Mitigation of qubit crosstalk induced errors in quantum computing and information processing systems

Abstract

The disclosure relates to mitigating qubit crosstalk induced errors within a quantum computing system (QCS). A compensation signal is provided to one or more qubits. The compensation signal at least partially "counteracts" (e.g., compensates for) crosstalk between pairs of qubits. Such crosstalk-induced errors may include leakage of quantum states of qubits from computational subspaces of the quantum system. Thus, these embodiments may be employed to reduce quantum computing errors that occur due to qubit transitions (or leaks) to excited states that are not within the computing subspace of the quantum system.

Description

[0001] Priority Claim

[0002] This application claims priority to U.S. Application No. 17 / 974,216, filed on October 26, 2022, and the benefit of such U.S. application is hereby claimed, and such U.S. application is incorporated herein by reference. Technical Field

[0003] This disclosure generally relates to quantum computing and information processing systems, and more particularly to mitigation of qubit crosstalk-induced errors in quantum computing and information processing systems. Background Art

[0004] Quantum computing is a computational method that utilizes quantum effects such as superposition of basis states and entanglement to perform specific computations more efficiently than classical digital computers. In contrast to digital computers that store and manipulate information in the form of bits (e.g., "1" or "0"), quantum computing systems can use qubits ("qubits") to manipulate information. A qubit can refer to a quantum device capable of superposing multiple states (e.g., data in the "0" and "1" states), and / or to the superposition of the data itself in multiple states. According to conventional terminology, the superposition of the "0" and "1" states in a quantum system can be expressed as, for example, a|0> + b|1>. The "0" and "1" states of a digital computer are analogous to the |0> and |1> basis states of a qubit, respectively. Summary of the Invention

[0005] Aspects and advantages of embodiments of the present disclosure will be set forth in part in the description that follows, or may be learned from the description, or may be learned through practice of the embodiments.

[0006] One example aspect of the present disclosure relates to a method implemented by a quantum computing system (QCS). The QCS can include a set of qubits. The method can be used to calibrate a compensation signal for mitigating qubit crosstalk-induced errors in quantum computing. The method can include determining a pulse delay for a selection of consecutive pulses in a series of qubit rotation pulses applied to each qubit in the set of qubits. Each qubit rotation pulse in the series of qubit rotation pulses applied to the qubits in the set of qubits can generate a rotation of the quantum state of the qubit. The selected pulse delay can increase the probability that the applied series of qubit rotation pulses generates leakage of at least a portion of the set of qubits from the computational subspace of the QCS to the excited subspace of the QCS. The selected pulse delay can be an optimal pulse delay. As the optimal pulse delay, the selected pulse delay can at least approximately maximize the probability that the applied series of qubit rotation pulses generates leakage of at least a portion of the set of qubits from the computational subspace of the QCS to the excited subspace of the QCS. Based on the selected pulse delay, qubit pairs in the set of qubits can be identified. The identified qubit pairs can contribute to leakage of a portion of the set of qubits from the computational subspace to the excited subspace. The qubit pair can include a source qubit and a recipient qubit. The identified qubit pairs can be used to determine values of a set of compensation parameters for the compensation signal. When a control signal is provided to the source qubit and the compensation signal is provided to the recipient qubit, the control signal generates a reduced probability of leakage of the recipient qubit from the computational subspace to the excited subspace.

[0007] Other aspects of the present disclosure relate to various systems, methods, devices, non-transitory computer-readable media, computer-readable instructions, and computing devices.

[0008] These and other features, aspects, and advantages of the various embodiments of the present disclosure will be better understood with reference to the following description and the appended claims. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate example embodiments of the present disclosure and together with the description explain the relevant principles. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] With reference to the drawings, a detailed discussion of embodiments for those of ordinary skill in the art is set forth in this specification, in which:

[0010] Figure 1 An example quantum computing system in accordance with an example embodiment of the present disclosure is depicted.

[0011] Figure 2A An example first qubit in accordance with various embodiments is depicted.

[0012] Figure 2B Depicted in accordance with various embodiments is located Figure 2AAn example second qubit in close proximity to the first qubit.

[0013] Figure 2C Depicts parasitic electromagnetic coupling between a first qubit and a second qubit according to various embodiments. Figure 2B Induced leakage from the computational subspace to the excited subspace of the second qubit, which is induced by a first control signal.

[0014] Figure 2D Depicts Figures 2B to 2C Induced leakage from the computational subspace of the second qubit, which is induced by Figures 2B to 2C A first control signal.

[0015] Figure 2E Depicts mitigation of induced leakage from the computational subspace by applying a compensation signal to the second qubit according to various embodiments. Figure 2D Induced leakage generated from the computational subspace.

[0016] Figure 3A Depicts a Ramsey error filtering pulse sequence applied to qubits to calibrate a compensation signal to mitigate qubit crosstalk-induced errors according to various embodiments.

[0017] Figure 3B Shows representative data of Ramsey error filtering versus delay time according to various embodiments.

[0018] Figure 3C Shows typical output of Ramsey error filtering at the optimal pulse delay during paired operations of all possible pairs including the receiver qubit.

[0019] Figure 3D Shows the leakage probability of the receiver qubit versus the amplitude and phase shift of the compensation signal during paired operations with the dominant source qubit at the optimal pulse delay.

[0020] Figure 4 Provides a flowchart of a method for calibrating a compensation signal to mitigate qubit crosstalk-induced errors according to various embodiments.

[0021] Figure 5 Provides a flowchart of a method for mitigating qubit crosstalk-induced errors in a quantum computing system according to various embodiments. Detailed Description

[0022] Embodiments relate to eliminating and / or mitigating computational errors in a quantum computing and / or information processing system. Embodiments are directed to eliminating and / or mitigating errors induced by qubit crosstalk in a quantum computing system (or apparatus) that includes a set of qubits that includes at least a first qubit and a second qubit. Embodiments eliminate and / or mitigate errors induced by qubit crosstalk by providing a compensation signal to one or more qubits. The compensation signal at least partially "cancels" (e.g., compensates for) the crosstalk between qubit pairs. Thus, the compensation signal may be referred to as a cancellation signal (or tone). Such crosstalk-induced errors may include leakage of the quantum state of a qubit from the computational subspace of the quantum system. Accordingly, these embodiments may be employed to reduce quantum computing errors that occur due to qubit transitions (or leakage) to excited states that are not within the computational subspace of the quantum system.

[0023] In addition to providing a compensation signal that eliminates and / or mitigates some quantum computing errors, embodiments also provide a method for characterizing the crosstalk between qubit pairs. Such characterization of the crosstalk enables calibration of the compensation signal for a qubit pair as a function of a parameter of a control signal intended for one of the qubits in any qubit pair. Embodiments provide such characterization of the crosstalk and calibration of the crosstalk compensation signal by a method involving Ramsey interferometry. That is, the transition frequency associated with a quantum state transition of a qubit may be determined as a function of the tuning of the qubit. The compensation signal (and to which qubits the compensation signal is provided) is calibrated according to Ramsey interferometry.

[0024] To control (or tune) each qubit in a set of qubits of a quantum computing system (QCS), each qubit in the set of qubits can have a separate and independently addressable control line. That is, to control (or tune) a first qubit (e.g., in a set of qubits of a QCS), a first control signal can be provided to the first qubit via a first control line terminating at the first qubit. Similarly, to control a second qubit (e.g., in a set of qubits of a QCS), a second control signal can be provided to the second qubit via a second control line terminating at the second qubit. Due to the physical proximity of the first qubit and the second qubit (and / or the first control line and the second control line) on the device implementing the set of qubits (and / or the associated control lines), the first qubit and the second qubit (and / or their associated control lines) can be electromagnetically coupled via parasitic capacitance, parasitic inductance, and / or other such electromagnetic (EM) coupling mechanisms. Thus, when an EM signal of sufficient frequency is transmitted to and / or from the first qubit and the second qubit, the first qubit and the second qubit (and / or their associated control lines) may be prone to "crosstalk". Such crosstalk between the first qubit and the second qubit can include inadvertently inducing an unwanted signal on a control line not associated with the qubit that the control signal is intended to control. That is, when a first control signal is provided to the first qubit via the first control line, at least a portion of the first control signal can couple to or parasitically drive (e.g., "leak" into) the second control line and / or otherwise be provided to the second qubit. The induced (or leaked) signal can cause an unintended operation within the qubit, resulting in a computational error. Embodiments relate to eliminating these qubit errors induced via such crosstalk. Note that physical adjacency of qubits or qubit control lines may not be a necessary condition for unwanted crosstalk to occur. Due to various EM coupling mechanisms, qubits and / or control lines do not need to be physically adjacent to produce crosstalk. The qubits and / or control lines need only be close enough such that the EM coupling mechanism is strong enough to induce unwanted crosstalk. Thus, as used herein, the term physical proximity (e.g., referring to qubits and / or control lines) is used to describe a situation where qubits and / or control lines are physically "close enough" such that the EM coupling mechanism is strong enough to induce unwanted crosstalk. The term "leakage" can refer to a situation where an EM coupling mechanism induces crosstalk in a way that disrupts the expected or intended behavior of the qubit and / or control line. That is, when unwanted and / or combined crosstalk occurs, it can be described as leakage.

[0025] Such crosstalk-induced errors may include inadvertently causing a second qubit to transition (or leak) the quantum state of one or more qubits out of the computational subspace of the QCS. In a non-limiting embodiment, the QCS relies on each qubit in its set of qubits being in any of the following: a "pure" state of one of its two lowest eigenstates (e.g., |0> and |1>), or a superposition of its pure states (e.g., α0|0> + α1|1>), where α0 and α1 ∈ C subject to the constraint The pure state |0> of a qubit can be referred to as the ground state of the qubit, and the other pure state |1> of the qubit can be referred to as the first excited state of the qubit. Thus, the computational subspace of such a QCS includes the tensor product: where N is a positive integer indicating the cardinality (or size) of the set of qubits. However, the quantum state space of many QCSs can be larger than the computational subspace. For example, some QCSs implement qubits using systems (or particles) with additional quantum eigenstates (e.g., additional excited states). Some QCSs implement qubits via a transmon, which is a quantum circuit implemented via a superconducting Josephson junction. A transmon can be modeled as a quantum harmonic oscillator (QHO) with an infinite number of eigenstates: |0>, |1>, |2>, |2>..., where the eigenstates: |2>, |3>... are excited states associated with an energy (or frequency) greater than the first excited state: |1>. The eigenstate |2> can be referred to as the second eigenstate of the qubit, the eigenstate |3> can be referred to as the third eigenstate of the qubit, and so on. Note that in other embodiments, the QCS may employ higher excited qubit states than just the first excited state such as |1>. For example, the QCS may compute using qubit states: 0>, |1>, |2> or other non-limiting ranges of states. Thus the term computational subspace may refer to 0>, |1>, |2> or other such ranges. The term computational subspace may refer to any set of qubit states used by the QCS for computation, and the term excitation subspace may refer to a disjoint set of qubit states not used by the QCS for computation. For example, in a non-limiting embodiment, the computational subspace may include the set of qubit states {0>, |1>}, while the excitation subspace includes the set of qubit states {2>, |3>,...}. In another non-limiting embodiment, the term computational subspace may refer to the set of qubit states {3>, |4>,...}. Depending on the range employed by the QCS, the terms computational subspace and excitation subspace may be defined for other ranges of qubit states. The term qubit subspace may refer to the set of qubit states: {0>, |1>}. The terms excitation subspace and leakage subspace may be used interchangeably therein.

[0026] The induced signal (or leakage signal) can induce the qubit to its second excited state, or even an excited state beyond the second excited state. When at least one qubit has transitioned to the second (or higher) excited state, it can be said that the qubit has transitioned (or leaked) into the excitonic subspace of the QCS. Note that the computational subspace of the QCS and the excitonic subspace of the QCS have no intersection. When a qubit has transitioned to the excitonic subspace of the QCS, the qubit may not be reliably used for quantum computing. Thus, when the first qubit is driven (or operated) by the first control signal, the induced signal can be transferred to the second qubit, causing the second qubit to transition (or leak) from the computational subspace into the excitonic subspace of the QCS. When this occurs, at least the second qubit may not be available for quantum computing, resulting in a quantum error induced by qubit crosstalk. In some embodiments, the qubits may not be suitable for high-performance quantum computing.

[0027] More specifically, when the first qubit is driven by a first control signal (e.g., a microwave control signal) on the control line of the first qubit, the second qubit may be inadvertently driven (or controlled) by the induced signal (e.g., via crosstalk-induced) on the associated control line of the second qubit (e.g., the second control line). That is, due to the physical proximity between the first qubit and the second qubit (and / or their associated control lines), a quantum computing error can be induced via crosstalk (e.g., parasitic coupling and / or leakage) between the first qubit and the second qubit. This embodiment eliminates at least a portion of such qubit-crosstalk-induced errors by providing a second control signal (e.g., a compensation control signal) to the second qubit, which "cancels" (e.g., compensates) the portion of the first control signal that leaks (via parasitic capacitance) into the second qubit. That is, when the first qubit is driven by the first control signal, the embodiment can provide a second control signal (e.g., a compensation signal) to the second qubit. The second control signal provided to the second qubit can at least partially compensate for the leakage of the first control signal to the second qubit. That is, the second control signal at least partially compensates for the leakage of the first control signal onto the second qubit, thereby eliminating potential crosstalk-induced errors in the second qubit.

[0028] Throughout the text, a first qubit (e.g., a qubit intended to be controlled by a first control signal) may be referred to as a source qubit. Since a second qubit (e.g., a qubit "inadvertently" controlled via the first control signal) is the target of a second control signal (e.g., a compensation signal), the second qubit may be referred to as a target qubit. The first control signal driving the source qubit may be referred to as a source signal, while the second control signal may be referred to as a compensation signal. In some embodiments, the source qubit may be referred to as an antagonistic qubit, and the portion of the first signal leaking (or induced) into the target qubit may be interchangeably referred to as an antagonistic signal, a leakage signal, an induced signal, and / or a parasitic signal. Note that driving a single source qubit via the source signal may inadvertently cause multiple target qubits to be driven inadvertently by the source signal leaking onto the drive line to the multiple target qubits. Their own compensation signals may be provided for each of the multiple target qubits to eliminate the errors in each of the multiple target qubits.

[0029] In addition to methods for eliminating such crosstalk-induced errors by providing a compensation signal to a second qubit, embodiments provide methods for calibrating such a compensation signal. Such methods can employ Ramsey interferometry, which characterizes the transition frequency and phase shift associated with transitioning a qubit to an excited state beyond its first excited state. That is, such calibration methods can be based on a Ramsey error filtering process that determines values for a set of compensation parameters that parameterize (or characterize) the compensation signal. An example method is a method for calibrating a compensation signal for mitigating crosstalk-induced errors in quantum computing, as discussed throughout the present document. The calibration method can be implemented by a QCS. The QCS can include a set of qubits. The method can include determining a pulse delay for a selection of consecutive pulses in a series of qubit rotation pulses applied to each qubit in the set of qubits. Note that the terms "pulse delay" and "time delay" can be used interchangeably throughout the present document. Each qubit rotation pulse in the series of qubit rotation pulses applied to the qubits in the set of qubits can generate a rotation of the quantum state of the qubit. The selected pulse delay can increase the probability that the applied series of qubit rotation pulses generates leakage of at least a portion of the set of qubits from the computational subspace of the QCS to the excited subspace of the QCS. The selected pulse delay can be an optimal pulse delay. As an optimal pulse delay, the selected pulse delay can at least approximately maximize the probability that the applied series of qubit rotation pulses generates leakage of at least a portion of the set of qubits from the computational subspace of the QCS to the excited subspace of the QCS. Each qubit rotation pulse in the series of rotation pulses applied to a qubit can be a pi rotation pulse. A pi rotation pulse can generate a rotation of the quantum state of the qubit. The generated rotation of the quantum state can be a rotation about at least one of the x-axis or y-axis of the Bloch sphere representation of the quantum state of the qubit.

[0030] The method can additionally include identifying qubit pairs in the set of qubits based on the selected pulse delay. The identified qubit pairs can contribute to leakage of a portion of the set of qubits from the computational subspace to the excited subspace. The qubit pairs can include a source qubit and a recipient qubit. The identified qubit pairs can be qubit pairs from all possible pairings of the set of qubits that dominate leakage of a portion of the set of qubits from the computational subspace to the excited subspace.

[0031] The method may further include determining values of a set of compensation parameters for a compensation signal using the identified qubit pairs. The set of compensation parameters may include a first parameter corresponding to the amplitude of the compensation signal and a second parameter corresponding to the phase of the compensation signal. When a control signal is provided to a source qubit and the compensation signal is provided to a recipient qubit, the control signal generates a reduced probability of leakage of the recipient qubit from a computational subspace to an excited subspace. Values of the set of compensation parameters for the compensation signal may be selected from a space of possible values of the set of compensation parameters. The selected value may be a value from the space of possible values that minimizes the probability of leakage of the recipient qubit from the computational subspace to the excited subspace generated by the control signal. The leakage of the recipient qubit from the computational subspace to the excited subspace may include a transition of the quantum state of the recipient qubit from a first excited state to a second excited state. Providing the compensation signal to the recipient qubit may compensate for an induced signal provided to the recipient qubit. The induced signal may be induced by the control signal provided to the source qubit. The compensation signal prevents leakage of the recipient qubit from the computational subspace to the excited subspace that would otherwise be caused by the induced signal.

[0032] An embodiment includes another method implemented by a QCS. The other method may be a method for mitigating errors induced by qubit crosstalk during quantum computing. The method may include determining to provide a control signal to a source qubit in a set of qubits for performing quantum computing by the QCS. In response to determining to provide the control signal to the source qubit, the control signal may be provided to the source qubit. Additionally, in response to determining to provide the control signal to the source qubit, a compensation signal may be provided to a recipient qubit in the set of qubits. The provided compensation signal may be according to (e.g., based on) values of a set of compensation parameters. Values of the set of compensation parameters may be determined such that providing the compensation signal to the recipient qubit compensates for an induced signal provided to the recipient qubit. The induced signal may be induced by the control signal provided to the source qubit. The compensation signal may prevent leakage of the recipient qubit from a computational subspace of the QCS to an excited subspace of the QCS that would otherwise be caused by the induced signal.

[0033] Values of the set of compensation signals may be determined according to any of the various embodiments discussed herein. For example, values of the set of compensation parameters may be determined based on a Ramsey error filtering process.

[0034] An embodiment includes a quantum computing system (QCS) (e.g., a quantum computing and / or quantum information processing device). At least in combination with Figure 1Various embodiments of a QCS are discussed. However, briefly stated here, a QCS can include a set of qubits, one or more processor devices (e.g., classical processor devices, quantum processor devices, or combinations thereof), and one or more memory devices. The one or more memory devices can store computer-readable instructions. When executed by the one or more processors, the instructions can cause the one or more processors to perform operations. The operations can include determining a pulse delay for a selection of consecutive pulses in a series of qubit rotation pulses applied to each qubit in the set of qubits. Each qubit rotation pulse in the series of qubit rotation pulses applied to the qubits in the set of qubits can generate a rotation of the quantum state of the qubit. The selected pulse delay can increase the probability that the applied series of qubit rotation pulses generates leakage of at least a portion of the set of qubits from the computational subspace of the QCS to the excited subspace of the QCS. The selected pulse delay can be an optimal pulse delay. As the optimal pulse delay, the selected pulse delay can at least approximately maximize the probability that the applied series of qubit rotation pulses generates leakage of at least a portion of the set of qubits from the computational subspace of the QCS to the excited subspace of the QCS. The operations can further include identifying qubit pairs in the set of qubits based on the selected pulse delay. The identified qubit pairs can contribute to leakage of a portion of the set of qubits from the computational subspace to the excited subspace. The qubit pairs can include a source qubit and a recipient qubit. The operations can further include using the identified qubit pairs to determine values of a set of compensation parameters for a compensation signal, wherein when a control signal is provided to the source qubit and the compensation signal is provided to the recipient qubit, the control signal generates a reduced probability of leakage of the recipient qubit from the computational subspace to the excited subspace.

[0035] Aspects of the present disclosure provide various technical effects and benefits. For example, embodiments mitigate (or eliminate) errors in quantum computing performed by a QCS and / or a quantum computing device (e.g., qubit crosstalk-induced errors). Accordingly, the performance of a QCS employing such embodiments is significantly improved because the QCS is less error-prone when performing quantum computing.

[0036] Figure 1 An example quantum computing system 100 is depicted. Quantum computing system 100 is an example of a system of one or more classical computers and / or quantum computing devices located at one or more locations in which the systems, components, and techniques described below can be implemented. One of ordinary skill in the art, using the disclosure provided herein, will understand that other quantum computing devices or systems can be used without departing from the scope of the present disclosure.

[0037] The quantum computing system 100 includes quantum hardware 102 that communicates data with one or more classical processors 104. The classical processor 104 can be configured to execute computer-readable instructions stored in one or more memory devices to perform operations, such as any of the operations described herein. The quantum hardware 102 includes components for performing quantum computing. For example, the quantum hardware 102 includes a quantum system 110, a control device 112, and a readout device 114 (e.g., a readout resonator). The quantum system 110 can include one or more multi-level quantum subsystems, such as a register of qubits (e.g., qubit 120). In some implementations, the multi-level quantum subsystem can include superconducting qubits, such as flux qubits, charge qubits, transmon qubits, gmon qubits, spin-based qubits, etc.

[0038] The type of multi-level quantum subsystem utilized by the quantum computing system 100 can vary. For example, in some cases, it may be convenient to include one or more readout devices 114 attached to one or more superconducting qubits (e.g., transmon qubits, flux qubits, gmon qubits, xmon qubits, or other qubits). In other cases, ion traps, photonic devices, or superconducting cavities (e.g., in which it may be possible to prepare states without the need for qubits) can be used. Further examples of implementations of multi-level quantum subsystems include fluxmon qubits, silicon quantum dots, or phosphorus-doped quantum dots.

[0039] A quantum circuit can be constructed and applied to the qubit register included in the quantum system 110 via a plurality of control lines coupled to one or more control devices 112. Example control devices 112 for operating on the qubit register can be used to implement quantum gates or quantum circuits having multiple quantum gates, such as Pauli gates, Hadamard gates, controlled-NOT (CNOT) gates, controlled-phase gates, T gates, multi-qubit quantum gates, coupler quantum gates, etc. One or more control devices 112 can be configured to operate on the quantum system 110 via one or more respective control parameters (e.g., one or more physical control parameters). For example, in some implementations, the multi-level quantum subsystem can be a superconducting qubit, and the control device 112 can be configured to provide control pulses to the control lines to generate a magnetic field to adjust the frequency of the qubit.

[0040] The quantum hardware 102 may further include a readout device 114 (e.g., a readout resonator). The measurement result 108 obtained via the measurement device may be provided to the classical processor 104 for processing and analysis. In some implementations, the quantum hardware 102 may include a quantum circuit, and the control device 112 and the readout device 114 may implement one or more quantum logic gates that operate on the quantum computing system 100 through physical control parameters (e.g., microwave pulses), which are sent through wires included in the quantum hardware 102. Further examples of control devices include arbitrary waveform generators, where a DAC (digital-to-analog converter) creates the signal.

[0041] The readout device 114 may be configured to perform a quantum measurement on the quantum system 110 and send the measurement result 108 to the classical processor 104. Additionally, the quantum hardware 102 may be configured to receive data from the classical processor 104 specifying the values 106 of the physical control qubit parameters. The quantum hardware 102 may use the received physical control qubit parameter values 106 to update the actions of the control device 112 and the readout device 114 on the quantum system 110. For example, the quantum hardware 102 may receive data that specifies a new value representing the voltage intensity of one or more DACs included in the control device 112, and the quantum hardware may update the actions of the DAC on the quantum system 110 accordingly. The classical processor 104 may be configured to initialize the quantum system 110 in an initial quantum state, for example, by sending data specifying a set of initial physical control qubit parameters 106 to the quantum hardware 102.

[0042] In some implementations, the readout device 114 may utilize the impedance difference between the |0> and |1> states of elements (such as qubits) of the quantum system to measure the state of the elements (e.g., qubits). For example, due to the non-linearity of the qubit, when the qubit is in the state |0> or the state |1>, the resonance frequency of the readout resonator may adopt different values. Therefore, the microwave pulse reflected from the readout device 114 carries an amplitude and a phase shift that depend on the qubit state. In some implementations, a Purcell filter may be used in combination with the readout device 114 to block the propagation of microwaves at the qubit frequency.

[0043] In some embodiments, the quantum system 110 may include, for example, a plurality of qubits 120 arranged in a two-dimensional grid 122. For clarity, Figure 1The two-dimensional grid 122 depicted in A includes 4×4 qubits. However, in some implementations, the quantum system 110 may include a smaller or larger number of qubits. In some embodiments, multiple qubits 120 may interact with each other via multiple qubit couplers (such as qubit coupler 124). The qubit couplers may define nearest-neighbor interactions between the multiple qubits 120. In some implementations, the strength of the multiple qubit couplers is an adjustable parameter. In some cases, the multiple qubit couplers included in the quantum computing system 100 may be couplers with a fixed coupling strength.

[0044] In some implementations, the multiple qubits 120 may include data qubits (such as qubit 126) and measurement qubits (such as qubit 128). Data qubits are qubits that participate in the calculations being performed by the quantum computing system 100. Measurement qubits are qubits that can be used to determine the results of the calculations performed by the data qubits. That is, during the calculation process, the unknown state of the data qubits is transferred to the measurement qubits using appropriate physical operations and measured via appropriate measurement operations performed on the measurement qubits.

[0045] In some implementations, each qubit in the multiple qubits 120 may be operated using a corresponding operating frequency, such as an idle frequency and / or an interaction frequency and / or a readout frequency and / or a reset frequency. The operating frequencies of different qubits may be different. For example, each qubit may idle at a different operating frequency. The operating frequencies of the qubits 120 may be selected before performing the calculations.

[0046] Figure 1 An example quantum computing system is depicted that can be used to implement the methods and operations in accordance with example aspects of the present disclosure. Other quantum computing systems may be used without departing from the scope of the present disclosure.

[0047] Figure 2AIllustrates an example first qubit 200 according to various embodiments. The first qubit 200 may be a transmon qubit (e.g., a qubit implemented by a transmon superconducting circuit). The transmon circuit implementing the first qubit 200 may include a first microwave drive 202 that drives a first control signal (e.g., a first microwave pulse V1(t)) along a first control line 204. This first control signal may be transmitted to the first qubit 200 via the first control line 204. To control the transmission of the first control signal to the first qubit 200, a first control line capacitor 206 may be positioned along the first control line 204. That is, the first control line capacitor 206 may capacitively couple the transmission capacitance of the first control signal to the first qubit 200. The first control line 204 may terminate at a first qubit loop 210 of the transmon circuit. The first qubit loop 210 includes a first qubit capacitor 212 and a first qubit Josephson junction pair 214. The first qubit loop 210 may be tied to a first qubit ground 216 such that the first qubit 200 does not float.

[0048] In various embodiments, qubits (e.g., Figure 2B the first qubit 200 and / or the second qubit 220) may be employed to implement quantum logic gates (e.g., Pauli-X gate, Pauli-Y gate, Pauli-Z gate, Hadamard gate, etc.). In other embodiments, the first qubit 200 (and / or the second qubit 220) may be used as an information encoding mechanism for quantum computing. Whether used as a quantum logic gate or an information encoding mechanism, a quantum computing system (QCS) of a quantum computing system 100 such as but not limited to Figure 1 may employ the first qubit 200 and / or the second qubit 220 when performing quantum computing and / or quantum information processing operations. Controlling the amplitude and phase of the first control signal (e.g., V1(t)) may selectively enable the implementation of quantum logic gates and / or enable the first qubit 200 to function as an information encoding mechanism. As described above, the first control line capacitor 206 may capacitively couple the first control signal (e.g., a microwave pulse) to the first qubit 200. Thus, the first microwave pulse implements the first quantum logic gate and / or the first information encoding mechanism.

[0049] Figure 2B Illustrates, according to various embodiments, positioned at Figure 2AAn example second qubit 220 in close proximity to the first qubit 200. For example, the first qubit 200 and the second qubit 220 may be located on a quantum integrated circuit (QIC). The second qubit 220 may be equivalent to (or at least similar to) the first qubit 200. In some embodiments, the qubits (e.g., the first qubit 200 and the second qubit 220) may have equivalent, similar, or different architectures that are similar enough such that there is a possibility of crosstalk. Thus, the second qubit 220 may be a transmon qubit. In other embodiments, the second qubit 220 may not be a transmon qubit, but the possibility of crosstalk between the first qubit 200 and the second qubit 220 may be a concern. Similar to the first qubit 200, the transmon circuit implementing the second qubit 220 may include a second microwave drive 222 that drives a second control signal (e.g., a second microwave pulse V2(t)) along a second control line 224. The second control signal may be transmitted to the second qubit 220 via the second control line 224. To control the transmission of the second control signal to the second qubit 220, a second control line capacitor 226 may be positioned along the second control line 224. The second control line 224 may terminate at a second qubit loop 230 of the transmon circuit. The second qubit loop 230 includes a second qubit capacitor 232 and a second qubit Josephson junction pair 234. The second qubit loop 230 may be tied to a second qubit ground 236.

[0050] The first control signal 218 (e.g., a microwave pulse transmitted along the first control line 204 to control the first qubit 200) is shown as an arrow Figure 2B transmitting along the first control line 204 of the first qubit 200. The first control signal 218 has a general functional form (e.g., as a function of time): V1(t) = V1·cos(ω1·t + φ1), where V1 indicates the amplitude of the first control signal 218, ω1 indicates the frequency of the first control signal 218, and φ1 indicates the phase shift associated with the first control signal 218. Similarly, the second control signal 238 (e.g., a microwave pulse transmitted along the second control line 224 to control the second qubit 220) is shown in Figure 2BAn arrow is shown above traveling along a second control line 224 of a second qubit 220. The second control signal 238 has a general functional form V2(t) = V2·cos(ω2·t + φ2), where V2 indicates the amplitude of the second control signal 238, ω2 indicates the frequency of the second control signal 238, and φ2 indicates the phase shift associated with the second control signal 238. In various embodiments, the values of the parameters of the first control signal 218 (e.g., V1, ω1, φ1) are calibrated (or tuned) to various characteristics of the first qubit 200, while the values of the parameters of the second control signal 238 (e.g., V2, ω2, φ2) are calibrated (or tuned) to various characteristics of the second qubit 220.

[0051] Figure 2C depicts, according to various embodiments, Figure 2B the parasitic electromagnetic (EM) coupling between a first qubit 200 and a second qubit 220. That is, Figure 2C illustrates the parasitic EM coupling between the first qubit 200 and the second qubit 220, where a first control signal 218 (e.g., for driving the first qubit 200) parasitically couples to the second qubit 220. The parasitic EM coupling of the first control signal 218 to the second qubit 220 generates an induced signal 240 (e.g., a leakage signal or an antagonistic signal) along the second control line 224. The induced signal 240 follows the general form of the first control signal 218, where the amplitude and phase shift of the first control signal 218 are modified (e.g., reduced). Thus, the general functional form of the induced signal 240 takes the form V P (t) = |r|·V1·cos cos(ω1·t + φ1 + δ φ )), where |r| < 1 indicates the reduction (e.g., due to weak parasitic coupling between the two qubits) of the amplitude of the first control signal 218, δ φ indicates the additional phase shift induced via parasitic coupling, and the subscript P indicates the parasitic (or induced) signal.

[0052] Figure 2D depicts Figures 2B to 2C the induced leakage (or transition) of the second qubit 220 from the computational subspace to the excited subspace, which is induced by Figures 2B to 2C the first control signal. As described throughout the text, transmon qubits (e.g., the first qubit 200 and / or the second qubit 220) can be modeled as quantum harmonic oscillators (QHOs). Figure 2DShows the potential well of the second qubit (modeled as a QHO) and the energy levels 260 of this potential well. The energy levels 260 of the second qubit 220 at least include the ground state 262 (e.g., indicated as the eigenstate |0>), the first excited state 264 (e.g., indicated as the eigenstate |1>), and the second excited state 266 (e.g., indicated as the eigenstate |2>). For simplicity, higher excited states of the second qubit 220 exist, but are omitted in Figure 2D . The ground state 262 and the first excited state 264 can be located within the computational subspace of the QCS employing the second qubit 220, while the second excited state 266 (and higher excited states) are located outside the computational subspace. That is, the second excited state 266 can be located within the excitation subspace. The excitation subspace can include the quantum states associated with the second excited state 266, as well as Figure 2D any higher excited states not shown in

[0053]

[0054] Figure 2C T P (t) = V2(t) + V(t) = V1·cos cos(ω1·t + φ1) + |r|V1·cos cos(ω1·t + φ1 + δ(t) = V1·cos cos(ω1·t + φ1) + |r|V1·cos cos(ω1·t + φ1 + δ φ ), where the subscript T indicates the total signal provided to the second qubit 220. Note that although not explicitly shown in Figure 2C , the second control signal 238 can induce additional induced signals on the first control line 204. Additionally, in some embodiments, V2 = 0 or V1 = 0. That is, in some embodiments, only one of the two qubits 200 / 220 is actively driven by a control signal. For example, the second control signal 238 can be absent, and thus the total signal transmitted to the second qubit 220 is the induced signal 240, e.g., V T (t) = VP I(t)=|r|V1·cos cos(ω1·t + φ1+δ φ )。

[0055] Figure 2E Depicts alleviating, according to various embodiments, the induced leakage generated from the computational subspace by applying a compensation signal 242 to the second qubit 220. More specifically, in response to providing a first control signal 218 to the first qubit 200 and the induction of an induced signal 240 transmitted to the second qubit, a second microwave drive 222 provides a compensation signal 242 to the second qubit 220. That is, the compensation signal 242 is transmitted along the second control line 224 to the second qubit 220. The compensation signal is tuned and / or calibrated to at least partially compensate for and / or at least partially cancel the effect of the induced signal 240. The functional form of the compensation signal 242 is: V Figure 2D (t)=|r|V1·cos cos(ω1·t + φ1+δ C (t)=|r|V1·cos cos(ω1·t + φ1+δ φ +π) where the subscript C indicates the compensation and / or cancellation effect of the compensation signal 242. Note that periodic functions (e.g., sin sin and cos cos) are anti-symmetric under a π rotation (or phase shift). Thus, the superposition of the induced signal 240 and the compensation signal 242 is at least approximately zero, e.g., V P (t)+V C (t)≈0. Thus, the compensation signal 242 can at least partially cancel the errors induced by qubit crosstalk. Thus, the compensation signal 242 can be referred to as a cancellation signal (or tone). Figures 3A to 3D Discusses a Ramsey-interference-based method for calibrating such compensation signals for a set of qubits employed by a QCS (e.g., Figure 1 the quantum computing system 100).

[0056] Note that the control signal, the induced signal, and the compensation signal can be modeled via complex functions. When transformed to the complex plane via Euler's formula, the functional form of manipulating periodic signals can be easier. It can be understood that a real signal can be interpreted as the pure real or pure imaginary part of a complex function when represented as a complex function. For example, the first control signal 218 can be represented as: And the compensation signal 242 can be represented as: V C (t)=V1(t)·|r|·e i·θ , where θ≡δ φ +π. Figures 3A to 3D Shows a Ramsey-interference-based method for determining (or calibrating) by a QCS (e.g., Figure 1Values of a set of compensation parameters (e.g., (r, θ)) for qubit pairs in a set of qubits implemented and / or employed by the quantum computing system 100). The set of compensation parameters includes at least a first parameter corresponding to the amplitude of the compensation signal (e.g., r) and a second parameter corresponding to the phase of the compensation signal (e.g., θ).

[0057] Figure 3A Depicts Ramsey error filtering pulse sequences according to various embodiments that are applied to qubits to calibrate a compensation signal to mitigate qubit crosstalk-induced errors. In Figure 3A a series of qubit rotation pulses are applied to at least two qubits in the set of qubits (e.g., at least one receiver qubit and at least one source qubit). Each qubit rotation pulse in the series of qubit rotation pulses applied to a qubit generates a rotation of the quantum state of that qubit (e.g., a π rotation). Note that the pulse sequence can be applied simultaneously to multiple “source” (or antagonist) qubits to determine the effect on at least one receiver qubit. In fact, the sequence of applied pulses can be applied simultaneously to all qubits in the set of qubits. As Figure 3A shown, consecutive pulses of the series of pulses are separated by a delay time (t). The pulses can be Ramsey error filtering pulses. The Ramsey error filtering pulse sequence (or series of Ramsey error filtering pulses) can consist of π rotation pulses that are separated by a variable delay t. The π rotation pulses applied to a qubit can generate a rotation about at least one of the x-axis or y-axis of the Bloch sphere representation of the quantum state of the qubit. For example, a π rotation pulse can generate a quantum state transition |0> → |1> or a quantum state transition |1> → |0>. Such rotations may generate resonance effects that cause coherent leakage of the qubit from the computational subspace to the excited subspace.

[0058] The applied pulse sequence can be repeated several times to amplify the coherent leakage, which can be observed by directly measuring the quantum state of one or more receiver qubits. A measurement of |2> (or higher excited state) indicates that the qubit has transitioned to an excited state outside the computational subspace. For certain delay times t, the sequence amplifies the coherent crosstalk leakage to facilitate calibration. This amplification can be understood as the result of constructive interference between the leakage amplitudes induced by consecutive pulses.

[0059] That is,[[]] Figure 3AIt shows iteratively providing a series of qubit rotation pulses to at least a portion of the qubits in the qubit set. During each iteration of providing the series of qubit rotation pulses, the pulse delay between consecutive pulses in the series of qubit rotation pulses remains constant. Between consecutive iterations of providing the series of qubit rotation pulses to the qubits, the pulse delay varies. During iteratively providing the series of qubit rotation pulses to each qubit in the qubit set, a window of pulse delay values is swept. In response to each iteration of providing the series of qubit rotation pulses to the qubits, the quantum states of at least a portion of the qubits can be measured. Each iteration corresponds to a specific value of the pulse delay within the window of pulse delay values.

[0060] In response to measuring the quantum states of each qubit in the qubit set for an iteration corresponding to a specific pulse delay, the probability of generating a transition of the quantum state of the qubit set from the ground state or the first excited state to one or more higher excited states for the specific pulse delay is measured. This probability can be referred to as the leakage probability (p2). The leakage probability (e.g., p2) can be measured as the fraction of qubits in the qubit set that transition to |2> (or higher excited states) via the application of a series of pulses. The leakage probability can be measured as a function of the pulse delay.

[0061] Figure 3B It shows representative data of Ramsey error filtering versus the delay time t. Figure 3B The curve graph shows the measurement of the leakage probability (e.g., p2) as a function of the pulse delay (e.g., t). This data can be acquired while driving all qubits in parallel to minimize the data acquisition time. More specifically, Figure 3B The curve graph shows the leakage probability p2 versus t during Ramsey error filtering. The t (e.g., the optimal pulse delay, as indicated as the optimal t in the curve graph) that at least approximately maximizes the leakage probability is identified. The optimal pulse delay can be identified as the pulse delay within the pulse delay window that at least approximately maximizes the probability of generating a transition of the quantum state of the qubit set from the first populated state to one or more higher excited states. The optimal pulse delay and / or the optimal t can be referred to as the selected pulse array throughout the process.

[0062] The optimal pulse delay is used for the entire remaining portion of the calibration sequence. That is, for subsequent steps in the calibration (as Figures 3C to 3D shown), t is held fixed at a value that at least approximately maximizes the leakage population and / or the leakage probability (e.g., p2). More specifically, Figure 3BThe curve diagram shows the determination of the optimal pulse delay for successive pulses in a series of qubit rotation pulses applied to qubits. The optimal pulse delay increases the probability (e.g., at least approximately maximizes the probability) of leakage of a set of qubits generated by the applied series of qubit rotation pulses from the computational subspace of the QCS (or qubit) to the excited subspace of the QCS (or qubit). The leakage of the receiver qubit from the computational subspace to the excited subspace includes the transition of the quantum state of the receiver qubit from the first excited state to the second excited state (or higher excited states).

[0063] Figure 3C Shows the typical output of Ramsey error filtering at the optimal t during paired operations for all possible pairs including the receiver qubit. This data identifies the source of parasitic drive. That is,[ Figure 3C The curve graph is a graph of p2 versus the source qubit during paired operations at the optimal t. The peak identifies the main source of leakage. More specifically, the curve graph shows the relationship of p2 versus the source qubit during paired operations at the optimal t. The peak identifies the main source. During paired operations with the main source, p2 after Ramsey error filtering versus the amplitude r and phase θ of the compensation tone for eliminating crosstalk leakage. Data for generating the Figure 3C curve graph can be obtained by selecting a qubit from the set of qubits as the target qubit and selecting another qubit as the source qubit for each data point on the x-axis. Therefore,[ Figure 3C The curve graph can be used to determine the maximum leakage source (to the excited subspace) of a specific target qubit. Therefore, to characterize the entire set of qubits, for each qubit in the set of qubits, generate Figure 3C the curve graph. The qubit corresponding to the Figure 3C curve graph can be regarded as the target qubit. Data can be obtained by providing a sequence of qubit rotation pulses to qubit pairs, where the pulse delay is set to the optimal pulse delay (or the selected pulse delay) found via the Figure 3B curve graph.

[0064] Can adopt Figure 3C the curve graph to identify, based on the optimal pulse delay (or the selected pulse delay), the qubit pairs in the set of qubits that contribute to the leakage of the set of qubits from the computational subspace to the excited subspace. The qubit pairs include the source qubit and the receiver qubit. Note that each data point along the x-axis corresponds to a separate qubit pair, but the target qubit remains constant along the x-axis. Therefore, each data point along the x-axis can correspond to a different source qubit in the qubit pair. As described above, for each qubit in the set of qubits, generate Figure 3C the curve graph. The qubit corresponding to the Figure 3CThe qubit corresponding to the curve can be used as the target qubit in the qubit pair associated with each data point along the x-axis.

[0065] More specifically, qubit pairs (with a specific receiver qubit) can be identified by generating Figure 3D the curve for each possible specific receiver qubit. Each possible qubit pair can be iteratively selected from the set of all possible qubit pairings. Each selected possible qubit pair includes a first qubit (e.g., the source qubit) and a second qubit (e.g., the receiver qubit). For each selected possible qubit pair, a series of qubit rotation pulses can be provided to at least one of the first qubit and the second qubit in the selected possible qubit pair according to (e.g., based on) the optimal (or selected) pulse delay. In response to providing a series of qubit rotation pulses to each of the first qubit and the second qubit, the quantum state of at least one of the first qubit and the second qubit in the selected possible qubit pair can be measured. For each selected possible qubit pair and based on measuring the quantum state of each of the first qubit and the second qubit, the probability of the transition of the quantum state of at least one of the first qubit or the second qubit generated by the provided series of qubit rotation pulses according to (e.g., based on) the optimal pulse delay to the second excited state (or a higher excited state) can be measured. As Figure 3C shown in the curve of, such qubit pairs in the set of qubits can be identified: the qubit pair that at least approximately maximizes the probability of the transition of the quantum state of at least one of the first qubit or the second qubit generated by the provided series of qubit rotation pulses according to (e.g., based on) the optimal pulse delay to the second excited state. The identified qubit pair can be a qubit pair from all possible pairings of the set of qubits, and the qubit pair dominates the leakage of the set of qubits from the computational subspace to the excited subspace.

[0066] Figure 3D Shows p2 on the receiver qubit relative to the amplitude r and phase θ of the compensation tone during paired operation with the dominant source qubit at the optimal t. The asterisk indicates the optimal r and θ used to mitigate crosstalk-induced leakage. That is, during paired operation at the optimal t, the phase space of the curve of p2 relative to the source qubit in the figure. The peak identifies the main source. During paired operation with the main source, p2 after Ramsey error filtering relative to the amplitude r and phase θ of the compensation tone used to eliminate crosstalk leakage.

[0067] Figure 3DThe curve graph can be used to determine the values of the set of compensation parameters for the compensation signal. When a control signal is provided to the source qubit and a compensation signal is provided to the recipient qubit, the control signal generates a reduced (e.g., minimized) probability of leakage of the recipient qubit from the computational subspace to the excited subspace. The value of the set of compensation parameters for the compensation signal is selected from the space of possible values of the set of compensation parameters, as shown in Figure 3D the curve graph shown. The selected value is a value from the space of possible values that minimizes the probability of leakage of the recipient qubit from the computational subspace to the excited subspace generated by the control signal.

[0068] In some embodiments, after calibrating the compensation signal, quantum computing can be performed by the QCS. To perform quantum computing by the QCS, it can be determined to provide a control signal to the first qubit (e.g., the source qubit). In response to determining to provide a control signal to the source qubit, a control signal can be provided to the source qubit. Additionally, in response to determining to provide a control signal to the source qubit, a compensation signal can be provided to the second qubit (e.g., the recipient qubit). The provided compensation signal can be based on (e.g., according to) the determined value of the set of compensation parameters for the qubit pair. Providing the compensation signal to the recipient qubit can compensate for the induced signal provided to the recipient qubit. The compensation signal can prevent leakage of the recipient qubit from the computational subspace to the excited subspace that would otherwise be caused by the induced signal. The induced signal can be induced by the control signal provided to the source qubit.

[0069] Method

[0070] Figures 4 to 5 The operations are depicted in a particular order for purposes of illustration and discussion. Those of ordinary skill in the art, using the disclosure provided herein, will understand that the operations of any of the methods described herein can be extended, including steps that are not illustrated, omitted, rearranged, and / or modified in various ways without departing from the scope of the present disclosure. Figure 4 Method 400 and Figure 5 Method 500 can be implemented using any suitable quantum computing system - such as the system described in Figure 1 - to be realized.

[0071] Figure 4 A flowchart of method 400 for calibrating a compensation signal to mitigate qubit crosstalk-induced errors according to various embodiments is provided. Method 400 begins at block 402, where a series of qubit rotation pulses are applied to each qubit in a set of qubits. Each qubit rotation pulse is applied to the qubit to generate a rotation of the quantum state of the qubit. At least in combination with Figure 3AA series of qubit rotation pulses applied to qubits is discussed. Each qubit rotation pulse in the series of rotation pulses applied to the qubits can be a pi rotation pulse. The rotation of the quantum state of a qubit can be a rotation about at least one of the x-axis or the y-axis of the Bloch sphere representation of the quantum state of the qubit.

[0072] At block 404, a selected pulse delay for consecutive pulses in the series of qubit rotation pulses applied to each qubit in the set of qubits is determined. At least in combination with Figure 3A The determination of the selected pulse delay is discussed. However, briefly, here, the selected pulse delay increases (e.g., at least approximately maximizes) the probability that the applied series of qubit rotation pulses generates leakage of the set of qubits from the computational subspace of the QCS to the excited subspace of the QCS. The selected pulse delay can be an optimal pulse delay. As the optimal pulse delay, the selected pulse delay can at least approximately maximize the probability that the applied series of qubit rotation pulses generates leakage of at least a portion of the set of qubits from the computational subspace of the QCS to the excited subspace of the QCS. Note that the terms "pulse delay" and "time delay" can be used interchangeably throughout the text.

[0073] At block 406, based on the selected pulse delay, qubit pairs in the set of qubits that contribute to (e.g., at least approximately maximize) the leakage of the set of qubits from the computational subspace to the excited subspace are identified. The identified qubit pairs can include a source qubit and a receiver qubit. At least in combination with Figure 3C the identification of such qubit pairs is discussed. The identified qubit pairs that contribute to the leakage of the set of qubits from the computational subspace to the excited subspace can be the qubit pairs among all possible pairings of the set of qubits that dominate the leakage of the set of qubits from the computational subspace to the excited subspace.

[0074] At block 408, the identified qubit pairs are used to determine values of a set of compensation parameters for a compensation signal. At least in combination with Figure 3D the determination of the values of the set of compensation parameters is discussed. When a control signal is provided to the source qubit and a compensation signal is provided to the receiver qubit, the control signal reduces (e.g., minimizes) the probability that the receiver qubit leaks from the computational subspace to the excited subspace. The leakage of the receiver qubit from the computational subspace to the excited subspace can include a transition of the quantum state of the receiver qubit from a first excited state to a second excited state. The set of compensation parameters can include a first parameter corresponding to the amplitude of the compensation signal and a second parameter corresponding to the phase of the compensation signal.

[0075] Figure 5A flowchart of a method 500 for mitigating qubit crosstalk-induced errors in a quantum computing system (QCS) in accordance with various embodiments is provided. Method 500 begins at block 502, where, for a quantum computation to be performed by the QCS, it is determined that a control signal is to be provided to a source qubit in a set of qubits. At block 504, in response to determining that a control signal is to be provided to the source qubit, the control signal may be provided to the source qubit. At block 506, in response to determining that a control signal is to be provided to the source qubit, a compensation signal may be provided to a recipient qubit in the set of qubits. The compensation signal provided is based on (e.g., determined by) values of a set of compensation parameters. The values of the set of compensation parameters are determined such that providing the compensation signal to the recipient qubit compensates for the induced signal provided to the recipient qubit. The compensation signal prevents leakage of the recipient qubit from the computational subspace of the QCS to the excitation subspace of the QCS, which otherwise would be caused by the induced signal. The induced signal is induced by the control signal provided to the source qubit.

[0076] Additional Embodiments

[0077] The digital, classical, and / or quantum subjects described in this specification, as well as the implementation of digital function operations and quantum operations, may be implemented in digital electronic circuitry, in suitable quantum circuitry or more generally a quantum computing system, in tangibly implemented digital and / or quantum computer software or firmware, in digital and / or quantum computer hardware (including the structures disclosed in this specification and their structural equivalents), or in a combination of one or more of them. The term "quantum computing system" may include, but is not limited to, a quantum computer / computing system, a quantum information processing system, a quantum cryptography system, or a quantum simulator.

[0078] The implementation of the digital and / or quantum subjects described in this specification may be implemented as one or more digital and / or quantum computer programs, i.e., one or more modules of digital and / or quantum computer program instructions encoded on a tangible non-transitory storage medium for execution by, or to control the operation of, a data processing apparatus. The digital and / or quantum computer storage medium may be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, one or more qubit / qubit structures, or a combination of one or more of them. Alternatively or additionally, the program instructions may be encoded on an artificially generated propagated signal (e.g., a machine-generated electrical, optical, or electromagnetic signal) capable of encoding digital and / or quantum information, the artificially generated propagated signal being generated to encode digital and / or quantum information for transmission to an appropriate receiver device for execution by the data processing apparatus.

[0079] The terms quantum information and quantum data refer to information or data carried, held, or stored by a quantum system, where the smallest non-trivial system is a qubit, i.e., the system that defines the unit of quantum information. It should be understood that the term "qubit" encompasses all quantum systems that can be appropriately approximated as two-level systems in the corresponding context. Such quantum systems can include multi-level systems, e.g., having two or more levels. By way of example, such systems can include atoms, electrons, photons, ions, or superconducting qubits. In many implementations, the computational basis states are identified with the ground state and the first excited state. However, it should be understood that other settings where the computational states are identified with higher-level excited states (e.g., qubits) are also possible.

[0080] The term "data processing device" refers to digital and / or quantum data processing hardware and includes all types of devices, apparatuses, and machines for processing digital and / or quantum data, such as including programmable digital processors, programmable quantum processors, digital computers, quantum computers, or multiple digital and quantum processors or computers, and combinations thereof. The device can also be or further include dedicated logic circuitry, such as an FPGA (field-programmable gate array) or an ASIC (application-specific integrated circuit), or a quantum simulator, i.e., a quantum data processing device designed to simulate or generate information about a particular quantum system. Specifically, a quantum simulator is a special-purpose quantum computer that does not have the ability to perform general quantum computing. In addition to the hardware, the device can optionally include code that creates an execution environment for digital and / or quantum computer programs, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them.

[0081] A digital or classical computer program, which can also be referred to as or described as a program, software, software application, module, software module, script, or code, can be written in any form of programming language (including compiled or interpreted languages or declarative or procedural languages); and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a digital computing environment. A quantum computer program, which can also be referred to as or described as a program, software, software application, module, software module, script, or code, can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and translated into a suitable quantum programming language, or can be written in a quantum programming language such as QCL, Quipper, Cirq, etc.

[0082] A digital and / or quantum computer program may or may not correspond to a file in a file system. The program may be stored as part of a file that holds other programs or data (such as one or more scripts stored in a markup language document), in a single file dedicated to the program in question, or in multiple coordinated files (such as files that store one or more modules, subroutines, or portions of code). A digital and / or quantum computer program may be deployed to execute on one digital computer or one quantum computer or on multiple digital and / or quantum computers, which are located at one site or distributed across multiple sites and interconnected by a digital and / or quantum data communication network. A quantum data communication network is understood to be a network that can transmit quantum data using a quantum system (such as qubits). Generally, a digital data communication network cannot transmit quantum data, while a quantum data communication network can transmit both quantum data and digital data simultaneously.

[0083] The processes and logical flows described in this specification may be executed by one or more programmable digital and / or quantum computers operating in conjunction with one or more digital and / or quantum processors, which, in appropriate cases, execute one or more digital and / or quantum computer programs to perform functions by operating on input digital and quantum data and generating output. The processes and logical flows may also be executed by dedicated logic circuitry (such as an FPGA or ASIC or quantum simulator), and the apparatus may also be implemented as the dedicated logic circuitry system, or by a combination of the dedicated logic circuitry or quantum simulator and one or more programmed digital and / or quantum computers.

[0084] For a system of one or more digital and / or quantum computers or processors “configured to” or “operable to” perform a particular operation or action, it means that the system has installed thereon software, firmware, hardware, or a combination thereof that, in operation, causes the system to perform these operations or actions. For one or more digital and / or quantum computer programs configured to perform a particular operation or action, it means that the one or more programs include instructions that, when executed by a digital and / or quantum data processing device, cause the device to perform these operations or actions. A quantum computer may receive instructions from a digital computer that, when executed by the quantum computing device, cause the device to perform an operation or action.

[0085] A digital and / or quantum computer adapted to execute digital and / or quantum computer programs may be based on general-purpose or special-purpose digital and / or quantum microprocessors or both, or any other kind of central digital and / or quantum processing unit. Generally, the central digital and / or quantum processing unit will receive instructions and digital and / or quantum data from read-only memory, or random access memory, or a quantum system suitable for transmitting quantum data (such as photons), or a combination thereof.

[0086] Some example elements of a digital and / or quantum computer are a central processing unit for executing or implementing instructions and one or more memory devices for storing instructions and digital and / or quantum data. The central processing unit and the memory may be supplemented by, or incorporated into, a dedicated logic circuit or a quantum simulator. Generally, a digital and / or quantum computer will also include one or more mass storage devices for storing digital and / or quantum data, such as magnetic disks, magneto-optical disks, or optical disks, or a quantum system suitable for storing quantum information, or operatively coupled to receive digital and / or quantum data from, or transfer digital and / or quantum data to, or both, such mass storage devices. However, a digital and / or quantum computer need not have such devices.

[0087] Digital and / or quantum computer-readable media suitable for storing digital and / or quantum computer program instructions and digital and / or quantum data include all forms of non-volatile digital and / or quantum memories, media, and memory devices, including, for example, semiconductor memory devices such as EPROM, EEPROM, and flash memory devices; magnetic disks such as internal hard disks or removable disks; magneto-optical disks; and CD-ROM and DVD-ROM disks; and quantum systems such as trapped atoms or electrons. It should be understood that a quantum memory is a device capable of storing quantum data with high fidelity and high efficiency over a long period of time, such as a light-matter interface that utilizes light for transmission, matter for storage, and preserves quantum features such as superposition or quantum coherence of quantum data.

[0088] The control of the various systems or portions thereof described in this specification may be implemented in a digital and / or quantum computer program product that includes instructions stored on one or more tangible, non-transitory machine-readable storage media and executable on one or more digital and / or quantum processing devices. The systems or portions thereof described in this specification may be implemented separately as a device, a method, or an electronic system, which may include one or more digital and / or quantum processing devices and a memory for storing executable instructions to perform the operations described in this specification.

[0089] Although this specification contains many specific implementation details, these details should not be construed as limiting the scope of what may be claimed, but rather as descriptions of features specific to particular implementations. Certain features that are described in this specification in the context of separate implementations may also be implemented in combination within a single implementation. Conversely, the various features that are described in the context of a single implementation may also be implemented separately or in any suitable sub-combination in multiple implementations. Additionally, although the features are described above as acting in certain combinations and even initially claimed as such, one or more features from the claimed combination may in some cases be excluded from the combination, and the claimed combination may be directed to a sub-combination or variation of a sub-combination.

[0090] Similarly, although the operations are depicted in the drawings in a particular order, this should not be understood as requiring that the operations be performed in the particular order shown or in a sequential order, or that all of the illustrated operations be performed, to achieve the desired result. In some cases, multitasking and parallel processing may be advantageous. Additionally, the separation of the various system modules and components in the implementations described above should not be understood as requiring such separation in all implementations, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged in multiple software products.

[0091] Specific implementations of the subject matter have been described. Other implementations are within the scope of the appended claims. For example, the acts recited in the claims may be performed in a different order and still achieve the desired result. As one example, the processes depicted in the drawings do not necessarily require the particular order or sequential order shown to achieve the desired result. In some cases, multitasking and parallel processing may be advantageous.

Claims

1. A method for operating a quantum computing system QCS comprising a set of qubits, the method comprising: Determining a pulse delay for a selection of consecutive pulses in a series of qubit rotation pulses applied to each qubit in the set of qubits, wherein each qubit rotation pulse in the series of qubit rotation pulses applied to the qubits in the set of qubits generates a rotation of the quantum state of the qubit, and the selected pulse delay increases the probability of leakage of at least a portion of the set of qubits from a computational subspace of the QCS to an excited subspace of the QCS; and Based on the selected pulse delay, identifying qubit pairs in the set of qubits that contribute to the leakage of the set of qubits from the computational subspace to the excited subspace, wherein the qubit pair includes a source qubit and a receiver qubit; and Using the qubit pair to determine values of a set of compensation parameters for a compensation signal, wherein when a control signal is provided to the source qubit and the compensation signal is provided to the receiver qubit, the control signal generates a reduced probability of leakage of the receiver qubit from the computational subspace to the excited subspace.

2. The method of claim 1, further comprising: Determining to provide the control signal to the source qubit; In response to determining to provide the control signal to the source qubit, providing the control signal to the source qubit; And In response to determining to provide the control signal to the source qubit, providing the compensation signal to the receiver qubit, wherein the compensation signal is at least partially based on the values of the set of compensation parameters.

3. The method according to claim 1, wherein, The set of compensation parameters includes a first parameter corresponding to an amplitude of the compensation signal and a second parameter corresponding to a phase of the compensation signal.

4. The method according to claim 1, wherein, Each qubit rotation pulse in the series of qubit rotation pulses applied to the qubit is a pi rotation pulse, the pi rotation pulse generates a rotation of the quantum state of the qubit, and the rotation is about at least one of the x-axis or the y-axis of the Bloch sphere representation of the quantum state of the qubit.

5. The method according to claim 1, wherein, The leakage of the receiver qubit from the computational subspace to the excited subspace includes a transition of the quantum state of the receiver qubit from a first excited state to a second excited state.

6. The method according to claim 1, wherein, Determining the selected pulse delay includes: Iteratively providing the series of qubit rotation pulses to each qubit in the set of qubits, wherein during each iteration of providing the series of qubit rotation pulses, the pulse delay between the consecutive pulses in the series of qubit rotation pulses remains constant, and between consecutive iterations of providing the series of qubit rotation pulses to each qubit in the set of qubits, the pulse delay varies such that a pulse delay window is swept during the iterative provision of the series of qubit rotation pulses to each qubit in the set of qubits; In response to each iteration of providing the series of qubit rotation pulses to each qubit in the qubit set, measure the quantum state of each qubit in the qubit set, wherein the iteration corresponds to a specific pulse delay in the pulse delay window; In response to measuring the quantum state of each qubit in the qubit set for the iteration corresponding to the specific pulse delay, determine the probability of generating a transition of the quantum state of the qubit set from a first excited state to one or more higher excited states for the specific pulse delay; and Identify the selected pulse delay as the pulse delay in the pulse delay window that increases the probability of the transition of the quantum state of the qubit set from the first excited state to the one or more higher excited states.

7. The method according to claim 1, wherein, The qubit pair that contributes to the leakage of the qubit set from the computational subspace to the excitation subspace is the qubit pair that dominates the leakage of the qubit set from the computational subspace to the excitation subspace among all possible pairings of the qubit set.

8. The method according to claim 1, wherein, Identifying the qubit pair that contributes to the leakage of the qubit set from the computational subspace to the excitation subspace includes: Iteratively select each possible qubit pair from the set of all possible qubit pairings, wherein each selected possible qubit pair includes a first qubit and a second qubit; For each selected possible qubit pair, provide the series of qubit rotation pulses to each of the first qubit and the second qubit in the selected possible qubit pair according to the selected pulse delay; In response to providing the series of qubit rotation pulses to each of the first qubit and the second qubit, measure the quantum state of each of the first qubit and the second qubit in the selected possible qubit pair; For each selected possible qubit pair and based on measuring the quantum state of each of the first qubit and the second qubit, determine the probability of generating a transition of the quantum state of at least one of the first qubit or the second qubit to a second excited state by the series of qubit rotation pulses according to the selected pulse delay; and Identify such a qubit pair in the qubit set: the qubit pair maximizes the probability of generating a transition of the quantum state of at least one of the first qubit or the second qubit to the second excited state by the series of qubit rotation pulses according to the selected pulse delay.

9. The method according to claim 1, wherein The value of the set of compensation parameters of the compensation signal is selected from the possible value space of the set of compensation parameters, and the selected value is a value from the possible value space that minimizes the probability of the control signal generating leakage of the receiver qubit from the computational subspace to the excitation subspace.

10. The method according to claim 1, wherein The compensation signal provided to the recipient qubit compensates for the induced signal provided to the recipient qubit such that the compensation signal prevents leakage of the recipient qubit from the computational subspace to the excited subspace, which otherwise would be caused by the induced signal, and the induced signal is induced by the control signal provided to the source qubit.

11. A method for operating a quantum computing system QCS comprising a set of qubits, the method comprising: Determining a control signal to be provided to a source qubit in the set of qubits; In response to determining that the control signal is to be provided to the source qubit, providing the control signal to the source qubit; And In response to determining that the control signal is to be provided to the source qubit, providing a compensation signal to a recipient qubit in the set of qubits, wherein the provided compensation signal is at least partially based on values of a set of compensation parameters, and the values of the set of compensation parameters are determined such that providing the compensation signal to the recipient qubit compensates for the induced signal provided to the recipient qubit, and the compensation signal prevents leakage of the recipient qubit from the computational subspace of the QCS to the excited subspace of the QCS, and the induced signal is induced by the control signal provided to the source qubit.

12. The method of claim 11, further comprising: Determining the values of the set of compensation parameters based on a Ramsey error filtering process.

13. The method according to claim 12, wherein, The Ramsey error filtering process includes actions, the actions including: Determining a pulse delay for a selection of consecutive pulses in a series of qubit rotation pulses applied to each qubit in the set of qubits, wherein each qubit rotation pulse in the series of qubit rotation pulses applied to the qubits in the set of qubits generates a rotation of the quantum state of the qubit, and the selected pulse delay increases the probability that the series of qubit rotation pulses generates leakage of the set of qubits from the computational subspace of the QCS to the excited subspace of the QCS; Based on the selected pulse delay, identifying qubit pairs in the set of qubits that contribute to the leakage of the set of qubits from the computational subspace to the excited subspace, wherein the qubit pairs include the source qubit and the recipient qubit; and Using the qubit pairs to determine the values of the set of compensation parameters of the compensation signal, wherein when the control signal is provided to the source qubit and the compensation signal is provided to the recipient qubit, the probability of leakage of the recipient qubit from the computational subspace to the excited subspace generated by the control signal is reduced.

14. The method according to claim 13, wherein, Each qubit rotation pulse in the series of qubit rotation pulses applied to the qubit is a pi rotation pulse, the pi rotation pulse generates a rotation of the quantum state of the qubit, and the rotation is about at least one of the x-axis or y-axis of the Bloch sphere representation of the quantum state of the qubit.

15. The method according to claim 13, wherein, The leakage of the receiver qubit from the computational subspace to the excited subspace includes a transition of the quantum state of the receiver qubit from a first excited state to a second excited state.

16. The method according to claim 13, wherein, Determining the selected pulse delay includes: Iteratively providing the series of qubit rotation pulses to each qubit in the qubit set, wherein during each iteration of providing the series of qubit rotation pulses, the pulse delay between consecutive pulses in the series of qubit rotation pulses remains constant, and between consecutive iterations of providing the series of qubit rotation pulses to each qubit in the qubit set, the pulse delay varies such that a pulse delay window is swept through during the iterative provision of the series of qubit rotation pulses to each qubit in the qubit set; In response to each iteration of providing the series of qubit rotation pulses to each qubit in the qubit set, measuring the quantum state of each qubit in the qubit set, wherein the iteration corresponds to a specific pulse delay in the pulse delay window; In response to measuring the quantum state of each qubit in the qubit set for the iteration corresponding to the specific pulse delay, determining the probability of generating a transition of the quantum state of the qubit set from a first excited state to one or more higher excited states for the specific pulse delay; and Identifying the selected pulse delay as the pulse delay in the pulse delay window that maximizes the probability of generating the transition of the quantum state of the qubit set from the first excited state to the one or more higher excited states.

17. The method according to claim 13, wherein, Identifying the qubit pairs contributing to the leakage of the qubit set from the computational subspace to the excited subspace includes: Iteratively selecting each possible qubit pair from the set of all possible qubit pairings, wherein each selected possible qubit pair includes a first qubit and a second qubit; For each selected possible qubit pair, providing the series of qubit rotation pulses to each of the first qubit and the second qubit in the selected possible qubit pair according to the selected pulse delay; In response to providing the series of qubit rotation pulses to each of the first qubit and the second qubit, measuring the quantum state of each of the first qubit and the second qubit in the selected possible qubit pair; For each selected possible qubit pair and based on measuring the quantum state of each of the first qubit and the second qubit, determining the probability of generating a transition of the quantum state of at least one of the first qubit or the second qubit to a second excited state for the provided series of qubit rotation pulses according to the selected pulse delay; and Identify such qubit pairs in the set of qubits in the set of qubits: the qubit pairs maximize the probability of the transition of the quantum state of at least one of the first qubit or the second qubit to the second excited state generated by a provided series of qubit rotation pulses according to the selected pulse delay.

18. The method according to claim 11, wherein The values of the set of compensation parameters of the compensation signal are selected from the space of possible values of the set of compensation parameters, the selected values are values from the space of possible values, and the values reduce the probability of leakage of the control signal generating the receiver qubit from the computational subspace to the excited subspace.

19. A quantum computing system QCS, comprising: A set of qubits; One or more processors; One or more memory devices storing computer-readable instructions that, when executed by the one or more processors, cause the one or more processors to perform operations including: Determine a control signal to be provided to a source qubit in the set of qubits; In response to determining to provide the control signal to the source qubit, provide the control signal to the source qubit; and In response to determining to provide the control signal to the source qubit, provide a compensation signal to a receiver qubit in the set of qubits, wherein the provided compensation signal is at least partially based on the value of a set of compensation parameters, and the value of the set of compensation parameters is determined such that providing the compensation signal to the receiver qubit compensates for the induced signal provided to the receiver qubit, and the compensation signal prevents leakage of the receiver qubit from the computational subspace of the QCS to the excited subspace of the QCS, and the induced signal is induced by the control signal provided to the source qubit.

20. The system QCS according to claim 19, wherein, The operations further include: Determine the value of the set of compensation parameters based on a Ramsey error filtering process.

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