

number

number

number

number

number

[0084] In the following, the evolution of occupations in non-computational states under the iSWAP operation is analyzed.

[0085] Here, the Hamiltonian of the system shown above

number

number

number

number

number

[0086] To quantify the impact on the non-computational state during the iSWAP gate operation, we consider the above approach using a three-state truncation of the transmon qubit. As a result, we obtain the following system Hamiltonian in the interaction picture:

number

number

number

number

number

[0087] In general, the iSWAP operation can be realized by evolving the above system when the first qubit 101 and the second qubit 102 are in resonance (ω1 = ω2) for duration τ = π / (2g). In the two-state truncation of the transmon, the interaction picture Hamiltonian

number

number

number

[0088] To calculate the error generated by the transition to the non-computing state during the iSWAP gate operation, we use the complete interaction picture Hamiltonian

number

number

number

[0089] Occupancy P in the |f〉 state of the computation qubitf The dynamics of (t) can be solved from the von Neumann equation, and the result can be written as

number

[0090] In the following, we will consider the worst-case estimate of the transmitted non-computational information of the iSWAP gate as

number

[0091] FIG. 4 is a block diagram of an embodiment of the present invention.

number

[0092] Rectangle 402 indicates that the single gate error 401

number

number

number

[0093] FIG. 5 shows a table of circuit parameters according to an embodiment.

[0094] The numerical simulations presented in the next section use the circuit parameters shown in the table in Figure 5. With these parameters,

number

number

number

[0095] In the rotating wave approximation, starting from an ancillary ground state, the dynamics of non-computational information is restricted to the Hilbert space spanned by the states {|f,g〉,|e,e〉,|g,f〉}. As a result, by choosing α2≫α1, we can suppress the transfer of occupation from |f,g〉→|g,f〉, which may guarantee inconsistent Rabi frequencies between |f,g〉→|e,e〉 and |e,e〉→|g,f〉.

[0096] Another possible source of error is generated when the first qubit 101 is coupled to the first energy dissipation structure 103. Ideally, the energy dissipation structure 103 would couple only to the computation qubit and be decoupled from the ancillary qubits, thus preserving the stored quantum information during depletion of non-computational information from the computation qubit 101. However, due to the coupling g between the computation qubit 101 and the ancillary qubit 102, the QCR is also indirectly coupled to the ancillary qubit 102. We now calculate the undesired effective decay rate of the ancillary qubit 102 and its dependence on circuit parameters.

[0097] The interaction between a two-qubit system and a QCR can be modeled by the Caldeira-Leggett model, in which the energy dissipation structure 103 is described by an infinite set of harmonic oscillators bilinearly and capacitively coupled to the computation qubit 101. The physical properties are captured by the following Hamiltonian:

number

number

number

[0098] When the computation qubit 101 and the ancillary qubit 102 are coupled (g>0), errors can arise from unwanted decay of the ancillary qubit 102. To analyze this, we consider two limiting regimes. When g≫κ, we can analytically calculate the dissipation rate γ of the ancillary qubit 102. Here, the results in the resonant (δ=0) and dispersive (δ≫g) limits are summarized as follows (δ=|ω1-ω2|).

number

[0099] In the opposite case, g<<κ, to obtain analytical results, the computation qubit 101 needs to be treated as part of the bath seen by the ancillary qubit 102. As a result, the computation qubit 101 acts as a filter between the ancillary qubit 102 and the energy dissipation structure 103. Approximating the computation qubit 101 as a linear resonator, the auxiliary damping rates for the resonance and dispersion limits can be derived as follows:

number

[0100] Now, upon depletion of the non-computational state of the first qubit 101, the QCR pulse is on and the first qubit is coupled to the energy dissipation structure 103, so that the rate κ=κ on ,

number

number

number

[0101] 6 illustrates a graphical representation of coordination between a first qubit and a second qubit, coordination between the first qubit and a first energy dissipation structure, and state occupancy, according to an embodiment. In the embodiment of FIG. 6, it is assumed that both transmon qubits include three states and the parameters from FIG. 5 are used. The protocol duration is

number

[0102] The resonant frequency ω2(t) of the ancillary qubit 102 is, for example, the Josephson energy

number

[0103] In the simulation of Figure 6, the initial state is a product state.

number

number

number

[0104] Curve 601 represents the ratio of the resonant frequency ω2 of the second qubit to the resonant frequency ω1 of the first qubit. During the time interval ω1t=[0,500], ω2 / ω1=1, and the first qubit 101 and the second qubit 102 are in resonance due to the first SWAP operation. During the time interval ω1t=[500,1500], ω2 / ω1=1.2, and the first qubit 101 and the second qubit 102 are not in resonance. During the time interval ω1t=[1500,2000], ω2 / ω1=1 again, and the first qubit 101 and the second qubit 102 are in resonance due to the second gate operation.

[0105] Curve 602 represents the ratio κ / ω1. Curve 602 therefore corresponds to the coupling between the first qubit 101 and the QCR in units of ω1. During the time interval ω1t=[500,1500], κ / ω1=0.01, and κ / ω1=0 otherwise.

[0106] Curve 603 represents the occupancy of the ground state |g〉 of computation qubit 101, curve 604 represents the occupancy of the lowest excited state |e〉 of computation qubit 101, and curve 605 represents the occupancy of the second lowest excited state |f〉 of computation qubit 101.

[0107] In the embodiment of Figure 6, dissipation is modeled using the local Lindblad equation for computation qubit 101. As a result, incoherent or dissipative dynamics ignores the ancillary qubit 102, which is effective in the limit of κ > g, i.e., when computation qubit 101 can be treated as part of the bath seen by the ancillary qubit. For the parameters of Figure 5, the coupling angular frequency is g = 2π × 0.016 GHz, and the value of the dissipation rate in the on state of the QCR is

number

number

[0108] As can be seen from the results disclosed herein, at least for the parameter values ​​and initial conditions used, the protocol executed by configuration 100 results in a decrease in the occupancy of the second excited state of computation qubit 101. The decay rate induced by energy dissipation structure 103

number

[0109] FIG. 7 shows a schematic diagram of the control unit 104 according to an embodiment.

[0110] The control unit 104 may include at least one processor 701. The at least one processor 701 may comprise one or more of a variety of processing devices, such as, for example, a coprocessor, a microprocessor, the control unit 104, a digital signal processor (DSP), processing circuitry 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.

[0111] The control unit 104 may further include a memory 702. The memory 702 may be configured to store, for example, computer programs. The memory 702 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 702 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)).

[0112] The control unit 104 may further comprise other components not shown in the embodiment of Figure 7. The control unit 104 may, for example, comprise an input / output bus for connecting the control unit 104 to the configuration 100. Furthermore, a user may control the control unit 104 via the input / output bus. A user may, for example, control the quantum computing operations performed by the configuration 100 via the control unit 104 and the input / output bus.

[0113] If the control unit 104 is configured to implement several functions, several components and / or elements of the control unit 104, such as the at least one processor 702 and / or memory 702, may be configured to implement this functionality. Furthermore, if the at least one processor 701 is configured to implement some functionality, this functionality may be implemented using program code contained in, for example, a memory.

[0114] The control unit 104 may be implemented using, for example, a computer, some other computing device, or the like.

[0115] FIG. 8 shows a flowchart representation of a method 800 for reducing qubit leakage errors according to an embodiment.

[0116] According to an embodiment, method 800 includes performing 801 a first quantum operation to transfer at least one characteristic of a quantum state from a first qubit to a second qubit.

[0117] The method 800 may further include coupling 802 the first qubit to the energy dissipation structure for the time interval.

[0118] The method 800 may further include, after the time interval, performing 803 a second quantum operation to transfer at least one characteristic of the quantum state from the second qubit to the first qubit.

[0119] The method 800 may be performed, for example, by the arrangement 100 and / or the control unit 104 .

[0120] 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.

[0121] 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.

[0122] 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 stated problems or have any or all of the stated benefits and advantages. It will be further understood that reference to "an" or "an" item can refer to one or more of those items.

[0123] 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.

[0124] As used herein, the term "comprising" is used to mean including identified methods, blocks, or elements, but such blocks or elements do not constitute an exclusive list and a method or apparatus may comprise additional blocks or elements.

[0125] It will be understood that the above description 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 the exemplary embodiments. While various embodiments have been described above with a certain degree of particularity, or with reference to one or more individual embodiments, those skilled in the art could 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: a first qubit (101) and a second qubit (102) that are selectively coupleable to each other; a first energy dissipation structure (103) selectively couplable to the first qubit, the first energy dissipation structure (103) configured to dissipate energy transferred to the first energy dissipation structure (103); and A control unit (104) comprising: performing a first quantum operation to transfer at least one characteristic of a quantum state from the first qubit (101) to the second qubit (102); coupling the first qubit (101) to the first energy dissipation structure (103) for a time interval; performing a second quantum operation after the time interval to transfer the at least one characteristic of the quantum state from the second qubit (102) to the first qubit (101); and the control unit (104) configured to:

2. a second energy dissipation structure (201) selectively couplable to the second qubit (102); the second energy dissipation structure (201) is configured to dissipate energy transferred to the second energy dissipation structure (201); The control unit (104) and / or, prior to performing the first quantum operation, initializing the second quantum bit (102) to a ground state by coupling the second quantum bit (102) to the second energy dissipation structure (201); 10. The arrangement (100) of claim 1, further configured to, after performing the second quantum operation, initialize the second quantum bit (102) to a ground state by coupling the second quantum bit (102) to the second energy dissipation structure (201).

3. The arrangement (100) of claim 2, wherein the first energy dissipation structure (103) and / or the second energy dissipation structure (201) comprises at least one normal metal-insulator-superconductor NIS junction.

4. 4. The arrangement (100) of claim 2 or 3, wherein the first energy dissipation structure (103) and / or the second energy dissipation structure (201) comprise a quantum circuit refrigerator (QCR), the QCR comprising a voltage-biased superconductor-insulator-normal metal-insulator-superconductor SINIS junction, and the first qubit (101) is electrically coupled to the normal metal of the SINIS junction of the first energy dissipation structure (103) and / or the second qubit (102) is electrically coupled to the normal metal of the SINIS junction of the second energy dissipation structure (201).

5. 5. The arrangement (100) of claim 4, wherein the control unit (104) is configured to couple the first quantum bit (101) to the first energy dissipation structure (103) during the time interval by adjusting a bias voltage of the SINIS junction of the first energy dissipation structure (103).

6. The arrangement (100) of any one of claims 1 to 5, wherein the first qubit (101) and / or the second qubit (102) comprise a superconducting qubit.

7. The arrangement (100) of any one of claims 1 to 6, wherein the first qubit (101) and / or the second qubit (102) comprise a transmon qubit.

8. 8. The arrangement (100) of claim 1, wherein the control unit (104) is configured to perform the first quantum operation and / or the second quantum operation by performing a SWAP or iSWAP operation between the first quantum bit (101) and the second quantum bit (102).

9. The arrangement (100) of any one of claims 1 to 8, wherein the control unit (104) is configured to perform the first quantum operation and / or the second quantum operation by causing the first quantum bit (101) and the second quantum bit (102) to resonate via shifting a resonant frequency of the first quantum bit / the second quantum bit.

10. 10. The arrangement (100) of claim 9, wherein the control unit (104) is configured to shift the resonant frequency of the first qubit / second qubit (101, 102) via magnetic flux adjustment.

11. a first plurality of qubits including the first qubit (101); a second plurality of qubits including the second qubit (102), wherein each qubit of the second plurality of qubits is selectively couplable to a corresponding qubit of the first qubit; a plurality of energy dissipation structures including the first energy dissipation structure (103), each energy dissipation structure of the plurality of energy dissipation structures selectively couplable to a corresponding qubit of the first plurality of qubits, and each energy dissipation structure of the plurality of energy dissipation structures configured to dissipate energy transferred to it; The control unit (104) performing a first quantum operation to transfer at least one characteristic of a quantum state from each qubit of the first plurality of qubits to a corresponding qubit of the second plurality of qubits; coupling each qubit of the first plurality of qubits to a corresponding energy dissipation structure of the plurality of energy dissipation structures for a time interval; and performing a second quantum operation to transfer the at least one characteristic of the quantum state from each qubit of the second plurality of qubits to the corresponding qubit of the first plurality of qubits.

12. A quantum computing system comprising the configuration according to any one of claims 1 to 11.

13. 1. A method (800) for reducing qubit leakage errors, comprising: performing a first quantum operation to transfer at least one characteristic of a quantum state from a first qubit to a second qubit (801); coupling the first qubit to an energy dissipation structure for a time interval (802); and performing (803) a second quantum operation to transfer the at least one characteristic of the quantum state from the second quantum bit to the first quantum bit after the time interval.

14. A computer program having instructions for performing the method according to claim 13 when the computer program is run on a computer.

Images