Quantum information system

Abstract

A quantum information system comprising a quantum information element and a control line, the quantum information element comprising: a first Josephson element and a second Josephson element, each Josephson element comprising a Josephson junction disposed between two superconducting islands, one of the superconducting islands is shared by the first Josephson element and the second Josephson element; wherein the superconducting island of the first Josephson element is coupled to the superconducting island of the second Josephson element such that the quantum information element comprises a plurality of states, the plurality of states comprising a first state, a second state, and a third state, where there is a single excitation transition between the third state and the first state, and there is a single excitation transition between the third state and the second state; and wherein the control line is configured to encode one of two states of the computing subspace into the quantum information element, a first state of the computing subspace corresponding to the first state, and a second state of the computing subspace corresponding to the second state.

Description

Technical Field

[0001] This application relates to a method and system for processing quantum information in a stable manner and performing error detection on a quantum information system. Background Technology

[0002] A quantum computer is a computer that stores and processes information in the form of qubits (or quantum bits). Quantum computers can utilize quantum mechanical phenomena to perform computations that are impossible on classical computers, including encoding and processing information in quantum states, to achieve faster processing times than classical computers.

[0003] To realize a practical quantum computer, qubits must be physically implemented and information encoded onto them in a stable manner. Instabilities in the encoded quantum states can lead to errors in the encoded information, which in turn can cause errors in any process performed on or read from the encoded quantum information. Therefore, quantum error detection techniques are needed to identify any errors in the encoded information caused by decoherence or noise. Attached Figure Description

[0004] Embodiments will now be described by way of example with reference to the accompanying drawings.

[0005] Figure 1A This schematically illustrates a quantum information element.

[0006] Figure 1B schematically shown Figure 1A Equivalent circuit diagram of quantum information element.

[0007] Figure 2 The energy level diagram of a quantum information element is shown.

[0008] Figure 3A A quantum information element is schematically shown.

[0009] Figure 3B schematically shown Figure 3A Equivalent circuit diagram of quantum information element.

[0010] Figure 4A A quantum information system including quantum information elements is schematically illustrated.

[0011] Figure 4B It shows Figure 4A The readout amplitude response signal of the quantum information system.

[0012] Figure 4C It shows Figure 4A The readout phase response signal of a quantum information system.

[0013] Figure 5A method for quantum information processing, including error detection, is shown.

[0014] Figure 6A and 6B An example quantum information processing method is shown.

[0015] Figure 6C The phase diagram of the state measurement for the quantum information element is shown in the error detection at the final readout.

[0016] Figure 6D A phase diagram for state measurement of a quantum information element in a continuous error detection scheme is shown.

[0017] Figure 7A and 7B An example quantum information performance method is shown.

[0018] Figure 8 An array of coupled quantum information elements is schematically shown.

[0019] Figure 9 The illustration shows including Figure 8 A quantum information system consisting of an array of quantum information elements. Detailed Implementation

[0020] In a first aspect, a quantum information system comprising a quantum information element and control lines is described, the quantum information element comprising:

[0021] First Josephson element and second Josephson element,

[0022] Each Josephson element includes a Josephson junction disposed between two superconducting islands, wherein one superconducting island is shared by both the first and second Josephson elements;

[0023] In this embodiment, the superconducting island of the first Josephson element is coupled to the superconducting island of the second Josephson element, such that the quantum information element includes multiple states, including a first state, a second state, and a third excited state, wherein there is a single excited transition between the third state and the first state, and wherein there is a single excited transition between the third state and the second state.

[0024] Furthermore, the control line is configured to encode one of the two states of the computational subspace into the quantum information element, with the first state in the computational subspace corresponding to the first state and the second state in the computational subspace corresponding to the second state.

[0025] The above embodiments relate to a quantum information system that provides accessible quantum states for use in a quantum computing subspace, wherein bit flip errors within the quantum computing subspace are minimized and an error detection process can be performed on them to accurately eliminate errors during or at the end of quantum computing.

[0026] Therefore, the energy levels of a quantum information element correspond to excitations above the ground state. Within the accessible energy levels, there are allowed and disallowed single-excitation transitions, and each state in the computational subspace is chosen to correspond to an energy level where no allowed single excitation exists. A single excitation is understood as a single-photon excitation, an excitation between two states resulting from the interaction of a single photon with the quantum information element. In some examples, the two states in the computational subspace correspond to two states with the two lowest-energy excitations of the quantum information element from the ground state, each corresponding to a single excitation from the ground state. However, other computational basis sets are also possible in the energy level diagram. Single excitations between states in the computational subspace correspond to the generation of dipole moments on the superconducting islands of a Josephson element.

[0027] The first excited state corresponds to an in-phase / parallel dipole excitation of the Josephson junction across the first and second Josephson elements, and the second excited state corresponds to an antiparallel / out-of-phase excitation of the Josephson junction across the first and second Josephson elements. There is no permitted lateral coupling between the two states in the quantum computing subspace. This means that any longitudinal relaxation of an excited state within a quantum information element will not manifest as a bit-flipping error in the computing subspace, but can instead be identified as an occupied ground state. Therefore, qubits identified as being in the ground state can be identified as errors and discarded from any computation.

[0028] In one embodiment, the coupling between the two superconducting islands within each Josephson element is substantially the same.

[0029] In another embodiment, the quantum information element includes a split superconducting electrode arranged coaxially with another superconducting electrode, the split superconducting electrode forming one of the superconducting islands of each of the first and second Josephson elements, and the other superconducting electrode forming a superconducting island common to the first and second Josephson elements.

[0030] In another embodiment, the control lines are arranged out of plane relative to the quantum information element.

[0031] In another embodiment, the quantum information system further includes a readout element configured to measure the quantum state of the quantum information element, wherein, optionally, the readout element is arranged out of plane relative to the quantum information element.

[0032] In another embodiment, the quantum information system further includes a processor configured to perform quantum information processing operations on the quantum information elements, the quantum information processing including:

[0033] The quantum state within the quantum information element is initialized via control lines;

[0034] Quantum information elements are addressed via pulse sequences through control lines;

[0035] The state of the quantum information element is measured via the readout line.

[0036] In another embodiment, the processor is configured to perform quantum information processing operations N times, where N is a number greater than 1000, and where each repeated measurement state is added to the dataset.

[0037] In another embodiment, the quantum information system further includes:

[0038] Determine which measurements from the measurement state dataset correspond to the third state of the quantum information element;

[0039] Discard measurements corresponding to the third state of the quantum information element from the measurement state dataset.

[0040] In another embodiment, during the process of addressing the quantum information element with a pulse sequence, the step of determining which measurements correspond to the third state is repeated.

[0041] In another embodiment, the quantum information system further includes:

[0042] Determine which measurements correspond to the first state and which correspond to the second state from the measurement state dataset; and

[0043] After discarding the measurement corresponding to the third state of the quantum information element, the measurements corresponding to the first and second states are renormalized.

[0044] In another embodiment, the quantum information system further includes one or more additional quantum information elements and one or more additional control lines, wherein each additional quantum information element includes:

[0045] First Josephson element and second Josephson element,

[0046] Each Josephson element includes a Josephson junction disposed between two superconducting islands, wherein one superconducting island is shared by both the first and second Josephson elements;

[0047] In this embodiment, the superconducting island of the first Josephson element is coupled to the superconducting island of the second Josephson element, such that the quantum information element includes multiple states, including a first state, a second state, and a third state, wherein there is a single-excitation transition between the third state and the first state, and wherein there is a single-excitation transition between the third state and the second state.

[0048] Furthermore, each additional control line is configured to encode one of the two states of the computational subspace into a corresponding one of the additional quantum information elements, with the first state of the computational subspace corresponding to the first state and the second state of the computational subspace corresponding to the second state.

[0049] In another aspect, a method for performing quantum information processing in a quantum information element, comprising a first Josephson element and a second Josephson element, is described.

[0050] Each Josephson element includes a Josephson junction disposed between two superconducting islands, wherein one superconducting island is shared by both the first and second Josephson elements;

[0051] In this embodiment, the superconducting island of the first Josephson element is coupled to the superconducting island of the second Josephson element, such that the quantum information element includes multiple states, including a first state, a second state, and a third state, wherein there is a single-excitation transition between the third state and the first state, and wherein there is a single-excitation transition between the third state and the second state.

[0052] And one of the two states of the computational subspace is encoded into the quantum information element, where the first state of the computational subspace corresponds to the first state, and the second state of the computational subspace corresponds to the second state.

[0053] In one embodiment, control lines are used to perform encoding.

[0054] In another embodiment, the coupling between the two superconducting islands within each Josephson element is substantially the same.

[0055] In another embodiment, the method further includes addressing the quantum information element via a control line to control the state of the quantum information element, wherein optionally, the control line is coaxially arranged relative to the quantum information element.

[0056] In another embodiment, the method further includes measuring the state of the quantum information element via a readout line, wherein optionally, the readout line is coaxially arranged relative to the quantum information element.

[0057] In another embodiment, the method further includes performing a quantum information processing operation, which includes the following steps:

[0058] Initialize the quantum state within the quantum information element;

[0059] Quantum information elements are addressed using pulse sequences;

[0060] Measuring the state of quantum information elements.

[0061] In another embodiment, the quantum information processing operation is repeated N times, where N is a number greater than 1000, and the measurement state of each repetition is accumulated into the dataset.

[0062] In another embodiment, the method further includes classifying each accumulated measurement state as a first measurement state corresponding to a first state of the quantum information element, a second measurement state corresponding to a second state of the quantum information element, or a third measurement state corresponding to a third state of the quantum information element, and designating the measurement state classified as the first measurement state as the first state of the computation subspace, designating the measurement state classified as the second measurement state as the second state of the computation subspace, and designating the measurement state classified as the third measurement state as an error state.

[0063] In another embodiment, the method further includes removing measurement states designated as error states from the dataset and renormalizing the remaining accumulated measurement states based on a designated first state and a designated second state.

[0064] On the other hand, a computer program is described that includes instructions, when executed by a processor, to cause the processor to perform quantum information processing in a quantum information element, which includes a first Josephson element and a second Josephson element.

[0065] Each Josephson element includes a Josephson junction disposed between two superconducting islands, wherein one superconducting island is shared by both the first and second Josephson elements;

[0066] In this embodiment, the superconducting island of the first Josephson element is coupled to the superconducting island of the second Josephson element, such that the quantum information element includes multiple states, including a first state, a second state, and a third state, wherein there is a single-excitation transition between the third state and the first state, and wherein there is a single-excitation transition between the third state and the second state.

[0067] It also provides control outputs to encode one of the two states of the computational subspace into the quantum information element, where the first state in the computational subspace corresponds to the first state and the second state in the computational subspace corresponds to the second state.

[0068] The embodiments disclosed herein provide an improved quantum information element and system. An apparatus and method for high-fidelity quantum information processing and quantum state storage are described.

[0069] Figure 1AA quantum information element 10 configured to store quantum states is schematically shown. The quantum information element 10 includes a first Josephson element and a second Josephson element. Each Josephson element includes a Josephson junction disposed between two superconducting islands, one of which is shared by both the first and second Josephson elements. Figure 1A As shown, the first Josephson element includes a first superconducting island (also called a superconducting electrode) 12 and a third superconducting island 16, and the second Josephson element includes a second superconducting island 14 and a third superconducting island 16.

[0070] Each pair of superconducting islands within each Josephson element is coupled via a Josephson junction and capacitively coupled together. This capacitive coupling is due to the spatial separation between the islands in each Josephson element and the capacitance of the Josephson junction. Referring to Figure 1, the first Josephson element includes a first Josephson junction J1 connecting a first superconducting island 12 to a third superconducting island 16, and the first superconducting island 12 and the third superconducting island 16 are capacitively coupled via a capacitor C1. The second Josephson element includes a second Josephson junction J2 connecting a second superconducting island 14 to the third superconducting island 16, and the second superconducting island 14 and the third superconducting island 16 are capacitively coupled via a capacitor C2. The first Josephson junction J1 has a Josephson energy E. J1 The second Josephson junction J1 has the Josephson energy E. J2 . Figure 1B It shows Figure 1A Circuit diagram 18 for component 10.

[0071] The superconducting island of the first Josephson element is coupled to the superconducting island of the second Josephson element via a coupling between the first superconducting island 12 and the second superconducting island 14. For example... Figure 1A As shown, due to the physical separation of the two superconducting islands, the coupling between the first and second Josephson elements is the capacitive coupling of the capacitance Cm between the first superconducting island 12 and the second superconducting island 14.

[0072] Two Josephson elements are capacitively coupled between two corresponding capacitive islands, thereby generating two weakly anharmonic quantum oscillator modes (or degrees of freedom). In some embodiments, the Josephson elements are fabricated such that EJ / Ec » 1 to operate within a charge-insensitive region (where EJ is the Josephson energy of the Josephson junction in the Josephson element, and Ec is the charge energy of the island in the Josephson element). In the excited state of the quantum information element, the electric field oscillates within each Josephson element to provide a dipole moment between each superconducting island of the Josephson element. The harmonics of the dipole moment of each Josephson element are accessible in higher-order excitations of the quantum information element.

[0073] Due to the shared superconducting island, the large capacitive coupling between the two modes leads to strong hybridization, resulting in two new normal modes in the system. The excited states of the quantum information element exist as multiple normal modes of the system, where each Josephson element contains an oscillating electric field passing through the Josephson junction. Normal modes correspond to either in-phase addition of the dipole moment modes of the Josephson element or out-of-phase addition of the dipole moment modes of the Josephson element. Out-of-phase addition of dipole moments produces dipole moments (Δ-modes) across the entire quantum information element as low-frequency modes, while in-phase addition of dipole moments produces quadrupole moments (Σ-modes) across the entire quantum information element as high-frequency modes.

[0074] Figure 2 The energy level diagram of quantum information element 10 is shown, in which the states of the system are... by The symbols are used to denote the number of Δ-mode excitations and the number of Σ-mode excitations. Figure 2 The first two normal modes (|01> and |10>) shown are split, with each mode corresponding to the addition of parallel or antiparallel dipole moments, thus forming Δ-modes and Σ-modes, respectively. The two states |10> and |01> represent the single-excitation manifold of the system with two normal modes. Higher excitation levels exist within the system, described by higher integer Δ-mode and Σ-mode excitations (e.g., |02>, |11>, and |02>), as... Figure 2 As shown in the diagram, a single excitation of a quantum information element corresponds to increasing n by 1 or increasing m by 1.

[0075] The |nm> state energy level is non-harmonic and addressable by photons of frequencies corresponding to the transition frequencies. The transition frequency from |00> to |01> is ω1, from |00> to |10> is ω2, from |01> to |11> is ω3, and from |10> to |11> is ω4, where ω1 ≠ ω2 and ω3 ≠ ω4. Therefore, the quantum information element 10 provides an energy level structure comprising a ground state, a first excited state, and a second excited state different from the first excited state. Thus, the quantum information element 10 can be labeled as a multimode transporter, a multimode qubit, or a dimon.

[0076] In the embodiments described herein, a bimodal computational subspace is created based on the two states of the quantum information element 10. For example, the two states of the computational subspace may correspond to two lowest-energy excited states. Figure 2 As shown, the computational subspace for this example can be formed as follows:

[0077]

[0078] This computational subspace is merely an example, and other states can be used based on the |01> and |10> states of the described quantum information element 10. For example:

[0079]

[0080] The selected basis can be prepared based on the appropriate logical encoding of the quantum information element 10, for example, through one or more single-qubit gates.

[0081] Using the above computational subspace significantly reduces the decay probability between states in the computational subspace. The two transition frequencies |00> to |01> and |00> to |10> are separated by the large capacitive coupling strength of the original modes, which allows the dipole and quadrupole modes to be addressed individually by microwave control pulses of appropriate frequencies. Excitation from the |00> state to the |01> or |10> state corresponds to excitation along the longitudinal quantization axis of the computational subspace of the |01> and |10> states. The |01> or |10> states are both located on the transverse quantization axis of the computational subspace.

[0082] Because the excited states of the computational subspace are separated from the ground state along the vertical quantization axis, there is a vertical coupling between the states of the computational subspace and the ground state. Therefore, there is a finite probability of vertical relaxation between the computational subspace and the ground state. For example, in Figure 2 At the lowest energy level, the excited |01> state can relax to the state |00>, or relax to the excited |10> state by relaxing to the state |00>. In both cases, energy is lost and dissipated through lossy elements of the circuit (including dielectric two-level systems within the fabricated device), coupling with the coaxial control line, or coupling with the readout resonator. The quantum information element is used as a nonlinear resonator with a resonance peak at the excitation frequency, which includes an internal quality factor and an external quality factor that determine the linewidth of the quantum state. Furthermore, since the states in the computational subspace are located on the transverse quantization axis, single-photon longitudinal relaxation between |01> states is prohibited. Therefore, transitions between two states in the computational subspace can only occur via longitudinal coupling through a two-photon process (e.g., relaxation from state |01> to state |00> and subsequent excitation from state |00> to state |01>), or via transverse coupling mediated by exchange interactions between the two states in the computational subspace. Two-photon longitudinal coupling and transverse exchange interaction coupling have a significantly lower probability of occurrence than single-photon longitudinal relaxation, with single-photon longitudinal relaxation being the main relaxation channel.

[0083] By encoding quantum information in a selected computational subspace, bit-flipping errors between states in the computational subspace are significantly reduced due to forbidden longitudinal single-photon coupling between states in the computational subspace. Furthermore, since the permitted single-photon relaxation channels are oriented towards states that do not form part of the computational subspace, quantum state relaxation from single-photon decay channels does not manifest as bit-flipping errors.

[0084] Therefore, compared to the computational subspace formed by qubits with longitudinally coupled normal modes (e.g., |0> and |1> of the transport subqubits), the quantum information element 10 provides an error detection mechanism. In this longitudinally coupled subspace, the excited states of the computational subspace can relax to lower states of the computational subspace. Therefore, the possibility of the states of the computational subspace being incorrectly filled is significant due to single-photon transitions between states of the subspace. In contrast, in the quantum information element described herein, single-photon transitions decay each state in the computational subspace into a |0> state. Therefore, these filled states can be accurately labeled as errors and error detection can be performed more accurately. Any filled excited state |0> L and |1> L This can be accurately identified as a filled state in the computational subspace. Although there will be a further single-photon transition from state |00> to state |0>. L OR state | 1> L The probability is finite, but the timescale of the quantum information process can be kept short enough (e.g., 50 μs) to minimize the effects of these transitions, thus providing high quantum state fidelity (e.g., about 99.5%, as described below).

[0085] Choosing the states |01> and |10> as the computational subspace is merely an example. Alternative computational subspaces can be chosen from the available energy levels formed by self-coupled Josephson elements. For example, the two states could be |00> and |20> (where |10> is the erase state), or |00> and |02> (where |01> is the erase state), or |00> and |11> (where either |01> or |10> is the erase state). Any two states can be chosen for the computational subspace, provided there is no single-excitation transition separating them (i.e., no single-photon transition exists between the two states in the computational subspace). However, the choice of |01> and |10> implies that attenuation from both computational bases results in a readily detectable ground state |00>.

[0086] In some embodiments, the error rate of the quantum information element described herein is improved by providing the first and second Josephson elements with the same or substantially the same coupling (including both capacitive and Josephson inductive coupling) within each Josephson element. By providing the same coupling, the two Josephson elements resonate. When in resonance, the splitting strength between states in the computational subspace increases, and the lateral coupling between the |01> state and the |10> state decreases. This results in fewer errors from the longitudinal relaxation to the ground state and the lateral state switching between excited states. In these embodiments, the superconducting island and the Josephson junction are fabricated such that the Josephson energies EJ1 and EJ2 are substantially equal (e.g., equal to within manufacturing tolerances that allow for a 2% to 3% variation in the total Josephson energy), and the capacitances C1 and C2 are substantially equal (e.g., within manufacturing tolerances).

[0087] In some embodiments, the same coupling within each Josephson element can be provided by providing the same physical properties to the Josephson elements. This can be accomplished by manufacturing the placement and orientation of the first superconducting island relative to the third superconducting island to be substantially the same as the placement and orientation of the first superconducting island relative to the third superconducting island. For example, the assembly of the first, second, and third superconducting elements is provided in a planar arrangement having in-plane rotational symmetry of 180 degrees.

[0088] An example of this arrangement is Figure 1A The quantum information element 10 shown is illustrated. Figure 3A The alternative quantum information element 30 is shown in the figure. Figure 3B The equivalent circuit diagram of component 30 is shown below, which shows its relationship with... Figure 1A The same applies. In these examples, the quantum information element comprises two superconducting electrode patterns formed coaxially, one of which forms a third superconducting island, and the second electrode pattern is split to form a first and a second superconducting island. Figure 1A In one embodiment, a split electrode pattern is formed at the center of the element, wherein the third superconducting island is a continuous ring surrounding the first and second superconducting islands. Each of the split electrodes is shown as having a hemispherical cross-section, for example, split into semicircles at a certain distance, but other cross-sections are possible. Figure 3A In one embodiment, the third superconducting pattern is placed at the center of a coaxial arrangement, wherein the first electrode pattern and the second electrode pattern are formed by split rings of superconducting material surrounding the third superconducting electrode to form two symmetrical arcs with the same radius centered on the third superconducting island. Figure 1AIn this embodiment, the outer ring has a diameter of approximately 1 mm, and the distance between the inner islands is approximately 250 μm. The Josephson junction inductances are each approximately 10 nH, corresponding to Josephson energies of approximately 15 GHz to approximately 20 GHz. The frequency ω2 of the dipole mode |10> of the quantum information element is approximately 4.5 GHz, and the frequency ω1 of the quadrupole mode |01> of the quantum information element is approximately 6 GHz.

[0089] As described above, fabricating the first and second Josephson elements symmetrically, with equal capacitance and Josephson energy, increases the value of level splitting. Furthermore, symmetry reduces the strength of the lateral coupling between the |01> and |10> states and significantly reduces the occurrence of bit-flipping errors via the lateral coupling channel. When the Josephson energy and capacitance of the Josephson elements are identical, the lateral coupling is completely removed. Small asymmetries in the coupling may be caused by manufacturing tolerances, but the resulting lateral coupling strength is significantly less than the longitudinal coupling between excitations. The lateral relaxation error between |01> and |10> occurs on a much longer timescale than the longitudinal relaxation error.

[0090] The previously described quantum information element (e.g., 10) is used to store quantum information and will be addressed to transition qubits between quantum states. To prepare the quantum information element for a logical state or to cause the quantum information element to transition between states, the quantum information element 10 is addressed via a control line. The control line is capacitively coupled to the quantum information element to provide control pulses to cause the quantum information element to transition between quantum states.

[0091] Figure 4 illustrates an example quantum information system, including quantum information element 40 (e.g., Figure 1A and 1B The quantum information system comprises element 40, control line 42, readout line 44, and resonator 46. The quantum information system is coupled to processor 50, which is configured to control control line 42 and readout line 44 to perform quantum information processing. Readout line 44 and resonator 46 together form a readout element. Resonator 46 and quantum information element 40 are disposed on opposite sides of substrate 48. Control line 42 and readout element are arranged out of plane relative to the superconducting island of quantum information element. Quantum information element 40, control line 42, readout line 44, and resonator 46 can be coaxially aligned, as shown in Figure 4.

[0092] Processor 50 is included in a computer system and coupled to an input / output interface, memory, and other elements configured to perform data processing. The processor is configured to execute a computer program, thereby performing the steps of the computer program to perform the processes described herein, including the generation of control pulses and readout pulses, and the processing, classification, and post-processing of raw data, as described below.

[0093] Control line 42 is configured to control the state of the element by providing control signals coupled to the modes of element 10. For example, the control line is arranged to address qubits using electromagnetic energy pulses such as microwave radiation. The length, amplitude, frequency, and phase of the control signal are varied to address element 10 in order to prepare the quantum state based on the computational subspace described above.

[0094] The readout element, comprising readout line 44 and resonator 46, is configured to read out the state of quantum information element 10 in a dispersive readout regime. The resonator is coupled to element 10, and the resonant frequency of the resonator is detuned to the excitation frequency of the qubit state. Therefore, the coupling between the qubit and the resonator causes a state-related shift in the resonator frequency. Readout line 44 is configured to interrogate / address the resonator using a control signal at a selected frequency (e.g., an electromagnetic pulse, such as a microwave pulse), and to measure the response reflected back from the resonator. The reflected pulse has an amplitude and phase shift relative to the interrogation pulse. By measuring the phase (including the real and imaginary parts, represented by the in-phase and quadrature phases of the voltage signal), the response from the resonator can be measured, and the state of element 10 can be inferred.

[0095] Figure 4B An example readout amplitude response of the readout line is shown when the resonator is addressed over a frequency range. Three different response lines are shown. Line 401 shows the resonator amplitude response as a function of the microwave probe frequency when element 10 is encoded in the ground state (|00>). Line 402 shows the resonator amplitude response when element 10 is encoded in the dipole state (|10>). Line 403 shows the resonator amplitude response when element 10 is encoded in the quadrupole state (|01>). Each response curve has a resonance peak at a different frequency, which corresponds to the excitation of the encoded state present in the quantum information element. By addressing the resonator at the resonance frequency of each state, the maximum intensity of the response received from the resonator at the readout line can be measured.

[0096] In addition to the amplitude response, there will be a phase response in the pulse reflected from the resonator, which has a real part and an imaginary part. Figure 4C Example readout phase responses of the readout lines are shown when addressing the resonator across a frequency range. Line 401p shows the resonator phase response as a function of the microwave probe frequency when element 10 is encoded in the ground state (|00>). Line 402p shows the resonator phase response when element 10 is encoded in the dipole state (|10>). Line 403p shows the resonator phase response when element 10 is encoded in the quadrupole state (|01>). The quantum states encoded on the qubits can be distinguished by observing the phase response of the reflected pulse.

[0097] In the embodiments described herein, the quantum information system is configured to distinguish all three states of |00>, |01>, and |10> by addressing a resonator with a single electromagnetic pulse. The single pulse is selected at a frequency that will non-resonantly drive the resonator to fill it with photons; the readout element pulse will generate a response from the resonator with different phase responses (formed by real and imaginary terms) corresponding to the resonator frequency offset from the |01> and |10> modes. The selected frequency ( Figure 4B 410) was chosen as the frequency response of the resonator when the quantum information element is in the |01> state and the frequency response of the resonator when the quantum information element is in the |10> state. For example... Figure 4B and Figure 4C As shown, this frequency provides the response with the maximum difference in phase shift of the pulse reflected from the resonator. This response can be measured and the in-phase and quadrature phase shifts of the response can be inferred to determine the measurement state.

[0098] Compared to other arrangements of coupled Josephson elements (e.g., where each Josephson element is a separate transport formed by two superconducting islands, with the two transports capacitively coupled), the embodiments of quantum information elements (and embodiments of quantum information systems utilizing this quantum information element) described herein, comprising two Josephson elements having a common superconducting island, offer significant improvements in coherence time, fidelity, and scalability. Due to the shared third electrode and the fabrication to provide equal coupling between the superconducting islands within the Josephson element, the coupling between the Josephson elements of quantum information element 10 is much stronger than that between a pair of coupled transports. This strong coupling results in a much wider bandgap (e.g., 1.5 GHz) between the first and second excited states in quantum information element 10 than the bandgap (e.g., 200 MHz) between a pair of coupled transports.

[0099] The aforementioned wide bandgap between the two modes |01> and |10> improves the control and readout provided above. Separation of the coding frequencies (e.g., 1.5 GHz) improves the differentiation between driven modes when driving modes with a single control line. Frequency separation also reduces control crosstalk in the coding (i.e., accidentally driving one mode while intending to drive another mode of element 10). The larger bandgap also protects the excited states from decoherence sources such as charge noise, photon shot noise dephasing, critical current noise, control electronics noise, non-resonant two-level systems, and 1 / f noise.

[0100] Furthermore, compared to the multiple control lines and multiple readout elements required for addressing and reading states within a coupled transporter architecture, a single control line 42 (control multiplexing) and a single readout element can be used to address the two states of the quantum information element 10. Therefore, the system is more hardware efficient and compact, thus improving scalability. Moreover, the coupled transporter architecture is sensitive to flux noise and requires precise flux tuning between the two coupled transporters to make them resonate (e.g., when g >> Δ, where g is the coupling strength between uncoupled modes due to capacitance and Δ is the detuning between modes; when resonating the uncoupled modes, Δ = 0 and there is a split of 2g ~ 200 MHz), which is not necessary for the quantum information element 10 (thus making the quantum information element insensitive to flux noise, which is the main reason for decoherence in the coupled transporter architecture).

[0101] Although Figure 4 illustrates a quantum information system with a single quantum information element, it should be understood that multiple elements within this element can be combined into an array, as will be described later. The aforementioned coaxial arrangement constitutes a compact, in-plane quantum information system, thereby allowing for greater scalability to include numerous quantum information elements without requiring minimal control wiring on the substrate. However, it will be appreciated that the described coaxial arrangement is merely an example, and alternative arrangements of control and readout lines are possible, including those coplanar with the quantum information elements.

[0102] Quantum information element 40 is formed on substrate 48 via a photolithography process, wherein one side of substrate 48 is patterned with a superconducting material (e.g., aluminum or tantalum) to form a first superconducting island, a second superconducting island, and a third superconducting island. Standard photolithography techniques can be used.

[0103] For example, the process includes providing a substrate, depositing a superconducting material over the substrate, and then covering the substrate with photoresist. A mask is used over the photoresist layer, and the photoresist is then exposed to UV light. The exposed portions of the photoresist are then removed (e.g., via a chemical agent) to leave a pattern on the substrate. The superconducting material is then etched away, thereby exposing the pattern on the substrate of the superconducting islands. The remaining photoresist is removed with a solvent.

[0104] A photolithography process is also performed on the opposite side of substrate 48 to pattern substrate 48 with a superconducting material (e.g., aluminum or tantalum) to form a resonator. The substrate may be sapphire or silicon. A Josephson junction is formed by a combination of electron beam lithography and metal deposition. The qubit side of the substrate is covered with electron beam resist. The pattern is defined by electron beam lithography before chemical development to remove the resist from the areas exposed by the electron beam. Standard bi-angle deposition is performed to deposit a first layer of superconducting material (e.g., aluminum) before oxidation to form a Josephson junction oxide barrier. Finally, a second metal evaporation is performed at different angles. The Josephson junction is formed at the location where the oxide barrier separates the superconducting material from the first and second superconducting depositions.

[0105] As described above, the quantum information element 10 can be used to store quantum information in a state where error detection can be performed. After performing error detection, the quantum bit state can be read out with high fidelity. Figure 5 Figure 7 illustrates an example of quantum state storage and readout for a single quantum information element.

[0106] Figure 5 A process 500 for performing quantum information processing to perform incorporation error detection is illustrated. The process begins with an initialization step, in which the quantum information element 10 is addressed to initialize it to a logical state to be stored in the quantum information element 10. For example, the quantum information element 10 is addressed via control lines in one or more single-qubit gate operations to excite the quantum information element to |0> L 、|1> L The prepared logical state can then be addressed by other pulses in step 520 as part of the quantum algorithm, or the initial prepared state can be maintained in the quantum information element 10 (i.e., step 520 is not executed when the initial state is just maintained). After a time delay, the process continues to the original data measurement process 530.

[0107] Figure 6A and Figure 6B An example embodiment of 500 is shown.

[0108] Figure 6A The diagram illustrates a process 610 for addressing and reading out a quantum state prepared in one of the physical states |10> and |01> (dipole / quadripolar) of the aforementioned quantum information element. In process 610, the initialization step 510 includes initializing the element to |0> by providing a pulse in a single-qubit gate operation to address the |10> dipole state (e.g., a microwave pulse at the resonant frequency of the dipole mode to perform a π-rotation from the |00> state to the |01> state). L=|10> state, or provide pulses to address the second logic state to initialize the element to the |01> state (e.g., microwave pulses at the resonant frequency of a quadrupole mode to perform a π rotation from the |00> state to the |01> state), to initialize the logic state. In step 520, for example as part of a quantum algorithm, a series of pulses may be executed to perform operations on the qubit. After the algorithm completes, a measurement process 530 is performed to read out the final quantum state of the algorithm.

[0109] Figure 6B An example procedure 620 is shown for addressing and reading out the quantum state prepared in the superposition of the physical states |10> and |01> (dipole / quadripolar) of the aforementioned quantum information element. In procedure 620, the initialization step 510 includes preparing the element for entry by applying a single-qubit gate to the quantum information element (e.g., by pulses configured to perform π rotations in the dipole mode and pulses configured to perform π / 2 rotations in the quadrupole mode). The physical state is converted into a superposition state to initialize the logical state. In step 520, for example as part of a quantum algorithm, a series of pulses can be executed to perform operations on the qubits. After the algorithm completes, another series of pulses can be executed to generate a logical π / 2 operation to rotate the state of the quantum element back to the measurement basis (|01>, |10> basis). Finally, process 530 is executed to read out the final quantum state of the algorithm. The measurement process 530 is executed by the readout element in the manner described above.

[0110] In processes 610 and 620 described above, pulses are used to address each element 10 as part of the quantum algorithm in step 520; however, some qubits may not be addressed by pulses during the algorithm. In an alternative embodiment, the algorithm is not executed and the qubits are stored for a finite time using quantum information elements.

[0111] Figure 6A and Figure 6B The above process is merely an example, and any choice of orthogonal ground state formed from the physical state can be used to encode quantum information in a two-state computational basis. To encode an arbitrary ground state, a series of pulses is generated for the initialization process 510 to address and rotate the physical state to the selected basis. Similarly, any series of pulses can be generated for the pulse sequence operation 522 to rotate the state generated by the algorithm back to the measurement basis.

[0112] In measurement step 530, the process measures the information stored in the quantum information element by addressing the resonator at the selected frequency as described above. When performing the final measurement of the quantum state, the measured mode is the ground state of the quantum information element and two excited states (i.e., |00>, |01>, and |10>) forming the computational subspace. Each of these modes will have a different resonator dispersion shift, where the reflected signal from the resonator has different amplitudes and complex phases. This allows for the combination of the above... Figure 4B The aforementioned joint frequency dispersion readout.

[0113] The computation subspace is selected to exclude |00> states, so any occurrence of a |00> state in the final measurement is a result of errors in the qubit (e.g., attributed to longitudinal relaxation of states in the computation subspace). In the error detection method described below, error states are discarded and the remaining measurement states are retained. Therefore, when the algorithm is performed on the quantum information element at least once, there is a probability that an error will occur or not occur. In the embodiments disclosed herein, the same process steps 510 to 530 are repeated many times (e.g., 1,000 repetitions) to obtain a large sample of measured qubit states, some of which will be in states in the computation subspace and some in error states. The output of the readout element in each repetition is recorded in a dataset, which is a cumulative record of all measurements. For N repetitions, the dataset will contain N entries of measured IQ values. The selected value of N will be chosen depending on the expected number L of accurate quantum state measurements and the bit erasure fraction β, where N = L / (1 - β). For example, if there is an erasure fraction of 0.2 (20% of all bits) and you want to measure L=5,000 qubits in the logic basis, then N is chosen to be 5000 / 0.8=6250.

[0114] Figure 6C The figure shows an example readout, illustrating polymorphic readouts of repeated measurements clustered in a Gaussian pattern around three locations in the IQ plane. The distribution pattern is generated by noise in the readout chain, where the width depends on the signal-to-noise ratio.

[0115] Return to Figure 5 At step 540, the original data signal (such as...) is extracted from the readout line of the self-addressed resonator. Figure 6CThe raw data signal is then graphically represented. The raw data is then processed in classification step 550. Classification is performed, for example, by a trained Gaussian Mixture Model (GMM). The GMM is trained on data collected through calibration measurements, with numerous measurements performed (e.g., 10,000 or more), wherein the quantum information element 10 is prepared in the state to be measured (states and erased states in the computational subspace, such as |00>, |10>, and |01>), and readout measurements are performed as described above. Training data is prepared during system calibration. The GMM can identify state boundaries in the IQ plane and classify each measurement in the IQ plane as being in one of three states. After classification step 550, identification step 560 is performed, where the measurement state classified as one of the three states in the IQ plane is assigned to a logical state—that is, assigned to one of the |01> state, |10> state, or |00> state.

[0116] After assigning a state, a post-selection process is performed at step 570. In the post-selection, the state assigned to state |00> is identified as an error and discarded from the dataset. The remaining states are renormalized to provide the final logical state to be read.

[0117] The aforementioned storage and readout process 500, which incorporates error detection, is configured to perform a final-state measurement and compensate for errors in that final-state measurement. In an alternative embodiment, the error detection process may be a "continuous error detection" process, which does not measure the |0> of the system. L State and |1> L In these alternative embodiments, errors can be detected by addressing the quantum information element 10 using pulses that do not distinguish between encoded quantum states. These alternative embodiments can be used, for example, to perform error detection during the execution of quantum algorithms.

[0118] The continuous error detection process is performed in a manner similar to process 500 described above. However, instead of providing a joint dispersion readout at step 524 (where the readout line is at |0> L With |1> L The resonator is addressed by frequencies between its resonant peaks. Readout elements are configured to address the resonator at a given frequency, for state |0> L and |1> L For each state, the phase and amplitude responses of the signal reflected from the resonator are identical. This frequency is close to the resonant frequency of the ground state |00> (e.g., within approximately 100 kHz). The selected readout signal pulse frequency is... Figure 4BThe frequency shift is shown as 440. This is because the frequency separation between the frequency 440 corresponding to the ground state |00> and each of the frequencies 420 and 430 corresponding to the computed subspace states is greater than the frequency separation between the two frequencies 420 and 430 of the computed substate. Since the pulses from the resonator have the same phase and amplitude response for the computed substates, addressing the resonator at frequency 440 will not distinguish between the two states |0>. L and |1> L Therefore, dephasing of states in the computational subspace is minimized. Dispersion offset can be increased by adjusting the resonator configuration to further reduce dephasing. Thus, states determined to be "non-|00>" maintain their quantum state and can be further addressed by control lines in subsequent pulse series (e.g., during the quantum algorithm).

[0119] Therefore, the continuous error detection process enables the identification of errors in the quantum states of a quantum information element during the execution of quantum information processes. As discussed above, errors in the quantum states can occur during the operation of a qubit via two-photon interactions. The first single-photon interaction can cause the excited |01> or |01> state to decay into the |00> state, and the subsequent second photon interaction can cause |00> to be excited into the |01> or |01> state. The characteristic rate Γ of single-photon relaxation... ↓ The characteristic rate Γ higher than that of single-photon excitation ↑ Therefore, the characteristic decay time (T) of relaxation ↓ =1 / Γ ↓ The characteristic decay time of the excitation is less than T. ↑ =1 / Γ ↑ (e.g., T) ↓ =50μs and T ↑ =100μs). Repeated execution of the continuous error detection process can identify errors between the interactions of two photons, thereby improving the accuracy of the error detection process and the reliability of the quantum information element. Continuous error detection can be performed at predetermined intervals, which are optimized between identifying a high degree of error during self-state relaxation and minimizing the situation where the quantum information element is addressed. For example, the predetermined interval is selected as the excitation T... ↑ The average single-photon decay time.

[0120] Similar to the previously described process 500, the continuous error detection process steps 510 to 530 are repeated many times (e.g., 1,000 times), and the output of the readout element for each repetition is recorded in a dataset, which is a cumulative record of all measurements. For N repetitions, the dataset will contain N entries of the measured IQ values. Figure 6DThe figure shows an example readout of a continuous error detection process, illustrating a polymorphic readout of repeated measurements clustered in a Gaussian pattern around three locations in the IQ plane. The distribution pattern is caused by noise or defects within the circuit.

[0121] The dataset of recorded measurements used in the continuous error detection process is classified using the classification algorithm described above. In this case, the classification algorithm is trained to classify states into one of two categories ("|00>" or "not|00>"), where boundaries in the phase diagram separate the IQ regions corresponding to each category. Measurements classified as "|00>" are identified as error states. Any results produced using states identified as error states in any subsequent algorithms are disregarded.

[0122] In some embodiments, the quantum information system is configured to perform a quantum information element performance method. This performance method is performed to determine the performance of the quantum information element, including the logic readout fidelity of the quantum information element. The performance method may evaluate the rate of error logic bit flipping and the degree of decoherence of superposition states.

[0123] Performing such performance checks periodically allows the performance of quantum information elements to be tracked over time. If the fidelity drops below a performance threshold, the corresponding element can be deactivated for use in any subsequent quantum algorithms.

[0124] In one embodiment, the performance measurement of a quantum information element includes performing the above-described combination of... Figure 6A The method described herein involves initializing a quantum information element to a logical state |01> or |10>. The encoded quantum state is then decayed for a given decay time, without addressing the quantum element using any control pulses. After the decay time has elapsed, the state is measured as identified above. The same process is repeated N times as described above, with an error detection process 540 performed, and the finally renormalized quantum state is measured. Based on this measurement, an error fraction is determined. The error fraction characterizes the bit-flipping rate of the system (i.e., how many of the population prepared in the first computational subspace state ultimately reside in the second computational subspace state).

[0125] Figure 7A and Figure 7B An example procedure is shown for measuring the coherence of the superposition of logical states of a quantum information element.

[0126] In one embodiment, the state in the quantum information element is initialized as a superposition of two states in the computational subspace. The initialized quantum state is then allowed to evolve freely for a predetermined time delay. The quantum information element is then addressed with a series of pulses to rotate the state back to the logic state subspace. At least one of these pulses includes a phase shift to induce oscillations in the measured signal. The decay constant of the oscillation signal is then determined to identify the decay time of the state. This embodiment is a logic Ramsey measurement, and in Figure 7A As shown in the image.

[0127] Figure 7A The process 710 begins with a step to prepare the element in a superposition of physical states |01> and |10>. For example, the element is prepared by providing pulses at the dipole mode frequency to perform a π rotation of the dipole mode and providing pulses at the quadrupole mode frequency to perform a π / 2 rotation of the quadrupole mode. The superposition state is then stored in the element for later readout and allowed to evolve freely for a time delay. After this time delay, another pulse is executed to rotate the quantum state stored in the quantum information element back to the measurement basis of the control lines (i.e., back to the physical state basis |01>, |10>). An additional step phase φ is provided to one of the physical states to generate oscillations in the system. Measurement procedure 530 is then performed, in which the physical states are directly addressed as described above. The logical population fraction of each of the logical states |01> and |10> that oscillate over time is measured. Thus, the decay time of the population fraction, corresponding to the decay time of each of the logical ground states, can be measured.

[0128] Figure 7B Another example process 720 is shown for storing and reading out a quantum state prepared in a superposition of the physical states |01> and |10> (dipole / quadripolar states) of the aforementioned quantum information element, wherein the stored quantum state has additional stability. In process 720, in accordance with the above description... Figure 6B Initialization step 510 is performed in the same manner. After the first time delay, another pulse is executed to refocus the element (e.g., by a pulse configured to perform π rotation in dipole mode, a pulse configured to perform π rotation in quadrupole mode, and then another pulse configured to perform π rotation in dipole mode). After the second delay, another pulse is executed to refocus the element. L The measurement basis of the control line is rotated back (i.e., rotated back to the physical state basis |01>, |10>). An additional step phase φ is provided to one of the physical states to generate oscillations in the system. Measurement procedure 530 is then performed, in which the two physical states are directly addressed as described above. In this example, step 520 is used to rotate the stored quantum information to the measurement basis of the readout line and also to stabilize the system. Procedure 720 forms a spin echo measurement.

[0129] Table 1 below shows the physical state specification matrix, which displays the overall score of each specified state for a given preparatory state.

[0130]

[0131] Table 1 — Physical State Specification Matrix

[0132] After the post-selection process, the "00" row and column are removed, and the remaining measured "01" and "10" states are renormalized to produce Table 2 below.

[0133]

[0134] After error detection process 500, high logic readout fidelity can be achieved at the cost of a high erase fraction of many measurement states. In the example results above, approximately 99.5% fidelity is achieved at the cost of a 20% average erase fraction. A small amount of error (approximately 0.5%) still exists in the system, which includes contributions from low-probability two-photon processes and logic specification errors (where elements are prepared in states different from the expected states).

[0135] Refer to the example to calculate the subspace state | 0> L = |01> and |1> L The states |10> and |00> are classified as erased states to illustrate the above examples. However, these specific states are cited only by way of example. As explained above, the computational subspace and erased states can be selected from other energy level states of the quantum information element, such that in |0> L With |1> L There are no single-excitation transitions between states, and in the erased state and |0> L and |1> L There are single excitations among the states. Control line 42, readout element 44, and processor 50 are each configured to perform the same method as described above for the example states. Each of the selected states can be encoded in a quantum information element via a pulse or a series of pulses, and each state will be coupled to a resonator to generate a corresponding resonator offset that can be interrogated by the readout line. A classifier can be trained on the corresponding training data, and the classification and recognition algorithm can select the selected states to perform error detection and post-selection processes.

[0136] The above embodiments pertain to a single quantum information element having associated resonators and control lines. In other embodiments of the invention, multiple quantum information elements may be provided together to form an array. Figure 8A schematic planar diagram of an example array of quantum information elements 810 is shown. However, it should be understood that the grid arrangement is only one example, and other arrangements of qubits, including hexagonal arrays, circular arrays, or other planar arrangements, are possible. The quantum information elements 810 are coupled together by coupling 820. Figure 8 The coupling is illustrated as capacitive coupling, but other forms of coupling can also be implemented (e.g., resonant coupling including inductors and capacitors). The coupled array of quantum information elements in the array can be individually addressed as part of a quantum algorithm, where the coupling between elements enables the execution of two or more qubit gate operations.

[0137] Figure 9 The above text is shown. Figure 8 An example quantum information system is an array of quantum information elements, wherein each quantum information element is coaxially aligned with individual control lines, readout lines and resonators in the same manner as shown in Figure 4. Figure 9 Only three are shown, but it should be understood that each quantum information element is equipped with the aforementioned coaxial assembly.

[0138] An array of M quantum information elements provides M independently addressable quantum memory cells, each configured to store a quantum state. Each of the quantum information elements can be individually addressed and measured as described above for a single quantum information element, and the error detection and compensation methods provided above can be applied independently to each element. Therefore, the array is configured to operate as a high-fidelity M-bit quantum processor with the stored and processed quantum information.

[0139] While certain embodiments have been described, these embodiments are presented by way of example only and are not intended to limit the scope of the invention. In fact, the novel apparatus and methods described herein can be embodied in many other forms; furthermore, various omissions, substitutions, and changes can be made to the form of the apparatus, methods, and products described herein without departing from the spirit of the invention. The appended claims and their equivalents are intended to cover such forms or modifications that fall within the scope and spirit of the invention.

Claims

1. A quantum information system, comprising a quantum information element and a control line, wherein the quantum information element comprises: First Josephson element and second Josephson element, Each Josephson element includes a Josephson junction disposed between two superconducting islands, wherein one of the superconducting islands is shared by both the first Josephson element and the second Josephson element; The superconducting island of the first Josephson element is coupled to the superconducting island of the second Josephson element, such that the quantum information element includes multiple states, including a first state, a second state, and a third state, wherein a single-excitation transition exists between the third state and the first state, and wherein a single-excitation transition exists between the third state and the second state. Furthermore, the control line is configured to encode one of two states of the computational subspace into the quantum information element, wherein the first state of the computational subspace corresponds to the first state, and the second state of the computational subspace corresponds to the second state.

2. The quantum information system according to claim 1, wherein, The coupling between the two superconducting islands within each Josephson element is substantially the same.

3. The quantum information system according to any one of the preceding claims, wherein, The quantum information element includes a split superconducting electrode arranged coaxially with another superconducting electrode, the split superconducting electrode forming one of the superconducting islands of each of the first Josephson element and the second Josephson element, the other superconducting electrode forming the superconducting island common to the first Josephson element and the second Josephson element.

4. The quantum information system according to any one of the preceding claims, wherein, The control lines are arranged out of plane relative to the quantum information element.

5. The quantum information system according to any one of the preceding claims further includes a readout element configured to measure the quantum state of the quantum information element, wherein, Optionally, the readout element is arranged out of plane relative to the quantum information element.

6. The quantum information system of claim 5, further comprising a processor configured to perform quantum information processing operations on the quantum information element, the quantum information processing comprising: The quantum state within the quantum information element is initialized via the control line; The quantum information element is addressed via the control line using a pulse sequence; The state of the quantum information element is measured via the readout line.

7. The quantum information system according to claim 6, wherein, The processor is configured to perform the quantum information processing operation N times, where N is a number greater than 1000, and where each repeated measurement state is added to the dataset.

8. The quantum information system according to claim 7, further comprising: Determine which measurements from the measurement state dataset correspond to the third state of the quantum information element; Discard the measurement corresponding to the third state of the quantum information element from the measurement state dataset.

9. The quantum information system according to claim 8, wherein, During the addressing of the quantum information element with the pulse sequence, the step of determining which measurements correspond to the third state is repeated.

10. The quantum information system according to claim 8 or claim 9, further comprising: Determine which measurements correspond to the first state and which measurements correspond to the second state from the measurement state dataset; as well as After discarding the measurement corresponding to the third state of the quantum information element, the measurements corresponding to the first and second states are renormalized.

11. The quantum information system according to any one of the preceding claims further includes one or more additional quantum information elements and one or more additional control lines, wherein, Each additional quantum information element includes: First Josephson element and second Josephson element, Each Josephson element includes a Josephson junction disposed between two superconducting islands, wherein one of the superconducting islands is shared by both the first Josephson element and the second Josephson element; The superconducting island of the first Josephson element is coupled to the superconducting island of the second Josephson element, such that the quantum information element includes multiple states, including a first state, a second state, and a third state, wherein a single-excitation transition exists between the third state and the first state, and wherein a single-excitation transition exists between the third state and the second state. Furthermore, each of the additional control lines is configured to encode one of two states of the computational subspace into a corresponding additional quantum information element in the additional quantum information element, wherein the first state of the computational subspace corresponds to the first state, and the second state of the computational subspace corresponds to the second state.

12. A method for quantum information processing in a quantum information element, said quantum information element comprising a first Josephson element and a second Josephson element. Each Josephson element includes a Josephson junction disposed between two superconducting islands, wherein, One of the superconducting islands is shared by both the first Josephson element and the second Josephson element; The superconducting island of the first Josephson element is coupled to the superconducting island of the second Josephson element, such that the quantum information element includes multiple states, including a first state, a second state, and a third state, wherein a single-excitation transition exists between the third state and the first state, and wherein a single-excitation transition exists between the third state and the second state; and One of the two states of the computational subspace is encoded into the quantum information element, wherein the first state of the computational subspace corresponds to the first state, and the second state of the computational subspace corresponds to the second state.

13. The method according to claim 11, wherein, The coupling between the two superconducting islands within each Josephson element is substantially the same.

14. The method according to any one of claims 11-13, further comprising: The quantum information element is addressed via a control line to control the state of the quantum information element, wherein optionally, the control line is coaxially arranged relative to the quantum information element.

15. The method according to any one of claims 11-14, further comprising: The state of the quantum information element is measured via a readout line, wherein optionally, the readout line is coaxially arranged with respect to the quantum information element.

16. The method according to any one of claims 11-15, further comprising: Performing quantum information processing operations includes the following steps: Initialize the quantum state within the quantum information element; The quantum information element is addressed using a pulse sequence; The state of the quantum information element is measured.

17. The method according to any one of claims 11-16, wherein, The quantum information processing operation is repeated N times, where N is a number greater than 1000, and the measurement state of each repetition is accumulated into the dataset.

18. The method of claim 17, further comprising: Each of the accumulated measurement states is classified into a first measurement state corresponding to the first state of the quantum information element, a second measurement state corresponding to the second state of the quantum information element, or a third measurement state corresponding to the third state of the quantum information element; as well as The measurement state that will be classified as the first measurement state is designated as the first state, the measurement state that will be classified as the second measurement state is designated as the second state of the computational subspace, and the measurement state that will be classified as the third measurement state is designated as the error state.

19. The method of claim 18, further comprising: The measurement states designated as error states are removed from the dataset, and the remaining accumulated measurement states are renormalized based on the designated first state and the designated second state.

20. A computer program comprising instructions that, when executed by a processor, cause the processor to perform a method of quantum information processing in a quantum information element, the quantum information element comprising a first Josephson element and a second Josephson element. Each Josephson element includes a Josephson junction disposed between two superconducting islands, wherein, One of the superconducting islands is shared by both the first Josephson element and the second Josephson element; The superconducting island of the first Josephson element is coupled to the superconducting island of the second Josephson element, such that the quantum information element includes multiple states, including a first state, a second state, and a third state, wherein a single-excitation transition exists between the third state and the first state, and wherein a single-excitation transition exists between the third state and the second state; and A control output is provided to encode one of two states of a computational subspace into the quantum information element, wherein a first state of the computational subspace corresponds to the first state, and a second state of the computational subspace corresponds to the second state.

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