Methods for tuning the interaction strength between at least two qubits in a quantum computer and quantum computers
By applying a periodic pulse sequence and tuning the time delay in a quantum computer, the problem of tuning the interaction strength between qubits was solved, improving the efficiency of quantum computing and reducing decoherence, thus achieving more stable quantum computing.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- ELEQTRON GMBH
- Filing Date
- 2024-11-14
- Publication Date
- 2026-06-02
AI Technical Summary
Existing technologies struggle to effectively tune the interaction strength between qubits in a quantum computer, resulting in low quantum computing efficiency.
The interaction strength between qubits is tuned by applying a periodic pulse sequence to the qubits using time offset, specifically by modulating the interaction strength by controlling the time delay of the first and second periodic pulse sequences.
Effective interaction between qubits was achieved, improving the efficiency of quantum computing. Furthermore, decoupling pulse sequences were used to reduce decoupling and enhance the stability of quantum computing.
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Figure CN122139197A_ABST
Abstract
Description
[0001] This article describes in detail the method for tuning the interaction strength between at least two qubits in a quantum computer and the quantum computer itself.
[0002] At least one objective of certain embodiments is to provide a method for tuning the interaction strength between at least two qubits in a quantum register of a quantum computer. This objective is achieved by a method having the features according to the independent claims.
[0003] Advantageous embodiments and other developments of the method are described in detail in the dependent claims.
[0004] According to an embodiment, a method for tuning the interaction strength between at least two qubits of a quantum computer includes the step of applying a first periodic pulse sequence to a first qubit. Specifically, each qubit is a quantum mechanical two-state system comprising two linearly independent ground states denoted below as |0> and |1>.
[0005] For example, at least two qubits are part of the same quantum register in a quantum computer. Specifically, a quantum register comprises multiple qubits, and the quantum computer performs quantum computations, such as gate operations, by manipulating the states of the qubits in the quantum register. For instance, qubits in the same quantum register interact with each other.
[0006] For example, the first periodic pulse sequence includes or consists of single-qubit gates acting on the first qubit. In other words, each pulse in the first periodic pulse sequence corresponds to one or more single-qubit gates. For example, a single-qubit gate is a rotation operator about the x-axis, y-axis, and / or z-axis. Specifically, a pulse in the first periodic pulse sequence rotates the state of the first qubit by a given angle about a given axis of the Bloch sphere. For example, each pulse in the first periodic pulse sequence flips the state of the first qubit, changing the ground state |0> to |1>, and vice versa.
[0007] Specifically, the first periodic pulse sequence is periodic in time. For example, one period of the first periodic pulse sequence consists of one pulse, and the pulse is repeatedly applied to the first qubit at equal time steps.
[0008] According to another embodiment, the method includes the step of applying a second periodic pulse sequence to a second qubit. All features disclosed for the first periodic pulse sequence can also be applied to the second periodic pulse sequence, and vice versa. For example, the second periodic pulse sequence includes or consists of single-qubit gates acting on the second qubit. In other words, each pulse of the second periodic pulse sequence corresponds to one or more single-qubit gates. For example, one pulse in the second periodic pulse sequence rotates the state of the second qubit by a given angle about a given axis of the Bloch sphere. For example, each pulse of the second periodic pulse sequence flips the state of the second qubit, changing the ground state |0> to |1>, and vice versa.
[0009] In particular, the second periodic pulse sequence is periodic in time. For example, one period of the second periodic pulse sequence consists of one pulse, and the pulse is repeatedly applied to the second qubit at equal time steps.
[0010] According to another embodiment of the method, the period of the first periodic pulse sequence is equal to the period of the second periodic pulse sequence. In other words, the time interval between the first periodic pulse sequence and the second periodic pulse sequence repeating themselves is the same for both the first periodic pulse sequence and the second periodic pulse sequence.
[0011] According to another embodiment of the method, the pulses of the second periodic pulse sequence are time-delayed relative to the pulses of the first periodic pulse sequence. For example, if the pulses of the first periodic pulse sequence are time-delayed with discrete equidistant time steps t... m When applied to the first qubit, the pulses of the second periodic pulse sequence occur in discrete, equidistant time steps t. m +Δt is applied to the second qubit, where Δt is a time delay. Specifically, 0 ≤ Δt ≤ T, where T is the period of the first and second periodic pulse sequences. For example, the second periodic pulse sequence is identical to the first periodic pulse sequence except that there is a time delay or time offset Δt between the first and second periodic pulse sequences.
[0012] According to another embodiment of the method, the interaction strength is tuned by controlling the time delay between the pulses of the second periodic pulse sequence and the pulses of the first periodic pulse sequence. For example, when the first periodic pulse sequence and the time-shifted second periodic pulse sequence are applied to the first qubit and the second qubit, respectively, the interaction strength between the first qubit and the second qubit is modulated as a function of time.
[0013] For example, the periods of the first and second periodic pulse sequences are much shorter than the timescale associated with the interaction strength between the first and second qubits. In other words, the energy scale associated with the pulses of the first and second periodic pulse sequences, such as Planck's constant multiplied by the Rabi frequency of a single-qubit rotation operation applied to the first and / or second qubit, is much larger than the energy scale of the interaction strength between the first and second qubits. For example, the energy scale of the pulses of the first and second periodic pulse sequences is at least 10 times the interaction strength.
[0014] Specifically, if the periods of the first and second periodic pulse sequences are much shorter than the time scale h / |J|, for example, at most one-tenth, where h is Planck's constant and J is the interaction strength in physical units of energy, then when the first and second periodic pulse sequences are applied, the first and second qubits interact effectively through a time-averaged interaction strength. Here, for example, time averaging can be performed over one period of the first and second periodic pulse sequences.
[0015] For example, the time-averaged interaction strength is a function of the time delay between the pulses of the second periodic pulse sequence and the pulses of the first periodic pulse sequence. For example, the absolute value of the interaction strength remains constant during one period of the first and second periodic pulse sequences, but the interaction flips its sign during the time interval between the pulses of the first periodic pulse sequence and the time-delayed pulses of the second periodic pulse sequence. Therefore, for example, the absolute value of the time-averaged interaction strength changes as the time delay increases. For example, if the time delay is equal to half the period of the first and second periodic pulse sequences, the time-averaged interaction strength is zero.
[0016] According to a preferred embodiment, a method for tuning the interaction strength between at least two qubits of a quantum computer includes the following steps:
[0017] - Apply the first periodic pulse sequence to the first qubit.
[0018] - Apply a second periodic pulse sequence to the second qubit, where
[0019] - The period of the first periodic pulse sequence is equal to the period of the second periodic pulse sequence.
[0020] - Delay the pulse time of the second periodic pulse sequence relative to the pulse time of the first periodic pulse sequence, and
[0021] - The interaction strength is tuned by controlling the time delay.
[0022] The method disclosed herein is based on the idea of tuning the interaction strength between qubits in a quantum register by applying a time-shifted sequence of periodic pulses to the respective qubits. For example, the periodic pulse sequence flips the state of the qubit at a frequency much higher than the frequency h / |J| associated with the interaction energy scale J. Therefore, the interaction between the qubits is effectively time-averaged over the period of the periodic pulse sequence, and the strength of the time-averaged interaction can be adjusted by tuning the time delay of the pulses between different periodic pulse sequences. Advantageously, these periodic pulse sequences have a dual function as dynamic decoupling pulse sequences to protect the state of the qubits from decoherence.
[0023] According to another embodiment of the method, the interaction between at least two qubits is a paired Ising or XY interaction. For example, all qubits in a quantum register interact through all-to-all paired Ising or XY interactions.
[0024] For example, in a quantum register comprising N qubits, the interaction takes the following form
[0025] (1).
[0026] Specifically, all pairs of qubits in the quantum register interact via the Ising or XY interaction. In equation (1) above, H int This refers to the interaction term in the Hamiltonian, where integer indices i and j list the N qubits in the quantum register, and (in ) represents the action on qubit i (where The three 2×2 Pauli matrices on the ground state of ) One of them. Here, the product of Pauli matrices acting on different qubits is understood as a tensor product. Furthermore, J ij It has units of energy and parameters the interaction strength between qubits i and j. For example, J ij = J is independent of i and j.
[0027] For α = β, the interaction specified in equation (1) is referred to below as the "Ising interaction," while for α ≠ β, the interaction is referred to below as the "XY interaction." For the Ising interaction with α = β, the ground states |0> and |1> of the qubit are preferably the corresponding Pauli matrices. The eigenstates of , and are represented below as the measurement ground state.
[0028] For example, pairwise Ising or XY interactions between qubits occur in various physical qubit implementations, such as superconducting qubits or trapped ion qubits. For instance, pairwise Ising or XY interactions between qubits can be used to implement two-qubit gates and / or gates for multiple qubits, particularly entangled gates, between the respective qubits. For example, a globally entangled gate, such as a generalized Mohr-Sorenson gate or a magnetic gradient-induced coupling gate, can be implemented by qubits in a time-evolution quantum register when the qubits interact via the Hamiltonian specified in equation (1). Therefore, controlling the interaction strength between pairs of qubits individually and simultaneously using the methods disclosed herein advantageously allows for the implementation of specific quantum circuits, such as those where entangled gates act on selected qubits in a predetermined manner.
[0029] According to another embodiment of the method, the first periodic pulse sequence includes π pulses, wherein each π pulse toggles the state of the first qubit. For example, a π pulse is a single qubit rotation that causes the state of the first qubit to rotate by an angle of π radians about the axis of the Bloch sphere. In particular, the π pulse changes the ground state |0> of the first qubit to the ground state |1> of the first qubit, and vice versa.
[0030] Specifically, the π pulse acts on a timescale that is the reciprocal of the Rabi frequency of the applied electromagnetic field between the two ground states |0> and |1> of the first qubit. For example, the Rabi frequency is greater than the interaction strength J between the first and second qubits. 12 Associated frequency | J 12 | / h is much larger, for example, at least 10 times larger. Therefore, the frequency of the first periodic pulse sequence can be greater than the frequency |J associated with the interaction strength. 12 | / h is much larger.
[0031] According to another embodiment of the method, the second periodic pulse sequence includes π pulses, wherein each π pulse toggles the state of the second qubit. All features disclosed for the π pulses of the first periodic pulse sequence can also be applied to the π pulses of the second periodic pulse sequence, and vice versa. In particular, the π pulses change the ground state |0> of the second qubit to the ground state |1> of the second qubit, and vice versa.
[0032] According to another embodiment of the method, the time-averaged interaction strength between at least two qubits, averaged over the periods of the first and second periodic pulse sequences, is a linear function of the time delay. For example, the first and second periodic pulse sequences flip the measurement ground states of the first and second qubits, respectively. Therefore, if the first and second qubits do not flip simultaneously, the interaction strength J in equation (1) is... 12 The sign actually changes from + to -, and vice versa. For example, the time-averaged interaction strength between the first and second qubits takes the value of
[0033] ,
[0034] Where Δt (where 0 ≤ Δt ≤ T) is the time delay, and T is the period of the first and second periodic pulse sequences. Therefore, by adjusting the time delay Δt accordingly, it is possible to achieve the desired effect in +J... 12 With –J 12 The interaction strength is continuously tuned over time.
[0035] According to another embodiment of the method, the first periodic pulse sequence is a dynamically decoupling pulse sequence configured to protect the first qubit from decoupling, and / or the second periodic pulse sequence is a dynamically decoupling pulse sequence configured to protect the second qubit from decoupling. Specifically, decoupling refers to the loss of quantum coherence of a qubit due to undesirable coupling between the qubit and its environment. For example, the dynamically decoupling pulse sequence suppresses decoupling of the qubit by at least approximately averaging the undesirable coupling between the qubit and its environment to zero.
[0036] For example, dynamic decoupling pulse sequences are based on periodically iterated Hahn spin echoes or the Carr-Purcell scheme used to reduce phase loss of qubits due to their coupling with ambient noise. In particular, the time interval between pulses in a dynamic decoupling pulse sequence is much shorter than the timescale of the undesirable coupling between the qubit and the environment, for example, the latter being at least ten times the time interval between pulses.
[0037] According to the method described above, the dynamic decoupling pulse sequence for qubits can be further used to tune the interaction strength between qubits by time-shifting the dynamic decoupling pulse sequences applied to different qubits relative to each other.
[0038] According to another embodiment of the method, the frequencies of the first and second periodic pulse sequences are matched to the ambient noise spectrum. Specifically, the frequencies are matched such that the coherence time of the first and second qubits increases in the presence of ambient noise compared to the case where the first and second periodic pulse sequences are not applied to the first and second qubits, respectively. For example, the frequencies of the first and second periodic pulse sequences are chosen such that they do not resonate with a resonance in the noise spectrum.
[0039] According to another implementation, the method is configured to independently tune the interaction strength between multiple pairs of qubits in a quantum register using the following steps:
[0040] - Apply different periodic pulse sequences to different qubits in a quantum register, where all periodic pulse sequences have the same period, and
[0041] - Adjust the time delay of pulses between different periodic pulse sequences to independently tune the interaction strength between multiple pairs of qubits. In particular, all the characteristics of the first and / or second periodic pulse sequences disclosed above can also be applied to all other periodic pulse sequences applied to different qubits in the quantum register.
[0042] According to another embodiment of the method, the ground state of each qubit corresponds to a different ultrafine state of the corresponding trapped ion. Specifically, each qubit is encoded in two different ultrafine states of the corresponding trapped ion. For example, a system of two or more ions trapped in the same ion trap forms a quantum register.
[0043] According to another embodiment of the method, at least two qubits interact via magnetic gradient-induced coupling. For example, a magnetic field gradient along the chain of trapped ions induces pairwise Ising interactions between all pairs of qubits in the ion trap. For example, in the presence of a magnetic field gradient, this Ising interaction is mediated by the co-vibrational motion of the ions in the ion trap.
[0044] Furthermore, this paper describes a quantum computer in detail. Specifically, the quantum computer implements the method described above for tuning the interaction strength between at least two qubits. All features of this method are also disclosed for use in the quantum computer, and vice versa.
[0045] According to the implementation of the quantum computer, the interaction strength between at least two qubits is tuned using the method described above.
[0046] Further advantageous and alternative embodiments of the quantum computer and the method may become apparent from the following exemplary embodiments described in conjunction with the accompanying drawings.
[0047] Figure 1 A schematic graph showing a first periodic pulse sequence, a second periodic pulse sequence, the states of the first and second qubits, and the interaction strength between the first and second qubits as a function of time, according to an exemplary embodiment of a method for tuning the interaction strength between at least two qubits of a quantum computer.
[0048] Figure 2 A schematic graph of a periodic pulse sequence applied to a quantum register according to an exemplary embodiment of a method for tuning the interaction strength between at least two qubits of a quantum computer is shown.
[0049] Figure 3 A schematic diagram of a quantum computer according to an example implementation is shown.
[0050] Elements that are identical, similar, or have the same effect are indicated by the same reference numerals in the accompanying drawings. The scale of the figures and elements shown in the figures is not considered to be true scale. Rather, for better representation and / or better understanding, individual elements may be exaggerated to appear large.
[0051] Figure 1 A first periodic pulse sequence 1 is shown, comprising pulse 11 applied to a first qubit qb1 in a quantum register of a quantum computer according to an exemplary embodiment of the method, and a second periodic pulse sequence 2, comprising pulse 21 applied to a second qubit qb2 in a quantum register of a quantum computer according to an exemplary embodiment of the method. The first periodic pulse sequence 1 and the second periodic pulse sequence 2 have the same period T as a function of time t.
[0052] The first quantum bit qb1 and the second quantum bit qb2 interact through the Ising interaction. And the interaction, in which This represents the z-Pauli matrix acting on the first qubit qb1. Let J denote the z-Pauli matrix acting on the second qubit qb2, and J be the interaction strength.
[0053] The first periodic pulse sequence 1's pulse 11 is a π pulse that flips the ground states |0> and |1> of the first qubit qb1 to each other. In other words, after applying a π pulse, state |0> changes to state |1>, and vice versa. Here, |0> and |1> are eigenvalues with eigenvalues -1 and +1, respectively. The eigenstates. Similarly, pulse 12 of the second periodic pulse sequence 2 is a π pulse, which flips the ground states |0> and |1> of the second qubit qb2 to each other. In other words, after applying a π pulse, state |0> changes to state |1>, and vice versa. Here, |0> and |1> are eigenvalues with eigenvalues -1 and +1, respectively. The eigenstates.
[0054] Pulse 21 of the second periodic pulse sequence 2 is time-shifted and therefore has a time delay Δt relative to pulse 11 of the first periodic pulse sequence 1. Thus, the second qubit qb2 is flipped by each corresponding π pulse at a time t different from that of the first qubit qb1.
[0055] Figure 1 The second and third subgraphs show the expected values of the first qubit qb1 as a function of time t, respectively. Expected value of the second quantum bit qb2 In this example, at time t=0, both the first qubit qb1 and the second qubit qb2 are initialized to the ground state |1>. Therefore, at time t=0, the expected value is... and Both are equal to 1. After the first π pulse is applied to the first qubit qb1, the state of the qubit changes to |0>, and the expected value changes accordingly to The second π pulse flips the state of the first qubit qb1 back to |1>, and the expected value... The same applies to the second qubit qb2, although with a time delay Δt at a later time.
[0056] The interaction energy between the first qubit qb1 and the second qubit qb2 as a function of time t Depicted in Figure 1 In the bottom subgraph. If two qubits are in the same state, for example, both qubits are in state |0> or both qubits are in state |1>, then the interaction energy is +J. If the first qubit qb1 and the second qubit qb2 are in different states, for example, the first qubit qb1 is in state |0> and the second qubit qb2 is in state |1>, or vice versa, then the interaction energy is -J.
[0057] Therefore, by tuning the time delay Δt, the time average of the interaction energy E can be tuned, and thus the time average of the effective interaction strength J can be tuned. Specifically, the frequencies 1 / T of the first periodic pulse sequence 1 and the second periodic pulse sequence 2 are much larger than the frequency scale J / h (where h represents Planck's constant) associated with the interaction strength J, for example, at least ten times larger. Thus, the first and second qubits interact effectively through an interaction with a time average of the effective interaction strength J, which is the time average of the interaction energy E over one period T of the periodic pulse sequences 1 and 2.
[0058] Figure 2 The illustration shows four distinct periodic pulse sequences 1, 2, 3, 4 applied to four different qubits qb1, qb2, qb3, qb4 according to an exemplary embodiment of the method, in order to tune the interaction strength J between each pair of the four qubits qb1, qb2, qb3, qb4. ij Besides the different time delays Δt, the pulse sequences and combinations Figure 1 The pulse sequences described are the same. Specifically, for example, the effective interaction strength J between qubits qb1 and qb2 is... 12 Depends on time delay The effective interaction strength J between qubits qb2 and qb3 23 Depends on time delay Generally, the effective interaction strength J between qubits qbi and qbj is... ij (in (Depends on time delay) By selecting the timing of the pulses in each periodic pulse sequence 1, 2, 3, 4, the interaction strength between each pair of qubits can thus be tuned independently.
[0059] according to Figure 3 The quantum computer 10 in the exemplary embodiment includes a quantum register with four qubits qb1, qb2, qb3, qb4. The two ground states |0> and |1> of each qubit qb1, qb2, qb3, qb4 are the two ultrafine states of the corresponding trapped ions. All ions belonging to the quantum register are trapped in the same ion trap, such as a Paul trap or a Penning trap. The magnetic gradient along the chain of trapped ions induces paired Ising interactions between all pairs of qubits in the quantum register.
[0060] This invention is not limited to the exemplary embodiments described herein. Rather, the invention covers any new features and any combination of features, particularly any combination of features in the patent claims and any combination of features in the exemplary embodiments, even if the feature or combination itself is not expressly specified in the patent claims or exemplary embodiments.
[0061] Figure Labels
[0062] 1. First periodic pulse sequence
[0063] 11 pulses
[0064] 2. Second periodic pulse sequence
[0065] 21 pulses
[0066] 3,4 periodic pulse sequences
[0067] 10 quantum computers
[0068] qb1…4 qubits
[0069] T cycle
[0070] Δt time delay
[0071] t time
[0072] J-interaction strength
[0073] E-interaction energy
Claims
1. A method for tuning the interaction strength (J) between at least two qubits (qb1, qb2) of a quantum computer (10), comprising the steps of: - Apply the first periodic pulse sequence (1) to the first qubit (qb1). - Apply the second periodic pulse sequence (2) to the second qubit (qb2), where, - The period (T) of the first periodic pulse sequence (1) is equal to the period (T) of the second periodic pulse sequence (2). - Delay the pulses (21) of the second periodic pulse sequence (2) relative to the pulses (11) of the first periodic pulse sequence (1), and - The interaction strength (J) is tuned by controlling the time delay (Δt).
2. The method according to the preceding claim, wherein, The interaction between the at least two qubits (qb1, qb2) is a pairwise Ising or XY interaction.
3. The method according to any one of the preceding claims, wherein, - The first periodic pulse sequence (1) includes π pulses, wherein each π pulse toggles the state of the first qubit (qb1), and - The second periodic pulse sequence (2) includes π pulses, wherein each π pulse flips the state of the second qubit (qb2).
4. The method according to any one of the preceding claims, wherein, The time-averaged interaction strength (J) between the at least two qubits (qb1, qb2) averaged over the period (T) of the first periodic pulse sequence (1) and the second periodic pulse sequence (2) is a linear function of the time delay (Δt).
5. The method according to any one of the preceding claims, wherein, - The first periodic pulse sequence (1) is a dynamically decoupling pulse sequence configured to protect the first qubit (qb1) from decoherence, and / or - The second periodic pulse sequence (2) is a dynamic decoupling pulse sequence configured to protect the second qubit (qb2) from decoherence.
6. The method according to any one of the preceding claims, wherein, The frequencies of the first periodic pulse sequence (1) and the second periodic pulse sequence (2) are matched with the ambient noise spectrum.
7. The method according to any one of the preceding claims, wherein, The method is configured to independently tune the interaction strength (J) between multiple pairs of qubits (qb1, qb2, qb3, qb4) in a quantum register using the following steps: - Different periodic pulse sequences (1, 2, 3, 4) are applied to different qubits (qb1, qb2, qb3, qb4) in the quantum register, wherein all periodic pulse sequences (1, 2, 3, 4) have the same period (T). - Adjust the time delay (Δt) of the pulses between different periodic pulse sequences (1, 2, 3, 4) to independently tune the interaction strength (J) between multiple pairs of qubits (qb1, qb2, qb3, qb4).
8. The method according to any one of the preceding claims, wherein, The ground state of each qubit (qb1, qb2, qb3, qb4) corresponds to a different ultrafine state of the captured ion.
9. The method according to the preceding claim, wherein, The at least two qubits (qb1, qb2) interact through magnetic gradient-induced coupling.
10. A quantum computer (10), wherein, The interaction strength (J) between at least two qubits (qb1, qb2) is tuned using the method according to any one of claims 1 to 9.