quantum computer

Abstract

The present invention relates to the field of quantum computing, and more particularly to a novel arrangement of qubits in a quantum processing unit and a novel method for performing multi-qubit gate operations on qubits. The system comprises a plurality of qubits coupled to a central resonator via tunable couplers. The system is particularly suitable for performing quantum algorithms that feature centrally significant elements, and may significantly reduce the number of quantum gate operations performed in such algorithms.

Description

[Technical Field]

[0001] The present invention relates to the field of quantum computing, and more particularly to a novel arrangement of qubits in a quantum processing unit and a novel method for performing multi-qubit gate operations on qubits. [Background technology]

[0002] Coupling a large number of qubits in a quantum processing unit is technically challenging because directly coupling one qubit to many qubits requires increased capacitance or inductance, resulting in larger qubit sizes. These constraints limit both the number of qubits that can be coupled and the number of qubits that can be formed on a single die or wafer. Furthermore, as many qubits are coupled into a single system, frequency congestion prevents reliable individual addressing of single qubits. Summary of the Invention

[0003] According to a first aspect of the present invention, there is provided a system comprising a plurality of qubits, a plurality of tunable couplers (102), and a resonator (103), wherein each of the plurality of qubits is coupled to the resonator via one of the plurality of tunable couplers, and each of the plurality of qubits is coupled to the resonator within a region of ±20% of the wavelength of the EM wave at or near a maximum of the EM wave in the resonator.

[0004] The system may further include control circuitry configured to prepare a first state in one of the qubits, transfer the first state to the resonator via the tunable coupler, and perform a multi-qubit gate between the resonator and one or more of the other qubits by operating the tunable coupler between the resonator and the other qubits.

[0005] The system may further include a central qubit coupled to the resonator via a capacitor, and control circuitry configured to prepare a first state in the central qubit, transfer the first state to the resonator via the capacitor coupling, and perform a multi-qubit gate between the resonator and one or more of the plurality of qubits by manipulating tunable couplings between the resonator and the other qubits.

[0006] The qubits, tunable couplers, and resonators may form a first set, where the plurality of qubits is a first plurality of qubits, the plurality of tunable couplers is a first plurality of tunable couplers, and the resonator is a first resonator, and the system may further comprise a second set including a second plurality of qubits, a second plurality of tunable couplers, and a second resonator (203). Each of the second plurality of qubits may be coupled to the second resonator via one of the second plurality of tunable couplers, each of the second plurality of qubits may be coupled to the second resonator at a maximum of the EM wave in the second resonator, and the second resonator may be coupled to the first resonator.

[0007] The second resonator may be coupled to the first resonator by at least one coupling chain including a first tunable coupler, a qubit, and a second tunable coupler.

[0008] The second resonator may be coupled to the first resonator by two coupling chains, each coupling chain comprising a first tunable coupler, a qubit, and a second tunable coupler.

[0009] The system may further comprise one or more additional sets of qubits, tunable couplers, and resonators, wherein the qubits are coupled to the resonators via the tunable couplers at a maximum of the EM wave in the resonators, and the resonators in each of the multiple sets are coupled.

[0010] The resonators in each of the first set, the second set, and the one or more further sets may be coupled in series.

[0011] Each of the plurality of qubits may be directly coupled to one or more of the other qubits in the plurality of qubits via a tunable coupler.

[0012] Each of the plurality of qubits may be directly coupled to fewer than 6, 7, 8, 9, or 10 other qubits.

[0013] The system can be configured to simulate a spin system by encoding the spin state of each particle into a separate qubit and performing multi-qubit gates on the qubits or qubits and resonators to simulate interactions between the particles.

[0014] According to a second aspect of the present invention, there is provided a method comprising providing a first state in a first qubit, transferring the first state to a resonator via a tunable coupler, and performing a multi-qubit gate between the resonator and one or more further qubits by operating the tunable coupler between the resonator and one or more further qubits.

[0015] The one or more further qubits may include a plurality of further qubits logically arranged in a series of further qubits. Preparing a first state in the first qubit may include preparing a state in the first qubit and applying a Hadamard gate to the first qubit, and performing a multi-qubit gate may include iteratively performing the following steps until there are no more qubits remaining in the sequence of further qubits: a) A controlled phase gate is applied sequentially to each qubit in the sequence of resonators and further qubits. b) applying a Hadamard gate to a first further qubit in the sequence of further qubits; c) swapping the state of a first further qubit in the sequence of further qubits with the resonator; d) removing the first further qubit from the sequence of further qubits. [Brief explanation of the drawings]

[0016] [Figure 1] 1 is a schematic diagram of an arrangement of quantum bits in a first embodiment of the present invention. [Figure 2] FIG. 1 is a schematic diagram of an embodiment of the present invention including multiple coupled resonators. [Figure 3] FIG. 1 is a schematic diagram of one embodiment of the present invention in which qubits are directly connected via tunable couplers. [Figure 4] 4 is a flow chart illustrating a method of operating the system shown in FIGS. 1 to 3. [Figure 5] FIG. 4 is a quantum circuit diagram illustrating how to perform a quantum Fourier transform on the system shown in FIGS. 1 to 3. DETAILED DESCRIPTION OF THE INVENTION

[0017] FIG. 1 shows a schematic diagram of a qubit arrangement in a first embodiment of the present invention. Individual qubits 101 (shown as filled circles) are coupled to a resonator 103 via tunable couplers 102 (shown as open circles). The qubits 101 may be transmon qubits, as described in detail in Koch et al., Charge-insensitive qubit design derived from the Cooper pair box, Phys. Rev. A 76, 042319 (doi:10.1103 / PhysRevA.76.042319). The tunable couplers 102 may also be transmon or other coupling circuits whose frequency characteristics can be externally controlled to selectively couple each qubit 101 to the resonator 103, i.e., so that coupling can be turned “on” or “off” as needed.

[0018] The resonator 103 may be, for example, a superconducting coplanar waveguide resonator. Such a resonator is formed by a single conductive track with a pair of return conductors, one on each side of the conductive track. Boundary conditions, i.e., zero current or zero voltage, are imposed at the ends of the conductive track, resulting in a set of resonant frequencies consistent with the boundary conditions. The resonator mode frequencies are close to the frequency of the qubit 101, but the default frequency of the tunable coupler 102 is higher or lower than the frequency of the qubit 101. The frequency difference between the qubit 101 and the resonator 103 is preferably less than the absolute value of the anharmonicity of the qubit 101. For transmon qubits, this is approximately 2% negative of the transition frequency between the |0> and |1> states.

[0019] The tunable couplers 102 are positioned at locations along the resonator 103 that correspond to the locations of voltage maxima of the electromagnetic standing wave occurring within the resonator 103. The tunable couplers 102 (and any direct qubit connections) to the resonator 103 are preferably located within a region of ±10% of the wavelength of the standing wave around each maximum. However, the tunable couplers 102 (and any direct qubit connections) to the resonator 103 may be positioned within a region of up to ±20% of the wavelength of the standing wave around each maximum. Thus, by scaling the length of the resonator 103, the number of maxima within the resonator can be increased, providing more locations at which qubits 101 can be coupled to the resonator 103 via tunable couplers 102. As shown in FIG. 1 , qubits 101 can be coupled to the resonator 103 (via tunable couplers 102) on each side of the resonator 103. Although Figure 1 shows one qubit / tunable coupler connected to each side of the resonator in a single location, up to 20 qubits can be connected to the resonator at each maximum.

[0020] In a first embodiment, to perform an operation on the qubit, a first arbitrary qubit state is prepared in one of the qubits 101, which can be considered a central qubit (although not necessarily centrally located). The first state is transferred from the central qubit to the resonator 103 via a tunable coupler 102, which couples the central qubit to the resonator 103. The first state may be prepared by applying a microwave pulse to the central qubit while the central qubit is decoupled from the resonator 103 by turning off the tunable coupler 102. The tunable coupler is turned off by tuning its resonant frequency to a specific frequency at which the interaction between the qubit and the resonator is canceled. Once the first state is prepared, the central qubit and the tunable coupler 102 are tuned to couple the central qubit to the resonator 103 for a specific length of time required to effectively transfer the first state from the central qubit to the resonator 103.

[0021] In a second embodiment, a central qubit (again, not necessarily centrally located) may be directly coupled to resonator 103 by a capacitor, i.e., without an intermediate tunable coupler. A first state is prepared in the central qubit, and the central qubit is brought into resonance with resonator 103 to transfer the prepared first state from the central qubit to resonator 103. This transfer operation corresponds to a Rabi swap.

[0022] Once the first state is transferred to the resonator 103, two-qubit gate operations, such as conditional phase gates, can be performed between the resonator and one or more other qubits by manipulating the tunable coupler between the resonator and the other qubits. In this way, the resonator functions as an information storage component, rather than simply an information bus, as is typically the case. Measurements can be performed by transferring the state of the resonator 103 back to the central qubit or any qubit whose state can be measured. This arrangement therefore allows any of the qubits 101 to couple with any of the other qubits 101 through the resonator 103, enabling all-to-all coupling by sequentially swapping the state of each qubit 101 into the resonator. For applications and algorithms requiring many-to-many coupling, this qubit arrangement significantly reduces the number of two-qubit gate operations that need to be performed compared to other qubit arrangements.

[0023] While FIG. 1 shows a total of 10 qubits 101 and 10 tunable couplers 102, it is possible to couple at least 48 qubits 101 and tunable couplers 102 to a single resonator 103. This upper limit is governed by the quality factor of the resonator 103, which decreases as the length of the resonator 103 increases, and the frequency separation of the resonator modes compared to the qubit linewidth. To further increase the number of qubits 101 that can be coupled, multiple groups on qubits, couplers, and resonators 200a-c may be coupled via resonators 203a-c, as shown in FIG. 2. Preferably, each resonator 203a-c is coupled to another resonator 203a-c by two CQC couplings 201a, 201b, each including a first tunable coupler (C), a qubit (Q), and a second tunable coupler (C) connected in series. Each tunable coupler in a CQC coupling is connected to a different one of the resonators 203a-c, linking the two resonators 203a-c. The two CQC couplings in each set 201, 201b are arranged in parallel between the resonators 103, 203. Each CQC coupling is connected to a resonator 203a-c at a maximum of an electromagnetic standing wave that forms within the resonator during operation. While Figure 2 shows three sets of qubits, couplers, and resonators 200a-c, additional resonators may be coupled to any of the resonators 203a-c to form a chain of resonators or any other architecture.

[0024] Alternatively, the resonators 203a-c of the sets 200a-c can be coupled by a single CQC coupling. However, if the target resonator is empty, i.e., in the ground state, a single CQC can be used to transfer state from one resonator to the other. To enable arbitrary state transfer between both resonators, two parallel paths, provided by two CQC couplings as shown in Figure 2, are required. The limitations imposed by using a single CQC coupling between the resonators may be desirable in certain application-specific implementations, for example, where the quantum algorithm running on the qubit does not require arbitrary state transfer between the resonators. When two CQC couplings are provided between the two resonators, the state from the first resonator is transferred to the qubit of the first CQC coupling, and the state from the second resonator is transferred to the qubit of the second CQC coupling. The state from the qubit of the first CQC coupling is then transferred to the second resonator, and the state from the second CQC coupling is transferred to the first resonator.

[0025] As a further alternative, the resonators may be connected by one CQC coupler and one direct coupler, i.e., a single tunable coupler. The quantum state from the first resonator is transferred to the qubit in the CQC coupler, and then an iSWAP gate operation is performed between the two resonators via the direct coupling to transfer the state from the second resonator to the first resonator. Finally, the state held in the CQC qubit is transferred to the second resonator. Compared to a system with two CQC couplers coupling the resonators, a single CQC and direct coupling results in a phase change in the state transferred via the direct coupling, while the state transferred via the CQC coupling maintains the same phase. However, this may be acceptable or even desirable depending on the algorithm.

[0026] It is also possible for qubits 101 to be directly coupled to other qubits 101 (i.e., not via resonators 103). Such direct coupling may still include tunable couplers, as shown in FIG. 3; alternatively, qubit-to-qubit coupling may be via capacitive or inductive coupling, i.e., without tunable couplers. FIG. 3 shows a simple example of a system including a single resonator 303, in which qubit 301 is coupled to resonator 303 via tunable coupling 302, but qubit 301 is also coupled directly, i.e., not via resonator 303, to adjacent qubits via tunable couplers 304. Each qubit 101 may not only be indirectly coupled to other qubits 101 via resonators 103, but may also be directly coupled to as many as six to ten other qubits. Furthermore, such direct qubit-to-qubit coupling may exist in systems with multiple resonators 103, and it will be understood that such direct qubit-to-qubit coupling may exist between qubits connected to the same resonator, or even to different resonators.

[0027] 4 is a flowchart illustrating a method for performing quantum operations on qubits of the system described above. In step 401, a first state is prepared in the central qubit (also referred to as the "first qubit"). The first state may be prepared, for example, by initializing the qubit at |0> and applying one or more single-qubit quantum gates to move the qubit to the desired state.

[0028] In step 402, a first state is transferred from the central qubit to the resonator. When the central qubit is connected to the resonator via a tunable coupler, the state may be transferred to the resonator by applying an appropriate stimulus to the tunable coupler to turn on the exchange interaction between the central qubit and the resonator. This transfer corresponds to an iSWAP gate applied to the central qubit and the resonator. In an alternative embodiment, when the central qubit is coupled to the resonator via a capacitor, the state prepared at the central qubit may be transferred to the resonator by a Rabi swap.

[0029] In step 403, two-qubit gate operations, such as conditional phase gates, can be performed between the resonator and one or more other qubits by manipulating the tunable couplers between the resonator and the other qubits. In this way, the resonator functions as an information storage component, rather than simply an information bus, as is typically the case. Measurements can be performed by transmitting the state of the resonator back to the central qubit.

[0030] The same basic process can be applied to more complex systems, such as that shown in Figure 2, by repeatedly performing transfers between coupled resonators and qubits.

[0031] The above-described system can be advantageously used in many practical applications, for example, in simulating physical systems with centrally affecting elements such as spin systems, e.g., NV at the center of a diamond, where the spin (or other properties) of multiple objects are interdependent. In such systems, the spin (or other properties) of each object or particle is represented or encoded by one or more qubits, and the interactions between each object or particle are represented by the connections and interactions between the qubits.

[0032] As a further example, the system is particularly suitable for simulating hyperpolarization protocols where qubit 0 represents the NV center and the remaining N-1 qubits represent atomic nuclei. The evolution of the system within one cycle is then given by the evolution operator, i.e.,

number

[0033] During the ceremony,

number

[0034] where X, Y, and Z are the Pauli operators,

number

[0035] Normal g jk The constants are negligible, resulting in two-qubit gates operating only on the central qubit and the non-central qubit. Simulation algorithms can be generated by decomposing the evolutionary operators using Trotter expansions. The algorithms require only a single-qubit gate and a two-qubit gate applied to the central qubit and the non-central element, but not two-qubit gates applied to the two non-central qubits. As a result, when simulations are performed using the system of the present invention, the algorithms can be run without swapping qubits, eliminating a significant number of steps required to simulate physical systems on quantum computing systems with other architectures.

[0036] The system may also be advantageously employed to perform quantum algorithms such as the quantum Fourier transform. As noted above, in a system consisting of a central qubit and N-1 additional qubits coupled to a resonator, the quantum Fourier transform may be performed by sequentially swapping the state of each qubit into the resonator to perform the required two-qubit gate with the other qubit.

[0037] First, the initial quantum state of each qubit is prepared with the required number of qubits, including the central qubit. A Hadamard gate is applied to the central qubit, swapping the state of the central qubit into the resonator.

[0038] The other qubit, 101, is then passed through the logical sequence, q2 to q N It can be thought of as being in the controlled phase gate CR k is the sequence q2 to q N and each qubit 101, i.e., the pair [R, qk ], where R is the resonator and qk ranges from k=2 to k=N. Controlled Phase Gate CR k can be expressed as the following matrix:

number

[0039] A Hadamard gate is then applied to q2, resulting in the state of q2 being swapped into the resonator.

[0040] The process is repeated by shifting the index of each qubit by one, i.e., q becomes q, or more generally, q i gaq i-1 and the previous q2 is removed from the sequence. The controlled phase gate again assigns a new resonator and each qubit in the sequence, starting with q2, i.e., the pair [R, q k ] are applied sequentially, R is the resonator, and q k where k=2 to k=N-1. This process is repeated until there are no more qubits remaining in the sequence of further qubits. An exemplary quantum circuit diagram for a five-qubit system is shown in Figure 5. While the process can be extended to any number of qubits using the current system, it will be understood that if multiple coupled resonators are used, an additional step of transferring the state between the resonators will be required.

Claims

1. 1. A system comprising: A plurality of quantum bits (101); a plurality of tunable couplers (102); a resonator (103), each of the plurality of quantum bits is coupled to the resonator via one of the plurality of tunable couplers, and each of the plurality of quantum bits is coupled to the resonator within a position corresponding to a maximum value of an EM wave in the resonator or within a region that is within 20% of a wavelength of the EM wave from a position corresponding to a maximum value of the EM wave.

2. The system comprises: preparing a first state in one of the plurality of qubits (101); transferring the first state to the resonator (103) via the tunable coupler (102); 10. The system of claim 1, further comprising control circuitry configured to perform a multi-qubit gate between the resonator and one or more qubits of the other qubits of the plurality of qubits by operating the tunable coupler between the resonator and one or more qubits of the other qubits of the plurality of qubits.

3. the system comprising: a central qubit coupled to the resonator (103) via a capacitor; providing a first state in the central qubit; transferring the first state to the resonator via coupling of the capacitor; 10. The system of claim 1, further comprising: control circuitry configured to perform a multi-qubit gate between the resonator and one or more qubits of the plurality of qubits by manipulating tunable couplings between the resonator and other qubits of the plurality of qubits.

4. the plurality of qubits is a first plurality of qubits (101a-j), the plurality of tunable couplers is a first plurality of tunable couplers (102a-j), and the resonator is a first resonator (103), the first plurality of qubits, the tunable coupler, and the first resonator forming a first set; the system further comprises a second set including a second plurality of qubits (101k-p), a second plurality of tunable couplers (102k-p), and a second resonator (203); each of the second plurality of qubits is coupled to the second resonator via one of the second plurality of tunable couplers, and each of the second plurality of qubits is coupled to the second resonator at a location corresponding to a maximum of the EM wave within the second resonator; The system of any one of claims 1 to 3, wherein the second resonator is coupled to the first resonator (103).

5. 5. The system of claim 4, wherein the second resonator is coupled to the first resonator by at least one coupling chain including a first tunable coupler, a quantum bit, and a second tunable coupler.

6. 6. The system of claim 5, wherein the second resonator (203) is coupled to the first resonator by two coupling chains, each coupling chain comprising a first tunable coupler, a quantum bit, and a second tunable coupler.

7. 7. The system of claim 4, further comprising one or more additional sets of qubits, tunable couplers, and resonators, the qubits being coupled to the resonators via the tunable couplers at locations corresponding to maxima of the EM wave in the resonators, and the resonators of each of the multiple sets being coupled.

8. 8. The system of claim 4, wherein the resonators in each of the first set, second set, and one or more further sets are coupled in series.

9. 9. The system of claim 1, wherein each qubit of the plurality of qubits is directly coupled to one or more other qubits in the plurality of qubits via capacitive or inductive coupling.

10. 9. The system of claim 1, wherein each qubit of the plurality of qubits is directly coupled to one or more other qubits in the plurality of qubits via a tunable coupler.

11. 11. The system of claim 9 or claim 10, wherein each of the plurality of qubits is directly coupled to fewer than 6, 7, 8, 9, or 10 other qubits.

12. 11. The system of claim 1, wherein the system is configured to simulate a spin system by encoding the spin state of each particle into a separate qubit and performing multi-qubit gates on the qubits or qubits and resonators to simulate interactions between particles.

13. 1. A method comprising: Preparing a first state in a first qubit (101); transferring said first state to a resonator (103) via a tunable coupler (102); performing a multi-qubit gate between the resonator and one or more additional qubits by manipulating a tunable coupler between the resonator and one or more additional qubits.

14. the one or more further qubits include a plurality of further qubits logically arranged in a series of further qubits; preparing the first state in the first qubit includes preparing a state in the first qubit and applying a Hadamard gate to the first qubit; Performing a multi-qubit gate involves iteratively performing the following steps until no more qubits remain in the sequence of further qubits: a) sequentially applying a controlled phase gate to each qubit in the sequence of said resonator and further qubits; b) applying a Hadamard gate to the first further qubit in the sequence of further qubits; c) swapping the state of the first further qubit in the sequence of further qubits with the resonator; and d) removing the first further qubit from the sequence of further qubits.

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