Implementing quantum bit gates using phase-shifted microwave pulses

Abstract

Systems and methods are provided for implementing arbitrary single-qubit quantum gates using a sequence of single-qubit quantum gates. The systems and methods can implement a first quantum gate in a sequence of gates by applying a first phase-shift pulse sequence to a qubit. After implementing the first quantum gate, a second quantum gate in the sequence of gates can be implemented by applying a second phase-shift pulse sequence to the qubit. The implementation of the second quantum gate can introduce additional rotations. This additional rotation can be independent of the implementation of the first quantum gate. The pulses in the second phase-shift pulse sequence can be configured to implement: a virtual Z gate with a first rotation angle; an X gate with a second rotation angle; a virtual Z gate with a negative value of the first rotation angle.

Description

Technical Field

[0001] This disclosure relates generally to quantum computing, and more specifically to the implementation of qubit gates using phase-shifted microwave pulses. Background Technology

[0002] Quantum computing is performed on qubits or quantum bits. This computation can be performed using quantum gates, which are analogous to logic gates in digital computing. Quantum computers can be configured to implement arbitrary quantum gates using other sequences of fundamental quantum gates. The performance of a quantum computer can depend on the choice of fundamental quantum gates and how these gates are combined to implement arbitrary quantum gates. For example, a quantum computer may only be able to apply a finite number of fundamental quantum gates before the target qubit becomes decoherent due to noise. Therefore, the length of the sequence used to implement arbitrary quantum gates determines the number of arbitrary quantum gates that a quantum computer can apply. Furthermore, the choice of fundamental quantum gates affects the fidelity of arbitrary quantum gates and the calibration requirements of the quantum computer. Summary of the Invention

[0003] The systems and methods disclosed herein relate to the implementation of arbitrary single-qubit gates using one or more phase-shifted microwave pulse sequences. Embodiments of this disclosure can reduce the calibration requirements of quantum computers, reduce the number of microwave pulses required to implement arbitrary single-qubit gates, or support improved integration of two-qubit gates with single-qubit gates implemented using phase-shifted microwave pulses.

[0004] Embodiments of this disclosure include a system for applying a single-qubit quantum gate, the unitary form of which is specified by at least a first real parameter, a second real parameter, and a third real parameter. The system may include a qubit and a quantum controller coupled to the qubit via a power transmission system. The quantum controller may be configured to apply a phase-shifted Pauli gate sequence to the qubit to realize the single-qubit quantum gate, each phase-shifted Pauli gate in the sequence having a rotation angle and a phase shift. The first, second, and third real parameters of the unitary form may correspond to the rotation angle and the phase shift in the phase-shifted Pauli gate sequence, or the phase shift in the phase-shifted Pauli gate sequence.

[0005] Embodiments of this disclosure include a method for applying a sequence of quantum gates to a qubit. The method may include implementing the operation of a first quantum gate in the gate sequence by applying a first phase-shift pulse sequence to the qubit. The method may include further operations on a second quantum gate in the gate sequence after applying the first quantum gate. The second quantum gate may be implemented by applying a second phase-shift pulse sequence to the qubit. The additional rotation introduced by the implementation of the second quantum gate may be independent of the implementation of the first quantum gate. The pulses in the second phase-shift pulse sequence may be configured to implement a virtual Z-gate with a first rotation angle, an X-gate with a second rotation angle, and a virtual Z-gate with a negative value of the first rotation angle.

[0006] Embodiments of this disclosure include a method for implementing a combination of two-qubit gates and a tensor product of a first single-qubit gate and a second single-qubit gate. The method may further include operations of applying a first phase-shift pulse sequence to a first qubit, applying a second phase-shift pulse sequence to a second qubit, and applying a two-qubit gate to the first and second qubits. Applying the first phase-shift pulse sequence to the first qubit implements a first single-qubit gate. The implementation of the first single-qubit gate may introduce additional rotations. Applying the second phase-shift pulse sequence to the second qubit implements an additional rotation and a product of a second single-qubit gate. A two-qubit gate can be applied to the first and second qubits to obtain a phase-shifted version of the combination of two-qubit gates and a tensor product of the first and second single-qubit gates.

[0007] Embodiments of this disclosure include a non-transitory computer-readable medium containing instructions executable by a processor of a quantum controller. The quantum controller may be coupled to a qubit. The instructions may be executable to cause the quantum controller to perform operations for applying single-qubit quantum gates to the qubit. The single-qubit quantum gates may have unitary characteristics specified by a first real parameter, a second real parameter, and a third real parameter. The operation may include applying a phase-shifted Pauli gate sequence to the qubit. Each phase-shifted Pauli gate in the phase-shifted Pauli gate sequence may have a rotation angle and a phase shift. The first real parameter, the second real parameter, and the third real parameter may correspond to the rotation angle and phase shift in the phase-shifted Pauli gate sequence; or the phase shift in the phase-shifted Pauli gate sequence.

[0008] It should be understood that the foregoing general description and the following detailed description are merely exemplary and explanatory, and not intended to limit the embodiments of this disclosure as claimed. Attached Figure Description

[0009] The accompanying drawings, which form part of this specification, illustrate several embodiments and, together with the specification, serve to explain the principles and features of the disclosed embodiments. In the drawings: Figure 1 A Bloch sphere representation of a quantum bit according to an embodiment of the present disclosure is shown.

[0010] Figure 2 A first approximate implementation of an arbitrary single-qubit quantum gate using phase-shifted microwave pulses according to an embodiment of the present disclosure is shown.

[0011] Figure 3A and 3B Two different implementations of an arbitrary single-qubit quantum gate using phase-shifted microwave pulses according to embodiments of the present disclosure are shown.

[0012] Figure 4A A sequence of quantum gates including a two-qubit quantum gate is shown according to an embodiment of the present disclosure.

[0013] Figures 4B to 4D An embodiment according to this disclosure is shown, using Figure 3A Or the single-qubit quantum gate implemented by 3B Figure 4A The realization of quantum gate sequences.

[0014] Figure 5 A quantum controller for applying quantum gates to one or more qubits is illustrated according to an embodiment of the present disclosure. Detailed Implementation

[0015] Exemplary embodiments will now be described in detail, and discussed in conjunction with the accompanying drawings. In some cases, the same reference numerals will be used throughout all the drawings and in the following description to refer to the same or similar parts. Unless otherwise defined, technical or scientific terms have the meanings commonly understood by one of ordinary skill in the art. Embodiments of this disclosure have been described in sufficient detail to enable those skilled in the art to practice them. It should be understood that other embodiments may be utilized, and changes may be made without departing from the scope of the embodiments of this disclosure. Therefore, the materials, methods, and examples are illustrative only and are not intended to be limiting.

[0016] Quantum computers offer the ability to perform certain tasks (equivalent to solving certain problems) that are considered difficult for classical computers to handle, including any possible future classical computers. To understand the advantages of quantum computers, it is useful to understand the contrast between quantum and classical computers. Classical computers operate based on digital logic. Digital logic refers to a logical system that operates on units of information called bits. A bit can have two values, typically represented as 0 and 1, and is the smallest unit of information in digital logic. Operations are performed on bits using logic gates, which take one or more bits as input and output one or more bits. Typically, a logic gate usually has only one bit as output (although that single bit can be sent as input to multiple other logic gates), and the value of that bit usually depends on the values ​​of at least some of the input bits. In modern computers, logic gates are typically composed of transistors, and bits are usually represented by the voltage level of the wires connected to the transistors. A simple example of a logic gate is an AND gate, which (in its simplest form) takes two bits as input and outputs one bit. If both input values ​​are 1, the output of the AND gate is 1; otherwise, it is zero. By connecting the inputs and outputs of various logic gates in a specific way, classical computers can implement arbitrarily complex algorithms to accomplish various tasks.

[0017] On the surface, quantum computers appear to operate similarly to classical computers. Quantum computers operate within quantum logic. Quantum logic, as used herein, refers to a logical system that operates on units of information called "qubits," or simply "qubits." A qubit is the smallest unit of information in a quantum computer and can have any linear combination of two values, typically represented as... and The value of a quantum bit can be represented as... Unlike numeric bits, which can have values ​​of "0" or "1", It can have a value Where α and β are complex numbers (called "amplitudes"), except Quantum bits are not subject to any constraints. They can be constructed in various forms and can be represented as quantum states of components of a quantum computer. For example, qubits can be physically realized using photons with polarization as their quantum state (e.g., in lasers), electrons or ions with spin as their quantum state (e.g., trapped in an electromagnetic field), Josephson junctions with charge, current flux, or phase as their quantum states (e.g., in superconducting quantum systems), quantum dots with point spin as their quantum state (e.g., in semiconductor structures), topological quantum systems, or any other system that can provide two or more quantum states. Quantum logic can be used to create, remove, or modify qubits using quantum logic gates (or simply "quantum gates").

[0018] Mathematically, a quantum gate is a propagator acting on a quantum state. A quantum gate can take one or more qubits as input and output one or more qubits, and therefore can be represented as a matrix. Unlike classical logic gates (such as AND gates), quantum gates have the characteristic that their inputs can be determined based on their outputs and the transformation information applied to them; this is called "reversibility." This reversibility requires that the number of outputs of a quantum gate equals or exceeds the number of its inputs, and ensures that a known set of inputs can always be constructed given the outputs.

[0019] In physics, quantum gates can be implemented as hardware devices capable of generating laser pulses, electromagnetic waves (e.g., microwave pulses), electromagnetic fields, or used to alter, maintain, or control the quantum states of qubits. Superconducting quantum circuits can be used to implement qubits and quantum gates. Such qubits can be based on current (e.g., flux qubits), charge (e.g., charge qubits), or energy (e.g., phase qubits). Different implementations can have different characteristics, such as sensitivity to external noise, coherence time, or anharmonicity. For example, the transmon qubit, a charge qubit comprising a capacitively shunt Josephson junction, can exhibit reduced sensitivity to charge noise. As an additional example, the fluxonium qubit, a flux qubit comprising a Josephson junction shunt by capacitors and inductors (the latter can be implemented using an array of additional Josephson junctions), can exhibit long coherence time and large anharmonicity.

[0020] One way to visualize the value of a qubit is to represent it as a point on the surface of a Bloch sphere. As an example, Figure 1 A diagram illustrating qubits represented in a Bloch sphere 100 consistent with some embodiments of this disclosure is shown. The Bloch sphere 100 can be conceptualized as existing in a three-dimensional (3D) space having coordinate axes x, y, and z, respectively. It requires two values ​​(e.g., latitude and longitude, or...). Figure 1 The angles φ and θ are used to represent points on the surface of the Bloch sphere 100. Figure 1 In the diagram, the positive and negative poles of the z-axis correspond to... and For qubits ,because and Is the recipient Complex number of constraints It can be represented as a complex number The values ​​of a and b can be mapped to the azimuth angle φ and the equatorial angle θ in a Bloch sphere of 100, and can also be expressed as... Figure 1 A point on the surface of the 100-meter Bloch sphere.

[0021] Typically, quantum algorithms can be represented using underlying quantum circuits. A quantum circuit consists of one or more quantum gates. This is because quantum gates can transform qubits in an infinite number of ways (e.g., by changing the qubit's position). middle and The value of , therefore, there are infinitely many types of quantum gates. For example, since there are infinitely many ways to perform a unitary transformation, there are infinitely many quantum gates for performing a unitary transformation on a qubit. One type of quantum gate, called a "Pauli operator" or "Pauli gate," can be used to perform a unitary transformation on a qubit. For four Pauli operators, denoted as I, X, Y, and Z, where I is the identity operator, and X, Y, and Z represent rotations of 180° around the x-axis, y-axis, and z-axis in three-dimensional space, respectively. For example, in a two-state qubit system, a Pauli gate can be represented as a matrix , , and . The set of Pauli operators on a quantum bit can be defined as and , where the subscript indicates the qubit involved in the operator's action. For Qubit set, there are Pauli matrices, each matrix represents Possible tensor products (in the form of) For example, in a system comprising three qubits... , and In a three-qubit system, the action of Pauli Gates and their effects Pauli A door can be represented as

[0022] .

[0023] Pauli gates can be understood as rotations around the three principal axes of a Bloch sphere. For example, see... Figure 1 Pauli Men, Pauli Men and Pauli A door can be understood as a gate that allows the represented point to... Rotate about the x-axis, y-axis and z-axis of Bloch 100 respectively.

[0024] A single quantum gate can be implemented using other sequences of quantum gates, such as by combining arbitrary Pauli rotations or continuously parameterized geometric gates. However, the relationship between the gate parameters and the physical control parameters of the system can be complex. For example, a Pauli X-gate can be obtained by supplying microwave pulses to a superconducting quantum circuit that implements a qubit. The rotation angle of the Pauli X-gate... This can depend on the combination of the waveform, length, and amplitude of the microwave pulse. Furthermore, this relationship can be affected by pulse distortion or leakage of quantum information outside the computational subspace. Therefore, in this example, an accurate implementation of the Pauli X-gate may require tuning or calibration of the microwave pulse's waveform, length, and amplitude.

[0025] like Figure 2 As shown, some single quantum gate implementations support a more direct relationship between gate parameters and physical control parameters. Figure 2 An exemplary gate sequence 200 is shown, comprising two single-qubit gates (gates 201 and 203). Figure 2 As shown, a single-qubit gate 201 can be implemented using gate sequence 205, as follows: , in, It is an arbitrary Z-rotation: , in, yes X rotation: , X, Y, and Z are Pauli operators.

[0026] The gate sequence 205 can be approximated using phase-shifted microwave (PMW) pulses. Given an implementation... The microwave pulses used to create gates can be phase-shifted to achieve gate sequences. In this way, given the calibration The gate can be controlled using only one physical parameter: phase shift. To generate additional "virtual" elements. Gate. Unlike typical microwave pulse waveforms, lengths, and amplitudes, in this case, physical control parameters (phase shift) are mapped to gate parameters (Z-rotation). In some cases, only calibration is required. This reduces the system's calibration requirements. Furthermore, phase shifts can be precisely controlled (e.g., using a global frequency reference such as an atomic clock).

[0027] Embodiments of this disclosure use phase-shifted microwave (PMW) pulses to implement arbitrary single-qubit gates (e.g., using superconducting circuits). In some embodiments, the PMW pulses can implement X-gates. This is achieved by adding a phase shift to the X-gate. X-door can be with Gate conjugate. In the first general case, two PMWs can be used. A door and a PMW A gate is used to implement an arbitrary single-qubit gate, wherein, and This indicates the rotation angle of the unshifted X-pulse. In some special cases, only one or two PMWs may be used. A gate is used to implement a single qubit gate. In the second general case, a PMW gate can be used. Doors and PMW Gates are used to implement arbitrary single-qubit gates, where, This represents a rotation based on the unitary selection of the realized arbitrary single-qubit gate. The systems and methods disclosed herein can support quantum computing on superconducting circuits with minimal necessary X-pulse calibration.

[0028] Figure 2 The gate sequence 206 shown can be approximately implemented using a PMW pulse sequence to achieve gate sequence 205. The PMW pulse sequence may include a first phase-shift pulse 207 and a second phase-shift pulse 209. Pulse 207 generates the gate sequence. Introducing additional Rotation. The second phase shift pulse 209 generates the gate sequence. This compensates for the effects introduced by the first phase shift pulse 207. Rotation. However, the second phase-shift pulse 209 introduces additional... Rotation. To implement gate sequence 205, gate sequence 206 requires additional... Gate 210 is used to compensate for the phase shift introduced by the second phase shift pulse 209. Rotate.

[0029] Known methods for implementing arbitrary single-qubit gates can provide compensability through phase-shifted subsequent single-qubit gates. Instead of providing additional rotations as part of the gate sequence 206, rotations are used. For example, to implement a single-qubit gate sequence. ,in: , , It can be shifted as follows: , Phase shifting can be achieved using two PMW pulses. Door: , , As mentioned earlier, additional rotations will be required (e.g., To achieve phase shift This rotation can be applied to the next single-qubit gate in the gate sequence.

[0030] While the phase-shifting method may be applicable to single-qubit gate sequences, it may not be suitable for certain two-qubit gates (such as...). , or (Door) is incompatible.

[0031] The system and method disclosed herein can support the generation of arbitrary single-qubit gates using PMW pulses. PMW pulses can be applied to realize... The gates of this form, through cascading, can realize arbitrary single-qubit gates. As described herein, these PMW pulses can realize arbitrary single-qubit gates without introducing an additional Z-rotation. Therefore, the systems and methods of this disclosure are compatible with any two-qubit gate while retaining the advantages of using PMW pulses (e.g., control parameter precision; reduced calibration requirements; explicit correlation between physical control parameters (e.g., phase shift) and gate parameters (e.g., Z-rotation angle), etc.). Thus, the systems and methods of this disclosure constitute an improvement in the field of quantum computing technology.

[0032] Figure 3A and 3B Two different methods for implementing arbitrary single-qubit quantum gates using phase-shifted microwave pulses according to embodiments of the present disclosure are illustrated. Both methods use one or more PMW pulse sequences. In some embodiments, the PMW pulses may be phase-shifted X-gates.

[0033] and Figure 3A Consistent with the given pattern, the real parameters of a single-qubit unitary can be mapped to the phase shifts of the gates in gate sequence 310. Therefore, for any single-qubit unitary, a system of linear equations can be solved to determine the appropriate phase shift used to implement that single-qubit unitary. In some embodiments, the phase shift X gate in gate sequence 310 can be derived from... and Choose from the set of doors.

[0034] In general, a single-qubit quantum gate 201 can be implemented using a gate sequence 310. This gate sequence can include three PMW pulses: a first phase-shift pulse 311 (to achieve phase shift). Gate), second phase shift pulse 313 (to achieve phase shift) (gate) and the third phase shift pulse 315 (to achieve phase shift) Door).

[0035] The cascading of three PMW pulses produces the following matrix: , The general form of a single-qubit gate can be represented as an element in a special unitary set of degree two, having the following three real parameters: , Upon inspection, the matrix of the three PMW pulses equals ,when: , , , Solving this system of linear equations directly yields: , , , Therefore, two PMWs can be used. A door and a PMW Gates can be used to implement arbitrary single-qubit gates as follows: , According to embodiments of this disclosure, in Door and After gate calibration, arbitrary single-qubit gates can be implemented without further calibration. Because Door and Gate calibration can be performed during the initialization or characterization of a quantum computer (e.g., as part of a Clifford-based random benchmark, T1 relaxation, T2 echo measurement, etc.), and embodiments of this disclosure can reduce the calibration requirements for performing quantum computing.

[0036] In some cases, fewer than three PMW pulses may be needed to realize a qubit. It can be decomposed into the Pauli operator:

[0037] when yes hour, The diagonal elements are zero. It can be decomposed into the Pauli operator as follows: , Apply a single PMW The following unit is generated: , Will and The coefficients are equal to produce Therefore, through appropriate selection A single PMW can be used Gates are used to implement only support and A single-qubit gate.

[0038] when yes hour, Off-diagonal elements are counted as zero. Decomposed into Pauli operators, it becomes: , Apply two PMWs The pulse generates the following unitary signal: , Will and The coefficients are equal to produce π. Therefore, by choosing appropriately and Two PMWs can be used Gates are used to implement only support and A single-qubit gate.

[0039] In addition, only one PMW per benchmark gate can be used. Pulses are used to generate gates for random benchmarking based on single-qubit Clifford.

[0040]

[0041]

[0042]

[0043]

[0044] and Figure 3B Consistent with the above, the real parameters of a single-qubit unitary can be mapped to a combination of gate phase shifts and gate rotation angles in the gate sequence 320. Therefore, for any single-qubit unitary, a system of linear equations can be solved to determine the appropriate phase shift and gate rotation angles for realizing that single-qubit unitary.

[0045] In some embodiments, one of the phase-shift X gates in the gate sequence 320 may be Gate. The unitary property of a single-qubit gate implemented by gate sequence 320 can determine the phase shift of another phase-shift X gate in gate sequence 320. .

[0046] Directly calculate arbitrary rotating PMW gates and PMW The gate cascade yields:

[0047] The first PMW pulse (e.g., the first phase shift pulse 321) can implement the gate sequence: , The second PMW pulse (e.g., the second phase shift pulse 323) can implement the gate sequence: , therefore, Figure 3B The method shown can be used to implement arbitrary single-qubit quantum gates using two PMW pulses. As mentioned above, unitary... It can be decomposed into the Pauli operator:

[0048] Equivalent variables produce a system of linear equations: , , , The system of linear equations can be solved to determine , and The appropriate value, thereby achieving unitary .

[0049] and Figure 3A Compared to the methods, Figure 3B This method can reduce the number of pulses required to implement quantum computing, thus providing implementation-dependent improvements in gate fidelity. However, this method may involve... Additional calibration of the door, because Door (for example, different from) and The gates may not be calibrated in other ways during the initialization or characterization of the quantum computer.

[0050] Consistent with embodiments of this disclosure, gate sequence 310 can be used to implement additional Z-rotations. In some embodiments, the need for additional Z-rotations can be determined during quantum computing (e.g., in response to frame offsets or other effects). In response to this determination, additional Z-rotations can be implemented during the application of the gate sequence by updating the PMW phase shift using the following update rule.

[0051] Given , , and (in , , and (The sum does not need to equal zero) a series of doors and the identity: , The gate sequence can be represented by the following PMW pulse:

[0052] .

[0053] Therefore, the final Z-rotation value can be updated by changing the phase shifts of the intermediate and final pulses. (For example, in order to achieve) The phase shift of the final pulse decreases. Furthermore, the phase shift of the intermediate pulse decreases. Similarly, the final Z-rotation value can be updated by changing the phase shifts of the first and intermediate pulses. (For example, in order to achieve) The phase shift of the first pulse increases Furthermore, the phase shift of the intermediate pulse increases. Similarly, the Z-rotation value can be updated by updating the phase shift of the intermediate pulse. and .

[0054] Figure 4A A sequence of quantum gates including two-qubit quantum gates according to embodiments of the present disclosure is shown. As shown, two single-qubit gates... and It can be applied in parallel to two independent qubits. Then, a two-qubit gate... It can be applied to two qubits. Then two single-qubit gates. and It can be applied in parallel to two independent qubits.

[0055] In general, single-qubit gates and They can be different. Therefore, when using Figure 2 When implementing the gate sequence, different additional rotations will be introduced for the two gates. In general, these different additional rotations cannot be passed through a two-qubit gate. accomplish.

[0056] However, in some cases, Z-rotation can be achieved through a two-qubit gate. Implementation. For symmetric phase-swapping two-qubit gates (e.g., Doors, etc.): .

[0057] Therefore, it can be achieved through a two-qubit gate. Perform common Z-rotation Potentially, some updates are made to each qubit (e.g., and In some embodiments, such as Figures 4A to 4D As shown, a two-qubit gate It could be a qubit gate with conserved excitation quantity. In such an embodiment, .

[0058] Figures 4B to 4D An embodiment according to this disclosure is shown, using Figure 3A Or a single-qubit quantum gate implemented with 3B Figure 4A Example implementation of quantum gate sequences.

[0059] like Figure 4B As shown, in the first step of this implementation, one can use Figure 2 The method shown will open the door Applied to the first qubit. Therefore, when: , Figure 2 The method shown can introduce additional rotations: .

[0060] In some embodiments, since only two PMW pulses are required, even if additional rotation is introduced, it is possible to use... Figure 2 The method shown (therefore, compared to implementations that require additional pulses, Figure 2 The method shown can support improved gate fidelity.

[0061] AND gate Application parallelism can be used Figure 3A The method shown Figure 3B The method shown may be achieved by updating the gate. The existing implementation will... The phase-shifted version is applied to the second quantum bit.

[0062] As Figure 3A Non-restrictive examples of the methods shown: .

[0063] As Figure 3B Non-restrictive examples of the methods shown: .

[0064] As a door Unrestricted examples of existing implementations: , By applying the update as described above: … .

[0065] According to any of these implementations, Therefore, as Figure 4C As shown, Rotation can be viewed as already being associated with a two-qubit gate. Exchange. For example... Figure 4D As shown, it can be used Figure 2 The method shown propagates the phase shift forward. Additionally or alternatively, Figure 3A or Figure 3B The method shown can be used by subsequent doors to compensate for additional rotation (e.g., subsequent doors). It can be implemented as (etc.). In this way, the system and method of this disclosure can be used with... Figure 2 The methods shown are used together to realize single-qubit gate and two-qubit gate sequences.

[0066] Although Pauli X-gates are described herein for convenience, the systems and methods disclosed herein are not limited thereto. In some embodiments, phase-shifted Pauli Y-gates may be used as an additional option or alternative to the phase-shifted Pauli X-gates described herein.

[0067] Figure 5 A quantum controller 510 for applying quantum gates to one or more qubits is illustrated according to an embodiment of the present disclosure. Figure 5 In the non-limiting example shown, the quantum controller 510 is coupled to a qubit implemented by a superconducting quantum circuit 520 using a microwave drive line. In this non-limiting example, the qubit is a transmon qubit and includes a series connection of a capacitor C. f The Josephson junction and capacitor C of the shunt d However, according to embodiments of this disclosure, other types of qubits, such as fluxonium qubits, can be used. In some embodiments, the superconducting quantum circuit 520 can be implemented using a chip comprising qubits and at least a portion of microwave drive lines coupling the qubits to the quantum controller 510.

[0068] The quantum controller 510 can be a digital computing device (e.g., a computing device including a central processing unit, a graphics processing unit, an application-specific integrated circuit, a field-programmable gate array, or other suitable processor). The quantum controller 510 can configure the quantum circuit 520 to perform computations, provide computation gates, and read state information from the quantum circuit 520.

[0069] Consistent with the disclosed embodiments, quantum controller 510 can configure quantum circuit 520 by enabling gate operations on one or more qubits of quantum circuit 520. In some embodiments, quantum circuit 520 can be configured by providing one or more bias drivers to move two qubits to a resonant state. Quantum controller 510 can provide one or more bias drivers directly to circuit 520, or it can provide instructions to a bias driving source (e.g., a waveform generator, etc.) to provide bias driving to circuit 520. In some embodiments, providing bias driving can include a coil that allows current to flow through an external coil of circuit 520. In various embodiments, providing bias driving can include a coil that allows current to flow through an on-chip coil. Embodiments of this disclosure are not limited to specific methods of providing bias driving or biasing qubits.

[0070] Consistent with embodiments of this disclosure, the quantum controller 510 may implement computation gates on circuit 520. In some embodiments, the quantum controller 510 may implement such gates by providing one or more PMW pulses (or other gate drivers) to the qubits in circuit 510. In various embodiments, the quantum controller 510 may implement such gates by providing instructions to a computation driving source (e.g., a waveform generator, etc.) such that the computation driving source provides such PMW pulses (or other gate drivers) to the qubits in circuit 520. As described herein, the PMW pulses may be selected to implement one or more quantum gates. One or more computation drivers may be provided to the qubits implemented by the quantum circuit 520 using one or more coils coupled to the corresponding qubits. The coils may be external to circuit 520 or on a chip included in circuit 520.

[0071] Consistent with embodiments of this disclosure, quantum controller 510 can be configured to determine state information of quantum circuit 520. In some embodiments, quantum controller 510 can measure the state of one or more qubits of circuit 520. This state can be measured when one or more quantum operation sequences are completed. In some embodiments, quantum controller 510 can provide a probe signal (e.g., a microwave probe tone) to the coupled resonator of circuit 520, or provide instructions to a readout device (e.g., an arbitrary waveform generator) that provides the probe signal. In various embodiments, quantum controller 510 can include a detector, or be configured to receive information from a detector configured to determine the amplitude and phase of an output signal received from the coupled resonator in response to the provision of a microwave probe tone. The amplitude and phase of the output signal can be used to determine the state of the probed qubit. Embodiments of this disclosure are not limited to any specific method of measuring the state of a qubit.

[0072] In some embodiments, a non-transitory computer-readable storage medium including instructions is also provided, and these instructions can be executed by a device (e.g., the encoder and decoder of this disclosure) to perform the methods described above. Common forms of non-transitory media include, for example, floppy disks, magnetic disks, hard disks, solid-state drives, magnetic tape or any other magnetic data storage media, CD-ROMs, any other optical data storage media, any physical media with a perforated pattern, RAM, PROMs and EPROMs, FLASH-EPROMs or any other flash memory, NVRAM, caches, registers, any other memory chips or cassette memories and their network versions. The device may include one or more processors (CPUs), input / output interfaces, network interfaces, and / or memory.

[0073] The foregoing description is for illustrative purposes. This description is not exhaustive and is not limited to the precise forms or embodiments disclosed. Modifications and adaptations to the embodiments will be apparent from the detailed description and practice of the embodiments of this disclosure. For example, the described implementations include hardware, but systems and methods conforming to this disclosure can be implemented in both hardware and software. Furthermore, while some components have been described as coupled to each other, these components may be integrated with each other or distributed in any suitable manner.

[0074] Furthermore, although illustrative embodiments have been described herein, the scope includes any and all embodiments based on this disclosure that have equivalent elements, modifications, omissions, combinations, adjustments, or alterations (e.g., aspects spanning various embodiments). Elements in the claims will be interpreted broadly based on the language used in the claims and are not limited to the examples described in this specification or in the application process, which will be interpreted as non-exclusive. Moreover, the steps of the disclosed method can be modified in any way, including reordering or inserting or deleting steps.

[0075] It should be noted that the relational terms used herein (e.g., “first” and “second”) are used only to refer to one entity or operation in relation to another entity or operation, and do not require or imply any actual relationship or order between these entities or operations. Furthermore, the words “including,” “having,” “containing,” and “comprising,” as well as other similar forms, are intended to be semantically equivalent and open-ended, as one or more elements following any of these words do not imply an exhaustive list of those elements, nor do they imply limitation to the listed elements.

[0076] The features and advantages of this disclosure are apparent from the detailed description, and therefore the appended claims are intended to cover all systems and methods falling within the true spirit and scope of this disclosure. As used herein, the indefinite articles “a” and “an” mean “one or more.” Similarly, the use of plural terms does not necessarily indicate multiple unless it is explicit in the given context. Furthermore, since many modifications and variations will readily arise from a study of this disclosure, it is not intended to limit this disclosure to the exact constructions and operations shown and described; therefore, all suitable modifications and equivalents may be considered to fall within the scope of this disclosure.

[0077] As used herein, unless expressly stated otherwise, the term "and / or" includes all possible combinations unless impractical. For example, if it is specified that a database may include A and / or B, then unless otherwise specified or impractical, the database may include A, B, or A and B. As a second example, if it is specified that a database may include A, B, and / or C, then unless otherwise specified or impractical, the database may include A, or B, or C, or A and B, or A and C, or B and C, or A and B and C.

[0078] It should be understood that the above embodiments can be implemented by hardware, software (program code), or a combination of hardware and software. If implemented by software, it can be stored in the above-described computer-readable medium. When executed by a processor, the software can perform the methods of this disclosure. The computing units and other functional units described in this disclosure can be implemented by hardware, software, or a combination of hardware and software. Those skilled in the art will also understand that multiple of the above modules / units can be combined into one module / unit, and each of the above modules / units can be further divided into multiple sub-modules / sub-units.

[0079] In the foregoing description, numerous specific details have been described with reference to embodiments, which may vary depending on the implementation. Certain adjustments and modifications may be made to the described embodiments. Other embodiments will be apparent to those skilled in the art in light of the detailed description and practice of this disclosure herein. The description and embodiments are to be considered exemplary only, and the true scope and spirit of the invention are indicated by the appended claims. The sequence of steps shown in the figures is also intended for illustrative purposes only and is not intended to limit one to any particular order of steps. Therefore, those skilled in the art will understand that these steps may be performed in a different order when implementing the same method.

[0080] The embodiments may be further described using the following terms: 1. A system for applying a single-qubit quantum gate, the unitary aspect of which is specified by at least a first real parameter, a second real parameter, and a third real parameter, the system comprising: a qubit; and a quantum controller coupled to the qubit via a power transmission system and configured to: apply a phase-shifted Pauli gate sequence to the qubit to realize the single-qubit quantum gate, each phase-shifted Pauli gate in the phase-shifted Pauli gate sequence having a rotation angle and a phase shift; and wherein the first real parameter, the second real parameter, and the third real parameter correspond to: the rotation angle and the phase shift in the phase-shifted Pauli gate sequence; or the phase shift in the phase-shifted Pauli gate sequence.

[0081] 2. The system according to Clause 1, wherein the quantum controller is further configured to solve a system of linear equations to determine the correspondence between: a first real parameter, a second real parameter, and a third real parameter, and a rotation angle and two phase shifts in a phase-shifted Pauli gate sequence; or a first real parameter, a second real parameter, and a third real parameter, and three phase shifts in a phase-shifted Pauli gate sequence.

[0082] 3. A system according to any one of clauses 1 to 2, wherein the phase-shifted bubble gate sequence comprises two phase-shifted bubble gates, and the first real parameter, the second real parameter, and the third real parameter correspond to the rotation angle and two phase shifts in the phase-shifted bubble gate sequence; or the phase-shifted bubble gate sequence comprises three phase-shifted bubble gates, and the first real parameter, the second real parameter, and the third real parameter correspond to three phase shifts in the phase-shifted bubble gate sequence.

[0083] 4. A system according to any one of clauses 1 to 3, wherein the first real parameter, the second real parameter, and the third real parameter correspond to three phase shifts in a phase-shifted Pauli gate sequence, and each of the three phase shifts is a distinct function of two of the first real parameter, the second real parameter, and the third real parameter.

[0084] 5. A system according to any one of clauses 1 to 4, wherein the first real parameter, the second real parameter, and the third real parameter correspond to three phase shifts in a phase-shifted bubble gate sequence, and the rotation angle in the phase-shifted bubble gate sequence is selected from a set containing π / 2, -π / 2, and π.

[0085] 6. The system according to Clause 1, wherein all elements on the diagonal of the unitary matrix are zero; the phase-shifted bubble gate sequence is a single-phase bubble gate; and wherein the first real parameter, the second real parameter, and the third real parameter correspond to the phase shift of the single-phase bubble gate.

[0086] 7. The system according to Clause 6, wherein a single-qubit quantum gate is derived from a system containing X π / 2 X -π / 2 Y -π / 2Choose from the set of Y-π / 2.

[0087] 8. According to Clause 1, in which: all elements outside the diagonal of the unitary matrix are zero; the phase-shift bubble gate sequence is two phase-shift bubble gates; the first real parameter, the second real parameter, and the third real parameter correspond to the phase shifts of the two phase-shift bubble gates; and the rotation angle of each of the two phase-shift bubble gates is π.

[0088] 9. A system according to any one of clauses 1 to 8, wherein: the implementation of a single-qubit quantum gate does not introduce additional rotations.

[0089] 10. A method for applying a sequence of gates of quantum gates to a qubit, comprising: implementing a first quantum gate in the gate sequence by applying a first phase-shift pulse sequence to the qubit; and, after applying the first quantum gate, implementing a second quantum gate in the gate sequence by applying a second phase-shift pulse sequence to the qubit, wherein an additional rotation introduced by the implementation of the second quantum gate is independent of the implementation of the first quantum gate, and the pulses in the second phase-shift pulse sequence are configured to implement: a virtual Z-gate having a first rotation angle; an X-gate having a second rotation angle; and a virtual Z-gate having a negative value of the first rotation angle.

[0090] 11. The method according to Clause 10, wherein the second phase-shift pulse sequence comprises three pulses, and the second rotation angle is selected from a set containing π / 2, -π / 2, and π.

[0091] 12. The method according to any one of clauses 10 to 11 further includes: determining an additional Z rotation angle during the application of the gate sequence; and the second phase shift pulse sequence is further configured to additionally realize the additional Z rotation angle.

[0092] 13. The method according to Clause 10, wherein the second phase-shift pulse sequence comprises two pulses, and the second rotation angle depends on the unitary nature of the second quantum gate.

[0093] 14. The method according to Clause 13, wherein all elements on the diagonal of the unitary matrix are zero; and the second phase-shift pulse sequence is a single pulse.

[0094] 15. According to the method of Clause 13, all elements outside the diagonal of the unitary matrix are zero; and the second phase-shift pulse sequence is two pulses.

[0095] 16. The method according to any one of clauses 10 to 15, wherein the additional rotation introduced by the implementation of the second quantum gate is zero.

[0096] 17. A method for realizing a combination of two-qubit gates and a tensor product of a first single-qubit gate and a second single-qubit gate, comprising: applying a first phase-shift pulse sequence to a first qubit to realize a first single-qubit gate, the realization of the first single-qubit gate introducing an additional rotation; applying a second phase-shift pulse sequence to a second qubit to realize the product of the additional rotation and the second single-qubit gate; and applying a two-qubit gate to the first qubit and the second qubit to obtain a phase-shifted version of the combination of two-qubit gates and a tensor product of the first single-qubit gate and the second single-qubit gate.

[0097] 18. The method according to Clause 17, wherein the first phase-shift pulse sequence is two pulses; and the second phase-shift pulse sequence is three pulses.

[0098] 19. The method according to Clause 18, wherein each of the two pulses in the first phase-shift pulse sequence realizes phase shift X. π / 2 Gate or phase shift X -π / 2 The gate; and one of the three pulses in the second phase-shift pulse sequence to achieve phase shift X. π Door.

[0099] 20. The method according to Clause 17, wherein the first phase-shift pulse sequence is two pulses; and the second phase-shift pulse sequence is two pulses.

[0100] 21. The method according to Clause 20, wherein each of the two pulses in the first phase-shift pulse sequence realizes a phase shift X. π / 2 Gate or phase shift X -π / 2 The phase-shift X-gate is implemented by one of two pulses in the second phase-shift pulse sequence, and the phase-shift X-gate has a rotation angle that depends on the second single-qubit gate.

[0101] 22. The method according to any one of clauses 17 to 21, wherein the two-qubit gate is symmetrically phase-swapping.

[0102] 23. A non-transitory computer-readable medium containing instructions executable by a processor of a quantum controller coupled to a qubit, such that the quantum controller performs operations for applying single-qubit quantum gates to the qubit, the single-qubit quantum gates having unitary characteristics specified by a first real parameter, a second real parameter, and a third real parameter, the operations comprising: applying a phase-shifted Pauli gate sequence to the qubit, each phase-shifted Pauli gate in the phase-shifted Pauli gate sequence having a rotation angle and a phase shift; and wherein the first real parameter, the second real parameter, and the third real parameter correspond to: the rotation angle and the phase shift in the phase-shifted Pauli gate sequence; or the phase shift in the phase-shifted Pauli gate sequence.

[0103] 24. A non-transitory computer-readable medium pursuant to Clause 23, wherein the first real parameter, the second real parameter, and the third real parameter correspond to three phase shifts in a phase-shifted Pauli gate sequence, and each of the three phase shifts is a distinct function of two of the first real parameter, the second real parameter, and the third real parameter.

[0104] 25. A non-transitory computer-readable medium pursuant to Clause 23, wherein the phase-shifted bubble gate sequence comprises two phase-shifted bubble gates, and the first real parameter, the second real parameter, and the third real parameter correspond to a rotation angle and two phase shifts in the phase-shifted bubble gate sequence; or the phase-shifted bubble gate sequence comprises three phase-shifted bubble gates, and the first real parameter, the second real parameter, and the third real parameter correspond to three phase shifts in the phase-shifted bubble gate sequence.

[0105] 26. A non-transitory computer-readable medium pursuant to Clause 23, wherein all elements on the diagonal of the unitary matrix are zero; the phase-shifted bubble gate sequence is a single-phase bubble gate; and wherein the first real parameter, the second real parameter, and the third real parameter correspond to the phase shift of the single-phase bubble gate.

[0106] 27. A non-transitory computer-readable medium pursuant to Clause 23, wherein all elements outside the diagonal of the unitary matrix are zero; the phase-shift bubble gate sequence is two phase-shift bubble gates; the first real parameter, the second real parameter, and the third real parameter correspond to the phase shifts of the two phase-shift bubble gates; and the rotation angle of each of the two phase-shift bubble gates is π.

[0107] Exemplary embodiments have been disclosed in the accompanying drawings and description. However, many variations and modifications can be made to these embodiments. Therefore, although specific terminology has been used, it is used only in a general and descriptive sense and not to limit or constrain the scope of the embodiments as defined by the appended claims.

Claims

1. A system for applying a single-qubit quantum gate, said single-qubit quantum gate having a unitary structure specified by at least a first real parameter, a second real parameter, and a third real parameter, said system comprising: Quantum bits; as well as A quantum controller, coupled to the qubit via a power transmission system and configured to: A phase-shift Pauli gate sequence is applied to the qubit to realize the single-qubit quantum gate, each phase-shift Pauli gate in the phase-shift Pauli gate sequence having a rotation angle and a phase shift; as well as Wherein, the first real parameter, the second real parameter, and the third real parameter correspond to: The rotation angle in the phase-shift bubble gate sequence and the two phase shifts in the phase-shift bubble gate sequence; or The three phase shifts in the phase-shift Pauli gate sequence, wherein the implementation of the single-qubit quantum gate does not introduce additional rotations.

2. The system according to claim 1, wherein, The quantum controller is further configured to solve a system of linear equations to determine the correspondence between the following parameters: The first real parameter, the second real parameter, and the third real parameter, as well as the rotation angle and two phase shifts in the phase-shift Pauli gate sequence; or The first real parameter, the second real parameter, the third real parameter, and the three phase shifts in the phase-shift Pauli gate sequence.

3. The system according to claim 1, wherein, The first real parameter, the second real parameter, and the third real parameter correspond to three phase shifts in the phase-shift Pauli gate sequence, and each of the three phase shifts is a different function of two of the first real parameter, the second real parameter, and the third real parameter.

4. The system according to claim 1, wherein, The first real parameter, the second real parameter, and the third real parameter correspond to the three phase shifts in the phase-shift Bubble gate sequence, and the rotation angle in the phase-shift Bubble gate sequence is selected from a set containing π / 2, -π / 2, and π. When the phase-shift Bubble gate sequence includes three pulses, two are used. A door and a A gate is used to implement a single-qubit gate.

5. The system according to claim 1, wherein, The phase-shift bubble gate sequence includes two phase-shift bubble gates, and the first real parameter, the second real parameter, and the third real parameter correspond to the rotation angle and the two phase shifts in the phase-shift bubble gate sequence; or The phase-shift bubble gate sequence includes three phase-shift bubble gates, and the first real parameter, the second real parameter, and the third real parameter correspond to the three phase shifts in the phase-shift bubble gate sequence.

6. The system according to claim 1, wherein, This indicates that all elements on the diagonal of the unitary matrix are zero; The phase shift bubble gate sequence is a single-phase bubble shift gate; and Wherein, the first real parameter, the second real parameter, and the third real parameter correspond to the phase shift of the single-phase shifting bubble gate.

7. The system according to claim 6, wherein, The single-qubit quantum gate contains X π / 2 X -π / 2 Y π / 2 and Y -π / 2 Choose from the set.

8. The system according to claim 1, wherein, This indicates that all elements of the unitary matrix except for the diagonal are zero; The phase-shifting bubble gate sequence consists of two phase-shifting bubble gates; The first real parameter, the second real parameter, and the third real parameter correspond to the phase shifts of the two phase-shift Pauli gates; and The rotation angle of each of the two phase-shifting bubble gates is π.

9. A method for applying a sequence of gates to a quantum bit, comprising: The first quantum gate in the gate sequence is realized by applying a first phase-shift pulse sequence to the qubit; as well as After applying the first quantum gate, a second quantum gate in the gate sequence is implemented by applying a second phase-shift pulse sequence to the qubit. The additional rotation introduced by the implementation of the second quantum gate is independent of the implementation of the first quantum gate. The pulses in the second phase-shift pulse sequence are configured to implement: A virtual Z-gate with a first rotation angle; An X-gate with a second rotation angle; and The virtual Z-gate having a negative value of the first rotation angle.

10. The method according to claim 9, wherein, The additional rotation introduced by the implementation of the second quantum gate is zero.

11. The method according to claim 9, wherein, The second phase-shift pulse sequence comprises three pulses, and the second rotation angle is selected from a set including π / 2, -π / 2, and π, wherein when the second phase-shift pulse sequence comprises three pulses, two [variables are used]. A door and a A gate is used to implement a single-qubit gate.

12. The method according to claim 9, wherein, The second phase-shift pulse sequence comprises two pulses, and the second rotation angle depends on the unitary nature of the second quantum gate.

13. The method according to claim 12, wherein, This indicates that all elements on the diagonal of the unitary matrix are zero; and The second phase-shift pulse sequence is a single pulse.

14. The method according to claim 12, wherein, The unitary matrix is ​​defined such that all elements except those on the diagonal are zero; and The second phase-shift pulse sequence consists of two pulses.

15. The method of claim 9, further comprising: During the application of the gate sequence, an additional Z-rotation angle is determined; and The second phase-shift pulse sequence is further configured to additionally achieve the additional Z-rotation angle.

16. A method for realizing the combination of two-qubit gates and the tensor product of a first single-qubit gate and a second single-qubit gate, comprising: The first phase-shift pulse sequence is applied to the first qubit to realize the first single-qubit gate, the realization of the first single-qubit gate introducing additional rotation; The second phase-shift pulse sequence is applied to the second qubit to achieve the product of the additional rotation and the second single-qubit gate; as well as The two-qubit gate is applied to the first qubit and the second qubit to obtain a phase-shifted version of the combination of the two-qubit gate and the tensor product of the first single-qubit gate and the second single-qubit gate.

17. The method according to claim 16, wherein, The first phase-shift pulse sequence consists of two pulses; and The second phase-shift pulse sequence consists of three pulses.

18. The method according to claim 17, wherein, Each of the two pulses in the first phase-shift pulse sequence achieves a phase shift X. π / 2 Gate or phase shift X -π / 2 Door; and One of the three pulses in the second phase-shift pulse sequence achieves phase shift X. π Door.

19. The method of claim 16, wherein, The first phase-shift pulse sequence consists of two pulses; and The second phase-shift pulse sequence consists of two pulses.

20. The method according to claim 19, wherein, Each of the two pulses in the first phase-shift pulse sequence achieves a phase shift X. π / 2 Gate or phase shift X -π / 2 Door; and One of the two pulses in the second phase-shift pulse sequence implements a phase-shift X-gate, which has a rotation angle that depends on the second single-qubit gate.

21. The method according to claim 16, wherein, The two-qubit gate is symmetrically phase-swapping.

22. A non-transitory computer-readable medium containing instructions executable by a processor of a quantum controller coupled to a qubit, such that the quantum controller performs an operation for applying a single-qubit quantum gate to the qubit, the single-qubit quantum gate having a unitary parameter specified by a first real parameter, a second real parameter, and a third real parameter, the operation comprising: A phase-shifted Pauli gate sequence is applied to the qubit, each phase-shifted Pauli gate in the sequence having a rotation angle and a phase shift; as well as Wherein, the first real parameter, the second real parameter, and the third real parameter correspond to: The rotation angle and the two phase shifts in the phase-shift Pauli gate sequence; or The three phase shifts in the phase-shift Pauli gate sequence, wherein the implementation of the single-qubit quantum gate does not introduce additional rotations.

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