Dual rail entangling gate via cross-kerr interaction activated by beam splitter

Abstract

This paper describes a system and method for executing entanglement gates between a first and a second dual-track qubit. The technique described herein can utilize static nonlinear interactions (e.g., static cross-Kerr interactions) to execute entanglement gates using coupled dual-track qubits. Entanglement gates can be executed by applying one or more driving waveforms to exchange the encoded states of the quantum oscillators in the dual-track qubits, thereby “turning on” and “turning off” the nonlinear interactions.

Description

[0001] Cross-references to related applications

[0002] This application claims priority and benefit to U.S. Provisional Patent Application No. 63 / 560,312, filed March 1, 2024, under Agent’s File No. Y0087.70174US00, entitled “DUAL-RAIL ENTANGLING GATES VIA BEAMSPLITTER-ACTIVATED CROSS KERR INTERACTIONS”, the entire contents of which are incorporated herein by reference.

[0003] Federally funded research

[0004] This invention was carried out with government support under license number W911NF-23-1-0051 granted by the U.S. Army Research Office. The government has certain rights to this invention. Background Technology

[0005] Quantum information processing techniques perform computations by manipulating one or more quantum objects. These techniques are sometimes referred to as "quantum computing." To perform computations, quantum information processors utilize quantum objects to reliably store and retrieve information. Based on some quantum information processing methods, quantum simulations of classical computational "bits" (equal to 1 or 0) have been developed, which are called quantum bits (qubits). A quantum bit can consist of any quantum system having two distinct states (which can be considered as a 1 state and a 0 state), but it also possesses the specific property that the system can be placed in a quantum superposition and thus potentially exist in both states simultaneously. Summary of the Invention

[0006] Some aspects described herein relate to quantum information processing systems. A quantum information processing system may include: a first dual-track qubit device; a second dual-track qubit device; a first coupling element coupled between the first and second dual-track qubit devices; at least one energy source; and at least one controller configured to operate the at least one energy source to perform an entanglement gate between the first and second dual-track qubit devices by: applying a first driving waveform to the first coupling element to induce a first exchange of the states of the quantum oscillators of the first and second dual-track qubit devices; and, after waiting for a predetermined time period following the induction of the first exchange, applying a second driving waveform to the first coupling element to induce a second exchange of the states of the quantum oscillators of the first and second dual-track qubit devices.

[0007] In some embodiments, the first dual-track qubit device and the second dual-track qubit device each include a first quantum oscillator, a second quantum oscillator, and a second coupling element that couples the first quantum oscillator to the second quantum oscillator; and the first coupling element is coupled between the first quantum oscillator of the first dual-track qubit device and the first quantum oscillator of the second dual-track qubit device.

[0008] In some embodiments, the first coupling element is dispersively coupled between the first quantum oscillator of the first dual-track qubit device and the first quantum oscillator of the second dual-track qubit device. In some embodiments, the first coupling element includes a flux-driven SQUID coupler. In some embodiments, the first coupling element is a transport sub-qubit device or a superconducting asymmetric inductor (SNAIL).

[0009] In some embodiments, the quantum information processing system further includes: a first auxiliary qubit device coupled to a first dual-track qubit device; and a second auxiliary qubit device coupled to a second dual-track qubit device. In some embodiments, the first auxiliary qubit device is coupled to a second quantum oscillator of the first dual-track qubit device, and the second auxiliary qubit device is coupled to a first quantum oscillator of the second dual-track qubit device. In some embodiments, the first and / or second auxiliary qubit devices are transport qubit devices. In some embodiments, the first and second quantum oscillators include microwave cavities. In some embodiments, at least one controller is configured to apply a first driving waveform and / or a second driving waveform to the first coupling element for a certain period of time. In some implementations, at least one controller is configured to have approximately After a predetermined time period of length, a second driving waveform is applied.

[0010] In some embodiments, at least one controller is further configured to apply a pulse sequence comprising applying a drive waveform to a respective coupling element to induce a state exchange between quantum oscillators coupled by the respective coupling elements. The pulse sequence includes: a first drive waveform applied to a first coupling element; a second drive waveform applied to the first coupling element; a third drive waveform applied to a second coupling element of the first dual-track qubit device, the third drive waveform being applied before the first drive waveform; and a fourth drive waveform applied to the second coupling element of the first dual-track qubit device, the fourth drive waveform being applied after the second drive waveform.

[0011] In some embodiments, at least one controller is further configured to apply a pulse sequence comprising applying a drive waveform to a corresponding coupling element to induce a state exchange between quantum oscillators coupled by the corresponding coupling element. The pulse sequence includes: a first drive waveform applied to a first coupling element; a second drive waveform applied to the first coupling element; a third drive waveform applied to a second coupling element of a first dual-track qubit device; a fourth drive waveform applied to a second coupling element of a second dual-track qubit device; a fifth drive waveform applied to the first coupling element; and a sixth drive waveform applied to the first coupling element after a second predetermined time period following the fifth drive waveform.

[0012] In some embodiments, the pulse sequence further includes: a seventh driving waveform applied to a second coupling element of the first dual-track qubit device; and an eighth driving waveform applied to a second coupling element of the second dual-track qubit device.

[0013] In some embodiments, at least one controller is further configured to apply a pulse sequence comprising applying a driving waveform to a corresponding coupling element to induce a state exchange between quantum oscillators coupled by the corresponding coupling element. The pulse sequence includes: a first driving waveform applied to a first coupling element; a second driving waveform applied to the first coupling element; a third driving waveform applied to a second coupling element of a first dual-track qubit device; and a fourth driving waveform applied to a second coupling element of a second dual-track qubit device, the third and fourth driving waveforms being applied between the first and second driving waveforms.

[0014] In some embodiments, the pulse sequence further includes: a fifth driving waveform applied to a second coupling element of the first dual-track qubit device; a sixth driving waveform applied to the first coupling element; a seventh driving waveform applied to the first coupling element after a second predetermined time period following the sixth driving waveform; and an eighth driving waveform applied to the second coupling element of the first dual-track qubit device.

[0015] In some embodiments, the first coupling element includes: a third quantum oscillator, a fourth quantum oscillator, and a third coupling element coupled between the first quantum oscillator and the second quantum oscillator; a fourth coupling element coupled between the first quantum oscillator and the third quantum oscillator of the first dual-track qubit device; and a fifth coupling element coupled between the first quantum oscillator and the fourth quantum oscillator of the second dual-track qubit device; applying a first driving waveform to the first coupling element includes applying the first driving waveform to the fourth coupling element and the fifth coupling element; and applying a second driving waveform to the first coupling element includes applying the second driving waveform to the fourth coupling element and the fifth coupling element.

[0016] Some aspects described herein relate to a method for performing an entanglement gate between a first two-track qubit device and a second two-track qubit device coupled via a first coupling element, each comprising a first quantum oscillator, a second quantum oscillator, and a second coupling element coupling the first quantum oscillator to the second quantum oscillator, wherein the first coupling element is coupled between the first quantum oscillator of the first two-track qubit device and the first quantum oscillator of the second two-track qubit device. The method may include: applying a first driving waveform to the first coupling element to induce a first exchange of the state of the first quantum oscillator of the first two-track qubit device with the state of the first quantum oscillator of the second two-track qubit device; and, after waiting for a predetermined time period after inducing the first exchange, applying a second driving waveform to the first coupling element to induce a second exchange of the state of the first quantum oscillator of the first two-track qubit device with the state of the first quantum oscillator of the second two-track qubit device.

[0017] In some embodiments, applying the first driving waveform and / or the second driving waveform includes applying the first driving waveform and / or the second driving waveform for a certain period of time. In some implementations, applying the second drive waveform includes having approximately The second driving waveform is applied after a predetermined time period of length.

[0018] In some embodiments, the method further includes applying a pulse sequence comprising a driving waveform configured to induce a state exchange between quantum oscillators coupled by respective coupling elements. Applying the pulse sequence includes: applying a third driving waveform to a second coupling element of the first dual-track qubit device, the third driving waveform being applied before the first driving waveform; and applying a fourth driving waveform to the second coupling element of the first dual-track qubit device, the fourth driving waveform being applied after the second driving waveform.

[0019] In some embodiments, the method further includes applying a pulse sequence comprising a driving waveform configured to induce a state exchange between quantum oscillators coupled by corresponding coupling elements. Applying the pulse sequence includes: applying a third driving waveform to a second coupling element of a first dual-track qubit device; applying a fourth driving waveform to a second coupling element of a second dual-track qubit device; applying a fifth driving waveform to a first coupling element; and applying a sixth driving waveform to the first coupling element after a second predetermined time period following the application of the fifth driving waveform.

[0020] In some embodiments, applying the pulse sequence further includes: applying a seventh driving waveform to the second coupling element of the first dual-track qubit device; and applying an eighth driving waveform to the second coupling element of the second dual-track qubit device.

[0021] In some embodiments, the method further includes applying a pulse sequence comprising a driving waveform configured to induce a state exchange between quantum oscillators coupled by respective coupling elements. Applying the pulse sequence includes: applying a third driving waveform to a second coupling element of a first dual-track qubit device; applying a fourth driving waveform to a second coupling element of a second dual-track qubit device, wherein the third and fourth driving waveforms are applied between the first and second driving waveforms.

[0022] In some embodiments, the pulse sequence further includes: after applying the second driving waveform: applying a fifth driving waveform to the second coupling element of the first dual-track qubit device; applying a sixth driving waveform to the first coupling element; after waiting for a second predetermined time period after the sixth driving waveform, applying a seventh driving waveform to the first coupling element; and applying an eighth driving waveform to the second coupling element of the first dual-track qubit device.

[0023] In some embodiments, the method further includes a first coupling element comprising: a third quantum oscillator, a fourth quantum oscillator, and a third coupling element coupled between the first quantum oscillator and the second quantum oscillator; a fourth coupling element coupled between the first quantum oscillator and the third quantum oscillator of the first dual-track qubit device; and a fifth coupling element coupled between the first quantum oscillator and the fourth quantum oscillator of the second dual-track qubit device; and the method further includes: applying a first driving waveform to the first coupling element comprising applying the first driving waveform to the fourth coupling element and the fifth coupling element; and applying a second waveform to the second coupling element comprising applying the second driving waveform to the fourth coupling element and the fifth coupling element.

[0024] The foregoing embodiments of the apparatus and methods can be implemented using any suitable combination of the embodiments, features, and operations described above or in further detail below. These and other aspects, embodiments, and features of this description can be more fully understood from the following description taken in conjunction with the accompanying drawings. Attached Figure Description

[0025] Various aspects and embodiments will be described with reference to the following accompanying drawings. It should be understood that the drawings are not necessarily drawn to scale. In the drawings, each identical or nearly identical component shown in the various figures is indicated by the same reference numerals. For clarity, not every component may be labeled in every figure.

[0026] Figure 1 An example block diagram of a system for implementing dual-track qubits according to some implementations of the techniques described herein is depicted;

[0027] Figure 2 An example schematic diagram of a system for achieving coupling between two dual-track qubits is depicted according to some implementations of the techniques described herein.

[0028] Figure 3 Some embodiments of the technology described herein are shown. Figure 2 A simplified schematic diagram of the system implementation illustrates the relative interaction strength between the system's oscillators;

[0029] Figure 4 This is a flowchart describing some implementations of the techniques described herein for performing an entanglement gate between two coupled dual-track qubits;

[0030] Figures 5A-1 to 5A-3 The following are some embodiments of the technique described herein for implementing an entanglement gate between two coupled dual-track qubits. Figure 4 Example operations of the process;

[0031] Figure 5B Some embodiments of the technology described herein are shown for implementation. Figure 4 The pulse sequence of the process;

[0032] Figure 5C Some embodiments of the technology described herein are shown. Figure 4 An example of the position of a quantum state during a process;

[0033] Figure 6A Some embodiments of the technology described herein are shown for use Figure 4An example of an alternative to the "wait" operation in the process, where the alternative operation is configured to minimize coherent leakage caused by nonlinear interactions;

[0034] Figure 6B Another example of a system for achieving coupling between two dual-track qubits according to some implementations of the techniques described herein is shown, the system including a buffer cavity coupled between the two dual-track qubits to minimize coherent leakage;

[0035] Figure 7 An example arrangement of five dual-track qubits according to some implementations of the techniques described herein is depicted for performing entanglement gates between pairs of dual-track qubits in the arrangement;

[0036] Figure 8A Another example arrangement of four dual-track qubits is depicted, illustrating some implementations of the techniques described herein, for performing entanglement gates between pairs of dual-track qubits in the arrangement;

[0037] Figure 8B Some embodiments of the technology described herein are depicted for use in Figure 8A A pulse sequence of entanglement gates is executed between the two-track qubits in the arrangement;

[0038] Figure 9 A schematic diagram of a long-range entangled double-track gate is shown, illustrating some embodiments of the technology described herein.

[0039] Figure 10 This is a flowchart describing some implementations of the techniques described herein for performing an entanglement gate replacement process between two coupled dual-track qubits, the replacement process using a reverse CPHASE angle;

[0040] Figure 11 Some embodiments of the technology described herein are shown for implementation. Figure 10 Example pulse sequences of the process;

[0041] Figure 12A A schematic representation of a process for applying a series of driving waveforms to perform an entangled gate configured to echo low-frequency dephase noise, according to some embodiments of the techniques described herein, is shown.

[0042] Figure 12B Another schematic representation of a process for applying a series of driving waveforms to perform a SWAP operation between two coupled dual-track qubits, according to some embodiments of the techniques described herein, is shown, wherein the SWAP operation is configured to eliminate accumulated CPHASE entanglement.

[0043] Figure 13 An illustrative implementation of a computer system 1300 that can be used in conjunction with any of the implementations of the techniques described herein is depicted. Detailed Implementation

[0044] Quantum multilevel systems, such as superconducting qubits, exhibit quantum states that decoherent within approximately ~100 µs, based on current experimental practice. While experimental techniques will undoubtedly improve this and produce qubits with longer decoherence times, it may be beneficial to couple a multilevel system to another system exhibiting a longer decoherence time. Systems configured with boson modes may be particularly desirable for coupling to multilevel systems. Through such coupling, the state of the multilevel system can be represented alternatively by the boson modes, thus retaining the same information as if it were otherwise existing alone in the multilevel system, even with a longer lifetime. When used in this way, boson systems are sometimes referred to as “logical” qubits, where a “logical” qubit is a collection of physical qubits (e.g., one or more devices supporting boson modes) that work together to represent quantum states (e.g., the state of a multilevel system).

[0045] Nevertheless, the quantum information stored in bosonic modes may still have a finite lifetime, making errors still possible within the bosonic system. Therefore, when errors occur in the state of a bosonic system, it may be desirable to manipulate the system to effectively correct those errors and thus restore the system to its previous state. If a wide range of errors can be corrected, it becomes possible to maintain the state of the bosonic system indefinitely (or at least over long periods) by correcting any type of error that may occur, thereby enabling longer computational cycles (e.g., allowing more quantum operations to be performed on the quantum state, thus permitting more complex or longer computations).

[0046] Therefore, when errors occur in the state of a boson system, it is desirable to manipulate the boson system to effectively correct those errors and thus restore the system to its previous state. In some cases, it may be sufficient to detect errors occurring only during operation. The expectation of detecting and / or correcting errors in quantum systems requires addressing a number of requirements simultaneously, including the number of physical qubits used to encode logical information, a suitable scheme for performing gates and measurements on the quantum system, and the precision of the system's physical components.

[0047] The inventors have recognized and understood that not all types of errors are equally likely to occur in a given quantum error correction architecture, nor are all types of errors equally detrimental to the logical information stored in the quantum system. Some types of errors, for example, require measuring a specific error syndrome to pinpoint the error precisely and obtain the information needed to correctly correct it. However, this does not always lead to successful error correction because sometimes sufficient information is unavailable to definitively identify the error. On the other hand, erasure errors—where the information in the qubit is erased, but in a manner that allows for the identification of the qubit—can be addressed more readily.

[0048] The inventors have further recognized and understood a technique for error correction that utilizes dual-track encoding of a single excitation in a pair of coupled quantum oscillators. Specifically, the dual-track qubit can be implemented as a circuit quantum electrodynamics (cQED) system comprising a pair of coupled resonators. In this dual-track encoding, the excitation is stored in one of the two resonators. The excitation of the first resonator is considered logic 0, while the excitation of the other resonator is considered logic 1. Thus, the two resonators together form a single logic dual-track qubit, where the logic state is... and This type of logical qubit has several advantages, including the following. First, photon loss manifests as an erasure error, which, as mentioned above, is a relatively easy-to-correct type of error. Second, the single-photon state is the lowest energy state of the oscillator, and thus has the lowest error rate for any state of the oscillator. Therefore, such dual-track encoding minimizes the loss error rate. Third, photon gain or loss can be easily detected by measuring the joint parity of the cavity.

[0049] A dual-track qubit can be implemented as a cQED system comprising two quantum oscillators (e.g., acoustic and / or optical microwave cavity resonators) coupled together via suitable nonlinear coupling elements (including, but not limited to, transport qubits, superconducting nonlinear asymmetric inductors (SNAILs), or superconducting quantum interference devices (SQUIDs)). One of the quantum oscillators can be coupled to an auxiliary qubit (e.g., transport qubits, flux qubits, or other suitable qubits). Although the auxiliary qubit is only coupled to one of the boson modes of the system, both boson modes interact with the auxiliary qubit due to beam splitter interactions provided by the coupling elements, enabling various dual-track operations. For example, a dual-track state can be prepared by applying energy (e.g., a microwave pulse) to the auxiliary qubit and / or to the coupling elements, and gates can be executed on the dual-track state, as further described below.

[0050] According to some implementations, the logical quantum state of a dual-track qubit is prepared by a single excitation of one of the two quantum oscillators used to prepare the dual-track qubit. For example, in order to prepare... The state (logic 0 state) allows two oscillators to be prepared as their respective ground states. And the first oscillator was excited to its The second oscillator remains in its state, while the second oscillator remains in its state. In this state. Similarly, in order to prepare The state (logic 1 state) allows two oscillators to be prepared as their respective ground states. And the second oscillator is excited to its The first oscillator remains in its state, while the second oscillator remains in its state. In this state, for example, in the case of a cQED dual-track qubit comprising two quantum resonators, one of the resonators can be fabricated by loading a single photon into the resonator. state.

[0051] The inventors have recognized and understood that quantum information processing systems comprising two or more dual-track qubits possess static nonlinear sources (e.g., cross-Kerr interactions or ZZ crosstalk). The inventors further recognize and understand that these static interactions between quantum oscillators can be effectively “turned on” and “turned off” by swapping the positions of photons between quantum oscillators of adjacent dual-track qubits. Two adjacent dual-track qubits can be entangled by swapping the positions of photons between quantum oscillators and “turning on” the nonlinear interactions between the two quantum oscillators (e.g., an entanglement gate can be implemented). Therefore, the inventors have developed a quantum information processing system configured to implement an entanglement gate between dual-track qubits, the entanglement gate being equivalent to a CPHASE gate, with at most a local Z-rotation phase difference.

[0052] In some implementations, the entanglement gate can be executed by implementing a first beamsplitter interaction between the first quantum oscillators of a first dual-track qubit and the first quantum oscillators of a second dual-track qubit, based on applying a first driving waveform to the coupling element coupled to the first quantum oscillator. In this way, photons can be exchanged between the first quantum oscillators of the first and second dual-track qubits. The controller can be configured to wait for a predetermined time period, such that a static cross-Kerr interaction causes phase accumulation during the predetermined time period. After the wait, the controller can then implement another beamsplitter interaction between the first and second quantum oscillators of the first and second dual-track qubits to exchange photons between the first quantum oscillators. The beamsplitter interaction can be implemented by applying a second driving waveform to the coupling element coupled to the first quantum oscillator.

[0053] Figure 1 An example block diagram of a system 100 for implementing a dual-track qubit according to some embodiments of the techniques described herein is depicted. In system 100, oscillators 101 and 102 are coupled to each other via coupling element 103. Oscillator 101 is also coupled to an auxiliary qubit 104. An energy source 105 can be operated by a controller 106 to direct energy to the auxiliary qubit 104, coupling element 103, and / or readout resonator 107.

[0054] According to some embodiments, oscillators 101 and 102 each include a cavity (e.g., a microwave cavity) that supports the quantum state of microwave photons. For example, in some embodiments, the first oscillator 101 and the second oscillator 102 may each include a resonator, such as a transmission line resonator or a three-dimensional cavity formed of a superconducting material (such as aluminum).

[0055] The coupling element 103 may include a nonlinear element coupled to oscillators 101 and 102. The coupling element 103 mediates coupling between the quantum states of the two oscillators to allow interaction between the first oscillator 101 and oscillator 102. In some embodiments, the coupling element 103 may be a superconducting nonlinear asymmetric inductor (SNAIL), a superconducting quantum interference device (SQUID), a Josephson junction, or some other nonlinear element. In some embodiments, the coupling element 103 may include a transport qubit dispersively coupled to both the first oscillator 101 and the second oscillator 102.

[0056] As shown in the illustrated embodiment, auxiliary qubit 104 is coupled (e.g., dispersively coupled) to oscillator 101. However, in some embodiments, auxiliary qubit 104 may be coupled to oscillator 102. In other embodiments, system 100 may include two auxiliary qubits 104, each coupled to one of oscillators 101 or 102. In some embodiments, auxiliary qubit 104 may be a transport qubit, flux qubit, charge qubit, SNAIL, SQUID, or some other nonlinear element.

[0057] In some embodiments, energy source 105 may include a microwave source configured to direct microwave pulses or drive waveforms of desired amplitude, frequency, and phase to one or more components of a dual-track qubit (e.g., auxiliary qubit 104, coupling element 103) or any other suitable component. In some embodiments, energy source 105 may be capacitively coupled to each of auxiliary qubit 104, coupling element 103, and / or readout resonator 107. As described below, in some embodiments, multiple instances of the illustrated dual-track qubits may be arranged to be coupled to each other. In some embodiments, energy source 105 may be coupled to some or all of the components of a plurality of dual-track qubits, such that microwave pulses can be directed to each of the dual-track qubits to which it may be coupled. In other embodiments, each dual-track qubit may be coupled to a different corresponding energy source 105.

[0058] Energy source 105 can be configured to provide microwave drive waveforms in response to receiving one or more control signals from controller 106. In embodiments employing dual-track qubits, controller 106 can be configured to control one or more of the energy sources 105 utilized in the system. Therefore, any suitable number of controllers 106 can be used.

[0059] As stated above, the inventors have recognized and understood that a quantum information processing system comprising two or more dual-track qubits as described above has a static nonlinear source that can be used to execute an entanglement gate, which is equivalent to a CPHASE gate, with at most a local Z-rotation phase difference. Figure 2 An example schematic diagram of a system 200 for achieving coupling between two dual-track qubits according to some embodiments of the technology described herein is depicted. In the illustrated embodiment, system 200 includes as described above regarding... Figure 1 The two dual-track qubits 210 and 220 and the coupling element 230 are described as being implemented.

[0060] The first dual-track qubit 210 includes oscillators 211 and 212 (e.g., microwave cavities), a coupling element 213, and an auxiliary qubit 214. The second dual-track qubit 220 includes oscillators 221 and 222 (e.g., microwave cavities), a coupling element 223, and an auxiliary qubit 224. While the illustrated embodiment depicts auxiliary qubit 214 coupled to oscillator 212 and auxiliary qubit 224 coupled to oscillator 222, the technique is not limited to this manner, and one or both cavities in each dual-track qubit may be coupled to an auxiliary qubit. In some embodiments, dual-track qubits may not include auxiliary qubits, or only one dual-track qubit may include an auxiliary qubit.

[0061] Coupler 230 is coupled between oscillator 211 of the first dual-track qubit 210 and oscillator 222 of the second dual-track qubit 220. Like coupling element 103, coupling element 230 coupling the two dual-track qubits, and coupling elements 213 and 223 coupling the cavities of each dual-track qubit, can be superconducting nonlinear asymmetric inductive elements (SNAILs), superconducting quantum interference devices (SQUIDs), Josephson junctions, and / or any other suitable nonlinear elements.

[0062] A two-track entanglement gate, as described herein, can be executed on two two-track qubits by directing energy (e.g., microwave energy from a microwave source) to the coupling element 230 between the two-track qubits, instead of (and / or otherwise) to the coupling elements 213 and 223 of the cavities coupling each of the respective two-track qubits 210 and 220. In previous two-qubit gate methods, different pulse sequences have been utilized, comprising different driving waveforms (e.g., provided by energy source 105) applied to both the inter-qubit coupling element (e.g., coupling element 230) and one or more auxiliary qubits (e.g., auxiliary qubit 224) coupled to the central cavity. As described above, the inventors have developed a technique for executing a two-qubit two-track entanglement gate that utilizes nonlinear static sources (e.g., cross-Kerr interactions) present in the system to open and close the interaction between cavities by applying driving waveforms to the coupling elements (e.g., 230, 213, and / or 223), without applying driving waveforms to one or more auxiliary qubits.

[0063] Figure 3 Some embodiments of the technology described herein are shown. Figure 2 A simplified schematic diagram of the implementation of System 200 illustrates the relative interaction strengths between the system's oscillators. To utilize the various nonlinear interactions between cavities in a dual-track entangled gate, different interaction strengths between cavities can be designed to provide high effective interaction strength between the two qubits, as well as a high on / off ratio for nonlinear interactions. For clarity, from... Figure 3 The auxiliary qubit is not initially depicted in the dual-track qubit diagram; however, it should be understood that the auxiliary qubit can be as described above. Figure 1 and Figure 2 As described, it exists because the various aspects of the technology described in this article are not limited in this respect.

[0064] In some implementations, including Figure 3 Those described herein can affect the strength of interactions within a dual-track qubit (e.g., between the cavity modes of oscillators 211 and 212 of the first dual-track qubit 210). Between the cavity modes of oscillators 221 and 222 of the second dual-track qubit 220 The interaction between dual-track qubits is greater than that between the cavity modes of coupled oscillators 211 and 222. By designing the relative interaction strength, it is possible to... The given effective entanglement interaction strength increases, and it can also make the entanglement interaction strength increase. The on / off ratio of the given entangled interaction becomes larger. Different interaction strengths can be designed in any suitable manner. In some embodiments, a first type of coupling element can be used for oscillators coupling two-track qubits (e.g., oscillators 211 and 212), and a second type of coupling element can be used for oscillators coupling the first two-track qubit and the second two-track qubit (e.g., oscillators 211 and 222). For example, the first type of coupling element can be one of SQUID, SNAIL, or transport qubit, while the second type of coupling element can be a different one of SQUID, SNAIL, or transport qubit. The first and second types of coupling elements can provide different coupling strengths. Additionally or alternatively, in some embodiments, the interaction strength can be adjusted by applying one or more driving waveforms (e.g., microwave driving pulses) to the coupling element to increase the nonlinear interaction strength. , and / or .

[0065] In some implementations, a driving waveform is applied to the coupling element 230 to exchange photons, and thus exchange the encoded states of cavities 211 and 222. For example, when the dual-track qubit 210 is in The 220 dual-track qubits were initialized and in During similar initialization, a driving waveform is applied to the coupling element 230 to exchange the positions of the photons, and thus exchange the encoded quantum states of cavities 211 and 222, such that the dual-track qubit 210 is placed... The state, and the 220 dual-track qubits are placed State. The interaction between the two photons of the dual-track qubit 210 will then be determined by... The interaction between the two photons of the dual-track qubit 220 will then be controlled by... Control. By leaving photons in the new exchanged state for a period of time, the time evolution of the quantum states in the two-track qubits 210 and 220 occurs, resulting in entanglement between photons in each of the two-track qubits 210 and 220. In this way, by applying a series of driving waveforms to various coupling elements, the encoded state of the system can be moved between the two-track qubits 210 and 220 to turn the nonlinear interactions between the encoded states on and off as needed, thereby executing various entanglement gates between the two-track qubits 210 and 220 as described herein.

[0066] The components used for executing the entanglement gate as described herein can be configured to have any suitable parameter values. For example, in some embodiments, one or more auxiliary qubits may have a parameter T1 value in the range of 100 μs to 400 μs and a T value in the range of 20 μs to 400 μs. 2R The value of . For example, in some implementations, T1 and T of one or more auxiliary qubits. 2R Both can be approximately 200 μs. In some implementations, the quantum oscillator can have a value for parameter T1 ranging from 300 μs to 900 μs and a value for parameter T ranging from 350 μs to 1000 μs. 2R The value of T1. For example, in some implementations, the T1 value of one or more oscillators may be approximately 500 μs, and the T1 value of one or more oscillators may be... 2R The value can be approximately 700 μs.

[0067] Furthermore, in some implementations, the beam splitter drive waveform can have a frequency ranging from 0.5 MHz to 2.5 MHz, and the nonlinear interaction strength... , and It can be in the range of 5 kHz to 50 kHz. As mentioned above, in some embodiments, and It can be configured to be greater than For example, in some implementations, and It can be 5 to 10 times larger. For example, It could be around 40 kHz. It can be approximately 40 kHz, and It can be approximately 8 kHz.

[0068] Figure 4This is a flowchart describing a process 400 for performing an entanglement gate between two coupled two-track qubits according to some embodiments of the technology described herein. Figure 5A depicts a process 400 for implementing an entanglement gate between two coupled two-track qubits according to some embodiments of the technology described herein. Figure 4 The process of 400 is an illustrative operation. Figure 5B The following are illustrated according to some embodiments. Figure 4 Example of a pulse sequence for process 400. Process 400 can use coupled dual-track qubits (e.g., as shown in the image). Figure 2 This can be achieved (as depicted in the example) to perform a two-qubit entanglement gate as described in this paper.

[0069] In some implementations, each of the two dual-track qubits is in its initial state (e.g., or After being initialized in ), process 400 can begin at step 402, as follows: Figure 5A-1 and Figure 5B As shown. At step 402, a first driving waveform 502 is applied (e.g., using an energy source, such as, but not limited to, a microwave source) to the coupling element (e.g., coupling element 230) between the quantum oscillator 211 of the first dual-track qubit 210 and the quantum oscillator 222 of the second dual-track qubit 220. The driving waveform 502 can be configured to perform a beam splitter SWAP operation (e.g., as described herein in conjunction with...). Figure 3 A to Figure 3 (as described in example B) to exchange the states of coupled quantum oscillators 211 and 222. In some implementations, the strength of the beam splitter drive can be determined by the following formula in order to apply the SWAP operation:

[0070] .

[0071] in It is the phase of the beam splitter interaction between oscillators 211 and 222 (which can indicate the effective interaction strength of the beam splitter interaction), and Describe the beam splitter drive waveform. When... (It represents the initial phase) During the flip, the beam splitter drives Implementing a SWAP operation results in the exchange of states in the cavity modes between quantum oscillators 211 and 222. Therefore, to implement the SWAP operation, in some embodiments, a drive waveform 502 can be applied to the coupling element. The time. For example, in In the 5 MHz implementation, the drive waveform can be applied for approximately 0.6 μs. However, this technique is not limited to this method, and the drive waveform can be applied for any suitable time corresponding to the frequency of the drive waveform (e.g., (In the range of 5 MHz to 50 MHz).

[0072] After the SWAP operation is performed in step 402, the entangled interaction between the two dual-track qubits can be resolved through static cross-Kerr interaction. and To open, such as Figure 5A-2 As shown, this leads to phase accumulation of the photon's state. For example, when both dual-track qubits 210 and 220 are in phase... When initialized in the state, performing the first SWAP operation at step 402 can place the dual-track qubit 210 in the state. And place the dual-track qubit 220 in the state This places two photons in a dual-track qubit 220, allowing the photons to interact through coupling element 223 of the dual-track qubit 220. Therefore, the SWAP operation can open the interaction between photons in the system. Interactions of control.

[0073] It is permissible to allow for a period of time (e.g., such as...) Figure 5B The "wait time" shown is used to allow the desired phase accumulation to occur. The selected wait time can be used to control the CPHASE angle (e.g., 0 < 0) associated with the two-qubit entanglement gate implemented by process 400. < 2π). In some implementations, the CPHASE angle can be defined as... This allows the scheduled time period to be changed from Given. In some implementations, process 400 can be used to implement having A controlled Z (CZ) gate. In such an implementation, In some implementations, An initial estimate of the predetermined waiting time can be given. The waiting time can then be fine-tuned to achieve the desired phase accumulation. For example, it can be... The results are within 5% to 15% of the initial estimate. Make minor adjustments.

[0074] In some implementations, during the predetermined waiting period Subsequently, process 400 can continue to step 404, where a second driving waveform 504 is applied to a coupling element (e.g., coupling element 230) to perform a second SWAP operation, resulting in an exchange of states between the quantum oscillator 211 of the first dual-track qubit 210 and the quantum oscillator 222 of the second dual-track qubit 220. In some embodiments, the second driving waveform 504 can be applied in the same manner as described above with respect to the first driving waveform 502. In some embodiments, the phase of the second driving waveform 504 can be reversed relative to the first driving waveform 502, such as... Figure 5B As shown, this is to reduce the impact of calibration errors. In some embodiments, in order to have the freedom to select the phase of the second drive waveform 504, It can be configured to be much larger than , and (For example, making) In some implementations, It can be configured to be in comparison , and / or The range is 10 to 500 times larger.

[0075] In some implementations, the nonlinear interaction during the latency period can be increased by applying one or more drive waveforms to the system. and / or To reduce latency, the effective interaction strength can be increased by applying one or more drive waveforms to the coupling elements (e.g., coupling elements 213 and / or 223) within the dual-track cavity. .along with Increase, Reduced. In some implementations, the pump tone can be a non-resonant pump tone, for example, 50 MHz higher than the resonant frequency of the dual-track inner coupler (e.g., coupling element 213 or 223), which downshifts the coupler's resonant frequency. By downshifting the coupler's resonant frequency, the effective coupling strength of the coupler increases (e.g., when the coupler's resonant frequency approaches the resonant frequency of the quantum oscillators (between which the coupler is coupled) and / or (Effective strength increased).

[0076] When implemented, applying a driving waveform to perform this SWAP-wait-SWAP entanglement gate can provide high gate fidelity without any state preparation and measurement (SPAM) correction, and can enable entanglement of two qubits. For example, in some implementations, the entanglement gate described herein can provide 99.20% fidelity without SPAM correction.

[0077] Figure 5C Some embodiments of the technology described herein are shown. Figure 4 An example of the position of the quantum state during process 400. Figure 5C The examples depict the quantum states within a pair of coupled two-track qubits during process 400 for different initialization states. (As along...) Figure 5C As shown in the top row, when the dual-track qubit is in When initialized in the state, the first SWAP operation is performed to place the first dual-track qubit 210 into the state. In the state, and place the second dual-track qubit 220 into In this state, photons interact through the coupling elements of the second double-track qubit. This interaction can be determined by the nonlinear interaction strength of the coupling elements between the cavities of the second double-track qubit 220. To control this. Therefore, the phase accumulated during the waiting time is... Perform a second SWAP operation (e.g., as in combination with...). Figure 4 (As described in step 404) Place both of the two-track qubits back into place. In progress.

[0078] In some implementations, such as along Figure 5C As shown in the bottom row, when the dual-track qubit is in When initialized in the state, the first SWAP operation is performed to place the first dual-track qubit 210 into the state. In the state, and place the second double-track qubit into In this state, photons in the first dual-track qubit 210 interact through the coupling element of the first dual-track qubit 210, such that the interaction is determined by the coupling strength of the coupling element of the first dual-track qubit 210. Control. Therefore, the phase accumulated during the waiting time is Perform a second SWAP operation (e.g., as in combination with...). Figure 4 (As described in step 404) Place both of the two-track qubits back into place. In progress.

[0079] like Figure 5C As shown in the second line, when the dual-track qubit is in When initialized, a first SWAP operation is performed to swap photons in each qubit. The interactions between qubits via coupling elements (e.g., coupling element 230) can be... Control, resulting in a cumulative total phase of Perform a second SWAP operation (e.g., as in combination with...). Figure 4(as described in step 404) to place the two photons back into their original qubits.

[0080] Finally, as Figure 5C As shown in the third line, when the dual-track qubit is in When initialized, neither photon may exchange, and there may be no interaction. Since no photon occupies the oscillator coupled via the inter-qubit coupling element (e.g., coupling element 230), applying a driving waveform to perform a SWAP operation does not cause any photon exchange between the qubits. Therefore, no interaction occurs.

[0081] In some implementations, the presence of nonlinear interactions caused by coupling elements between different quantum oscillators can introduce coherent leakage into the quantum processing system, potentially causing information encoded in quantum states to leak into non-computational energy states. Therefore, the inventors have recognized and understood methods for providing improved resistance to coherent leakage. For example, after a second SWAP operation, the resulting state of a two-track qubit system is... Leaks can be detected at that time. (Refer to...) Figure 6A and / or Figure 6B As described, adjustments can be made to the different coupling strengths between each pair of quantum oscillators to reduce coherent leakage.

[0082] Figure 6A Some embodiments of the technology described herein are shown. Figure 4 An example of an alternative to the "wait" operation in process 400, where the alternative operation is configured to minimize coherent leakage caused by nonlinear interactions. Figure 6A In the example, by The nonlinear interaction of the first dual-track qubit 210 is designed to be greater than the interaction between other oscillators (e.g., When the amplitude of the beam splitter drives the waveform... Approximately equal to a large nonlinear interaction At this time, coherent leakage can be reduced by preventing photons from leaking from oscillator a2 to oscillator b1. It should be understood that, although Figure 6A The nonlinear interaction of the first dual-track qubit 210 is shown. It is a large nonlinear interaction in the system, but in some implementations, Can be replaced by greater than Figure 6B Other nonlinear interactions of the system (e.g., ).

[0083] Figure 6BAnother example of a system for achieving coupling between two dual-track qubits, according to some embodiments of the techniques described herein, is shown. The system includes a buffer cavity coupled between the two dual-track qubits to minimize coherent leakage. Figure 6B In the example, the strength of the nonlinear interaction is large only at one location—for example, between the oscillator of the first two-track qubit 210A and the buffer oscillator 250. In this way, the nonlinear interaction between the two two-track qubits 210A and 220A is "on" only when a SWAP is performed to exchange the states of the other two-track qubit 220A with the buffer oscillator 250. Therefore, since there is no interaction between the two two-track qubits when the buffer oscillator is empty, coherent leakage can be reduced to zero or close to zero.

[0084] It is understood that a quantum information processing system implementing the two-track entanglement gate described in this paper can include more than two coupled two-track qubits. Therefore, depending on the arrangement of the two-track qubits in the quantum information processing system, the entanglement gate described in this paper can be executed between different two-track qubits.

[0085] Figure 7 An example arrangement of five dual-track qubits according to some embodiments of the techniques described herein is depicted for performing entanglement gates between pairs of dual-track qubits in the arrangement. Each of the dual-track qubits 710 to 750 can be configured as described above and can include two quantum oscillators, coupling elements, and / or auxiliary qubits respectively coupled to one or both of the quantum oscillators of the dual-track qubits.

[0086] In the illustrated embodiment, connection scheme 701 depicts various connections, among which a two-track entanglement gate can be executed in a given arrangement. For example, by applying the driving waveform sequence described herein (e.g., as per [reference to...]) to various coupling elements between the two-track qubits... Figures 4 to 5B and Figures 11 to 12B As described, entanglement gates can be executed between dual-track qubits 710 and 750, 720 and 750, 730 and 750, and / or 740 and 750. For example, to execute an entanglement gate between dual-track qubits 710 and 750, first and second drive waveforms performing a beam splitter SWAP operation can be applied to coupling element 1, and executing an entanglement gate between dual-track qubits 720 and 750 can be accomplished by applying a drive waveform to coupling element 2.

[0087] Figure 8AAnother example arrangement of four dual-track qubits according to some embodiments of the techniques described herein is depicted for performing entanglement gates between pairs of dual-track qubits in this arrangement. In the illustrated embodiment, connection scheme 801 depicts various connections between which dual-track entanglement gates can be performed in a given arrangement. Although depicted as with Figure 7 A similar arrangement is used, but the difference in Figure 8 is that the central dual-track qubit 750 is replaced by two vacant quantum oscillators 852 and 854 (e.g., buffer cavities). Therefore, entanglement gates can be executed between the next nearest neighbors. For example, entanglement gates can be executed between dual-track qubits 810 and 830, 810 and 840, 820 and 830, and 820 and 840.

[0088] To implement the entanglement gate in this arrangement, a pulse sequence (e.g., in...) Figure 4 (and as described in 5A) can be as follows Figure 8B The description in the original text has been modified. Because each dual-track qubit is separated by an empty quantum oscillator, in order to perform the entanglement gate, instead of applying the first and second drive waveforms to a single coupling element, the first and second drive waveforms can be applied to both coupling elements simultaneously. Figure 8B A pulse sequence for executing an entanglement gate between dual-track qubits 810 and 840 is described. To execute the gate, first and second pulse sequences 802 and 804 are simultaneously applied to both coupling elements 1 and 4. In this way, the simultaneous pulses exchange the state of the quantum oscillator of dual-track qubit 810 to the vacant oscillator 852, and exchange the state of the quantum oscillator of dual-track qubit 840 to the vacant oscillator 854. Therefore, the interaction can be opened and closed as a gate as described above, but the coupling strength is affected by the coupling elements between the vacant oscillators 852 and 854. To control. In some implementations, coupling strength It can be greater than the coupling strength between the two-track qubit and the vacant oscillator (e.g., 10 to 100 times).

[0089] In some implementations, the techniques described herein can be used to perform entanglement gates between long-distance dual-track qubits that are indirectly coupled through a series of other dual-track qubits. Figure 9A schematic diagram of a long-range entangled two-track gate is shown according to some embodiments. In the illustrated embodiment, system 900 includes four two-track qubits 910 to 940 (although system 900 may include more or fewer). To execute the entanglement gate described herein between the first two-track qubit 910 and the fourth two-track qubit 940, a series of SWAPs 902 to 904 can be performed to exchange the state of the quantum oscillator in the fourth two-track qubit 940 until it reaches the interaction region 901. SWAP 905 can then be used to exchange the state of the quantum oscillator in the two-track qubit 910 into the interaction region 901, enabling entanglement interaction to be performed. To complete the gate (e.g., in...), Afterwards, the reverse sequence of SWAP can be executed to swap the states back to their original oscillators in the first two-track qubits 910 and 940.

[0090] Although the entanglement gate described in this paper can be implemented as described above, the inventors understand that, optionally, additional measures can be applied to the dual-track qubits besides those concerning... Figure 4 Driving waveforms other than those described can provide additional functionality and improvements to the dual-track entanglement gate described herein.

[0091] Figure 10 This is a flowchart describing some embodiments of the technology described herein for performing an entanglement gate replacement process 1000 between two coupled two-track qubits, the replacement process 1000 using a reverse CPHASE angle. The process 1000 includes a series of driving waveforms applied to various coupling elements within the coupled two-track entanglement gate described herein, including: a first driving waveform applied to the coupling element of the first two-track qubit (at 1001), a second driving waveform applied to the coupling element between the first and second two-track qubits (at 1002), a third driving waveform applied to the coupling element between the first and second two-track qubits (at 1004), and a fourth driving waveform applied to the coupling element of the first two-track qubit (at 1005).

[0092] Steps 1002 and 1004 of process 1000 can be related to the above regarding Figures 4 to 5B The process is performed in the same manner as described. However, process 1000 can additionally be written before and after the driving waveform applied to the inter-qubit coupling element (e.g., coupling element 230) with a driving waveform applied to the coupling element (e.g., coupling element 213 or 223) of one of the dual-track qubits. In this way, the waiting time between the driving waveforms applied in steps 1002 and 1004 can be shortened.

[0093] Because entanglement gates can be equivalent to The gate (Gundam Z-Rotation) is used to represent this, therefore, the gate identity is utilized. To achieve angle The CPHASE gate can reduce waiting time. X1 is executed by applying a book-based SWAP pulse, instead of having to implement the necessary parameters for the angle. The door can be implemented only for realizing the angle. The door. For example, to achieve an angle. The CPHASE door, instead of having to wait The book-standing pulse applied to the first dual-track qubit can reverse the CPHASE angle ( ), allowing the use of only The maximum latency for implementing any CPHASE gate can be [the maximum latency]. Among them, the CZ gate ( It has the maximum waiting time.

[0094] Figure 11 Some embodiments of the technology described herein are shown for implementation. Figure 10 Example pulse sequence of the process. (Refer to...) Figure 10 and Figure 11 At step 1001 of process 1000, the first driving waveform 1101 is applied to the coupling element c of the first dual-track qubit 210. a (or the coupling element c of the second double-track qubit 220) b The first driving waveform 1101 can be configured to cause a state swap between the quantum oscillators of the first dual-track qubit 210. The SWAP operation can be performed in accordance with the above reference. Figure 4 It is implemented in the same way as described.

[0095] At steps 1002 and 1004 of process 1000, the second drive waveform 1102 and the third drive waveform 1104 can be compared with those above. Figure 4 The same manner described is applied to the coupling element c. ab However, it's not about waiting. The waiting time between waveforms 1102 and 1104 can be For example, regarding Figure 4 As described, in some implementations An initial estimate can be provided, and the waiting time can be fine-tuned within 5% to 15% of the initial estimate.

[0096] At step 1005, in the same manner as waveform 1101, the fourth driving waveform 1105 is applied to the coupling element c of the first dual-track qubit 210. a(or the coupling element c of the second double-track qubit 220) b In some implementations, the phase of the fourth driving waveform 1105 may be reversed relative to the driving waveform 1101.

[0097] Figures 12A to 12B Additional schematic representations of example procedures for performing entanglement gates between two coupled two-track qubits, according to some embodiments, are shown.

[0098] Figure 12A A schematic representation of a process for applying a series of driving waveforms to perform entanglement gate configured to echo low-frequency dephase noise, according to some embodiments of the technique described herein, is shown. The pulse sequence 1200 can be used to echo low-frequency dephase noise present on any of the four quantum oscillators of a dual-track qubit. Utilizing identities... This allows for the echoing of low-frequency dephase noise without affecting the results of circuit operations implemented using this gate. In a given pulse sequence of 1200, each "half" of each dual-track qubit spends the same amount of time in both quantum oscillators.

[0099] The initial two pulses 1201 and 1202 can be related to the above. Figures 4 to 5B The same method described is used to implement the first half of the entanglement gate. Therefore, the waiting time between pulses 1201 and 1202 can be about... Figure 4 Half of the described waiting time. For example, Following the second SWAP operation via pulse 1202, the third drive waveform 1203 and the fourth drive waveform 1204 can be applied to the coupling element c (e.g., of the dual-track qubits 1010 and 1020), respectively. a and c b This allows for a SWAP operation to be performed between the quantum oscillators in each corresponding dual-track qubit. In some implementations, a third and a fourth drive waveform can be applied simultaneously.

[0100] The next two pulses, 1205 and 1206, can be implemented in the same way as pulses 1201 and 1202 to achieve the second half of the entanglement gate. The waiting time can similarly be about Figure 4 Half of the described waiting time makes Therefore, the total waiting time for the two halves of the entanglement gate implemented by pulses 1201, 1202, 1205, and 1206 is For example, regarding Figure 4 As described, in some implementations An initial estimate can be provided, and the waiting time can be fine-tuned within 5% to 15% of the initial estimate.

[0101] Following the second SWAP operation via pulse 1206, two additional driving waveforms 1207 and 1208 can be applied to the coupling element c (e.g., of the dual-track qubits 1010 and 1020), respectively. a and c b This allows a SWAP operation to be performed between the quantum oscillators in each corresponding dual-track qubit. In this way, the state of each quantum oscillator in the system can be returned to its initial state.

[0102] In some implementations, the entanglement gates described herein can be used to extend other operations performed on coupled two-track qubit gates, such as the two-track SWAP operation. The two-track SWAP operation can swap the encoded states of two coupled two-track qubits. For example, this can be done via inter-qubit coupling elements (e.g., coupling element 230, c...). ab A first pulse is applied to cause the states of the coupled quantum oscillators to exchange. Then, pulses can be applied to the coupling elements within each qubit (e.g., coupling elements 213 and 223, c). a and c b A SWAP is applied to exchange states between the quantum oscillators within each dual-track qubit. Finally, a second pulse can be applied to the inter-qubit coupling element to exchange states between the two qubits. (Regarding...) Figure 12B Pulses 1221 to 1224 describe the above pulse sequence.

[0103] Figure 12B Another schematic representation of a process for applying a series of driving waveforms to perform a SWAP operation between two coupled two-track qubits, according to some embodiments of the technology described herein, is shown. This SWAP operation is configured to eliminate accumulated CPHASE entanglement. Pulse sequence 1220 can be used to remove any entanglement caused by the two-track logic SWAP operation. The two-track logic SWAP operation entangles the two two-track qubits due to the nonlinear interaction between the quantum oscillators of the first two-track qubit coupled to the quantum oscillator of the second two-track qubit, and introduces a small accumulation angle (typically less than 0.2 radians). Therefore, an inverse CPHASE gate (e.g., as described above regarding...) can be implemented after the two-track logic SWAP. Figures 10 to 11 (As described) to eliminate the cumulative angle of 0.2 radians. Therefore, pulses 1221 to 1224 implement the dual-track logic SWAP operation as described above. Subsequently, the entanglement gate can be used as described above regarding... Figures 10 to 11 The described reverse CPHASE angle pulse sequence is achieved by pulses 1225 to 1228.

[0104] Figure 13An illustrative implementation of computer system 1300 is depicted, which can be used in conjunction with any of the embodiments of the techniques described herein (e.g., controller 106 may be implemented as computer system 1300, or may be operatively coupled to computer system 1300). Computer system 1300 includes one or more processors 1310 and one or more articles of manufacture including non-transitory computer-readable storage media (e.g., memory 1320 and one or more non-volatile storage media 1330). Processor 1310 can control the writing of data to memory 1020 and the reading of data from memory 1020 and non-volatile storage media 1330 in any suitable manner, because the aspects of the techniques described herein are not limited to any particular technique for writing or reading data. In order to perform any of the functions described herein, processor 1310 may execute one or more processor-executable instructions stored in one or more non-transitory computer-readable storage media (e.g., memory 1320), which may be used as a non-transitory computer-readable storage medium for storing the processor-executable instructions executed by processor 1310.

[0105] The computer system 1300 may also include a network input / output (I / O) interface 1340 through which the computing device can communicate with other computing devices (e.g., via a network), and may also include one or more user I / O interfaces 1350 through which the computing device can provide output to and receive input from the user. The user I / O interfaces may include devices such as a keyboard, mouse, microphone, display device (e.g., monitor or touchscreen), speaker, camera device, and / or various other types of I / O devices.

[0106] The above-described embodiments can be implemented in any of a variety of ways. For example, the embodiments can be implemented using hardware, software, or a combination thereof. When implemented in software, the software code can execute on any suitable processor (e.g., a microprocessor) or set of processors, whether provided in a single computing device or distributed across multiple computing devices. It should be understood that any component or set of components performing the above-described functions can generally be considered as one or more controllers controlling the above-described functions. One or more controllers can be implemented in a variety of ways, such as utilizing dedicated hardware or utilizing general-purpose hardware (e.g., one or more processors) programmed using microcode or software to perform the above-described functions.

[0107] In this regard, it should be understood that one implementation of the embodiments described herein includes at least one computer-readable storage medium (e.g., RAM, ROM, EEPROM, flash memory or other storage technologies, CD-ROM, digital versatile disc (DVD) or other optical disc storage, cassette tape, magnetic tape, disk storage or other magnetic storage devices, or other tangible, non-transitory computer-readable storage media) encoding a computer program (i.e., a plurality of executable instructions), the computer program performing the functions described above in one or more embodiments when executed on one or more processors. The computer-readable medium may be transportable, such that the program stored thereon can be loaded onto any computing device to implement the aspects of the techniques discussed herein. Furthermore, it should be understood that references to computer programs that perform any of the functions described above when executed are not limited to applications running on a host computer. Rather, the terms computer program and software are used herein in a general sense to refer to any type of computer code (e.g., application software, firmware, microcode, or any other form of computer instructions) that can be used to program one or more processors to implement the aspects of the techniques discussed herein.

[0108] The foregoing description of the implementation methods provides illustration and description, but is not intended to be exhaustive or to limit the implementation methods to the precise forms disclosed. Modifications and variations are possible, or can be derived from the practice of the implementation methods, based on the above teachings. In other implementation methods, the methods depicted in these diagrams may include fewer operations, different operations, operations in different orders, and / or additional operations. Furthermore, non-dependent blocks can be executed in parallel.

[0109] It will be apparent that the example aspects described above can be implemented in many different forms of software, firmware, and hardware in the implementation shown in the figures. Furthermore, certain parts of the implementation can be implemented as "modules" performing one or more functions. These modules can include hardware such as processors, application-specific integrated circuits (ASICs), or field-programmable gate arrays (FPGAs), or a combination of hardware and software.

[0110] Therefore, several aspects of at least one embodiment of the present invention have been described, and it should be understood that various changes, modifications and improvements will be readily apparent to those skilled in the art.

[0111] Such changes, modifications, and improvements are intended to be part of this disclosure and within the spirit and scope of the invention. Furthermore, while advantages of the invention have been pointed out, it should be understood that not every implementation of the technology described herein will include every described advantage. Some implementations may not implement any of the features described herein as advantageous, and in some cases, one or more of the described features may be implemented to achieve other implementations. Therefore, the foregoing description and figures are used as examples only.

[0112] All definitions defined and used in this document should be understood as control dictionary definitions, definitions in referenced and incorporated literature, and / or the general meaning of the defining terms.

[0113] The indefinite articles “a” and “an” used in the specification and claims shall be understood to mean “at least one” unless expressly indicated otherwise.

[0114] The use of "coupling" or "connection" refers to elements or signals being directly linked to each other or linked through an intermediate component. Elements without "coupling" or "connection" are "decoupled" or "disconnected".

[0115] The use of "between" in a coupled signal chain does not imply a requirement for a specific direction of signal flow within the chain, unless otherwise stated. For example, when element B is described as being coupled between elements A and C in a signal chain, a signal can flow from element A to element C through element B, and / or from element C to element A through element B, unless otherwise stated.

[0116] The phrase “and / or” as used herein in the specification and claims should be understood to mean “any one or both” of the elements so combined, that is, elements that exist together in some cases and separately in others. Multiple elements listed with “and / or” should be interpreted in the same way, that is, “one or more” of the elements so connected. Other elements may optionally be present in addition to those specifically identified by the “and / or” statement, whether related to or unrelated to those specifically identified. Therefore, as a non-limiting example, when used in conjunction with open-ended language such as “comprising,” the reference to “A and / or B” can: in one embodiment refer only to A (optionally including elements other than B); in another embodiment refer only to B (optionally including elements other than A); in yet another embodiment refer to both A and B (optionally including other elements); and so on.

[0117] As used herein in this specification and claims, the phrase "at least one" referring to a list of one or more elements should be understood to mean at least one element selected from any one or more elements in the list, but not necessarily including at least one of every element specifically listed in the list, and does not exclude any combination of elements in the list. This definition also allows for the optional presence of elements other than those specifically identified in the list referred to by the phrase "at least one," whether related to or not related to those specifically identified elements. Thus, as a non-limiting example, "at least one of A and B" (or equivalently, "at least one of A or B," or equivalently, "at least one of A and / or B") can: in one embodiment, refer to at least one, optionally including more than one A without the presence of B (and optionally including elements other than B); in another embodiment, refer to at least one, optionally including more than one B without the presence of A (and optionally including elements other than A); in yet another embodiment, refer to at least one, optionally including more than one A, and at least one, optionally including more than one B (and optionally including other elements); and so on.

[0118] In the claims and in the foregoing description, all transitional phrases, such as “comprising,” “including,” “carrying,” “having,” “containing,” “involving,” “holding,” etc., shall be understood as open-ended, meaning including but not limited to. Only the transitional phrases “consisting of…” and “consisting substantially of…” shall be closed or semi-closed transitional phrases, respectively.

[0119] The use of "coupled" or "connected" refers to circuit elements or signals that are either directly linked to each other or linked through intermediate components. Elements that are not "coupled" or "connected" are "decoupled" or "disconnected".

[0120] The terms “about” and “approximately” can be used to mean within ±20% of the target value in some embodiments, within ±10% of the target value in some embodiments, within ±5% of the target value in some embodiments, and within ±2% of the target value in some embodiments. The terms “about” and “approximately” can include the target value.

[0121] The use of ordinal terms such as “first,” “second,” “third,” etc., to modify a claim element does not imply any priority, order, or sequence of one claim element relative to another, or the chronological order in which the actions of a process are performed. Rather, it is merely used as a label to distinguish one claim element with a certain name from another element with the same name (but using ordinal terms) to differentiate claim elements.

Claims

1. A quantum information processing system, comprising: The first dual-track quantum bit device; Second dual-track quantum bit device; A first coupling element is coupled between the first dual-track qubit device and the second dual-track qubit device; At least one energy source; as well as At least one controller, configured to operate the at least one energy source to perform an entanglement gate between the first dual-track qubit device and the second dual-track qubit device by: By applying a first driving waveform to the first coupling element, the state of the quantum oscillator of the first dual-track qubit device is exchanged with the state of the quantum oscillator of the second dual-track qubit device for the first time. as well as After a predetermined time period following the first exchange, a second exchange is initiated by applying a second driving waveform to the first coupling element, thereby inducing a second exchange between the states of the quantum oscillator of the first dual-track qubit device and the quantum oscillator of the second dual-track qubit device.

2. The quantum information processing system according to claim 1, wherein: The first dual-track qubit device and the second dual-track qubit device each include a first quantum oscillator, a second quantum oscillator, and a second coupling element coupling the first quantum oscillator to the second quantum oscillator; and The first coupling element is coupled between the first quantum oscillator of the first dual-track qubit device and the first quantum oscillator of the second dual-track qubit device.

3. The quantum information processing system according to claim 2, wherein, The first coupling element is dispersively coupled between the first quantum oscillator of the first dual-track qubit device and the first quantum oscillator of the second dual-track qubit device.

4. The quantum information processing system according to any one of claims 1 to 3, wherein, The first coupling element includes a flux-driven SQUID coupler.

5. The quantum information processing system according to any one of claims 1 to 3, wherein, The first coupling element is a transport quantum bit device or a superconducting asymmetric inductor (SNAIL).

6. The quantum information processing system according to any one of claims 1 to 3, further comprising: A first auxiliary qubit device coupled to the first dual-track qubit device; as well as A second auxiliary qubit device coupled to the second dual-track qubit device.

7. The quantum information processing system according to claim 6, wherein: The first auxiliary qubit device is coupled to the second quantum oscillator of the first dual-track qubit device, and The second auxiliary qubit device is coupled to the first quantum oscillator of the second dual-track qubit device.

8. The quantum information processing system according to any one of claims 6, wherein, The first auxiliary qubit device and / or the second auxiliary qubit device are transport qubit devices.

9. The quantum information processing system according to any one of claims 2 to 3, wherein, The first quantum oscillator and the second quantum oscillator include microwave cavities.

10. The quantum information processing system according to any one of claims 1 to 3, wherein, The at least one controller is configured to apply the first drive waveform and / or the second drive waveform to the first coupling element for a certain period of time. .

11. The quantum information processing system according to any one of claims 1 to 3, wherein, The at least one controller is configured to have approximately The second driving waveform is applied after a predetermined time period of length.

12. The quantum information processing system according to any one of claims 2 to 3, wherein, The at least one controller is further configured to apply a pulse sequence comprising applying a drive waveform to a corresponding coupling element to induce a state exchange between the quantum oscillators coupled by the corresponding coupling element, the pulse sequence comprising: The first driving waveform applied to the first coupling element; The second driving waveform applied to the first coupling element; A third driving waveform is applied to the second coupling element of the first dual-track qubit device, the third driving waveform being applied before the first driving waveform; and A fourth driving waveform is applied to the second coupling element of the first dual-track qubit device, the fourth driving waveform being applied after the second driving waveform.

13. The quantum information processing system according to any one of claims 2 to 3, wherein, The at least one controller is further configured to apply a pulse sequence comprising applying a drive waveform to a corresponding coupling element to induce a state exchange between the quantum oscillators coupled by the corresponding coupling element, the pulse sequence comprising: The first driving waveform applied to the first coupling element; The second driving waveform applied to the first coupling element; The third driving waveform applied to the second coupling element of the first dual-track qubit device; The fourth driving waveform applied to the second coupling element of the second dual-track qubit device; The fifth drive waveform applied to the first coupling element; and A sixth driving waveform is applied to the first coupling element after a second predetermined time period following the fifth driving waveform.

14. The quantum information processing system according to claim 13, wherein, The pulse sequence further includes: The seventh driving waveform applied to the second coupling element of the first dual-track qubit device; and The eighth driving waveform applied to the second coupling element of the second dual-track qubit device.

15. The quantum information processing system according to any one of claims 2 to 3, wherein, The at least one controller is further configured to apply a pulse sequence comprising applying a drive waveform to a corresponding coupling element to induce a state exchange between the quantum oscillators coupled by the corresponding coupling element, the pulse sequence comprising: The first driving waveform applied to the first coupling element; The second driving waveform applied to the first coupling element; The third driving waveform applied to the second coupling element of the first dual-track qubit device; and A fourth driving waveform is applied to the second coupling element of the second dual-track qubit device, wherein the third driving waveform and the fourth driving waveform are applied between the first driving waveform and the second driving waveform.

16. The quantum information processing system according to claim 15, wherein, The pulse sequence further includes: The fifth driving waveform applied to the second coupling element of the first dual-track qubit device; The sixth driving waveform applied to the first coupling element; A seventh drive waveform is applied to the first coupling element after a second predetermined time period following the sixth drive waveform; and The eighth driving waveform applied to the second coupling element of the first dual-track qubit device.

17. The quantum information processing system according to any one of claims 2 to 3, wherein: The first coupling element includes: A third quantum oscillator, a fourth quantum oscillator, and a third coupling element coupled between the first quantum oscillator and the second quantum oscillator; A fourth coupling element, coupled between the first quantum oscillator and the third quantum oscillator of the first dual-track qubit device; and A fifth coupling element is coupled between the first quantum oscillator and the fourth quantum oscillator of the second dual-track qubit device; Applying the first drive waveform to the first coupling element includes applying the first drive waveform to the fourth coupling element and the fifth coupling element; and Applying the second drive waveform to the first coupling element includes applying the second drive waveform to the fourth coupling element and the fifth coupling element.

18. A method for performing an entanglement gate between a first two-track qubit device and a second two-track qubit device coupled via a first coupling element, each of the first two-track qubit device and the second two-track qubit device including a first quantum oscillator, a second quantum oscillator, and a second coupling element coupling the first quantum oscillator to the second quantum oscillator, wherein the first coupling element is coupled between the first quantum oscillator of the first two-track qubit device and the first quantum oscillator of the second two-track qubit device, the method comprising: A first driving waveform is applied to the first coupling element to cause a first exchange between the state of the first quantum oscillator of the first dual-track qubit device and the state of the first quantum oscillator of the second dual-track qubit device. as well as After a predetermined time period following the induction of the first exchange, a second driving waveform is applied to the first coupling element to induce a second exchange between the state of the first quantum oscillator of the first dual-track qubit device and the state of the first quantum oscillator of the second dual-track qubit device.

19. The method according to claim 18, wherein, Applying the first drive waveform and / or the second drive waveform includes applying the first drive waveform and / or the second drive waveform for a certain period of time. .

20. The method according to any one of claims 18 to 19, wherein, Applying the second driving waveform includes having approximately The second driving waveform is applied after a predetermined time period of length.

21. The method of any one of claims 18 to 19, further comprising applying a pulse sequence including a driving waveform configured to induce a state exchange between the quantum oscillators coupled by respective coupling elements, wherein applying the pulse sequence comprises: A third driving waveform is applied to the second coupling element of the first dual-track qubit device, the third driving waveform being applied before the first driving waveform; as well as A fourth driving waveform is applied to the second coupling element of the first dual-track qubit device, the fourth driving waveform being applied after the second driving waveform.

22. The method of any one of claims 18 to 19, further comprising applying a pulse sequence including a driving waveform configured to induce a state exchange between the quantum oscillators coupled by respective coupling elements, wherein applying the pulse sequence comprises: A third driving waveform is applied to the second coupling element of the first dual-track qubit device; A fourth driving waveform is applied to the second coupling element of the second dual-track qubit device; Apply the fifth driving waveform to the first coupling element; as well as After a second predetermined time period following the application of the fifth driving waveform, a sixth driving waveform is applied to the first coupling element.

23. The method of claim 22, further comprising applying the pulse sequence: A seventh driving waveform is applied to the second coupling element of the first dual-track qubit device; as well as An eighth driving waveform is applied to the second coupling element of the second dual-track qubit device.

24. The method of any one of claims 18 to 19, further comprising applying a pulse sequence including a driving waveform configured to induce a state exchange between the quantum oscillators coupled by respective coupling elements, wherein applying the pulse sequence comprises: A third driving waveform is applied to the second coupling element of the first dual-track qubit device; A fourth driving waveform is applied to the second coupling element of the second dual-track qubit device, wherein the third driving waveform and the fourth driving waveform are applied between the first driving waveform and the second driving waveform.

25. The method according to claim 24, wherein, Applying the pulse sequence further includes: After applying the second drive waveform: A fifth driving waveform is applied to the second coupling element of the first dual-track qubit device; Apply a sixth driving waveform to the first coupling element; After waiting for a second predetermined time period after the sixth driving waveform, a seventh driving waveform is applied to the first coupling element; and An eighth driving waveform is applied to the second coupling element of the first dual-track qubit device.

26. The method according to any one of claims 18 to 19, wherein, The first coupling element includes: A third quantum oscillator, a fourth quantum oscillator, and a third coupling element coupled between the first quantum oscillator and the second quantum oscillator; A fourth coupling element, coupled between the first quantum oscillator and the third quantum oscillator of the first dual-track qubit device; and A fifth coupling element, said fifth coupling element being coupled between the first quantum oscillator and the fourth quantum oscillator of the second dual-track qubit device; and The method further includes: Applying the first drive waveform to the first coupling element includes applying the first drive waveform to the fourth coupling element and the fifth coupling element; and Applying the second drive waveform to the second coupling element includes applying the second drive waveform to the fourth coupling element and the fifth coupling element.

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