Frequency Configuration in Quantum Gates for Leakage Removal

Abstract

A quantum computing system configured to eliminate the leaky state can include quantum hardware including a first qubit and a second qubit, where the first qubit is configured to have a first transition frequency and the second qubit is configured to have a second transition frequency, where the first transition frequency is higher than the second transition frequency. The quantum computing system can include one or more quantum control devices configured to control operations of at least the first qubit and the second qubit, where the one or more quantum control devices are configured to implement quantum gate operations on the first qubit and the second qubit based at least in part on the first transition frequency and the second transition frequency, and where the one or more quantum control devices are configured to periodically reset a quantum state of the first qubit.

Description

Technical Field

[0001] Priority Claim This application claims the benefit of priority of U.S. Provisional Application Serial No. 63 / 161,180, filed on March 15, 2021, entitled "Frequency Configuration in Quantum Gates for Leakage Removal", the content of which is incorporated herein by reference.

[0002] Field The present disclosure generally relates to frequency configuration in quantum gates for leakage removal.

Background Art

[0003] Background Quantum computing is a computing technique that utilizes quantum effects such as superposition and entanglement of ground states to execute certain calculations 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 manipulate information using quantum bits (qubits). A qubit may refer to a quantum device that enables superposition of multiple states (e.g., data in both the "0" and "1" states), and / or a quantum device that enables superposition of the data of multiple states itself. According to conventional terminology, the superposition of the "0" and "1" states in a quantum system can be expressed, for example, as a|0> + b|1>. The "0" and "1" states of a digital computer are respectively similar to the |0> and |1> ground states of a qubit.

Summary of the Invention

[0004] Summary Aspects and advantages of embodiments of the present disclosure are described in part in the following description, or can be learned from the following description, or can be learned through the practice of the embodiments.

[0005] Certain exemplary aspects of the present disclosure relate to a quantum computing system configured to remove leakage states. The quantum computing system may comprise quantum hardware including a first qubit and a second qubit, the first qubit being configured to have a first transition frequency, the second qubit being configured to have a second transition frequency, and the first transition frequency being higher than the second transition frequency. The quantum computing system may comprise one or more quantum control devices configured to control the operation of at least the first qubit and the second qubit, the one or more quantum control devices being configured to implement quantum gate operations on the first qubit and the second qubit based at least in part on the first transition frequency and the second transition frequency, and the one or more quantum control devices being configured to periodically reset the quantum state of the first qubit.

[0006] Other exemplary aspects of the present disclosure relate to a quantum computing system configured to remove leakage states. The quantum computing system may comprise quantum hardware including a plurality of qubits arranged in a qubit grid, the plurality of qubits including one or more data qubits configured to implement quantum gate operations using a plurality of measurement qubits, each of the quantum gate operations including a high frequency side and a low frequency side, the low frequency side being configured to be implemented in the one or more data qubits.

[0007] Other exemplary aspects of the present disclosure relate to a method implemented by a computer to implement quantum gate operations. The method implemented by the computer may include one or more quantum control devices setting a first qubit of the quantum hardware to a first transition frequency. The method implemented by the computer includes one or more quantum control devices setting a second qubit of the quantum hardware to a second transition frequency, where the first transition frequency is higher than the second transition frequency. The method implemented by the computer can include one or more quantum control devices implementing a quantum gate operation on the first qubit and the second qubit based at least in part on the first transition frequency and the second transition frequency, and the one or more quantum control devices are configured to periodically reset the quantum state of the first qubit.

[0008] Other aspects of the present disclosure relate to various systems, devices, non-transitory computer-readable media, user interfaces, and electronic devices.

[0009] 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 herein and constitute a part of this specification, illustrate exemplary embodiments of the present disclosure and, together with the description, serve to explain the relevant principles.

[0010] A detailed discussion of embodiments directed to those of ordinary skill in the art is set forth in this specification with reference to the accompanying drawings.

Brief Description of the Drawings

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[0012] Detailed Description Exemplary aspects of the present disclosure relate to frequency configurations in quantum gates for leak removal, and more particularly, to frequency configurations in a quantum grid (e.g., including measurement qubits and data qubits) for separating potential leak points for removal from a quantum computing system. Some quantum gates (e.g., a controlled-Z adiabatic quantum gate) can be implemented based at least in part on a frequency difference between the operating frequencies (e.g., transition frequencies) of a first qubit and a second qubit. The quantum gate can be implemented in one of two configurations, including a configuration where the operating frequency of the first qubit is higher than the operating frequency of the second qubit, or a configuration where the operating frequency of the second qubit is higher than the operating frequency of the first qubit. According to an exemplary aspect of the present disclosure, a quantum gate operation can be configured such that the high-frequency side of the quantum gate operation is provided to a measurement qubit and the low-frequency side of the quantum gate operation is provided to a data qubit. The measurement qubit can be periodically refreshed to remove leaky states. This configuration can reduce the impact of leaky states on the operation of the quantum computing system.

[0013] A quantum computing system can include a qubit grid that includes a plurality of qubits arranged in a grid configuration. The qubit grid can include one or more data qubits and one or more measurement qubits. For example, in some implementations, the qubit grid can be an interleaved grid of data qubits and measurement qubits such that each data qubit is surrounded within the grid by measurement qubits and / or each measurement qubit is surrounded within the grid by data qubits (e.g., other than at the edges of the qubit grid). The data qubits can perform calculations for the evaluation of one or more quantum algorithms. Additionally and / or alternatively, the measurement qubits can be configured to read out and / or monitor the parity of the quantum computing system (e.g., the data qubits). For example, the quantum readout can be read out periodically (e.g., at intervals on the order of microseconds) from the measurement qubits.

[0014] This qubit grid can be implemented according to various quantum error correction codes, such as, for example, a quantum surface code or a repetition code, which is a simplified version thereof. For example, the repetition code can be a simplified version of the quantum surface code that is useful for certain tasks such as testing. Exemplary aspects of the present disclosure can be useful in a quantum computing system according to a quantum error correction code having an alternating grid of qubits.

[0015] The qubits can be frequency-variable qubits such that the operating frequency of the qubits (e.g., the transition frequency) can be changed. For example, in some implementations, the transition frequency of the qubits can be changed, such as within a range of candidate transition frequencies. In some implementations, the operating frequency (e.g., the transition frequency) can be changed by one or more quantum control devices.

[0016] Among quantum gate operations (referred to as quantum gates in this specification), there are some that can be realized at least partially based on the operating frequency of qubits (e.g., transition frequency). As an example, a quantum gate can be a non-adiabatic quantum gate. A non-adiabatic quantum gate can be realized by resonance of the transition frequencies between a first qubit and a second qubit. For example, a non-adiabatic controlled-Z (also called CZ) quantum gate can be realized based on resonance between the 01 transition frequency of the first qubit and the 12 transition frequency of the second qubit.

[0017] While realizing a gate (e.g., non-adiabatic controlled-Z) between a first qubit and a second qubit, the operating frequencies of the first qubit and the second qubit can be adjusted based on a target frequency difference |f1 - f2| between the operating frequency f1 of the first qubit and the operating frequency f2 of the second qubit. For example, the first qubit and / or the second qubit can be adjusted to realize a quantum gate in one of two configurations where f1 > f2 or f1 < f2, but in either case, a common frequency difference is defined between the two qubits. Both configurations are effective in realizing the same quantum gate.

[0018] However, aspects of the present disclosure recognize that while both configurations are effective for the implementation of (e.g., non-adiabatic controlled-Z) quantum gates, these two configurations have a slight operational difference that may be useful for reducing the likelihood of leakage states, such as non-computational leakage states from computational quantum states |0> and |1> to, for example, |2>, |3>, and higher, in exemplary aspects of the present disclosure. Leakage states in data qubits can be significantly more destructive to quantum code evaluation than other errors such as bit flips, phase flips, and gate errors. Qubits preferably operate in the states |0> and |1>, or superpositions thereof. However, qubits sometimes leak out of the computational space of |0> and |1> and enter the excitation space or non-computational space of leakage states |2> or higher. Such leakage states can cause inaccurate evaluation of quantum algorithms. Further, in some cases, leakage states may also propagate to other qubits.

[0019] As an example, consider the rule where f 01 means the frequency difference between the |0> state and the |1> state. The frequencies of two qubits can be offset by qubit detuning represented by the symbol η. Due to this interval, for example, resonance occurs between f 12 of one qubit and f 01 of another qubit. In one example implementation of a non-adiabatic controlled-Z gate, the initial two-qubit state |11> is involved in Rabi oscillations with the state |20> of approximately the same energy. In this example, since f1 > f2, |2> is on the higher-frequency qubit. Due to incomplete calibration and / or other factors, leakage state |2> is generally generated more frequently on the higher-frequency qubit compared to the lower-frequency qubit.

[0020] Furthermore, a physical mechanism can remove the leakage state |2> from the low-frequency qubits, resulting in a reduction of leakage in the low-frequency qubits. This physical mechanism is due to the fact that the energies of states |12> and |30> are approximately equal. For example, due to the anharmonic offset described above, resonance-like occurs between the f of one qubit 23 and the f of another qubit 12 such that the energies of states |12> and |30> become approximately equal. This approximately equal energy causes resonance between the states. Therefore, when the |12> state exists, the |2> state is removed and reset to the |0> state. However, this mechanism results in creating the |3> state on the high-frequency qubits. In this way, the leakage is essentially moved from the low-frequency qubits to the high-frequency qubits. For example, in one implementation of the repetition code and / or surface code, the probability that the leakage state moves from the low-frequency side of the non-adiabatic controlled-Z gate to the high-frequency side of this gate is about 20%. Thus, when the leakage state deteriorates the performance of some more vulnerable qubits more than other qubits, it may be beneficial to place the more vulnerable qubits (e.g., non-adiabatic controlled-Z) on the low-frequency side of the quantum gate.

[0021] This principle can also be applied to quantum error correction codes such as the repetition code and surface code. For example, at least in these codes (or other suitable quantum grid configurations), there can be two types of qubits including data qubits and measurement qubits. A quantum gate (e.g., non-adiabatic CZ gate) can be applied between the data qubit and the measurement qubit. According to an exemplary aspect of the present disclosure, the measurement qubit can be periodically reset from any state (e.g., |1>, |2>, |3>) to |0>. Therefore, the leakage state of the measurement qubit can significantly reduce the degradation to the quantum computing system compared to the leakage state in the data qubit.

[0022] Thus, exemplary aspects of the present disclosure relate to defining qubit frequencies for realizing the high-frequency side and the low-frequency side of quantum gate operations in order to reduce the possibility of leakage states existing in a quantum computing system. For example, according to an exemplary aspect of the present disclosure, the high-frequency side of a (e.g., non-adiabatic controlled-Z) quantum gate can be realized in a measurement qubit such that a potential leakage state is more likely to move to the measurement qubit. The measurement qubit can be periodically refreshed or reset (e.g., by one or more quantum control devices) such that the leakage state can be removed from the quantum computing system, for example, during some of the normal quantum computing operations and / or supplementary to the normal quantum computing operations.

[0023] For example, one exemplary implementation according to an exemplary aspect of the present disclosure provides a quantum computing system configured to remove leakage states. The quantum computing system includes quantum hardware including a first qubit and a second qubit. The quantum computing system may further include one or more quantum control devices configured to control the operation of at least the first qubit and the second qubit. For example, the one or more quantum control devices may be configured to perform quantum gate operations on the first qubit and the second qubit. In some implementations, the quantum gate operations can be non-adiabatic quantum gate operations and / or controlled gate operations, such as controlled-Z gate operations such as non-adiabatic controlled-z gate operations.

[0024] The first qubit can be configured to have a first transition frequency, and / or the second qubit can be configured to have a second transition frequency, such as for the realization of quantum gate operations. The first transition frequency can be higher than the second transition frequency. For example, the first qubit and the second qubit can be on the side of quantum gate operations based on a frequency difference, such as being at least partially based on the first transition frequency and the second transition frequency. For example, by configuring the first transition frequency to be higher than the second transition frequency, there can be a higher possibility that a leakage state exists in the first qubit according to an exemplary aspect of the present disclosure.

[0025] Furthermore, one or more quantum control devices can be configured to periodically reset the quantum state of the first qubit. Accordingly, the leakage state existing in the first qubit can be removed from the quantum computing system. As an example, the first qubit can be a measurement qubit. Further and / or alternatively, the second qubit can be a data qubit. For example, the first (e.g., measurement) qubit can be periodically reset or refreshed in response to a quantum measurement or a quantum readout (e.g., a parity measurement) being performed from the measurement qubit. The first qubit can be periodically reset at any suitable interval, such as on the order of microseconds (e.g., about 1 microsecond).

[0026] Another exemplary aspect of the present disclosure provides a method implemented by a computer for realizing quantum gate operations. The method implemented by the computer can be realized by any suitable computing system, such as a quantum computing system including quantum hardware communicating with one or more quantum control devices.

[0027] The method may include configuring, e.g., by one or more quantum control devices, a first qubit of the quantum hardware at a first transition frequency. The method may include configuring, e.g., by one or more quantum control devices, a second qubit of the quantum hardware at a second transition frequency. The first transition frequency can be higher than the second transition frequency. For example, there may be a frequency difference between the first transition frequency and the second transition frequency. By configuring the first transition frequency to be higher than the second transition frequency, there may be an increased likelihood of a leakage state existing in the first qubit according to an exemplary aspect of the present disclosure.

[0028] The method may include, e.g., by one or more quantum control devices, performing a quantum gate operation on the first qubit and the second qubit based at least in part on the first transition frequency and the second transition frequency. For example, each of the first qubit and the second qubit can perform one side of the quantum gate operation. The quantum gate operation can be performed based at least in part on a frequency difference between the first qubit and the second qubit, such as being based at least in part on the first transition frequency and the second transition frequency. In some implementations, the quantum gate operation can be, or can include, a non-adiabatic controlled-Z quantum gate.

[0029] One or more quantum control devices may be configured to periodically reset the quantum state of a first qubit. Accordingly, leak states present in the first qubit can be removed from the quantum computing system. As an example, the first qubit can be a measurement qubit. Further and / or alternatively, the second qubit can be a data qubit. Additionally, in some implementations, the quantum hardware can be arranged in a quantum surface code. The first (e.g., measurement) qubit can be periodically reset or refreshed in response to a quantum measurement or quantum readout (e.g., parity measurement) having been performed on the measurement qubit. The first qubit can be periodically reset at any suitable interval, such as intervals on the order of microseconds (e.g., about 1 microsecond).

[0030] In some embodiments, this principle can be applied to a qubit grid that includes a plurality of qubits. In the qubit grid, a subset or all combinations of data qubits and measurement qubits can be configured that define a frequency difference for implementing quantum gate operations, where the operating frequency of the data qubits is lower than the operating frequency of the measurement qubits. For example, in some implementations, only a subset of the quantum gate operations in a particular (e.g., data) qubit are realized in a configuration where the operating frequency of the data qubit is lower than the operating frequency of the measurement qubit. In some implementations, all of the quantum gate operations in a particular (e.g., data) qubit can be realized in a configuration where the operating frequency of that qubit is lower than the operating frequency of an adjacent (e.g., measurement) qubit. It is desirable to avoid situations where a data qubit is on the high-frequency side of all (e.g., four) non-adiabatic controlled-Z gates connected to it, because leakage can accumulate on the data qubit where it may not be removed. For example, it can be beneficial for a data qubit to realize the low-frequency side of at least one quantum gate operation in the data qubit.

[0031] Another exemplary aspect of the present disclosure provides a quantum computing system configured to remove a leakage state. The quantum system may include quantum hardware including a plurality of qubits arranged in a qubit grid. The plurality of qubits may include one or more data qubits and / or a plurality of measurement qubits. For example, the plurality of qubits can be arranged in a quantum surface code, a repetition code, or the like.

[0032] One or more data qubits can be configured to implement quantum gate operations using a plurality of measurement qubits. Each quantum gate operation can include a high-frequency side and a low-frequency side. According to an exemplary aspect of the present disclosure, the low-frequency side is implemented in one or more data qubits. For example, according to an exemplary aspect of the present disclosure, by configuring the first transition frequency to be higher than the second transition frequency, the possibility of the leakage state existing in the first qubit becomes higher. In some implementations, the quantum gate operation can be a non-adiabatic quantum gate operation and / or a control gate operation, such as a control Z gate operation such as a non-adiabatic control z gate operation.

[0033] The quantum gate operation can be implemented between a first qubit and a second qubit. For example, to implement the quantum gate operation, the first qubit can be configured to have a first transition frequency and / or the second qubit can be configured to have a second transition frequency. When the first qubit is on the high-frequency side of the quantum gate operation and / or the second qubit is on the low-frequency side of the quantum gate operation, the first transition frequency can be made higher than the second transition frequency. For example, the first qubit and the second qubit can be on the side of the quantum gate operation based on a frequency difference, such as at least partially based on the first transition frequency and the second transition frequency.

[0034] In some exemplary implementations, the low-frequency side of the quantum gate operation is realized on the data qubit. Further and / or alternatively, the high-frequency side of the quantum gate operation can be realized in the measurement qubit. For example, if the data qubit is provided in a qubit grid surrounded by a plurality (e.g., four) of measurement qubits and configured to realize a plurality (e.g., four) of quantum gate operations using the plurality of measurement qubits, the data qubit can be provided on the low-frequency side of each of those quantum gate operations. Further and / or alternatively (e.g., in the case of a total of four quantum gate operations in the data qubit), the low-frequency side of two of the quantum gate operations can be realized in the data qubit among one or more data qubits, and / or the high-frequency side of two of the quantum gate operations can be realized in the data qubit. These configurations can be provided randomly and / or regularly throughout the quantum grid. For example, the grid may form a regular pattern of quantum gate operation configurations, and / or these configurations may be provided randomly or arbitrarily to satisfy other optimization constraints.

[0035] For example, in a surface code where four control-Z gates are provided for each data qubit and each code cycle, before the leakage state can be removably removed by resetting the measurement qubit, it may first move from the data qubit to the measurement qubit, and then from the measurement qubit to another data qubit, for the second time. One approach to reducing the likelihood of such occurrences according to an exemplary aspect of the present disclosure is to configure the data qubit with four control-Z gates such that the data qubit is on the low-frequency side of two of the four CZ gates and on the high-frequency side of the other two of the four CZ gates. Such a configuration can be provided randomly and / or regularly across the entire quantum grid. For example, by making it either a random or regular configuration, this can free up optimization considerations regarding other operational constraints.

[0036] Exemplary aspects are discussed herein with reference to implementations that include non-adiabatic control-Z gates for purposes of illustration. Note that the exemplary aspects of the present disclosure can be applied in several other suitable quantum computing systems, such as a quantum computing system that requires a settable frequency difference between two qubits where the qubits are susceptible to the effects of the leakage state and / or the leakage state can be removed from at least some of the qubits within the quantum computing system.

[0037] The systems and methods according to exemplary aspects of the present disclosure can provide many technical effects and advantages, including improvements in computing technology. As an example, the systems and methods according to exemplary aspects of the present disclosure comprise quantum hardware having a first qubit and a second qubit, the first qubit being configured to have a first transition frequency, the second qubit being configured to have a second transition frequency, the first transition frequency being higher than the second transition frequency, and the systems and methods further comprising one or more quantum control devices configured to control the operation of at least the first qubit and the second qubit, the one or more quantum control devices being configured to implement quantum gate operations on the first qubit and the second qubit based at least in part on the first transition frequency and the second transition frequency, and the one or more quantum control devices being configured to periodically reset the quantum state of the first qubit. For example, the systems and methods according to exemplary aspects of the present disclosure can provide an effective implementation of a quantum algorithm (e.g., a quantum gate operation) with improved robustness against leakage states.

[0038] The systems and methods according to exemplary aspects of the present disclosure can separate leakage states in qubits (e.g., measurement qubits) that are periodically refreshed or reset to a computational state so that the leakage states do not exist in a quantum computing system for a long period of time. For example, in some exemplary implementations, the lifetime of the leakage state |2> can be reduced to less than 3 cycles even without natural energy relaxation of the leakage state. Natural energy relaxation refers to the ability of a qubit to relax over time to a computational energy state. This can improve the accuracy of implementing a quantum algorithm. Further and / or alternatively, this can reduce the amount of computational time and / or other resources lost to the leakage state.

[0039] Next, with reference to the figures, exemplary embodiments of the present disclosure will be described in further detail. Here, when the term "about" is used with a value, it refers to within 20% of that value.

[0040] FIG. 1 shows an exemplary quantum computing system 100 according to an exemplary embodiment of the present disclosure. The exemplary system 100 is an example of a system on one or more classical computers or quantum computing devices in one or more locations and can implement the systems, components, and techniques described below. One of ordinary skill in the art will understand that other quantum computing architectures or systems can be used without departing from the scope of the present disclosure by using the disclosure provided herein.

[0041] System 100 includes quantum hardware 102 that communicates data with one or more classical processors 104. The quantum hardware 102 includes components for performing quantum computations. For example, the quantum hardware 102 includes a quantum system 110, control device(s) 112, and readout device(s) 114 (e.g., readout resonator(s)). The quantum system 110 may include one or more multi-level quantum subsystems such as a register of qubits. In some implementations, the multi-level quantum subsystem may include superconducting qubits such as flux qubits, charge qubits, transmon qubits, gmon qubits, etc.

[0042] The types of multi-level quantum subsystems utilized by system 100 can be diverse. For example, in some cases, it may be advantageous to include one or more readout devices (s) 114 attached to one or more superconducting qubits, such as transmon qubits, flux qubits, gmon qubits, xmon qubits, or other qubits. In other cases, ion traps, photonic devices, or superconducting cavities (e.g., capable of preparing states without the need for qubits) can be used. Yet another example of a multi-level quantum subsystem includes fluxmon qubits, silicon quantum dots, or phosphorus impurity qubits.

[0043] A quantum circuit can be constructed and applied to a register of qubits included in quantum system 110 via a plurality of control lines coupled to one or more control devices 112. Exemplary control devices 112 operating on a register of qubits can be used to implement quantum gates or quantum circuits having a plurality of 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 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 may be a superconducting qubit, and the control device 112 may be configured to supply control pulses to a control line for generating a magnetic field to adjust the frequency of the qubit.

[0044] 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 can include a quantum circuit, and the control device(s) 112 and the readout device(s) 114 can implement one or more quantum logic gates operating on the quantum system 102 via physical control parameters (e.g., microwave pulses) transmitted via the wires included in the quantum hardware 102. As yet another example of a control device, any waveform generator in which a digital to analog converter (DAC) creates a signal can be mentioned.

[0045] The readout device(s) 114 can be configured to perform a quantum measurement on the quantum system 110 and transmit the measurement result 108 to the classical processor 104. Further, the quantum hardware 102 can be configured to receive data specifying the physical control qubit parameter value 106 from the classical processor 104. The quantum hardware 102 can use the received physical control qubit parameter value 106 to update the operation of the control device(s) 112 and the readout device(s) 114 on the quantum system 110. For example, the quantum hardware 102 can receive data specifying a new value representing the voltage strength of one or more DACs included in the control device 112, and accordingly update the operation of the DAC on the quantum system 110. The classical processor 104 can be configured to initialize the quantum system 110 in an initial quantum state, for example, by transmitting data specifying an initial set of the parameters 106 to the quantum hardware 102.

[0046] The readout device(s) 114 can measure the state of an element such as a qubit by utilizing the impedance difference between the |0> state and the |1> state of a quantum system element like a qubit. For example, the resonance frequency of the readout resonator can take different values when the qubit is in the |0> state or the |1> state due to the non-linearity of the qubit. Therefore, the microwave pulse reflected from the readout device 114 carries an amplitude and a phase shift that depend on the state of the qubit. In some implementations, a perself filter can be used together with the readout device(s) 114 to prevent microwave propagation at the qubit frequency.

[0047] FIG. 2 shows an exemplary qubit grid 200 according to an exemplary embodiment of the present disclosure. For example, the qubit grid 200 can be provided according to a quantum surface code, a repetition code, etc. As shown in FIG. 2, the qubit grid 200 can be an interleaved qubit grid of one or more data qubits 202 and / or one or more measurement qubits 204. The measurement qubit 204 can be configured to provide readout at the output of the data qubit 202 and / or measure an error (e.g., parity). For example, using some or all of the data qubits 202, a time series of quantum gate operations that define a quantum algorithm can be realized across some or all of the data qubits 202. As shown in FIG. 2, the data qubits 202 can be surrounded by the measurement qubits 204. Further and / or alternatively, the measurement qubits 204 can be arranged within a square or other in-plane area defined by two or more (e.g., four) data qubits 202.

[0048] FIG. 3 shows an exemplary qubit grid 300 used to implement quantum gate operations according to an exemplary embodiment of the present disclosure. For example, the qubit grid 300 can be provided according to a quantum surface code, a repetition code, or the like. As shown in FIG. 3, the qubit grid 300 can be an interleaved qubit grid of one or more data qubits 202 and / or one or more measurement qubits 204. The measurement qubit 204 can be configured to provide a readout at the output of the data qubit 202 and / or measure an error (e.g., parity). For example, using some or all of the data qubits 202, a time series of quantum gate operations defining a quantum algorithm can be implemented across some or all of the data qubits 202.

[0049] As shown in FIG. 3, a quantum gate operation 302 (e.g., a non-adiabatic controlled-Z gate operation) can be implemented between two qubits such as the data qubit 202 and the measurement qubit 204. The quantum gate operation 302 can include a high-frequency side (indicated by f h shown) and a low-frequency side (indicated by f l shown). According to an exemplary aspect of the present disclosure, the low-frequency side is implemented in the data qubit 202. Further and / or alternatively, the high-frequency side is implemented in the measurement qubit 204. For example, according to an exemplary aspect of the present disclosure, by configuring the transition frequency of the measurement qubit 204 (e.g., f h ) to be higher than the transition frequency of the data qubit 202 (e.g., f l ), the probability of the leakage state existing in the first qubit can be higher. In some implementations, the quantum gate operation 302 can be a non-adiabatic quantum gate operation and / or a controlled gate operation, such as a controlled-Z gate operation such as a non-adiabatic controlled-z gate operation.

[0050] FIG. 4 shows an exemplary qubit grid 400 used to implement quantum gate operations according to an exemplary embodiment of the present disclosure. In the configuration shown in FIG. 4, the data qubit(s) 202 are implemented on the low-frequency side of each quantum gate operation 302. For example, if the data qubit 202 is provided in the qubit grid 400 so as to be surrounded by four quantum gate operations 302 (for example, four measurement qubits 204), the data qubit 202 can be provided on the low-frequency side of each of those four quantum gate operations 302.

[0051] FIG. 5 shows an exemplary qubit grid 500 used to implement quantum gate operations according to an exemplary embodiment of the present disclosure. In the qubit grid 500 of FIG. 5, the data qubit 202 is used to implement the low-frequency side of two of the quantum gate operations 502 and the high-frequency side of two of the quantum gate operations 504. These arrangements can be provided randomly and / or regularly throughout the quantum grid 500. For example, the grid 500 may form a regular pattern of quantum gate configurations 502, 504, and / or the configurations may be provided randomly or arbitrarily, such as to satisfy other optimization constraints.

[0052] For example, in a surface code where four control Z gates are provided for each data qubit 202 per code cycle, before the leakage state can be removably reset by resetting the measurement qubit 204, it can potentially move twice, first from the data qubit 202 to the measurement qubit 204, and then from the measurement qubit 204 to another data qubit 202. According to an exemplary aspect of the present disclosure, one approach to reducing the likelihood of such occurrences is to configure the data qubit 202 having four control Z gates 502, 504 such that the data qubit 202 is on the low-frequency side of two of the four CZ gates 502 and on the high-frequency side of the other two of the four CZ gates 504. Such a configuration can be provided randomly and / or regularly throughout the quantum grid 500. For example, by either a random or regular arrangement, this can free up optimization considerations regarding other operational constraints.

[0053] FIG. 6 is a frequency diagram 600 showing an exemplary configuration of state frequencies on qubits according to an exemplary aspect of the present disclosure. As used in FIG. 6, f 01 refers to, for example, the frequency difference between the |0> state and the |1> state, and other subscripts similarly refer to frequency differences. The frequencies of two qubits can be offset by a qubit anharmonicity 615 represented by the symbol η. As shown between the first qubit frequency diagram 610 and the second qubit frequency diagram 620, this spacing can cause, for example, a resonance between f 23 of one qubit and f 12 of another qubit. This resonance can contribute to the realization of an adiabatic control Z quantum gate operation between the f 12 level in the first qubit and the f 01 frequency in the second qubit, as shown in FIG. 6.

[0054] FIG. 7 is a flowchart diagram showing an exemplary method 700 for implementing quantum gate operations, according to an exemplary embodiment of the present disclosure. FIG. 7 shows steps that are executed in a particular order for purposes of illustration and discussion, but the methods of the present disclosure are not limited to the particularly illustrated order or arrangement. The various steps of method 700 can be omitted, rearranged, combined, and / or adapted in various ways without departing from the scope of the present disclosure. Method 700 can be implemented by any suitable computing system, such as a quantum computing system that includes quantum hardware that communicates with one or more quantum control devices, such as the quantum computing system 100 of FIG. 1.

[0055] Method 700 can include, at 702, configuring a first qubit of the quantum hardware at a first transition frequency (e.g., where one or more quantum control devices). Method 700 can include, at 704, configuring a second qubit of the quantum hardware at a second transition frequency (e.g., where one or more quantum control devices). The first transition frequency may be higher than the second transition frequency. For example, there may be a frequency difference between the first transition frequency and the second transition frequency. According to an exemplary aspect of the present disclosure, by configuring the first transition frequency to be higher than the second transition frequency, the likelihood of a leakage state existing in the first qubit can be made higher.

[0056] Method 700 can include, at 706, implementing a quantum gate operation on the first qubit and the second qubit, at least partially based on the first transition frequency and the second transition frequency (e.g., where one or more quantum control devices). For example, the first qubit and the second qubit can be used to implement aspects of a frequency-difference-based quantum gate operation, such as being at least partially based on the first transition frequency and the second transition frequency. In some implementations, the quantum gate operation can be, or can include, a non-adiabatic controlled-Z quantum gate.

[0057] One or more quantum control devices may be configured to periodically reset the quantum state of the first qubit. Thus, leakage states present in the first qubit can be removed from the quantum computing system. As an example, the first qubit may be a measurement qubit. Further and / or alternatively, the second qubit may be a data qubit. Further, in some implementations, quantum hardware can be placed in a quantum surface code. The first (e.g., measurement) qubit can be periodically reset or refreshed in response to a quantum measurement or quantum readout (e.g., parity measurement) being performed on the measurement qubit. The first qubit can be periodically reset at any suitable interval, such as at intervals on the order of microseconds (e.g., about 1 microsecond).

[0058] FIG. 8 is a block diagram showing an exemplary computing system 1000 that can be used to implement systems and methods according to exemplary embodiments of the present disclosure, such as the system described with reference to FIG. 1. System 1000 includes a control system 1010 and a quantum computing system 1030 communicatively coupled via a network 1050. One or more aspects of any of the methods described herein can be implemented on control system 1010 and / or quantum computing system 1030.

[0059] The control system 1010 can include any type of computing device (e.g., a classical computing device). The control system 1010 includes one or more processors 1012 and a memory 1014. The one or more processors 1012 can include any suitable processing device (e.g., a processor core, a microprocessor, an ASIC, an FPGA, a controller, a microcontroller, etc.) and can be one processor or multiple processors operably connected. The memory 1014 can include one or more non-transitory computer-readable storage media such as RAM, ROM, EEPROM, EPROM, flash memory devices, magnetic disks, and combinations thereof. The memory 1014 can store data 1016 (e.g., qubit parameters, measurements, etc.) and instructions 1018 that are executed by the processor 1012 to cause the control system 1010 to perform operations such as one or more aspects of the methods disclosed herein. The control system 1010 can be configured to process error information 1020 obtained by measuring the output of a quantum system (e.g., quantum system 1040) to identify errors in quantum computing according to an exemplary embodiment of the present disclosure. Further, the quantum control system 1010 can be configured to control the operation (e.g., transition frequency) of the quantum system 1040.

[0060] The quantum computing system 1030 includes one or more processors 1032 and a memory 1034. The one or more processors 1032 can include a suitable processing device (e.g., a processor core, a microprocessor, an ASIC, an FPGA, a controller, a microcontroller, etc.) and can be one processor or multiple processors operably connected. The memory 1034 can include one or more non-transitory computer-readable storage media such as RAM, ROM, EEPROM, EPROM, flash memory devices, magnetic disks, and combinations thereof. The memory 1034 stores data 1036 and instructions 1038 that are executed by the processor 1032 to cause the quantum computing system 1030 to perform operations such as realizing a quantum circuit having one or more quantum gates on a quantum system 1040 having a plurality of qubits and obtaining associated measurement values (e.g., error information 1020). The quantum computing system 1030 can be similar to the quantum computing system discussed and described with reference to FIG. 1. Without departing from the scope of the present disclosure, other suitable quantum computing systems can be used.

[0061] The network 1050 can be any type of communication network such as a local area network (e.g., an intranet), a wide area network (e.g., the Internet), or some combination thereof, and can include any number of wired or wireless links. Generally, communication on the network 1050 can be transmitted via any type of wired and / or wireless connection using a variety of communication protocols (e.g., TCP / IP, HTTP, SMTP, FTP), encodings or formats (e.g., HTML, XML), and / or protection schemes (e.g., VPN, secure HTTP, SSL). In some implementations, the network 1050 can be omitted so that the control system 1010 directly signals with the quantum computing system 1030.

[0062] The digital, classical, and / or quantum subject matters described herein, as well as the examples of digital functional operations and quantum operations, may be tangibly realized in digital electronic circuits, appropriate quantum circuits, or, more generally, in digital and / or quantum computer software or firmware realized in a quantum computing system, in digital and / or quantum computer hardware including the structures disclosed herein and their structural equivalents, or in 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 cryptographic system, or a quantum simulator.

[0063] Examples of the digital and / or quantum subject matters described herein may be realized 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 to control the operation of, a data processing apparatus. The digital and / or quantum computer storage medium can 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 these. Alternatively or additionally, the program instructions can be encoded in an artificially generated propagated signal (e.g., an electrical, optical, or electromagnetic signal generated by a machine) capable of encoding digital and / or quantum information and generated to encode digital and / or quantum information to be transmitted to an appropriate receiving device and executed by a data processing apparatus.

[0064] The terms "quantum information" and "quantum data" refer to information or data that is carried, held, or stored in a quantum system, and the smallest non-trivial system defines a qubit, i.e., the unit of quantum information. Note 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, for example, multi-level systems having two or more levels. As examples, such systems can include atoms, electrons, photons, ions, or superconducting qubits. In many realizations, the computational basis states are identified with the ground state and the first excited state, but it is understood that other settings are possible where the computational states are identified with higher-level excited states (e.g., qubits).

[0065] The term "data processing device" refers to digital and / or quantum data processing hardware and encompasses any kind of device, apparatus, and machine for processing digital and / or quantum data, including, as examples, programmable digital processors, programmable quantum processors, digital computers, quantum computers, or multiple digital and quantum processors, or computers, and combinations thereof. Also, the device can be, or further include, dedicated logic circuits, such as field programmable gate arrays (FPGAs), or application-specific integrated circuits (ASICs), or quantum simulators, i.e., quantum data processing devices designed to simulate or generate information about a particular quantum system. In particular, a quantum simulator is a dedicated quantum computer that does not have the ability to perform universal quantum computing. The device can optionally include, in addition to the hardware, code that creates an execution environment for digital and / or quantum computer programs, such as code that constitutes processor firmware, protocol stacks, database management systems, operating systems, or combinations of one or more of them.

[0066] A digital or classical computer program (also called or described as a program, software, software application, module, software module, script, or code) can be written in any form of programming language, including compiler languages or interpreter languages or declarative languages or procedural languages, and can be deployed in any form, such as 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 (also called or described as a program, software, software application, module, software module, script, or code) can be written in any form of programming language, including compiler languages or interpreter languages or declarative languages or procedural languages, can be converted into a suitable quantum programming language, or can be written in a quantum programming language (e.g., QCL, Quipper, Cirq, etc.).

[0067] Digital and / or quantum computer programs can, but need not, correspond to files in a file system. The program can be stored in part of a file that holds 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 related files (e.g., files storing one or more modules, subprograms, or portions of code). Digital and / or quantum computer programs can be deployed and executed on one digital computer or one quantum computer, or on multiple digital and / or quantum computers distributed across one site or multiple sites 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). In general, digital data communication networks cannot transmit quantum data, but quantum data communication networks can transmit both quantum data and digital data.

[0068] The processes and logical flows described herein can be performed by one or more programmable digital and / or quantum computers operating using one or more digital and / or quantum processors and, as necessary, executing one or more digital and / or quantum computer programs to process input digital and quantum data and generate an output. The processes and logical flows can also be performed by, or by a combination of, dedicated logic circuitry (e.g., an FPGA or ASIC) or a quantum simulator and can be embodied as such a device.

[0069] For one or more digital and / or quantum computers or systems of processors to be "configured to" or "operable to" perform a particular operation or action means that software, firmware, hardware, or a combination thereof is installed on the system and, when operating, causes the system to perform the operation or action. For one or more digital and / or quantum computer programs to be configured to perform a particular operation or action means that the one or more programs include instructions that, when executed by a digital and / or quantum data processing apparatus, cause the apparatus to perform the operation or action. A quantum computer may receive from a digital computer instructions that, when executed by the quantum computing apparatus, cause the apparatus to perform the operation or action.

[0070] Digital and / or quantum computers suitable for the execution of 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 digital and / or quantum central processing unit. In general, a digital and / or quantum central processing unit receives instructions as well as digital and / or quantum data from read-only memory, random access memory, or a quantum system suitable for transmitting quantum data (e.g., photons), or a combination thereof.

[0071] Examples of 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 as well as digital and / or quantum data. The central processing unit and the memory may be supplemented by or incorporated into dedicated logic circuits or quantum simulators. Generally, a digital and / or quantum computer also includes, or is operably connected to a mass storage device (e.g., a magnetic disk, a magneto-optical disk, an optical disk, or a quantum system suitable for storing quantum information) for storing one or more digital and / or quantum data, or both, to transmit and receive digital and / or quantum data between such a mass storage device. However, a digital and / or quantum computer does not necessarily have such a device.

[0072] Digital and / or quantum computer program instructions and digital and / or quantum computer-readable media suitable for storing digital and / or quantum data include all forms of non-volatile digital and / or quantum memory, media, and memory devices, including, by way of example, semiconductor memory devices (e.g., EPROM devices, EEPROM devices, and flash memory devices), magnetic disks (e.g., internal hard disks or removable disks), magneto-optical disks, CD-ROM disks and DVD-ROM disks, and quantum systems (e.g., trapped atoms or trapped electrons). Note that quantum memory is a device capable of storing quantum data with high fidelity and high efficiency for a long time, for example, an optical-matter interface that uses light for transmission and uses matter to store and preserve quantum characteristics of quantum data such as superposition or quantum coherence.

[0073] The control of the various systems described herein, or portions thereof, can be implemented by a digital and / or quantum computer program product that includes instructions. These instructions are stored on one or more tangible, non-transitory, machine-readable storage media and are executable on one or more digital and / or quantum processing devices. The systems described herein, or portions thereof, can be realized as an apparatus, method, or electronic system that includes one or more digital and / or quantum processing devices and a memory that stores executable instructions for performing the operations described herein.

[0074] Although this specification contains many details, these details are not intended to limit the scope of what may be claimed and should instead be considered as descriptions of features specific to particular examples. Features described in the context of separate examples may be combined in a single example. Conversely, various features described in the context of a single example may be realized separately in multiple examples or in any suitable sub-combination. Additionally, features may be described as acting in a particular combination and may even initially be claimed as such, but one or more features of the claimed combination may be excluded from the combination, and the claimed combination may be directed to a sub-combination or a variation of a sub-combination.

[0075] Similarly, while the drawings illustrate operations in a particular order, it should not be understood that these operations must be performed in the particular order shown or sequentially to achieve desirable results, nor that all of the illustrated operations must be performed. In some situations, multitasking and parallel processing may be advantageous. Further, the separation of the various system modules and components in the examples described above should not be understood to be required in all examples, and the described program components and systems can generally be integrated into a single software product or packaged into multiple software products.

[0076] Specific examples of the subject matter have been described above. The following claims also include other examples. For example, desirable results can be obtained even if the operations recited in the claims are performed in a different order. As an example, in order to obtain desirable results, the processes shown in the accompanying drawings do not necessarily have to follow the specific order or sequence shown. In some cases, multitasking and parallel processing are advantageous.

Claims

1. A quantum computing system configured to remove a leakage state, comprising quantum hardware including measurement qubits and data qubits, wherein the measurement qubits are configured to have a first transition frequency, the data qubits are configured to have a second transition frequency, the first transition frequency is higher than the second transition frequency, and the quantum computing system further comprises one or more quantum control devices configured to control at least the operations of the measurement qubits and the data qubits, the one or more quantum control devices being configured to perform quantum gate operations on the measurement qubits and the data qubits based at least in part on the first transition frequency and the second transition frequency, and the one or more quantum control devices being configured to periodically reset the quantum state of the measurement qubits. A quantum computing system.

2. The quantum computing system according to claim 1, wherein the quantum gate operation includes a non-adiabatic quantum gate operation.

3. The quantum computing system according to claim 1 or 2, wherein the quantum gate operation includes a control gate operation.

4. The quantum computing system according to claim 3, wherein the control gate operation includes a controlled-Z gate operation.

5. The quantum computing system according to any one of claims 1 to 4, wherein the one or more quantum control devices are configured to periodically reset the quantum state of the measurement qubits to the |0> state.

6. A quantum computing system configured to remove a leakage state, Quantum hardware comprising a plurality of qubits arranged in a qubit grid, wherein the plurality of qubits includes one or more data qubits configured to implement quantum gate operations using a plurality of measurement qubits. Each of the quantum gate operations includes a high-frequency side and a low-frequency side, the high-frequency side being implemented in some or all of the plurality of measurement qubits, and the low-frequency side being configured to be implemented in the one or more data qubits. A quantum computing system. **Claim 7** The quantum computing system according to claim 6, wherein the plurality of qubits are arranged in a quantum surface code. **Claim 8** The quantum computing system according to claim 6 or 7, wherein the quantum gate operation includes a non-adiabatic quantum gate operation. **Claim 9** The quantum computing system according to any one of claims 6 to 8, wherein the quantum gate operation includes a controlled-Z gate operation. **Claim 10** For each quantum gate operation implemented in a data qubit among the one or more data qubits, the low-frequency side of the quantum gate operation is implemented in the data qubit. The quantum computing system according to any one of claims 6 to 9. **Claim 11** The low-frequency sides of two quantum gate operations among the quantum gate operations are implemented in a data qubit among the one or more data qubits, and the high-frequency sides of the two quantum gate operations among the quantum gate operations are implemented in the data qubit. The quantum computing system according to any one of claims 6 to 10. **Claim 12** Each data qubit of the one or more data qubits implements four quantum gate operations. The quantum computing system according to claim 11. **Claim 13** A method implemented by a computer to realize quantum gate operations, comprising: one or more quantum control devices setting a measurement qubit of the quantum hardware to a first transition frequency; the one or more quantum control devices setting a data qubit of the quantum hardware to a second transition frequency, wherein the first transition frequency is higher than the second transition frequency, and the method implemented by the computer further comprises: the one or more quantum control devices realizing a quantum gate operation on the measurement qubit and the data qubit based at least in part on the first transition frequency and the second transition frequency; the one or more quantum control devices being configured to periodically reset the quantum state of the measurement qubit. A method implemented by a computer. Claim 14 The method implemented by a computer according to claim 13, wherein the quantum gate operation includes a non-adiabatic controlled-Z quantum gate. Claim 15 A method implemented by a computer according to claim 13 or 14, wherein there is a frequency difference between the first transition frequency and the second transition frequency, and the quantum gate operation is realized based at least in part on the frequency difference. Claim 16 The method implemented by a computer according to any one of claims 13 to 15, wherein the quantum hardware is arranged in a quantum surface code.

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