Quantum computing device using two gate types to prevent frequency conflicts in superconducting quantum computers

Abstract

A quantum computing device includes a first plurality of qubits having a first resonant frequency and a second qubit having a second resonant frequency, the second resonant frequency being different from the first resonant frequency; and a first tunable frequency bus configured to couple the first plurality of qubits to the second qubit.

Description

[0001] STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] This invention was made with government support under Contract W911NF-14-1-0124 awarded by the Army Research Office (ARO). The Government has certain rights in this invention. Background Art

[0003] The presently claimed embodiments of the invention relate to superconducting quantum computers, and more particularly, to superconducting quantum computers that combine two gate types to avoid frequency conflicts.

[0004] Quantum computing is based on the reliable control of quantum bits (referred to herein as qubits). The basic operations required to implement quantum algorithms are a collection of single-qubit operations and double-qubit operations that establish correlations between two individual qubits. In order to reach the error threshold of quantum computing and to achieve reliable quantum simulations, the implementation of high-fidelity double-qubit operations may be desirable.

[0005] Currently for superconducting qubits, single-qubit gates are implemented using microwave control. There are three main types of two-qubit gates: gates based on tunable frequency qubits, gates based on microwave-driven qubits (e.g., cross-resonance, flick fork, Bell Rabi, MAP, sideband transition, and geometric phase-based gates (e.g., resonant induced phase gate, full-term gate)).

[0006] For tunable frequency qubit-based gates, the qubit itself is tuned in frequency to activate the resonant interaction. These gates essentially have two operating points: an "off" position where the coupling is essentially zero, and an "on" position when the qubit has a strong two-qubit interaction. These gates have very good on-off ratios, but because the qubit is tunable by an externally applied magnetic flux, they can be limited by 1 / f noise, which limits the coherence of the qubit to a few microseconds.

[0007] For gates based on microwave-driven qubits, the qubits can be designed to be fixed in frequency, so they are not affected by magnetic flux noise. However, microwave pulses are required to activate the gates. The problem with these gates is that they have a low on-off ratio and it is difficult to address the gate of interest without activating unwanted interactions.

[0008] Geometric phase-based gates are based on the path of a quantum state in its state space and the acquired quantum phase associated with its offset. Adiabatic geometric gates are robust to certain types of noise, but are generally slow and require control adiabatic. Non-adiabatic gates can be faster and potentially share the noise resilience of adiabatic gates.

[0009] Superconducting Josephson junction qubits are a promising technology for building quantum computers. Transmon type superconducting qubits operate at a relatively high ratio of Josephson energy to charge energy, which allows transmon (transmission-line shunted plasma oscillation) qubits to operate with reduced charge noise sensitivity while still allowing coupling between qubits and between qubits and transmission lines or buses. This allows transmon qubits to be coupled in a 2D arrangement with nearest neighbor interactions via fixed frequency microwave resonators (e.g., in a two-dimensional lattice). Fixed frequency transmission qubits (single junction transmons) are highly coherent (i.e., essentially have a single resonant frequency). Therefore, it is necessary to achieve interactions between qubits. Cross-resonance (CR) interactions between qubits can be used to couple qubits. In cross-resonance, qubits are driven by microwave tones of adjacent qubit frequencies to establish interactions between qubits. In order to enable CR interactions between multiple qubits, the qubits are relatively closely spaced in frequency (e.g., less than 200MHz). However, this leads to frequency collision problems and crosstalk between qubits.

[0010] Since future quantum computers may use a large number of qubits (hundreds to thousands, or more), it may be desirable to limit frequency conflicts or crosstalk between qubits. While CR may provide the benefit of allowing coupling between adjacent qubits, CR may not be sufficient to establish coupling between more distantly located qubits. Therefore, a solution is still needed that addresses the frequency conflict problem and crosstalk when using CR to couple qubits. Summary of the invention

[0011] One aspect of the present invention is to provide a quantum computing device, including a first plurality of qubits having a first resonant frequency and a second qubit having a second resonant frequency, the second resonant frequency being different from the first resonant frequency. The quantum computing device also includes a first fixed frequency bus configured to couple the first plurality of qubits, the first plurality of qubits being configured to interact via cross resonance through the first fixed frequency bus. The quantum computing device further includes a first tunable frequency bus configured to couple at least one qubit of the first plurality of qubits to the second qubit.

[0012] In one embodiment, the quantum computing device quantum computing device further includes a second plurality of qubits having the second resonant frequency; and a second fixed frequency bus configured to couple the second plurality of qubits, the second plurality of qubits configured to interact via cross resonance through the second fixed frequency bus. In one embodiment, the first plurality of qubits are arranged in a first row or a first column and are configured to interact via cross resonance through the first fixed frequency bus, and the second plurality of qubits are arranged in a second row or a second column and are configured to interact via cross resonance through the second fixed frequency bus.

[0013] In one embodiment, the quantum computing device further includes a third plurality of qubits having the first resonant frequency, the third plurality of qubits arranged in one of a third row or a third column; and a third fixed frequency bus configured to couple the third plurality of qubits, the third plurality of qubits configured to interact via cross resonance through the third fixed frequency bus.

[0014] In one embodiment, the first plurality of qubits arranged in the first row or the first column are configured to interact with the second plurality of qubits arranged in the second row or the second column via the first tunable frequency bus, and the second plurality of qubits arranged in the second row or the second column are configured to interact with the third plurality of qubits arranged in the third row or the third column via the first tunable frequency bus. In one embodiment, the second plurality of qubits are arranged between the first plurality of qubits and the third plurality of qubits so as to prevent cross-resonance interactions between the first plurality of qubits and the third plurality of qubits.

[0015] In one embodiment, the quantum computing device further includes a third plurality of qubits having a third resonant frequency, the third plurality of qubits being arranged in one of a third row or a third column, the third resonant frequency being different from the first resonant frequency and different from the second resonant frequency; a third fixed frequency bus configured to couple the third plurality of qubits, the third plurality of qubits being configured to interact via cross resonance through the third fixed frequency bus; and a second tunable frequency bus configured to couple at least one of the third plurality of qubits to the second plurality of qubits.

[0016] In one embodiment, the first plurality of qubits arranged in the first row or the first column are configured to interact with the second plurality of qubits arranged in the second row or the second column via the first tunable frequency bus, and the second plurality of qubits arranged in the second row or the second column are configured to interact with the third plurality of qubits arranged in the third row or the third column via the second tunable frequency bus.

[0017] Another aspect of the present invention is to provide another quantum computing device. The quantum computing device includes a first plurality of qubits having a first resonant frequency and a second qubit having a second resonant frequency, the second resonant frequency being different from the first resonant frequency. The quantum computing device further includes a first tunable frequency bus configured to couple the first plurality of qubits to the second qubit.

[0018] In one embodiment, the first plurality of qubits are configured to interact with each other via cross resonance through the first tunable frequency bus. In one embodiment, at least one of the first plurality of qubits and the second qubit are configured to interact through a parametric iSWAP gate.

[0019] In one embodiment, the first plurality of qubits includes three qubits configured to interact with each other via cross resonance through the first tunable frequency bus, and the second qubit is configured to interact with the three qubits via a parametric iSWAP gate through the first tunable frequency bus.

[0020] In one embodiment, the quantum computing device further comprises a second plurality of qubits having the second resonant frequency and a third qubit having the first resonant frequency; and a second tunable frequency bus configured to connect the third qubit to the second plurality of qubits. In one embodiment, the second plurality of qubits are configured to interact with each other through the second tunable frequency bus via cross resonance. In one embodiment, the third qubit is prevented from interacting with the first plurality of qubits via cross resonance.

[0021] In one embodiment, the quantum computing device further includes a second plurality of qubits having the second resonant frequency and a third qubit having a third resonant frequency that is different from the first resonant frequency and the second resonant frequency; and a second tunable frequency bus configured to couple the third qubit to the second plurality of qubits.

[0022] Another aspect of the present invention is to provide a method for producing a quantum computing device. The method includes producing a first plurality of qubits having a first resonant frequency and a second qubit having a second resonant frequency on a qubit chip, the second frequency being different from the first frequency; at least one of producing a first fixed frequency bus on the qubit chip or attaching the qubit chip to a chip including the first frequency bus to enable interaction between the first plurality of qubits via cross resonance; and at least one of the following: producing a first tunable frequency bus on the qubit chip or attaching the qubit chip to a chip including the first tunable frequency bus to enable coupling of at least one qubit of the first plurality of qubits to the second qubit using the first tunable frequency bus.

[0023] Another aspect of the present invention is to provide a method for producing a quantum computing device. The method includes producing a first plurality of qubits having a first resonant frequency and a second qubit having a second resonant frequency on a qubit chip, the second frequency being different from the first frequency; and at least one of the following: producing a first tunable frequency bus on the qubit chip or attaching the qubit chip to a chip including the first tunable frequency bus so as to enable coupling of at least one qubit of the first plurality of qubits to the second qubit using the first tunable frequency bus.

[0024] The frequency of a qubit corresponds to the transition energy between two states of the qubit being used, such as the transition energy between a ground state and a first excited state. A qubit has two quantum states (e.g., a ground state and a first excited state) that are sufficiently separated in energy to form separate energy levels and / or decoupled from any additional quantum states such that the qubit approximates a two-quantum-state structure under operating conditions. The transition energy between the two states defines the resonant frequency of the qubit. For some qubits, for example, the transition energy can be varied by applying a magnetic field.

[0025] The term "resonant frequency" of a qubit as used in this specification corresponds to the frequency resonance of the energy separation between two energy levels (e.g., a ground state energy level and an excited state energy level) of the qubit. The resonant frequency defines an energy transition from one energy level to another. Each "energy level" of a qubit corresponds to an energy level defined within a relatively narrow energy or frequency bandwidth. The term "narrower" is used herein to refer to a bandwidth that is smaller than the transition energy between energy states of the qubit. For example, the generation of multiple qubits intended to have the same resonant frequency can actually result in qubits with a small difference in resonant frequency but still within the bandwidth. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] The functionality of the related elements of the present disclosure and the methods of operation and structure and the economy of combination of parts and manufacture will become more apparent after considering the following description and appended claims with reference to the accompanying drawings, all of which form a part of this specification, wherein like reference numerals indicate corresponding parts in the various figures. It is to be expressly understood, however, that the drawings are for illustration and description purposes only and are not intended as a definition of the limits of the invention.

[0027] Figure 1 is a schematic diagram of a quantum computing device having a plurality of qubits according to an embodiment of the present invention;

[0028] Figure 2A is a schematic diagram of a quantum circuit including two qubits interacting via a first fixed frequency bus (CR bus) according to an embodiment of the present invention;

[0029] Figure 2B is a schematic diagram of a quantum circuit including two qubits interacting via a first tunable frequency bus according to one embodiment of the present invention;

[0030] Figure 3 is a schematic diagram of a quantum computing device having multiple qubits according to another embodiment of the present invention;

[0031] Figure 4A A schematic diagram showing a quantum circuit comprising four qubits interacting via a first tunable frequency bus according to an embodiment of the present invention;

[0032] Figure 4B A schematic diagram showing four qubits interacting via a first tunable frequency bus according to an embodiment of the present invention;

[0033] Figure 4C is an image of a quantum computing device on a chip including four qubits and a tunable frequency bus according to an embodiment of the present disclosure;

[0034] Figure 5A is an energy diagram showing first excitation energy levels of four qubits Q1, Q2, Q3, and Q4 according to an embodiment of the present invention;

[0035] Figure 5B is a graph of the energy or frequency of the first excitation energy levels of four qubits Q1, Q2, Q3, and Q4 according to an embodiment of the present invention; and

[0036] Figure 6 is a graph of the population of qubits Q3 as a function of frequency of modulating the tunable bus versus time in accordance with an embodiment of the present invention. DETAILED DESCRIPTION

[0037] Figure 1 is a schematic diagram of a quantum computing device having a plurality of qubits according to one embodiment of the present invention. Quantum computing device 10 includes a first plurality of qubits 12 having a first resonant frequency. Quantum computing device 10 also includes one or more second qubits 14 having a second resonant frequency. The second resonant frequency is different from the first resonant frequency. For example, the second resonant frequency of the one or more second qubits may be relatively higher than the first resonant frequency of the first plurality of qubits. For example, the first plurality of qubits may have a first resonant frequency in the range of 4.8-5.0 GHz, and the one or more second qubits may have a second resonant frequency in the range of 5.6-5.8 GHz.

[0038] Despite Figure 1 Four first qubits are shown in , but it must be recognized that more than two qubits may be used. Similarly, although in Figure 1 Four second qubits are shown in FIG, but it must be understood that one, two, or more second qubits may be used. However, in actual implementations, more than two first qubits and more than two second qubits are often used.

[0039] like Figure 1 As shown, the quantum computing device 10 further includes a first fixed frequency bus 16 (depicted as a dashed line), the first fixed frequency bus is configured to couple the first plurality of qubits 12, the first plurality of qubits 12 are configured to interact via cross resonance (CR) through the first fixed frequency bus 16, and the quantum computing device 10 further includes a first tunable frequency bus 18, the first tunable frequency bus is configured to couple at least one qubit in the first plurality of qubits 12 to the second qubit 14. In one embodiment, the first tunable frequency bus 18 is configured to couple the first plurality of qubits 12 (e.g., Figure 1 1) are coupled to a second plurality of qubits 14 (e.g., Figure 1 In one embodiment, first tunable frequency bus 18 is configured to couple at least one qubit in first plurality of qubits 12 and second plurality of qubits 14 via a parametric iSWAP gate. In one embodiment, first tunable frequency bus 18 is configured to couple first plurality of qubits 12 and second plurality of qubits 14 via a parametric iSWAP gate.

[0040] In one embodiment, quantum computing device 10 further includes a second fixed frequency bus 17 configured to couple a second plurality of qubits 14 , and second plurality of qubits 14 are configured to interact via cross resonance (CR) through second fixed frequency bus 17 .

[0041] Figure 2Ais a schematic diagram of a quantum circuit according to an embodiment of the present invention, the quantum circuit comprising two qubits interacting via a first fixed frequency bus (CR bus). Figure 2A As shown in , a first qubit Q1 in the first plurality of qubits 12 and a second qubit Q2 in the first plurality of qubits 12 interact with each other via a first fixed frequency bus 16 (CR bus). In one embodiment, first fixed frequency bus 16 is a microwave transmission line connecting qubit Q1 to qubit Q2. Similarly, although in Figure 2A Not illustrated, the first qubit Q1 in the second plurality of qubits 14 and the second qubit Q2 in the second plurality of qubits 14 interact via a second fixed frequency bus (CR bus) 17, which in one embodiment is a microwave transmission line connecting qubit Q1 to qubit Q2. In qubits Q1 and Q2, the vertical lines "|" correspond to capacitors, while the "X" symbols correspond to Josephson junctions. Although the qubits shown have a single Josephson junction (JJ) and a single capacitor, any number of Josephson junctions and any number of capacitors may be used. Additionally, other elements may also be included in the circuits of qubits Q1 and Q2 as well as the first fixed frequency bus 16 (CR bus) and / or the second fixed frequency bus 17 (CR bus).

[0042] Figure 2B 1 is a schematic diagram of a quantum circuit according to an embodiment of the present invention, the quantum circuit comprising two qubits interacting via a first tunable frequency bus 18. Figure 2B As shown, a first qubit Q1 in the first plurality of qubits 12 and a second qubit Q2 in the first plurality of qubits 12 interact with each other via a first tunable frequency bus 18 (e.g., via a parametric iSWAP gate). Figure 2B As shown, the first tunable frequency bus 18 includes a gate (e.g., a parametric iSWAP gate) "G" that connects qubit Q1 to qubit Q2 via a transmission line. Gate "G" is activated by applying a magnetic field "B". Figure 2ASimilarly, in qubits Q1 and Q2, the vertical line "|" corresponds to a capacitor and the "X" symbol corresponds to a Josephson junction. Although qubits Q1 and Q2 are shown as having a single Josephson junction and a single capacitor, any number of Josephson junctions and any number of capacitors may be used. In addition, other elements may also be included in the circuits of qubits Q1 and Q2. In addition, although the first tunable frequency bus 18 is shown as having a gate "G" (e.g., a parametric iSWAP gate) using two Josephson junctions, it will be understood that other types of gates with other numbers of Josephson junctions may be used. In one embodiment, the first tunable frequency bus 18 includes a superconducting quantum interference device (SQUID). The term parametric iSWAP gate is understood in the field of superconducting quantum computing as a gate that performs a swap in a phase matrix through an imaginary number "i".

[0043] like Figure 1 As shown, the first plurality of qubits 12 are arranged in a column. However, the first plurality of qubits 12 may also be arranged in a first row. The first plurality of qubits 12 are configured to interact via cross resonance (CR) through a first fixed frequency bus 16. Also as Figure 1 As shown, the second plurality of qubits 14 are arranged in a second column. However, the second plurality of qubits 14 may also be arranged in a second row. The second plurality of qubits 14 are configured to interact via cross resonance (CR) through the second fixed frequency bus 17.

[0044] Likewise Figure 1 As shown, in one embodiment, the quantum computing device 10 also includes a third plurality of qubits 13 having a first resonant frequency similar to the first plurality of qubits 12. Figure 1 As shown, the third plurality of qubits 13 are arranged in a third column. However, the third plurality of qubits 13 may also be arranged in a third row. The quantum computing device further includes a third fixed frequency bus 19 configured to couple the third plurality of qubits 13, and the third plurality of qubits 13 are configured to interact via cross resonance (CR) through the third fixed frequency bus 19.

[0045] Likewise Figure 1 As shown, in one embodiment, quantum computing device 10 also includes a fourth plurality of qubits 15 having a second resonant frequency similar to that of second plurality of qubits 14. Figure 1 As shown in , the fourth plurality of qubits 15 are arranged in a fourth column. However, the fourth plurality of qubits 15 may also be arranged in a fourth row. The quantum computing device 10 also includes a fourth fixed frequency bus 21 configured to couple the fourth plurality of qubits 15, and the fourth plurality of qubits 15 are configured to interact via cross resonance (CR) through the fourth fixed frequency bus 21.

[0046] In one embodiment, first plurality of qubits 12 arranged in a first row or column are configured to interact with second plurality of qubits 14 arranged in a second row or column via first tunable frequency bus 18, in one embodiment, second plurality of qubits 14 arranged in the second row or column are configured to interact with third plurality of qubits 13 arranged in a third row or column via first tunable frequency bus 18, and in one embodiment, third plurality of qubits 13 arranged in the third row or column are configured to interact with fourth plurality of qubits 15 arranged in a fourth row or column via first tunable frequency bus 18.

[0047] In one embodiment, second plurality of qubits 14 is arranged between first plurality of qubits 12 and third plurality of qubits 13 so as to prevent cross-resonance interactions and thereby substantially reduce or eliminate frequency conflicts and crosstalk between first plurality of qubits and third plurality of qubits 13, and similarly, third plurality of qubits 13 is arranged between second plurality of qubits 14 and fourth plurality of qubits 15 so as to prevent cross-resonance interactions and thereby substantially reduce or eliminate frequency conflicts and crosstalk between second plurality of qubits 14 and fourth plurality of qubits 15.

[0048] In one embodiment, the third plurality of qubits 13 has a third resonant frequency. Figure 1 As shown, the third plurality of qubits 13 are arranged in a third column. However, the third plurality of qubits 13 may also be arranged in a third row. However, in this embodiment, the third resonant frequency is different from the first resonant frequency of the first plurality of qubits 12 and different from the second resonant frequency of the second plurality of qubits 14. In one embodiment, the third fixed frequency bus 19 is configured to couple the third plurality of qubits 13, which are configured to interact via cross resonance (CR) through the third fixed frequency bus 19. In one embodiment, the quantum computing device includes a second tunable frequency bus 22, which is configured to couple at least one of the third plurality of qubits 13 to the second plurality of qubits 14.

[0049] In one embodiment, first plurality of qubits 12 arranged in a first row or column are configured to interact with second plurality of qubits 14 arranged in a second row or column via first tunable frequency bus 18, and in one embodiment, second plurality of qubits 14 arranged in a second row or column are configured to interact with third plurality of qubits 13 arranged in a third row or column via second tunable frequency bus 22.

[0050] In one embodiment, the first, second, third and / or fourth plurality of qubits may be transport sub-qubits.

[0051] Figure 3 is a schematic diagram of a quantum computing device with multiple qubits according to another embodiment of the present invention. Quantum computing device 30 includes a first plurality of qubits 32 having a first resonant frequency and a second qubit 34 having a second resonant frequency. The second resonant frequency is different from the first resonant frequency. In one embodiment, the second frequency is, for example, higher than the first frequency. In one embodiment, for example, the second frequency can be in the range of 4.8-5.0 GHz, and the first frequency can be in the range of 5.6-5.8 GHz. The quantum computing device further includes a first tunable frequency bus 36, which is configured to couple the first plurality of qubits 32 to the second qubit 34.

[0052] In one embodiment, first plurality of qubits 32 are configured to interact with each other via cross resonance (CR) through first tunable frequency bus 36 .

[0053] Figure 4A A schematic diagram of a quantum circuit comprising four qubits interacting via a first tunable frequency bus 36 is shown according to an embodiment of the present invention. Figure 4B A schematic diagram showing four qubits interacting via a first tunable frequency bus 36 according to an embodiment of the present invention is shown. Figure 4C is an image of a quantum computing device on a chip including four qubits and a tunable frequency bus according to an embodiment of the present disclosure. Figure 4A As shown, qubits Q1 , Q2 , and Q4 of first plurality of qubits 32 interact with each other and with qubit Q3 corresponding to second qubit 34 via first tunable frequency bus 36 (eg, via parametric iSWAP gates).

[0054] In one embodiment, Figure 4AAs shown, the first tunable frequency bus 36 includes a gate (e.g., a parametric iSWAP gate) "G" that connects qubits Q1, Q2, Q3, and Q4 using a transmission line connected to the quantum gate "G". The gate "G" is activated by applying a magnetic field "B". In the qubits Q1, Q2, Q3, and Q4, the vertical lines "|" correspond to capacitors, and the "X" symbols correspond to Josephson junctions. Although the qubits Q1, Q2, Q3, and Q4 are shown as having a single Josephson junction and a single capacitor, any number of Josephson junctions and any number of capacitors can be used. In addition, other elements can also be included in the circuits of the qubits Q1, Q2, Q3, and Q4. In addition, although the first tunable frequency bus 36 is shown as having a gate "G" (e.g., a parametric iSWAP gate) using two Josephson junctions, it can be understood that other types of gates can be used, which use other numbers of Josephson junctions. In one embodiment, the first tunable frequency bus 36 includes a superconducting quantum interference device (SQUID). Thus, in one embodiment, first plurality of qubits 32 and second qubits 34 are configured to interact with first tunable frequency bus 36 (via a parametric iSWAP gate).

[0055] In one embodiment, Figure 3 , 4A As shown in Figures 4B and 4B, the first plurality of qubits 32 includes three qubits (e.g., Q1, Q2, and Q4). The three qubits 32 (Q1, Q2, and Q4) are configured to interact with each other via cross resonance (CR) through the first tunable frequency bus 36. The second qubit 34 (Q3) is configured to interact with the three qubits 32 (Q1, Q2, and Q4) through the first tunable frequency bus 36 (through a parametric iSWAP gate).

[0056] Figure 5A : is an energy diagram showing the first excitation energy levels of four qubits Q1, Q2, Q3 and Q4 according to an embodiment of the present invention. The first excitation energy level of qubit Q1 is represented as |0001>, the first excitation energy level of qubit Q2 is represented as |0010>, the first excitation energy level of qubit Q4 is represented as |1000>, and the first excitation energy level of qubit Q3 is represented as |0100>. The frequency of each of the above excited energy states corresponds to the transition energy (or frequency) between the ground state (energy or frequency equal to zero) and the first excited energy level, respectively, Q1 is 4.605 GHz, Q2 is 4.685 GHz, Q4 is 4.727, and Q3 is 5.478. As shown in Figure 5AAs shown, the excited energy levels |0001>, |0010>, and |1000> of qubits Q1, Q2, and Q4 are close to each other, respectively, with an energy difference of 80 MHz between |0001> and |0010>, 42 MHz between |0010> and |1000>, and 122 MHz between |0001> and |1000>. This allows qubits Q1, Q2, and Q4 to interact via CR. On the other hand, the energy difference between the excitation level |0100> of qubit Q3 and the energy level |0001> of qubit Q1, the energy difference between the excitation level |0100> of qubit Q3 and the energy level |0010> of qubit Q2, and the energy difference between the excitation level |0100> of qubit Q3 and the energy level |1000> of qubit Q4 are 873 MHz, 793 MHz, and 751 MHz, respectively, which are greater than any of 80 MHz, 42 MHz, and 122 MHz. As a result, in this case, the interaction between qubits Q1, Q2, Q4, and Q3 is achieved by the first tunable frequency bus 36 (e.g., using a parametric iSWAP gate). The inventors have achieved a quantum computing device having four qubits Q1, Q2, Q3, and Q4 coupled to a tunable frequency bus using a parametric iSWAP gate. The inventors report results showing the successful implementation of the interaction between various qubits. The inventors plot the results.

[0057] Figure 6 is a graph of the population in qubit Q3 as a function of the frequency of the modulated tunable bus relative to time according to an embodiment of the present invention. The region where the population of qubit Q3 is reduced corresponds to the frequency (energy) difference between the excitation energy levels. The figure shows that the energy (or frequency) difference between the excitation energy level |0100> of qubit Q3 and the energy level |0001> of qubit Q1, the energy (or frequency) difference between the excitation energy level |0100> of qubit Q3 and the energy level |0010> of qubit Q2, and the energy (or frequency) difference between the excitation energy level |0100> of qubit Q3 and the energy level |1000> of qubit Q4 are 873 MHz, 793 MHz, and 751 MHz, respectively. The figure shows that the interaction is stable over a time range of at least 5 μs, and gives a typical time scale for the interaction (less than about 1 μs).

[0058] Figure 5Bis a graph of the energy or frequency difference of the first excitation energy levels of four qubits Q1, Q2, Q3, and Q4 according to an embodiment of the present invention. The three lower horizontal lines in the graph below about 200 MHz correspond to transitions between the three states |0001>, |0010>, and |1000> of qubits Q1, Q2, Q3, and Q4. These three are located within a relatively narrow energy or frequency bandwidth. The term "narrower" as used herein means that the bandwidth (about 122 MHz in this case) is less than the energy difference between each of the three qubits and the energy state of the fourth qubit (about 800 MHz). The three upper horizontal lines in the graph between about 750 MHz and about 900 MHz correspond to the excitation manifold that includes the excitation energy level |0100> of qubit Q3. Transitions that leave the qubit space (e.g., transitions between state |1001> and state |0002>) are located between the lower and upper horizontal lines in the graph. The figure shows that a tunable bus interaction by itself is not sufficient because transitions between qubits of similar frequency are within the same bandwidth as transitions outside the qubit subspace.

[0059] Back to Figure 3 , quantum computing device 30 further includes a second plurality of qubits 38 having a second resonant frequency and a third qubit 40 having a first resonant frequency. Quantum computing device 30 further includes a second tunable frequency bus 42 configured to couple third qubit 40 to second plurality of qubits 38. In one embodiment, second plurality of qubits 38 includes second qubit 34.

[0060] In one embodiment, second plurality of qubits 38 are configured to interact with each other via cross resonance (CR) through second tunable frequency bus 42. In one embodiment, third qubit 40 and second plurality of qubits 38 are configured to interact (via parametric iSWAP gates) through second tunable frequency bus 42. In one embodiment, third qubit 40 is prevented from interacting with first plurality of qubits 32 via cross resonance.

[0061] In one embodiment, quantum computing device 30 further includes a second plurality of qubits 38 having a second resonant frequency and a third qubit 40 having a third resonant frequency. In this embodiment, the third resonant frequency is different from the first resonant frequency of first plurality of qubits 32 and different from the second resonant frequency of second plurality of qubits 38. Second tunable frequency bus 42 is configured to couple third qubit 40 to second plurality of qubits 38. In one embodiment, second plurality of qubits 38 are configured to interact with each other via cross resonance (CR) through second tunable frequency bus 42. In one embodiment, third qubit 40 and second plurality of qubits 38 are configured to interact via a parametric iSWAP gate through second tunable frequency bus 42.

[0062] In one embodiment, second plurality of qubits 38 includes three qubits. The three qubits are configured to interact with each other via cross resonance (CR) via second tunable frequency bus 42, and third qubit 40 is configured to interact with three qubits 38 via parametric iSWAP gates via second tunable frequency bus 42.

[0063] As can be understood from the above paragraphs, a method for producing a quantum computing device (e.g., quantum computing device 10) according to an embodiment of the present invention is also provided. The method includes producing a first plurality of qubits 12 having a first resonant frequency and a second qubit 14 having a second resonant frequency (e.g., as shown in FIG. 1 ) on a qubit chip. Figure 4C ). The second frequency is different from the first frequency. The method further includes at least one of producing a first fixed frequency bus 16 on the qubit chip or attaching the qubit chip to a chip including the first fixed frequency bus 16 to enable interaction between the first plurality of qubits 12 via cross resonance (CR). The method also includes at least one of producing a first tunable frequency bus 18 on the qubit chip or attaching the qubit chip to a chip including the first tunable frequency bus 18 to enable coupling of at least one qubit in the first plurality of qubits 12 to the second qubit 14 using the first tunable frequency bus 18.

[0064] According to one embodiment of the present invention, as can be understood from the above paragraphs, a method of producing a quantum computing device (e.g., quantum computing device 30) is further provided. The method includes on a qubit chip (e.g., Figure 4CThe method further comprises producing a first plurality of qubits 32 having a first resonant frequency and a second qubit 34 having a second resonant frequency on a qubit chip (as shown in FIG. 1 ). The second frequency is different from the first frequency. The method further comprises at least one of producing a first tunable frequency bus 36 on the qubit chip or attaching the qubit chip to a chip including the first tunable frequency bus 36. To enable coupling of at least one qubit in the first plurality of qubits 32 to the second qubit 34 using the first tunable frequency bus 36.

[0065] The description of various embodiments of the present invention has been given for the purpose of illustration, but it is not intended to be exhaustive or limited to the disclosed embodiments. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terms used herein are selected to best explain the principles of the embodiments, practical applications, or technical improvements existing in the market, or to enable other persons of ordinary skill in the art to understand the embodiments disclosed herein.

Claims

1. A quantum computing device, comprising: a plurality of qubits, the plurality of qubits comprising a first plurality of qubits having a first resonant frequency and a second plurality of qubits having a second resonant frequency different from the first resonant frequency; a first fixed frequency bus configured to couple the first plurality of qubits, the first plurality of qubits configured to interact via cross resonance through the first fixed frequency bus; as well as a first tunable frequency bus configured to couple at least one qubit of the first plurality of qubits to the second qubit, wherein pairs of adjacent qubits in the plurality of qubits having the same resonant frequency are coupled only through cross resonances, and pairs of adjacent qubits in the plurality of qubits having different resonant frequencies are coupled only through respective parametric iSWAP gates, and wherein the first plurality of qubits is different from the second qubits, and wherein a pair of adjacent qubits has no intervening qubits on an associated frequency bus connecting the pair of adjacent qubits.

2. The quantum computing device of claim 1 , wherein the first tunable frequency bus is configured to couple the at least one qubit in the first plurality of qubits to the second qubit via a parametric iSWAP gate.

3. The quantum computing device according to claim 1, in, the plurality of qubits further comprising a second plurality of qubits having the second resonant frequency; The quantum computing device further comprises: and a second fixed frequency bus configured to couple the second plurality of qubits, the second plurality of qubits configured to interact via cross resonance through the second fixed frequency bus, wherein the first plurality of qubits is different from the second plurality of qubits, and wherein the first fixed frequency bus is different from the second fixed frequency bus.

4. The quantum computing device of claim 3 , wherein the first plurality of qubits are arranged in one of a first row or a first column and are configured to interact via cross resonance through the first fixed frequency bus, and wherein the second plurality of qubits are arranged in one of a second row or a second column and are configured to interact via cross resonance through the second fixed frequency bus.

5. The quantum computing device according to claim 4, further comprising: a third plurality of qubits having the first resonant frequency, the third plurality of qubits arranged in one of a third row or a third column; as well as and a third fixed frequency bus configured to couple the third plurality of qubits, the third plurality of qubits configured to interact via cross resonance through the third fixed frequency bus, wherein the first plurality of qubits, the second plurality of qubits, and the third plurality of qubits are all different.

6. The quantum computing device according to claim 5, wherein the first plurality of qubits arranged in the first row or the first column are configured to interact with the second plurality of qubits arranged in the second row or the second column via the first tunable frequency bus; and in, The second plurality of qubits arranged in the second row or in the second column are configured to interact with the third plurality of qubits arranged in the third row or in the third column via the first tunable frequency bus.

7. The quantum computing device of claim 5, wherein the second plurality of qubits is arranged between the first plurality of qubits and the third plurality of qubits so as to prevent cross-resonance interactions between the first plurality of qubits and the third plurality of qubits.

8. The quantum computing device of claim 4, further comprising: a third plurality of qubits having a third resonant frequency, the third plurality of qubits arranged in one of a third row or a third column, the third resonant frequency being different from the first resonant frequency and different from the second resonant frequency; a third fixed frequency bus configured to couple the third plurality of qubits, the third plurality of qubits configured to interact via cross resonance through the third fixed frequency bus; as well as a second tunable frequency bus configured to couple at least one qubit in the third plurality of qubits to the second plurality of qubits, wherein the first plurality of qubits, the second plurality of qubits, and the third plurality of qubits are all different, and wherein the first fixed frequency bus, the second fixed frequency bus, and the third fixed frequency bus are all different.

9. The quantum computing device of claim 8, wherein the first plurality of qubits arranged in the first row or the first column are configured to interact with the second plurality of qubits arranged in the second row or the second column via the first tunable frequency bus, Wherein the second plurality of qubits arranged in the second row or in the second column are configured to interact with the third plurality of qubits arranged in the third row or in the third column via the second tunable frequency bus.

10. The quantum computing device of claim 1, wherein the first plurality of qubits and the second qubit are transport sub-qubits.

11. The quantum computing device of claim 1, wherein: The first tunable frequency bus includes a superconducting quantum interference device (SQUID).

12. A quantum computing device, comprising: a plurality of qubits, the plurality of qubits comprising a first plurality of qubits having a first resonant frequency and a second plurality of qubits having a second resonant frequency different from the first resonant frequency; and a first tunable frequency bus configured to couple the first plurality of qubits to the second qubits, wherein pairs of adjacent qubits in the plurality of qubits having the same resonant frequency are coupled only through cross resonances, and pairs of adjacent qubits in the plurality of qubits having different resonant frequencies are coupled only through respective parametric iSWAP gates, and wherein the first plurality of qubits is different from the second qubits, and wherein a pair of adjacent qubits has no intervening qubits on an associated frequency bus connecting the pair of adjacent qubits.

13. The quantum computing device of claim 12, wherein the first plurality of qubits are configured to interact with each other via cross resonance through the first tunable frequency bus.

14. The quantum computing device of claim 12, wherein at least one of the first plurality of qubits and the second qubit is configured to interact via a parametric iSWAP gate.

15. The quantum computing device of claim 12, wherein the first plurality of qubits comprises three qubits configured to interact with each other via cross resonance through the first tunable frequency bus, and the second qubit is configured to interact with the three qubits via a parametric iSWAP gate through the first tunable frequency bus.

16. The quantum computing device according to claim 12, in, The plurality of qubits also includes a second plurality of qubits having the second resonant frequency and a third qubit having the first resonant frequency; The quantum computing device further comprises: a second tunable frequency bus configured to couple the third qubit to the second plurality of qubits, wherein the first plurality of qubits, the second plurality of qubits, and the third qubits are all different, and wherein the first tunable frequency bus is different from the second tunable frequency bus.

17. The quantum computing device of claim 16, wherein the second plurality of qubits are configured to interact with each other via cross resonance through the second tunable frequency bus.

18. A quantum computing device according to claim 16, wherein the third qubit and the second plurality of qubits are configured to interact via a parametric iSWAP gate through the second tunable frequency bus.

19. The quantum computing device of claim 16, wherein via positioning of at least one of the second plurality of qubits, the third qubit is prevented from interacting with the first plurality of qubits via cross resonance.

20. The quantum computing device of claim 12, further comprising: a second plurality of qubits having the second resonant frequency and a third qubit having a third resonant frequency that is different from the first resonant frequency and the second resonant frequency; as well as a second tunable frequency bus configured to couple the third qubit to the second plurality of qubits, wherein the first plurality of qubits, the second plurality of qubits, and the third plurality of qubits are all different, and wherein the first tunable frequency bus is different from the second tunable frequency bus.

21. The quantum computing device of claim 20, wherein the second plurality of qubits are configured to interact with each other via cross resonance through the second tunable frequency bus.

22. A quantum computing device according to claim 21, wherein the third qubit and the second plurality of qubits are configured to interact via a parametric iSWAP gate through the second tunable frequency bus.

23. The quantum computing device of claim 21 , wherein the second plurality of qubits comprises three qubits configured to interact with each other via cross resonance through the second tunable frequency bus, and the third qubit is configured to interact with the three qubits via a parametric iSWAP gate through the second tunable frequency bus.

24. A method of producing a quantum computing device, comprising: producing a plurality of qubits on a qubit chip, the plurality of qubits comprising a first plurality of qubits having a first resonant frequency and a second qubit having a second resonant frequency, the second resonant frequency being different from the first resonant frequency, wherein pairs of adjacent qubits in the plurality of qubits having the same resonant frequency are coupled only through cross resonances and pairs of adjacent qubits in the plurality of qubits having different resonant frequencies are coupled only through respective parametric iSWAP gates, and wherein the first plurality of qubits are different from the second qubits, and wherein a pair of adjacent qubits have no intervening qubits on an associated frequency bus connecting the pair of adjacent qubits; At least one of: producing a first fixed frequency bus on the qubit chip or attaching the qubit chip to a chip including the first fixed frequency bus to enable interaction between the first plurality of qubits via cross resonance; and At least one of: producing a first tunable frequency bus on the qubit chip or attaching the qubit chip to a chip including the first tunable frequency bus to enable coupling of at least one qubit of the first plurality of qubits to the second qubit using the first tunable frequency bus.

25. A method of producing a quantum computing device, comprising: producing a plurality of qubits on a qubit chip, the plurality of qubits comprising a first plurality of qubits having a first resonant frequency and a second qubit having a second resonant frequency, the second resonant frequency being different from the first resonant frequency, wherein pairs of adjacent qubits in the plurality of qubits having the same resonant frequency are coupled only through cross resonances and pairs of adjacent qubits in the plurality of qubits having different resonant frequencies are coupled only through respective parametric iSWAP gates, and wherein the first plurality of qubits are different from the second qubits, and wherein a pair of adjacent qubits have no intervening qubits on an associated frequency bus connecting the pair of adjacent qubits; and At least one of: producing a first tunable frequency bus on the qubit chip or attaching the qubit chip to a chip including the first tunable frequency bus to enable coupling of at least one qubit of the first plurality of qubits to the second qubit using the first tunable frequency bus.

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