Mitigating Qubit Crosstalk-Induced Errors in Quantum Computing and Quantum Information Processing Systems

Abstract

The present disclosure is directed to mitigating errors induced by qubit crosstalk in a quantum computing system (QCS). A compensation signal is provided to one or more qubits. The compensation signal at least partially "cancels" (e.g., compensates for) crosstalk between pairs of qubits. Such crosstalk-induced errors may include leakage of the qubit's quantum state out of the quantum system's computational subspace. Thus, the present embodiments may be used to reduce quantum computation errors arising from qubit transitions (or leakage) into excited states that are not within the quantum system's computational subspace.

Description

[Technical Field]

[0001] Priority claims This application is based on and claims priority to U.S. Application No. 17 / 974,216, filed October 26, 2022, which is incorporated herein by reference.

[0002] The present disclosure relates generally to quantum computing and information processing systems, and more particularly to mitigating qubit crosstalk induced errors in quantum computing and information processing systems. [Background technology]

[0003] Quantum computing is a computing method that exploits quantum effects such as superposition and entanglement of basis states to perform certain calculations more efficiently than classical digital computers. Quantum computing systems may manipulate information using quantum bits ("qubits"), as opposed to digital computers, which store and manipulate information in the form of bits, e.g., "1" or "0." A qubit can refer to a quantum device that allows for the superposition of data in multiple states, e.g., both "0" and "1," and / or the superposition of data in multiple states itself. According to conventional terminology, the superposition of "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 equivalent to the |0〉 and |1〉 basis states of the qubit, respectively. Summary of the Invention

[0004] 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 by practice of the embodiments.

[0005] One exemplary aspect of the present disclosure is directed to a method implemented by a quantum computing system (QCS). The QCS may include a set of qubits. The method may be for calibrating a compensating signal used to mitigate errors induced by qubit crosstalk in quantum computation. The method may include determining a selected pulse delay for successive pulses of a series of qubit rotation pulses applied to each qubit of the set of qubits. Each qubit rotation pulse of the series of qubit rotation pulses applied to a qubit of the set of qubits may cause a rotation of the quantum state of the qubit. The selected pulse delay may increase a probability that the applied series of qubit rotation pulses causes leakage of at least a portion of the set of qubits from a computation subspace of the QCS to an excitation subspace of the QCS. The selected pulse delay may be an optimal pulse delay. The selected pulse delay may be an optimal pulse delay that at least approximately maximizes a probability that the applied series of qubit rotation pulses causes leakage of at least a portion of the set of qubits from a computation subspace of the QCS to an excitation subspace of the QCS. Based on the selected pulse delay, a pair of qubits in the set of qubits may be identified. The identified pair of qubits may contribute to leakage of a portion of the set of qubits from the computation subspace to the excitation subspace. The pair of qubits may include a source qubit and a receiver qubit. The identified pair of qubits may be used to determine values ​​for a set of compensation parameters of the compensation signal. When the control signal is provided to the source qubit and the compensation signal is provided to the receiver qubit, the probability that the control signal will cause leakage of the receiver qubit from the computation subspace to the excitation subspace is reduced.

[0006] Other aspects of the present disclosure are directed to various systems, methods, apparatus, non-transitory computer-readable media, computer-readable instructions, and computing devices.

[0007] These and other features, aspects, and advantages of various embodiments of the present disclosure will become better understood with reference to the following detailed description and the appended claims. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the present disclosure and, together with the detailed description, explain the basic principles involved.

[0008] Detailed descriptions of embodiments directed to those skilled in the art are set forth herein with reference to the accompanying drawings, in which: [Brief explanation of the drawings]

[0009] [Figure 1] 1 illustrates an exemplary quantum computing system according to an exemplary embodiment of the present disclosure. [Figure 2A] 1 illustrates an exemplary first qubit according to various embodiments. [Figure 2B] 2B illustrates an exemplary second qubit located near the first qubit of FIG. 2A, according to various embodiments. [Figure 2C] 2C illustrates parasitic electromagnetic coupling between the first qubit and the second qubit of FIG. 2B, according to various embodiments. [Figure 2D] 2B-2C illustrate induced leakage of the second qubit of FIGS. 2B-2C from the computation subspace to the excitation subspace induced by the first control signal of FIGS. 2B-2C. [Figure 2E] 2E illustrates mitigation of induced leakage from the computation subspace of FIG. 2D via application of a compensation signal to the second qubit, according to various embodiments. [Figure 3A] 10 illustrates a Ramsey error filter pulse sequence applied to a qubit to calibrate a compensation signal for mitigating crosstalk-induced errors in the qubit, according to various embodiments. [Figure 3B]10 illustrates representative data from a Ramsey error filter versus delay time, according to various embodiments. [Figure 3C] 10 shows typical outputs of the Ramsey error filter at optimal pulse delays during pairwise operations for all possible pairs involving a receiver qubit. [Figure 3D] 10 shows the leakage probability of the receiver qubit during pairwise operations on the primary source qubit at optimal pulse delays versus the amplitude and phase shift of the compensation signal. [Figure 4] 1 provides a flowchart of a method for calibrating a compensation signal to mitigate qubit crosstalk-induced errors, according to various embodiments. [Figure 5] 1 provides a flowchart of a method for mitigating qubit crosstalk-induced errors in a quantum computing system, according to various embodiments. DETAILED DESCRIPTION OF THE INVENTION

[0010] Embodiments are directed to avoiding and / or mitigating computational errors in quantum computing systems and / or information processing systems. The embodiments aim to avoid and / or mitigate errors induced by qubit crosstalk in a quantum computing system (or device) including a set of qubits, including at least a first qubit and a second qubit. The embodiments avoid 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 the pair of qubits. Thus, the compensation signal is sometimes referred to as a cancellation signal (or tone). Such crosstalk-induced errors may include leakage of the qubit's quantum state out of the computational subspace of the quantum system. Thus, the embodiments may be used to reduce quantum computational errors arising from qubit transitions (or leakage) to excited states that are not within the computational subspace of the quantum system.

[0011] In addition to providing a compensation signal that avoids and / or mitigates certain quantum computing errors, embodiments provide a method for characterizing crosstalk between pairs of qubits. Such characterization of crosstalk allows for calibration of the compensation signal for any pair of qubits as a function of parameters of a control signal intended for one of the pair of qubits. Embodiments provide such characterization of crosstalk, and calibration of the crosstalk compensation signal, by methods performed for Ramsey interferometry measurements. That is, the transition frequency associated with the quantum state transition of the qubit can be determined as a function of the qubit's tuning. The compensation signal (and the qubit providing the compensation signal) are calibrated taking into account Ramsey interferometry measurements.

[0012] To control (or adjust) each qubit in a set of qubits of a quantum computing system (QCS), each qubit in the set may have a separate, independently addressable control line. That is, to control (or adjust) a first qubit (e.g., in a set of qubits of a QCS), a first control signal may 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 may be provided to the second qubit via a second control line terminating at the second qubit. Due to the physical proximity of the first and second qubits (and / or the first and second control lines) on a device implementing the set of qubits (and / or their associated control lines), the first and second qubits (and / or their associated control lines) may be electromagnetically coupled via parasitic capacitance, parasitic inductance, and / or other such electromagnetic (EM) coupling mechanisms. Thus, when EM signals of sufficient frequency are transmitted to and / or from a first qubit and a second qubit, the first qubit and the second qubit (and / or their associated control lines) may become susceptible to “crosstalk.” Such crosstalk between a first qubit and a second qubit may involve unintentionally inducing unwanted signals on control lines that are not associated with the qubit that the control signal is intended to control. That is, when a first control signal is provided to a first qubit via a first control line, at least a portion of the first control signal may couple to a second control line or parasitically drive (“leak” onto) the second control line and / or be otherwise provided to the second qubit. The induced (or leaked) signal may cause inadvertent operations within the qubit, resulting in computational errors.Embodiments are implemented with the goal of avoiding these qubit errors induced through such crosstalk. Note that physical proximity of qubits or qubit-control lines may not be required to result in unwanted crosstalk. Due to various EM coupling mechanisms, qubits and / or control lines do not need to be physically adjacent for crosstalk to occur. Qubits and / or control lines only need to be close enough that the EM coupling mechanisms are strong enough to induce unwanted crosstalk. Thus, as used herein, the term physical proximity (e.g., with respect to qubits and / or control lines) is used to describe situations in which qubits and / or control lines are physically “close enough” that the EM coupling mechanisms are strong enough to induce unwanted crosstalk. The term “leakage” may refer to situations in which EM coupling mechanisms induce crosstalk in a way that disrupts the expected or intended behavior of qubits and / or control lines. That is, when unwanted and / or coupled crosstalk occurs, it may be described as leakage.

[0013] Such crosstalk-induced errors may include causing a second qubit to accidentally transition (or leak) the quantum state of one or more qubits out of the computational subspace of the QCS. In a non-limiting embodiment, a QCS relies on each qubit in its set of qubits being in either 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 satisfy the constraint

number

number

[0014] An induced signal (or leak) signal may induce a qubit into its second excited state or into an excited state beyond the second excited state. When at least one qubit transitions to a second (or higher) excited state, the qubit can be said to have transitioned (or leaked) into the excitation subspace of QCS. Note that there is no intersection between the computation subspace of QCS and the excitation subspace of QCS. When a qubit transitions into the excitation subspace of QCS, the qubit is unreliable and cannot be used for quantum computing. Therefore, when a first qubit is driven (or manipulated) via a first control signal, an induced signal may be sent to a second qubit, causing the second qubit to transition (or leak) from the computation subspace into the excitation subspace of QCS. When this occurs, at least the second qubit will not be used for quantum computing and may result in quantum errors induced by qubit crosstalk. In some embodiments, the qubit may not be suitable for high-performance quantum computing.

[0015] More specifically, when a first qubit is driven by a first control signal (e.g., a microwave control signal) via the first qubit's control line, a second qubit may be unintentionally driven (or controlled) by an induced signal (e.g., induced via crosstalk) on the second qubit's associated control line (e.g., a second control line). That is, due to the physical proximity between the first qubit and the second qubit (and / or their associated control lines), quantum computing errors may be induced via crosstalk (e.g., parasitic coupling and / or leakage) between the first qubit and the second qubit. Embodiments avoid 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 that “cancels” (e.g., compensates for) the portion of the first control signal that leaks to the second qubit (via parasitic capacitance). That is, when a first qubit is driven by a first control signal, embodiments may 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 leakage of the first control signal to the second qubit. That is, the second control signal at least partially compensates for leakage of the first control signal to the second qubit to avoid errors induced by potential second qubit crosstalk.

[0016] Throughout, a first qubit (e.g., a qubit intended to be controlled by a first control signal) may be referred to as a source qubit. A second qubit (e.g., a qubit “accidentally” controlled via a first control signal) may be referred to as a target qubit because it is the target of a second control signal (e.g., a compensation signal). A first control signal that drives a source qubit may be referred to as a source signal, and a second control signal may be referred to as a compensation signal. In some embodiments, a source qubit may be referred to as an antagonist qubit, and the portion of the first signal that leaks (or is induced) to the target qubit may be referred to interchangeably as an antagonist signal, leakage signal, induced signal, and / or parasitic signal. Note that driving a single source qubit via a source signal may result in multiple target qubits accidentally driven by the source signal leaking onto the drive lines of multiple target qubits. Each of the multiple target qubits may be provided with a unique compensation signal to avoid errors in each of the multiple target qubits.

[0017] In addition to methods for avoiding such crosstalk-induced errors by providing a compensation signal to a second qubit, embodiments provide methods for calibrating such compensation signals. Such methods may use Ramsey interferometry measurements to characterize the transition frequency and phase shift associated with a qubit transitioning beyond its first excited state to one of its excited states. That is, such calibration methods may be based on a Ramsey error filter procedure that determines values ​​for a set of compensation parameters that parameterize (or characterize) the compensation signal. One exemplary method, as described throughout, is a method for calibrating a compensation signal used to mitigate qubit crosstalk-induced errors in quantum computing. The calibration method may be implemented by a QCS. The QCS may include a set of qubits. The method may include determining a selected pulse delay for successive 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” may be used interchangeably throughout. Each qubit rotation pulse in a series of qubit rotation pulses applied to a qubit in the set of qubits may generate a rotation of the qubit's quantum state. The selected pulse delay may increase the probability that the applied series of qubit rotation pulses causes leakage of at least a portion of the set of qubits from the computation subspace of the QCS to the excitation subspace of the QCS. The selected pulse delay may be an optimal pulse delay. The selected pulse delay may be an optimal pulse delay that at least approximately maximizes the probability that the applied series of qubit rotation pulses causes leakage of at least a portion of the set of qubits from the computation subspace of the QCS to the excitation subspace of the QCS. Each qubit rotation pulse in the series of rotation pulses applied to the qubit may be a π rotation pulse. The π rotation pulse may cause a rotation of the quantum state of the qubit. The generated rotation of the quantum state may 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.

[0018] The method may further include identifying a pair of qubits of the set of qubits based on the selected pulse delay. The identified pair of qubits may contribute to leakage of a portion of the set of qubits from the computation subspace to the excitation subspace. The pair of qubits may include a source qubit and a receiver qubit. The identified pair of qubits may be a pair of qubits from all possible pairings of the set of qubits that dominates the leakage of the portion of the set of qubits from the computation subspace to the excitation subspace.

[0019] The method may further include using the identified pair of qubits to determine values ​​for a set of compensation parameters of the compensation signal. The set of compensation parameters may include a first parameter corresponding to a magnitude of the compensation signal and a second parameter corresponding to a phase of the compensation signal. When the control signal is provided to the source qubit and the compensation signal is provided to the receiver qubit, a probability that the control signal causes leakage of the receiver qubit from the computation subspace to the excitation subspace is reduced. Values ​​of the set of compensation parameters of the compensation signal may be selected from a space of possible values ​​for the set of compensation parameters. The selected value may be a value from the space of possible values ​​that minimizes the probability that the control signal causes leakage of the receiver qubit from the computation subspace to the excitation subspace. The leakage of the receiver qubit from the computation subspace to the excitation subspace may include a transition of the quantum state of the receiver qubit from a first excited state to a second excited state. Providing the compensation signal to the receiver qubit can compensate for an induced signal provided to the receiver qubit. The induced signal may be induced from the control signal provided to the source qubit. The compensation signal prevents leakage of the receiver qubit from the computation subspace into the excitation subspace, which the stimulation signal would normally cause.

[0020] Embodiments include other methods implemented by QCS. The other method may be a method for mitigating errors induced by qubit crosstalk during quantum computation. The method may include determining that a control signal should be provided to a source qubit of a set of qubits to perform a quantum computation by QCS. In response to determining that the control signal should be provided to the source qubit, the control signal may be provided to the source qubit. Also, in response to determining that the control signal should be provided to the source qubit, a compensation signal may be provided to a receiver qubit of the set of qubits. The compensation signal provided may be according to (e.g., based on) values ​​of a set of compensation parameters. The values ​​of the set of compensation parameters may be determined such that providing the compensation signal to the receiver qubit compensates for an induced signal provided to the receiver qubit. The induced signal may be induced from the control signal provided to the source qubit. The compensation signal may prevent leakage of the receiver qubit from the computation subspace of QCS into the excitation subspace of QCS, which the induced signal would normally cause.

[0021] The values ​​of the set of compensation signals may be determined according to any of the various embodiments discussed herein. For example, the values ​​of the set of compensation parameters may be determined based on a Ramsey error filter procedure.

[0022] Embodiments include a quantum computing system (QCS) (e.g., a quantum computing device and / or a quantum information processing device). Various embodiments of a QCS are described in connection with at least FIG. 1 . Briefly, however, a QCS may include a set of qubits, one or more processor devices (e.g., classical processor devices, quantum processor devices, or a combination thereof), and one or more memory devices. The one or more memory devices may store computer-readable instructions. The one or more processors may be caused to perform an operation when the instructions are executed by the one or more processors. The operation may include determining a selected pulse delay for successive pulses of a series of qubit rotation pulses applied to each qubit of the set of qubits. Each qubit rotation pulse of the series of qubit rotation pulses applied to a qubit of the set of qubits may cause a rotation of the quantum state of the qubit. The selected pulse delay may increase the probability that the applied series of qubit rotation pulses causes leakage of at least a portion of the set of qubits from a computation subspace of the QCS to an excitation subspace of the QCS. The selected pulse delay may be an optimal pulse delay. The selected pulse delay may be an optimal pulse delay that at least approximately maximizes the probability that the applied series of qubit rotation pulses causes leakage of at least a portion of the set of qubits from the computation subspace of the QCS to the excitation subspace of the QCS. The operations may further include identifying a pair of qubits in the set of qubits based on the selected pulse delay. The identified pair of qubits may contribute to the leakage of the portion of the set of qubits from the computation subspace to the excitation subspace. The pair of qubits may include a source qubit and a receiver qubit.The operations may further include using the identified pair of qubits to determine values ​​for a set of compensation parameters of a compensation signal, where when the control signal is provided to the source qubit and the compensation signal is provided to the receiver qubit, the probability that the control signal causes leakage of the receiver qubit from the computation subspace to the excitation subspace is reduced.

[0023] Aspects of the present disclosure provide several technical effects and advantages. For example, embodiments mitigate (or avoid) errors (e.g., errors induced by qubit crosstalk) in quantum computations performed by a QCS and / or quantum computing device. Thus, the performance of a QCS employing embodiments is significantly improved because the QCS is less prone to errors while performing quantum computations.

[0024] 1 illustrates an exemplary quantum computing system 100. Quantum computing system 100 is one example of a system of one or more classical computers and / or quantum computing devices, at one or more locations, that may implement the systems, components, and techniques described herein below. Using the disclosure provided herein, one skilled in the art will understand that other quantum computing devices or systems may be used without departing from the scope of the present disclosure.

[0025] Quantum computing system 100 includes quantum hardware 102 in data communication with one or more classical processors 104. Classical processor 104 may 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. Quantum hardware 102 includes components for performing quantum computations. For example, quantum hardware 102 includes quantum system 110, control device(s) 112, and readout device(s) 114 (e.g., readout resonator(s)). Quantum system 110 may include one or more multilevel quantum subsystems, such as a register of qubits (e.g., qubit 120). In some implementations, the multilevel quantum subsystems may include superconducting qubits, such as flux qubits, charge qubits, transmon qubits, Gmon qubits, and spin-based qubits.

[0026] The type of multilevel quantum subsystem utilized by quantum computing system 100 may vary. For example, in some cases it may be advantageous to include one or more readout device(s) 114 attached to one or more superconducting qubits, e.g., transmon, fluxmon, Gmon, Xmon, or other qubits. In other cases, ion traps, photonic devices, or superconducting cavities (which may prepare states without the need for qubits) may be used. Further examples of implementations of multilevel quantum subsystems include Fluxmon qubits, silicon quantum dots, or phosphorus impurity qubits.

[0027] Quantum circuits may be constructed and applied to a register of qubits included in quantum system 110 via multiple control lines coupled to one or more control devices 112. Exemplary control devices 112 operating on a register of qubits may be used to implement a quantum circuit having a quantum gate or multiple quantum gates, e.g., 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 may be configured to operate on quantum system 110 via one or more respective control parameters (e.g., one or more physical control parameters). For example, in some implementations, a multilevel quantum subsystem may be a superconducting qubit, and control device 112 may be configured to provide control pulses on control lines to generate a magnetic field that tunes the frequency of the qubit.

[0028] The quantum hardware 102 may further include a readout device 114 (e.g., a readout resonator). Measurements 108 obtained via the measurement device may be provided to the classical processor 104 for processing and analysis. In some embodiments, the quantum hardware 102 may include quantum circuits, and the control device(s) 112 and readout device(s) 114 may implement one or more quantum logic gates that operate on the quantum computing system 100 via physical control parameters (e.g., microwave pulses) transmitted through wires included in the quantum hardware 102. Further examples of control devices include arbitrary waveform generators, from which a DAC (digital-to-analog converter) produces a signal.

[0029] The readout device(s) 114 may be configured to perform quantum measurements on the quantum system 110 and send the measurement results 108 to the classical processor 104. Additionally, the quantum hardware 102 may be configured to receive data from the classical processor 104 specifying the physical control qubit parameter values ​​106. The quantum hardware 102 may use the received physical control qubit parameter values ​​106 to update the action of the control device(s) 112 and the readout device(s) 114 on the quantum system 110. For example, the quantum hardware 102 may receive data specifying new values ​​representing voltage magnitudes of one or more DACs included within the control device 112 and may update the action of the DACs on the quantum system 110 accordingly. The classical processor 104 may be configured to initialize the quantum system 110 to an initial quantum state, for example, by sending data to the quantum hardware 102 specifying an initial set of physical control qubit parameters 106.

[0030] In some implementations, readout device(s) 114 may measure the state of an element (e.g., a qubit) of a quantum system, such as a qubit, by utilizing the difference in impedance for the |0> and |1> states of the element. For example, the resonant frequency of the readout resonator may be different when the qubit is in the |0> or |1> state due to the nonlinearity of the qubit. Thus, microwave pulses reflected from readout device 114 convey amplitude and phase shifts that depend on the qubit state. In some implementations, a Purcell filter may be used in conjunction with readout device(s) 114 to prevent microwave propagation at the qubit frequency.

[0031] In some embodiments, quantum system 110 may include multiple qubits 120 arranged, for example, in a two-dimensional lattice 122. For clarity, two-dimensional lattice 122 depicted in FIG. 1A includes 4×4 qubits, although in some implementations, quantum system 110 may include a fewer or greater number of qubits. In some embodiments, multiple qubits 120 may interact through multiple qubit couplers, such as qubit coupler 124. The qubit coupler may define nearest-neighbor interactions between multiple qubits 120. In some implementations, the strength of the multiple qubit couplers is a tunable parameter. In some cases, the multiple qubit couplers included in quantum computing system 100 may be couplers with fixed coupling strengths.

[0032] In some embodiments, plurality of qubits 120 may include data qubits, such as qubit 126, and measurement qubits, such as qubit 128. A data qubit is a qubit that participates in a computation being performed by quantum computing system 100. A measurement qubit is a qubit that can be used to determine the output result of a computation performed by a data qubit. That is, during a computation, the unknown state of a data qubit is transferred to a measurement qubit using an appropriate physical operation and measured via an appropriate measurement operation performed on the measurement qubit.

[0033] In some implementations, each qubit of plurality of qubits 120 may operate using a respective operating frequency, such as an idle frequency, an interaction frequency, a readout frequency, and / or a reset frequency. The operating frequency may vary from qubit to qubit. For example, each qubit may idle at a different operating frequency. The operating frequency of qubit 120 may be selected before a computation is performed.

[0034] 1 illustrates one exemplary quantum computing system that may be used to implement methods and operations according to exemplary aspects of the present disclosure. Other quantum computing systems may be used without departing from the scope of the present disclosure.

[0035] FIG. 2A shows an exemplary 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. The first control signal may be transmitted to the first qubit 200 via the first control line 204. A first control line capacitor 206 may be disposed along the first control line 204 to control the transmission of the first control signal to the first qubit 200. That is, the first control line capacitor 206 may capacitively couple the transmission of the first control signal to the first qubit 200. The first control line 204 may terminate in a first qubit loop 210 of the transmon circuit. First qubit loop 210 includes first qubit capacitor 212 and first qubit Josephson junction pair 214. First qubit loop 210 may be coupled to first qubit ground 216 so that first qubit 200 does not float.

[0036] In various embodiments, the qubits (e.g., first qubit 200 and / or second qubit 220 of FIG. 2B) may be used to implement quantum logic gates (e.g., Pauli-X gates, Pauli-Y gates, Pauli-Z gates, Hadamard gates, etc.). In other embodiments, the first qubit 200 (and / or 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), such as, but not limited to, quantum computing system 100 of FIG. 1, may use the first qubit 200 and / or the second qubit 220 in performing quantum computations and / or quantum information processing processes. 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 as an information encoding mechanism. As described above, first control line capacitor 206 can capacitively couple a first control signal (e.g., a microwave pulse) to first qubit 200. Thus, the first microwave pulse enables a first quantum logic gate and / or a first information encoding mechanism.

[0037] FIG. 2B illustrates an exemplary second qubit 220 located near the first qubit 200 of FIG. 2A , according to various embodiments. For example, the first qubit 200 and the second qubit 220 may be disposed on a quantum integrated circuit (QIC). The second qubit 220 may be equivalent (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 be of similar, equivalent, similar, or non-identical architectures that are sufficiently similar to present the 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. A second control line capacitor 226 may be disposed along the second control line 224 to control the transmission of the second control signal to the second qubit 220. 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 coupled to a second qubit ground 236.

[0038] 2B, a first control signal 218 (e.g., a microwave pulse transmitted along first control line 204 to control first qubit 200) is shown as an arrow transmitted along first control line 204 of first qubit 200. First control signal 218 has a general functional form (e.g., as a function of time): V(t)=V·cos(ω·t+Φ), where V denotes the amplitude of first control signal 218, ω denotes the frequency of first control signal 218, and Φ denotes a phase shift associated with first control signal 218. Similarly, FIG. 2B shows a second control signal 238 (e.g., a microwave pulse transmitted along second control line 224 to control second qubit 220) as an arrow transmitted along second control line 224 of second qubit 220. The second control signal 238 has the general functional form: V(t)=V·cos(ω·t+Φ), where V denotes the amplitude of the second control signal 238, ω denotes the frequency of the second control signal 238, and Φ denotes a 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., V, ω, Φ) 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., V, ω, Φ) are calibrated (or tuned) to various characteristics of the second qubit 220.

[0039] 2C illustrates parasitic electromagnetic (EM) coupling between first qubit 200 and second qubit 220 of FIG. 2B in accordance with various embodiments. That is, FIG. 2C illustrates parasitic EM coupling between first qubit 200 and second qubit 220, where first control signal 218 (e.g., for driving first qubit 200) is parasitic coupled to second qubit 220. The parasitic EM coupling of first control signal 218 to second qubit 220 generates an induced signal 240 (e.g., a leakage signal or antagonist signal) along second control line 224. The induced signal 240 follows a generalized form of first control signal 218, with the amplitude and phase shift of first control signal 218 modified (e.g., reduced). Thus, the generalized functional form of induced signal 240 is V P (t)=|r|·V1·coscos(ω1·t+Φ1+δ Φ ), where |r|<1 indicates a reduction in the magnitude of the first control signal 218 (e.g., due to weak parasitic coupling between the two qubits), and δ Φ denotes the additional phase shift introduced through parasitic coupling, and the subscript P denotes the parasitic (or induced) signal.

[0040] FIG. 2D illustrates the induced leakage (or transition) of the second qubit 220 of FIGS. 2B-2C from the computation subspace to the excitation subspace, induced by the first control signal of FIGS. 2B-2C. As noted throughout, the transmon qubits (e.g., the first qubit 200 and / or the second qubit 220) may be modeled as quantum harmonic oscillators (QHOs). The potential energy well of the second qubit (modeled as a QHO) and the energy levels 260 of the potential energy well are shown in FIG. 2D. The energy levels 260 of the second qubit 220 include at least a ground state 262 (e.g., denoted as eigenstate |0〉), a first excited state 264 (e.g., denoted as eigenstate |1〉), and a second excited state 266 (e.g., denoted as eigenstate |2〉). For simplicity, higher-lying excited states of the second qubit 220 exist but are omitted from FIG. 2D. Ground state 262 and first excited state 264 may be within the computational subspace of QCS using second qubit 220, while second excited state 266 (and higher excited states) are outside the computational subspace. That is, second excited state 266 may be within the excitation subspace. The excitation subspace may include quantum states associated with second excited state 266 and any higher excited states (e.g., |3〉, |4〉, |5〉...) not shown in FIG. 2D .

[0041] In some embodiments, the second control signal 238 may be tuned to induce a first quantum state transition 272 from the ground state 262 to the first excited state 264 (via a resonance phenomenon associated with the QHO). The inducement signal 240 may induce a second quantum state transition 274 from the first excited state 264 to the second excited state 266 (via a resonance phenomenon associated with the QHO). Thus, parasitic coupling of the first control signal 218 to the second qubit 220 may induce a transition of the second qubit 220 from the computation subspace to the excitation subspace (via a resonance phenomenon associated with the QHO). The inducement signal 240 may cause qubit errors due to leakage into this excitation subspace and / or other effects associated with crosstalk between the first qubit 200 and the second qubit 220.

[0042] Thus, the total control signal provided to second qubit 220 is the superposition of second control signal 238 and inducer signal 240: V T (t)=V2(t)+V P (t)=V1·coscos(ω1·t+Φ1)+|r|V1·coscos(ω1·t+Φ1+δ Φ ), where the subscript T denotes the total signal provided to the second qubit 220. Note that, although not explicitly shown in FIG. 2C , the second control signal 238 may induce an additional induced signal on the first control line 204. Furthermore, 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 may be absent, and thus the total signal transmitted to the second qubit 220 is the induced signal 240, e.g., V T (t)=V P (t)=|r|V1·coscos(ω1·t+Φ1+δ Φ )

[0043] 2E illustrates mitigation of induced leakage from the computational subspace of FIG. 2D via application of a compensation signal 242 to a second qubit 220, according to various embodiments. More specifically, in response to providing a first control signal 218 to the first qubit 200 and inducing an inducing signal 240 transmitted to the second qubit, a second microwave drive 222 provides the compensation signal 242 to the second qubit 220. That is, the compensation signal 242 is transmitted along a second control line 224 to the second qubit 220. The compensation signal is adjusted and / or calibrated to at least partially compensate for and / or at least partially cancel the effect of the inducing signal 240. The functional form of the compensation signal 242 is V C (t)=|r|V1·coscos(ω1·t+Φ1+δ Φ +π), where the subscript C denotes the compensating and / or canceling effect of the compensation signal 242. Note that periodic functions (e.g., sinsin and coscos) are antisymmetric under a π rotation (or phase shift). As a result, the superposition of the induced signal 240 and the compensation signal 242 is at least approximately zero, e.g.

number

[0044] It should be noted that the control signal, induced signal, and compensation signal may be modeled via complex functions. Manipulation of the functional form of a periodic signal may be easier when transformed to the complex plane via Euler's equation. When represented as a complex function, it may be understood that a real signal may be interpreted as a purely real or purely imaginary component of the complex function. For example, the first control signal 218 may be

number

[0045] FIG. 3A illustrates a Ramsey error filter pulse sequence applied to a qubit to calibrate a compensation signal for mitigating errors induced by qubit crosstalk, according to various embodiments. In FIG. 3A, a series of qubit rotation pulses is applied to at least two qubits (e.g., at least one receiver qubit and at least one source qubit) of a set of qubits. Each qubit rotation pulse of the series of qubit rotation pulses applied to the qubit generates a rotation (e.g., a π rotation) of the qubit's quantum state. Note that the sequence of pulses can be applied simultaneously to multiple "source" (or antagonist) qubits to determine their effect on at least one receiver qubit. In practice, the applied sequence of pulses can be applied simultaneously to all qubits of the set of qubits. As shown in FIG. 3A, consecutive pulses in the series of pulses are separated by a delay time (t). The pulses can be Ramsey error filter pulses. The sequence of Ramsey error filter pulses (or series of Ramsey error filter pulses) can consist of π rotation pulses separated by a variable delay t. A π rotation pulse applied to a qubit can generate a rotation about at least one of the x- or y-axes of the Bloch sphere representation of the qubit's quantum state. For example, a π rotation pulse can generate a quantum state transition |0〉→|1〉 or a quantum state transition |1〉→|0〉. Such a rotation can generate resonance effects, resulting in coherent leakage from the qubit's computation subspace into the excitation subspace.

[0046] The application of the pulse sequence can be repeated several times to amplify the coherent leakage, which can be observed by direct measurement of the quantum state of one or more receiver qubits. Measurement of |2〉 (or a higher excited state) indicates that the qubit has transitioned to an excited state outside the computational subspace. At a specific delay time t, this sequence amplifies the coherent crosstalk leakage, facilitating calibration. This amplification can be understood as a result of constructive interference between the leakage amplitudes induced by successive pulses.

[0047] That is, FIG. 3A illustrates repeatedly providing a series of qubit rotation pulses to at least some of the qubits of the set of qubits. During each iteration of providing the series of qubit rotation pulses, the pulse delay between successive pulses of the series of qubit rotation pulses is held constant. The pulse delay varies between successive iterations of providing the series of qubit rotation pulses to the qubits. A window of pulse delay values ​​is swept over the repeatedly providing the series of qubit rotation pulses to each qubit of the set of qubits. In response to each iteration of providing the series of qubit rotation pulses to the qubits, the quantum states of at least some of the qubits can be measured. Each iteration corresponds to a particular value of pulse delay within the window of pulse delay values.

[0048] In response to measuring the quantum state of each qubit of the set of qubits for the iteration corresponding to a particular pulse delay, a probability of causing the quantum state of the set of qubits to transition from the ground state or the first excited state to one or more higher excited states for the particular pulse delay is measured. This probability may be referred to as the leakage probability (p2). The leakage probability (e.g., p2) may be measured as the fraction of qubits in the set of qubits that transition to |2〉 (or a higher excited state) through the application of a series of pulses. The leakage probability may be measured as a function of pulse delay.

[0049] FIG. 3B shows representative data from the Ramsey error filter versus delay time t. The plot in FIG. 3B shows a measurement of the leakage probability (e.g., p2) as a function of pulse delay (e.g., t). This data may be acquired while driving all qubits in parallel to minimize data acquisition time. More specifically, the plot in FIG. 3B shows the leakage probability p2 versus t in the Ramsey error filter. A t (e.g., an optimal pulse delay, denoted as optimal t in the plot) that at least approximately maximizes the leakage probability is identified. The optimal pulse delay can be identified as a pulse delay in a window of pulse delays that at least approximately maximizes the probability of generating a quantum state transition of the set of qubits from a first excited state to one or more higher excited states. The optimal pulse delay and / or optimal t may be referred to throughout as the selected pulse array.

[0050] The optimal pulse delay is used throughout the remainder of the calibration sequence. That is, in the next step of the calibration (shown in Figures 3C-3D), t is held fixed at a value that at least approximately maximizes the leakage population and / or leakage probability (e.g., p2). More specifically, the plot in Figure 3B illustrates determining the optimal pulse delay for successive pulses of a series of qubit rotation pulses applied to the qubit. The optimal pulse delay increases (e.g., at least approximately maximizes) the probability that the applied series of qubit rotation pulses will cause leakage of a set of qubits from the computation subspace of the QCS (or qubits) to the excitation subspace of the QCS (or qubits). Leakage of a receiver qubit from the computation subspace to the excitation subspace involves a transition of the quantum state of the receiver qubit from a first excited state to a second excited state (or a higher excited state).

[0051] FIG. 3C shows a typical output of the Ramsey error filter at optimal t during pairwise operation for all possible pairs including a receiver qubit. This data identifies the source of parasitic drive. That is, the plot of FIG. 3C is a plot of p2 for the source qubit during pairwise operation at optimal t. The peak identifies the dominant source of leakage. More specifically, the plot shows p2 for the source qubit during pairwise operation at optimal t. The peak identifies the dominant source of p2 after the Ramsey error filter during pairwise operation for the dominant source with respect to r and θ, the magnitude and phase of the compensation tone used to null the crosstalk leakage. The data used to generate the plot of FIG. 3C can be obtained by selecting a qubit from a set of qubits as the target qubit and, for each data point on the x-axis, selecting another qubit as the source qubit. Consequently, the plot of FIG. 3C can be used to determine the source of the largest leakage (into the excitation subspace) for a particular target qubit. Thus, to characterize the entire set of qubits, the plot of Figure 3C may be generated for each qubit in the set of qubits. The qubit corresponding to the plot of Figure 3C may be considered the target qubit. Data may be acquired by providing a sequence of qubit rotation pulses to the pair of qubits, with the pulse delay set to the optimal pulse delay (or selected pulse delay) found via the plot of Figure 3B.

[0052] The plot of FIG. 3C can be used to identify pairs of qubits in the set of qubits that contribute to leakage of the set of qubits from the computation subspace to the excitation subspace based on the optimal pulse delay (or selected pulse delay). The pairs of qubits include a source qubit and a receiver qubit. Note that each data point along the x-axis corresponds to a distinct qubit pair, while the target qubit is held constant along the x-axis. Thus, each data point along the x-axis may correspond to a differential source qubit of the qubit pair. As described above, the plot of FIG. 3C may be generated for each qubit in the set of qubits. The qubit corresponding to the plot of FIG. 3C may be used as the target qubit for the qubit pairs associated with all data points along the x-axis.

[0053] More specifically, qubit pairs (including a particular receiver qubit) can be identified by generating the plot of FIG. 3D for each possible particular receiver qubit. Each possible qubit pair can be iteratively selected from a set of all possible pairings of qubits. Each selected possible qubit pair includes a first qubit (e.g., a source qubit) and a second qubit (e.g., a 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 according to (e.g., based on) an optimal (or selected) pulse delay. In response to providing the 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 of the selected possible qubit pair can be measured. For each selected possible qubit pair, and based on measuring the respective quantum states of the first qubit and the second qubit, the probability that the provided series of qubit rotation pulses will cause a transition of the quantum state of at least one of the first qubit or the second qubit to a second excited state (or a higher excited state) according to (e.g., based on) an optimal pulse delay can be measured. As shown in the plot of FIG. 3C , a qubit pair of the set of qubits can be identified that at least approximately maximizes the probability that the provided series of qubit rotation pulses will cause a transition of the quantum state of at least one of the first qubit or the second qubit to a second excited state according to (e.g., based on) an optimal pulse delay. The identified qubit pair can be a qubit pair from all possible pairings of the set of qubits that dominates the leakage of the set of qubits from the computation subspace to the excitation subspace.

[0054] Figure 3D shows p2 at the receiver qubit during pairwise operations on the primary source qubit at optimal t for the amplitude r and phase θ of the compensation tone. The stars indicate the optimal r and θ for mitigating crosstalk-induced leakage. That is, the phase space diagram plots p2 for the source qubit during pairwise operations at optimal t. The peaks identify the primary source of p2 after the Ramsey error filter during pairwise operations on the primary source for r and θ, the magnitude and phase of the compensation tone used to null the crosstalk leakage.

[0055] The plot of FIG. 3D may be employed to determine values ​​for a 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 receiver qubit, the probability that the control signal causes leakage of the receiver qubit from the computation subspace to the excitation subspace is reduced (e.g., minimized). As shown in the plot of FIG. 3D, values ​​for the set of compensation parameters for the compensation signal are selected from a space of possible values ​​for the set of compensation parameters. The selected value may be a value from the space of possible values ​​that minimizes the probability that the control signal causes leakage of the receiver qubit from the computation subspace to the excitation subspace.

[0056] In some embodiments, after calibrating the compensation signal, a quantum computation may be performed by the QCS. To perform a quantum computation by the QCS, it may be determined that a control signal be provided to a first qubit (e.g., a source qubit). In response to determining that the control signal should be provided to the source qubit, the control signal may be provided to the source qubit. Also, in response to determining that the control signal should be provided to the source qubit, a compensation signal may be provided to a second qubit (e.g., a receiver qubit). The compensation signal provided may be according to (e.g., based on) a value determined for a set of compensation parameters for the pair of qubits. Providing the compensation signal to the receiver qubit may compensate for the induced signal provided to the receiver qubit. The compensation signal may prevent leakage of the receiver qubit from the computation subspace to the excitation subspace, which the induced signal would normally cause. The induced signal may be induced from the control signal provided to the source qubit.

[0057] method 4-5 depict operations occurring in a particular order for purposes of illustration and explanation. Those skilled in the art, using the disclosure provided herein, will understand that the operations of any of the methods described herein may be extended in various ways, may include steps not shown, may be omitted, may be rearranged, and / or may be modified without departing from the scope of the present disclosure. Method 400 of FIG. 4 and method 500 of FIG. 5 may be implemented using any suitable quantum computing system, such as the system described in FIG. 1.

[0058] FIG. 4 provides a flowchart of a method 400 for calibrating a compensation signal to mitigate errors induced by qubit crosstalk, according to various embodiments. Method 400 begins at block 402, where a series of qubit rotation pulses is applied to each qubit in a set of qubits. Each qubit rotation pulse is applied to a qubit to generate a rotation of the qubit's quantum state. The application of the series of qubit rotation pulses to a qubit is described at least as in conjunction with FIG. 3A . Each qubit rotation pulse in the series of rotation pulses applied to a qubit may be a π rotation pulse. The rotation of the qubit's quantum state is a rotation about at least one of the x-axis or y-axis of the Bloch sphere representation of the qubit's quantum state.

[0059] At block 404, a selected pulse delay is determined for successive pulses of the series of qubit rotation pulses to be applied to each qubit of the set of qubits. Determining the selected pulse delay is described at least in connection with FIG. 3A . However, briefly described here, the selected pulse delay increases (e.g., at least approximately maximizes) the probability that the applied series of qubit rotation pulses will cause leakage of the set of qubits from the computation subspace of the QCS to the excitation subspace of the QCS. The selected pulse delay may be an optimal pulse delay. The selected pulse delay may be an optimal pulse delay that at least approximately maximizes the probability that the applied series of qubit rotation pulses will cause leakage of at least some of the set of qubits from the computation subspace of the QCS to the excitation subspace of the QCS. Note that the terms “pulse delay” and “time delay” may be used interchangeably throughout.

[0060] At block 406, pairs of qubits in the set of qubits are identified that contribute (e.g., at least approximately maximize) leakage of the set of qubits from the computation subspace to the excitation subspace based on the selected pulse delay. The identified qubit pairs may include a source qubit and a receiver qubit. Identifying such qubit pairs is described at least in connection with FIG. 3C . The identified qubit pairs that contribute to leakage of the set of qubits from the computation subspace to the excitation subspace may be pairs of qubits from all possible pairings of the set of qubits that dominate the leakage of the set of qubits from the computation subspace to the excitation subspace.

[0061] At block 408, the identified qubit pair is used to determine values ​​for a set of compensation parameters for the compensation signal. Determining values ​​for the set of compensation parameters is described at least in connection with FIG. 3D . When the control signal is provided to the source qubit and the compensation signal is provided to the receiver qubit, the probability that the control signal causes leakage of the receiver qubit from the computation subspace to the excitation subspace is reduced (e.g., minimized). The leakage of the receiver qubit from the computation subspace to the excitation subspace may 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 may include a first parameter corresponding to the magnitude of the compensation signal and a second parameter corresponding to the phase of the compensation signal.

[0062] FIG. 5 provides a flowchart of a method 500 for mitigating errors induced by qubit crosstalk in a quantum computing system (QCS) according to various embodiments. Method 500 begins at block 502, where it is determined that a control signal is to be provided to a source qubit of a set of qubits to perform a quantum computation by the QCS. At block 504, in response to determining that the control signal should be provided to the source qubit, the control signal may be provided to the source qubit. At block 506, in response to determining that the control signal should be provided to the source qubit, a compensation signal is provided to a receiver qubit of the set of qubits. The compensation signal provided is according to (e.g., based on) 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 receiver qubit compensates for an induced signal provided to the receiver qubit. The compensation signal prevents leakage of the receiver qubit from the computation subspace of the QCS to the excitation subspace of the QCS, which the induced signal would normally cause. The induced signal is induced from the control signal provided to the source qubit.

[0063] Additional Embodiments Implementations of the digital, classical, and / or quantum subject matter, and digital functional and quantum operations described herein may be implemented in digital electronic circuitry, suitable quantum circuitry, or more generally, quantum computing systems, tangibly embodied digital and / or quantum computer software or firmware, digital and / or quantum computer hardware, including the structures disclosed herein and their structural equivalents, or one or more combinations thereof. 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.

[0064] Embodiments of the digital and / or quantum subject matter described herein may be implemented as one or more digital and / or quantum computer programs, i.e., as one or more modules of digital and / or quantum computer program instructions encoded on a tangible, non-transitory storage medium for execution by or controlling 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 qubits or a single qubit, or a combination of one or more thereof. 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, generated to encode the digital and / or quantum information for transmission to a suitable receiver device for execution by a data processing apparatus.

[0065] The terms quantum information and quantum data refer to information or data conveyed by, held by, or stored within a quantum system, with the smallest nontrivial system being a qubit, i.e., a system defining a unit of quantum information. The term "qubit" is understood to encompass all quantum systems that can be appropriately approximated as a two-level system in the corresponding context. Such quantum systems may include, for example, multi-level systems having two or more levels. By way of example, such systems may include atoms, electrons, photons, ions, or superconducting qubits. In many implementations, the computational basis state is specified in the ground state and the first excited state, although it is understood that other setups are possible in which the computational state is specified in a higher-level excited state (e.g., a qubit).

[0066] The term "data processing apparatus" refers to digital and / or quantum data processing hardware and encompasses all types of apparatus, devices, and machines for processing digital and / or quantum data, including, by way of example, a programmable digital processor, a programmable quantum processor, a digital computer, a quantum computer, or multiple digital and quantum processors or computers, as well as combinations thereof. An apparatus may also be or include special-purpose logic circuits, such as FPGAs (field-programmable gate arrays), ASICs (application-specific integrated circuits), or quantum simulators, i.e., quantum data processing apparatuses designed to simulate or generate information about specific quantum systems. In particular, quantum simulators are special-purpose quantum computers that do not have the capability to perform universal quantum computations. In addition to hardware, an apparatus may also optionally include code that creates an execution environment for digital and / or quantum computer programs, such as code constituting processor firmware, protocol stacks, database management systems, operating systems, or one or more combinations thereof.

[0067] A digital or classical computer program may also be referred to or described as a program, software, software application, module, software module, script, or code, and may be written in any form of programming language, including compiled or interpreted languages, declarative or procedural languages, and may 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 may also be referred to as a program, software, software application, module, software module, script, or code, and may be written in any form of programming language, including compiled or interpreted languages, declarative or procedural languages, and may be converted to or written in a suitable quantum programming language, such as QCL, Quipper, Cirq, etc.

[0068] A digital and / or quantum computer program may correspond to a file in a file system, but this is not necessarily the case. A program may be stored in a portion of a file holding other programs or data, e.g., one or more scripts stored in a markup language document, in a single file dedicated to the program, or in multiple linked files, e.g., files storing one or more modules, subprograms, or code portions. A digital and / or quantum computer program may be deployed to run on one digital or quantum computer, or on multiple digital and / or quantum computers located at one location, or on multiple computers distributed across multiple locations and interconnected by a digital and / or quantum data communication network. A quantum data communication network is understood to be a network capable of transmitting quantum data using quantum systems, e.g., qubits. While digital data communication networks generally cannot transmit quantum data, quantum data communication networks can transmit both quantum data and digital data.

[0069] The processes and logic flows described herein may be performed by one or more programmable digital and / or quantum computers equipped with one or more digital and / or quantum processors, as appropriate, executing one or more digital and / or quantum computer programs that perform functions by operating on input digital and quantum data to generate output. The processes and logic flows may also be implemented by special purpose logic circuitry, e.g., FPGAs or ASICs, or quantum simulators, or a combination of special purpose logic circuitry or quantum simulators with one or more programmed digital and / or quantum computers.

[0070] A system of one or more digital and / or quantum computers or processors is "configured" or "operable" to perform a particular operation or action means that the system has installed thereon software, firmware, hardware, or a combination thereof that causes the system to perform the operation or action when in operation. One or more digital and / or quantum computer programs are configured to perform a particular operation or action means that the program or programs contain instructions that, when executed by a digital and / or quantum data processing device, cause the device to perform the operation or action. A quantum computer may receive instructions from a digital computer that, when executed by a quantum computing device, cause the device to perform the operation or action.

[0071] A digital and / or quantum computer suitable for executing a digital and / or quantum computer program may be based on a general-purpose or dedicated digital and / or quantum microprocessor, or both, or any other kind of central digital and / or quantum processing unit. Typically, the central digital and / or quantum processing unit receives instructions and digital and / or quantum data from a read-only memory, a random access memory, or a quantum system suitable for transmitting quantum data, e.g., photons, or a combination thereof.

[0072] Some exemplary elements of a digital and / or quantum computer are a central processing unit for performing or executing instructions and one or more memory devices for storing instructions and digital and / or quantum data. The central processing unit and memory may be supplemented by or incorporated into special-purpose logic circuitry or a quantum simulator. Generally, a digital and / or quantum computer includes one or more mass storage devices for storing digital and / or quantum data, such as, for example, magnetic, magneto-optical, optical disks, or quantum systems suitable for storing quantum information, or is operably coupled to receive digital and / or quantum data from them, transfer digital and / or quantum data to them, or both. However, a digital and / or quantum computer need not have such devices.

[0073] Digital and / or quantum computer-readable media suitable for storing digital and / or quantum computer program instructions and digital and / or quantum data include, by way of example, all forms of non-volatile digital and / or quantum memories, media, and memory devices, including semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices, magnetic disks, e.g., internal hard disks or removable disks, magneto-optical disks, and CD-ROM and DVD-ROM disks, and quantum systems, e.g., trapped atoms or electrons. Quantum memory is understood to be a device capable of long-term storage of quantum data with high fidelity and efficiency, such as, for example, a light-matter interface where light is used for transmission and matter is used for storage and preservation of quantum properties of the quantum data, such as superposition or quantum coherence.

[0074] Control of the various systems described herein, or portions thereof, may be implemented in a digital and / or quantum computer program product stored on one or more tangible, non-transitory, machine-readable storage media and including instructions executable on one or more digital and / or quantum processing devices. The systems described herein, or portions thereof, may each be implemented as an apparatus, method, or electronic system that may include one or more digital and / or quantum processing devices and memory for storing executable instructions for performing the operations described herein.

[0075] While this specification contains many details of specific embodiments, these should not be construed as limiting the scope of what may be claimed, but rather as descriptions of features that may be inherent in particular embodiments. Certain features described herein in the context of separate embodiments may also be implemented in combination in a single embodiment. Conversely, various features of the invention that are described in the context of a single embodiment may also be provided in multiple embodiments separately or in any suitable subcombination. Furthermore, while features may be described above as operating in a particular combination and may initially be claimed as such, one or more features from a claimed combination may, in some cases, be deleted from the combination, and the claimed combination may be directed to a subcombination or a variation of the subcombination.

[0076] Similarly, while operations are shown in the figures in a particular order, this should not be understood as requiring that such operations be performed in the particular order or sequence shown, or that all of the illustrated operations be performed, to achieve desirable results. In certain situations, multitasking and parallel processing may be advantageous. Furthermore, the separation of various system modules and components in the above-described embodiments should not be understood as requiring such separation in all embodiments, and it should be understood that the above-described program components and systems may generally be integrated together in a single software product or packaged in multiple software products.

[0077] Specific embodiments of the present invention have been described. Other embodiments are within the scope of the following claims. For example, the actions recited in the claims may be performed in a different order and still produce desirable results. By way of example, the processes depicted in the accompanying figures do not necessarily require the particular order shown or sequential order to achieve desirable results. In some cases, multitasking and parallel processing may be advantageous.

Claims

1. 1. A method for operating a quantum computing system (QCS) including a set of qubits, comprising: determining selected pulse delays for successive pulses of a series of qubit rotation pulses applied to each qubit of the set of qubits, wherein each qubit rotation pulse of the series applied to a qubit of the set of qubits causes a rotation of the quantum state of the qubit, and wherein the selected pulse delays increase a probability that the series of qubit rotation pulses causes leakage of at least a portion of the set of qubits from a computation subspace of the QCS to an excitation subspace of the QCS; identifying a pair of qubits in the set of qubits that contribute to the leakage of the set of qubits from the computation subspace to the excitation subspace based on the selected pulse delay, the pair of qubits comprising a source qubit and a receiver qubit; determining values ​​for a set of compensation parameters of a compensation signal using the pair of qubits, wherein when a control signal is provided to the source qubit and the compensation signal is provided to the receiver qubit, the probability that the control signal causes leakage of the receiver qubit from the computation subspace to the excitation subspace is reduced; A method comprising:

2. determining that the control signal should be provided to the source qubit; providing the control signal to the source qubit in response to determining that the control signal should be provided to the source qubit; providing the compensation signal to the receiver qubit in response to determining that the control signal should be provided to the source qubit, the compensation signal being based at least in part on the values ​​of the set of compensation parameters; The method of claim 1 further comprising:

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

4. 2. The method of claim 1 , wherein each qubit rotation pulse of the series of qubit rotation pulses applied to the qubit is a π rotation pulse that generates a rotation of the quantum state of the qubit, the rotation about at least one of an x-axis or a y-axis of a Bloch sphere representation of the quantum state of the qubit.

5. The method of claim 1 , wherein the leakage of the receiver qubit from the computation subspace to the excitation subspace comprises a transition of the quantum state of the receiver qubit from a first excited state to a second excited state.

6. Determining the selected pulse delay comprises: repeatedly providing the series of qubit rotation pulses to each qubit of the set of qubits, wherein during each repetition of providing the series of qubit rotation pulses, a pulse delay between successive pulses of the series of qubit rotation pulses is held constant, and the pulse delay is varied between successive repetitions of providing the series of qubit rotation pulses to each qubit of the set of qubits such that a window of pulse delay is swept over the repeated provision of the series of qubit rotation pulses to each qubit of the set of qubits; measuring a quantum state of each qubit of the set of qubits in response to each iteration of providing the series of qubit rotation pulses to each qubit of the set of qubits, the iteration corresponding to a particular pulse delay in the window of pulse delays; determining a probability that, for the particular pulse delay, the quantum state of the set of qubits will transition from a first excited state to one or more higher excited states in response to measuring the quantum state of each qubit of the set of qubits for the iteration corresponding to the particular pulse delay; identifying the selected pulse delay as a pulse delay of the window of pulse delays that increases the probability of generating the transition of the quantum state of the set of qubits from the first excited state to the one or more higher excited states; The method of claim 1 , comprising:

7. 2. The method of claim 1 , wherein the pairs of qubits that contribute to the leakage of the set of qubits from the computation subspace to the excitation subspace are pairs of qubits from all possible pairings of the set of qubits that dominate the leakage of the portion of the set of qubits from the computation subspace to the excitation subspace.

8. Identifying the pairs of qubits that contribute to the leakage of the set of qubits from the computation subspace to the excitation subspace comprises: iteratively selecting each possible pair of qubits from a set of all possible pairings of qubits, each selected possible qubit pair including 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 of the selected possible qubit pair according to the selected pulse delay; measuring a quantum state of each of the first qubit and the second qubit of the selected possible qubit pair in response to providing the series of qubit rotation pulses to each of the first qubit and the second qubit; determining, for each selected possible qubit pair, and based on measuring the quantum state of each of the first qubit and the second qubit, a probability that the series of qubit rotation pulses will cause the quantum state of at least one of the first qubit or the second qubit to transition to a second excited state according to the selected pulse delay; identifying a pair of qubits in the set of qubits that maximizes the probability that the series of qubit rotation pulses will cause the transition of the quantum state of the at least one of the first qubit or the second qubit to the second excited state according to the selected pulse delay; The method of claim 1 , comprising:

9. 2. The method of claim 1 , wherein the value of the set of compensation parameters for the compensation signal is selected from a space of possible values ​​of the set of compensation parameters, the selected value being a value from the space of possible values ​​that minimizes the probability that the control signal will produce leakage of the receiver qubit from the computation subspace to the excitation subspace.

10. 2. The method of claim 1 , wherein providing the compensation signal to the receiver qubit compensates for the stimulating signal provided to the receiver qubit such that the compensation signal prevents the leakage of the receiver qubit from the computation subspace to the excitation subspace that a stimulating signal would normally cause, and the stimulating signal is induced from the control signal provided to the source qubit.

11. 1. A method for operating a quantum computing system (QCS) including a set of qubits, comprising: determining that a control signal should be provided to a source qubit of the set of qubits; providing the control signal to the source qubit in response to determining that the control signal should be provided to the source qubit; providing a compensation signal to a receiver qubit of the set of qubits in response to determining that the control signal should be provided to the source qubit, the provided compensation signal being based at least in part on a value of a set of compensation parameters, the value of the set of compensation parameters being determined such that providing the compensation signal to the receiver qubit compensates for an induced signal provided to the receiver qubit, the compensation signal preventing leakage of the receiver qubit from a computation subspace of the QCS to an excitation subspace of the QCS, the induced signal being induced by providing the control signal to the source qubit; A method comprising:

12. The method of claim 11 , further comprising determining the values ​​of the set of compensation parameters based on a Ramsey error filter procedure.

13. The Ramsey error filter procedure includes the action: determining selected pulse delays for successive pulses of a series of qubit rotation pulses applied to each qubit of the set of qubits, wherein each qubit rotation pulse of the series of qubit rotation pulses applied to a qubit of the set of qubits causes a rotation of the quantum state of the qubit, and wherein the selected pulse delays increase the probability that the series of qubit rotation pulses causes leakage of the set of qubits from a computation subspace of the QCS to an excitation subspace of the QCS; identifying a pair of qubits in the set of qubits that contribute to the leakage of the set of qubits from the computation subspace to the excitation subspace based on the selected pulse delay, the pair of qubits including the source qubit and the receiver qubit; determining the values ​​of the set of compensation parameters of the compensation signal using the pair of qubits, wherein when the control signal is provided to the source qubit and the compensation signal is provided to the receiver qubit, the probability that the control signal will cause leakage of the receiver qubit from the computation subspace to the excitation subspace is reduced; 13. The method of claim 12, comprising:

14. 14. The method of claim 13, wherein each qubit rotation pulse of the series of qubit rotation pulses applied to the qubit is a π rotation pulse that generates a rotation of the quantum state of the qubit, the rotation about at least one of an x-axis or a y-axis of a Bloch sphere representation of the quantum state of the qubit.

15. The method of claim 13 , wherein the leakage of the receiver qubit from the computation subspace to the excitation subspace comprises a transition of the quantum state of the receiver qubit from a first excited state to a second excited state.

16. Determining the selected pulse delay comprises: repeatedly providing the series of qubit rotation pulses to each qubit of the set of qubits, wherein during each repetition of providing the series of qubit rotation pulses, a pulse delay between successive pulses of the series of qubit rotation pulses is held constant, and the pulse delay is varied between successive repetitions of providing the series of qubit rotation pulses to each qubit of the set of qubits such that a window of pulse delay is swept over the repeated provision of the series of qubit rotation pulses to each qubit of the set of qubits; measuring the quantum state of each qubit of the set of qubits in response to each iteration of providing the series of qubit rotation pulses to each qubit of the set of qubits, the iteration corresponding to a particular pulse delay in the window of pulse delays; determining a probability that, for the particular pulse delay, the quantum state of the set of qubits will transition from a first excited state to one or more higher excited states in response to measuring the quantum state of each qubit of the set of qubits for the iteration corresponding to the particular pulse delay; identifying the selected pulse delay as a pulse delay in the window of pulse delays that maximizes the probability of generating the transition of the quantum state of the set of qubits from the first excited state to the one or more higher excited states; 14. The method of claim 13, comprising:

17. Identifying the pairs of qubits that contribute to the leakage of the set of qubits from the computation subspace to the excitation subspace comprises: iteratively selecting each possible pair of qubits from a set of all possible pairings of qubits, each selected possible qubit pair including 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 of the selected possible qubit pair according to the selected pulse delay; measuring a quantum state of each of the first qubit and the second qubit of the selected possible qubit pair in response to providing the series of qubit rotation pulses to each of the first qubit and the second qubit; determining, for each selected possible qubit pair, and based on measuring the quantum state of each of the first qubit and the second qubit, a probability that the provided series of qubit rotation pulses will cause the quantum state of at least one of the first qubit or the second qubit to transition to a second excited state according to the selected pulse delay; identifying a pair of qubits in the set of qubits that maximizes the probability that the provided series of qubit rotation pulses will cause the transition of the quantum state of the at least one of the first qubit or the second qubit to the second excited state according to the selected pulse delay; 14. The method of claim 13, comprising:

18. 12. The method of claim 11 , wherein the value of the set of compensation parameters for the compensation signal is selected from a space of possible values ​​of the set of compensation parameters, the selected value being a value from the space of possible values ​​that reduces the probability that the control signal will cause leakage of the receiver qubit from the computation subspace to the excitation subspace.

19. 1. 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, the operations including: determining that a control signal should be provided to a source qubit of the set of qubits; providing the control signal to the source qubit in response to determining that the control signal should be provided to the source qubit; providing a compensation signal to a receiver qubit of the set of qubits in response to determining that the control signal should be provided to the source qubit, the provided compensation signal being based at least in part on values ​​for a set of compensation parameters, the values ​​of the set of compensation parameters being determined such that providing the compensation signal to the receiver qubit compensates for an induced signal provided to the receiver qubit, the compensation signal preventing leakage of the receiver qubit from a computation subspace of the QCS to an excitation subspace of the QCS, the induced signal being induced by providing the control signal to the source qubit; 1. A quantum computing system (QCS) comprising:

20. The operation is determining the values ​​for the set of compensation parameters based on a Ramsey error filter procedure; 20. The QCS of claim 19, further comprising:

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