A quantum lock-in detection method based on entanglement enhancement

Abstract

The application discloses a quantum phase-locked detection method based on entanglement enhancement, encodes quantum bits in a ground state and an excited state, and prepares the quantum bits as initial quantum states; a periodic multi-pulse sequence is loaded on the quantum bits; a carrier wave pulse resonating with the ground state and the excited state is loaded; a final quantum state of the quantum bits is detected; curves of each component of a measured density matrix and a theoretical density matrix changing with a pulse time interval of the periodic multi-pulse sequence are compared; and a half period and an amplitude of a to-be-measured sinusoidal wave are obtained. The application can effectively suppress measurement noise under the condition of existing rotation angles and detuning errors, and can maintain high measurement precision under the condition of existing rotation angles and detuning errors. The robustness makes the application more reliable in practical application.

Description

Technical Field

[0001] This invention relates to the fields of quantum metrology and quantum sensing technology, specifically to an entanglement-enhanced quantum lock-in detection (QLID) method for improving the measurement accuracy of alternating signal frequencies. Background Technology

[0002] Currently, the second quantum revolution, represented by quantum information technology, is underway. Utilizing the fundamental principles of quantum mechanics and quantum control techniques, quantum information technology can break through the classical limits of information technology. For example, quantum computers offer extremely high computing power with extremely low energy consumption, quantum communication provides unconditionally secure communication, and quantum precision measurement offers extremely high sensitivity and accuracy. This revolution is expected to achieve breakthroughs in quantum communication, quantum computing, and quantum simulation, becoming a powerful tool for addressing major challenges in information, energy, environment, and medicine.

[0003] The standard quantum limit refers to the theoretical limit of the measurement accuracy of an observable physical quantity under classical measurement conditions, which is limited by quantum noise. The main sources of noise are shot noise and quantum projection noise. Its measurement accuracy With the number of particles used in the measurement It is inversely proportional to the square root of (such as photons, atoms, etc.), that is... This represents the best accuracy achievable by classical measurement methods. It can be seen that, with... As the quantity increases, the measurement accuracy of physical quantities also increases, but the rate of increase is limited. The standard quantum limit is of great significance in many fields of quantum measurement and quantum sensing. For example, in optical or atomic interferometers, the measurement of phase is limited by shot noise; in atomic clocks, the measurement of atomic transition frequencies is limited by quantum projection noise; and in laser interferometric gravitational wave detectors, the shot noise of the photon number limits the detection sensitivity.

[0004] The Heisenberg limit refers to the optimal measurement precision achievable in quantum measurement using quantum resources (such as quantum entanglement and quantum coherence). Its physical basis is the Heisenberg uncertainty principle, which states that in quantum mechanics, certain pairs of physical quantities (such as position and momentum, phase and particle number) cannot be simultaneously measured precisely; this uncertainty limits the measurement precision. The Heisenberg limit is the theoretical limit of measurement precision allowed by quantum mechanics for an observable physical quantity. Its measurement accuracy Compared with the number of particles typically used in measurements (e.g., photons, atoms, etc.) are inversely proportional, that is The Heisenberg limit further demonstrates that by utilizing quantum resources (such as entangled states and squeezed states), measurement precision can be improved to a level unattainable by classical measurement, showcasing the advantage of quantum mechanics in measurement accuracy.

[0005] Traditional quantum phase-locked detection methods typically use non-entangled states for measurement, and their accuracy is limited by the standard quantum limit. This invention utilizes many-body quantum entanglement to provide a quantum phase-locked detection method based on entanglement enhancement. This method can break through the standard quantum limit and achieve measurement accuracy close to the Heisenberg limit. Summary of the Invention

[0006] The purpose of this invention is to provide an entanglement-enhanced quantum lock-in detection (QLID) method. By utilizing multi-body quantum entangled states (such as GHZ states) and optimized multi-pulse sequences, alternating signals can be extracted from noise through dynamic decoupling, which can significantly improve the measurement accuracy of alternating signal frequency and enhance robustness to rotation angle and detuning errors.

[0007] The above-mentioned objectives of the present invention can be achieved by the following technical means:

[0008] A quantum phase-locked detection method based on entanglement enhancement includes the following steps:

[0009] Step 1: During the center pulse time interval The pulse time interval of a periodic multipulse sequence is selected within the upper and lower fluctuation range. ;

[0010] Step 2: Encode the qubit in the ground state and excited state to prepare the qubit into an initialized quantum state;

[0011] Step 3: Apply a periodic multi-pulse sequence to the qubit;

[0012] Step 4: Load a carrier wave that resonates with the ground and excited states. The pulse is used to detect the final quantum state of the qubit and obtain the corresponding measurement density matrix.

[0013] Step 5: During the pulse time interval The pulse time interval traverses the upper and lower fluctuation range. Repeat steps 2-4 until all pulse time intervals have been traversed. The pulse time intervals of each component of the measurement density matrix as a function of a periodic multipulse sequence are obtained. A changing curve;

[0014] Step 6: Set a reference sinusoidal signal and use the Schrödinger equation to solve for the theoretical density matrix corresponding to the final quantum state after each repetition of steps 2 to 4;

[0015] Step 7: Compare the components of the measured density matrix and the theoretical density matrix with the pulse time interval of the periodic multipulse sequence. Do the changing curves overlap?

[0016] Step 8: If they coincide, then the half-cycle of the sine wave to be measured is... The center pulse time interval The amplitude of the reference sine wave is the amplitude of the sine wave to be measured;

[0017] If they cannot coincide, change the amplitude of the reference sinusoidal signal and recalculate the pulse time interval of each component of the theoretical density matrix with respect to the periodic multipulse sequence. The curve changes, and the process returns to step 7. If, after iterating through and changing the amplitude of all reference sinusoidal signals, they still cannot coincide, then the pulse time interval of the periodic multipulse sequence at the center of step 1 is changed. Then return to step 1.

[0018] As described above, the center pulse time interval The range of fluctuation is .

[0019] As described above, the quantum state is initialized as a maximally entangled state or a product state.

[0020] In the periodic multi-pulse sequence described above, each pulse represents the ground state of the qubit. and excited state resonant carrier pulse.

[0021] As described above, carrier Pulses can flip qubits between the ground state and the excited state.

[0022] As described above, carrier A pulse can flip a qubit from its ground state to a new state. , It is the ground state. It is an excited state.

[0023] carrier The loading of pulse and periodic multi-pulse sequences is based on the following steps:

[0024] An arbitrary waveform generator produces a radio frequency (RF) signal, which is then applied to an acousto-optic modulator. The acousto-optic modulator controls the frequency, intensity, and phase of the laser light passing through it by modulating the RF signal. The laser light then passes through an optical fiber and is incident on an ion trap, completing the carrier wave. Loading of pulse and periodic multi-pulse sequences.

[0025] As described above, the preparation of a quantum bit into an initialized quantum state includes the following steps: using a resonant laser between the ground state and the excited state, the quantum bit is prepared into an initialized quantum state by controlling the phase, intensity, and duration of the resonant laser.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] This invention has broad application potential in the field of quantum sensing, especially in scenarios requiring high-precision measurement of alternating signal frequencies. By optimizing the periodic multi-pulse sequence, measurement noise in the presence of rotation angle and detuning errors can be effectively suppressed, while maintaining high measurement accuracy even with these errors. This robustness makes it more reliable in practical applications. When using entangled states, the measurement accuracy of alternating signal frequencies approaches the Heisenberg limit, while when using superposition states, the measurement accuracy only approaches the standard quantum limit. This further demonstrates that entangled states have significant advantages in quantum sensing, significantly improving measurement accuracy. Future research could explore the entanglement enhancement effect in many-body quantum phase-locked detection and combine it with single-particle independent resolution detection technology to achieve even higher measurement accuracy. Attached Figure Description

[0028] Figure 1 for 40 Ca + Ion energy level diagram;

[0029] In Example 1, the qubits are encoded in |0>=|S 1 / 2 ,m=1 / 2> and |1>=|D 5 / 2 The above, where m=3 / 2, includes: a 397nm laser for laser cooling and quantum state detection; and an 866nm laser as a return pump to prevent ion states from falling into the D-phase. 3 / 2 Above; a 792nm laser is used to manipulate the transitions between |0> and |1> in the quantum bit encoding; an 854nm quenching light is used to pump the |1> state configuration to P. 3 / 2 It then spontaneously radiates back to its ground state;

[0030] Figure 2 This is a schematic diagram of the process of the present invention;

[0031] Figure 3 This is a schematic diagram illustrating the results of the present invention. The red line represents the measurement accuracy curve of the measured sinusoidal signal frequency when in the entangled state, and the blue line represents the measurement accuracy curve of the measured sinusoidal signal frequency when in the product state. The horizontal axis is... The vertical axis represents the measurement accuracy of the frequency of the sinusoidal signal under test, in Hz. The measurement accuracy with the initial state prepared as an entangled state reaches the Heisenberg limit, and the measurement accuracy with the initial state prepared as a product state reaches the standard quantum limit. This shows that the measurement uncertainty with the initial state prepared as an entangled state is less than that with the initial state prepared as a product state, indicating an improvement in measurement accuracy. The pulse time interval of a periodic multi-pulse sequence. This represents the half-cycle of the sine wave to be measured. Detailed Implementation

[0032] To facilitate understanding and implementation of the present invention by those skilled in the art, the present invention will be further described in detail below with reference to embodiments. It should be understood that the embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0033] Example 1:

[0034] A quantum phase-locked detection method based on entanglement enhancement, such as Figure 2 As shown, it includes the following steps:

[0035] Step 1: Select the pulse time interval of a periodic multi-pulse sequence as the center pulse time interval. During the central pulse time interval Select pulse time interval within the upper and lower fluctuation range ;

[0036] In some embodiments, the center pulse time interval The range of fluctuation is Within the range.

[0037] Step 2: Encode the qubits in two energy levels of the ion with relatively long coherence times, namely the ground state. and excited state Using the ground state and excited state By precisely controlling the phase, intensity, and duration of a resonant laser, qubits can be prepared into an initialized quantum state, which is then a maximally entangled state. (GHZ state, , The imaginary unit, , (representing the direct product or product state of two qubit states) ( ).

[0038] Figure 1 for 40 Ca +Ion level diagram, in this embodiment, using an ion trap (linear Porro trap) to trap two ion levels. 40 Ca + Ions, cooled by laser 40 Ca + Ions are dynamically cooled to their ground state and the qubits are encoded in 40 Ca + The ground state of an ion |0>=|S 1 / 2 ,m=1 / 2> and excited state |1>=|D 5 / 2 ,m=3 / 2>above, where, S 1 / 2 for 40 Ca + One energy level of an ion, D 5 / 2 for 40 Ca + Another energy level of the ion, m, is the magnetic quantum number of the Zeeman sublevel; the transition between these two energy levels has a relatively long coherence time, suitable for quantum information processing. The phase, intensity, and duration of the resonant laser are controlled by controlling the waveform output from the first channel of an arbitrary waveform generator (AWG, Keysight 33622A, two-channel), thereby achieving quantum state initialization of the qubit by the resonant laser. In this step, the initialized quantum state in this embodiment is the maximally entangled state (GHZ state). After completing the quantum state initialization operation, the first channel of the arbitrary waveform generator stops outputting signals.

[0039] Step 3: The first channel of the arbitrary waveform generator generates a periodic multi-pulse sequence, which is then applied to the qubit, i.e., added to the acousto-optic modulator controlling the laser. The acousto-optic modulator can control the frequency, intensity, and phase of the laser passing through it by controlling the applied radio frequency signal. The laser passing through the acousto-optic modulator is then incident on the ion trap through an optical fiber, completing the loading of the periodic multi-pulse sequence. In this periodic multi-pulse sequence, each pulse corresponds to the ground state of the qubit. and excited state resonant carrier Pulse, i.e., carrier wave Pulses can bring qubits to their ground state. and excited state Flip between (a carrier is applied in this step) Before the pulse, the qubits are prepared in an initialized quantum state. The pulse time interval of the periodic multi-pulse sequence is controlled. This is used to change the phase acquired by the qubit after being subjected to a periodic multi-pulse sequence, thereby achieving phase accumulation of the qubit.

[0040] Step 4: After the periodic multi-pulse sequence is loaded, the first channel of the arbitrary waveform generator is loaded with a pulse similar to the ground state. and excited state resonant carrier A pulse, which can bring a qubit from its ground state... Flip to The final quantum state of the qubit at this time is detected, and the measurement density matrix corresponding to the final quantum state is obtained.

[0041] Step 5: During the pulse time interval The pulse time interval traverses the upper and lower fluctuation range. Repeat steps 2-4 until the pulse time interval is reached. Iterate through all pulse time intervals within the upper and lower fluctuation range. ;

[0042] Each time interval of the periodic multi-pulse sequence is changed This yields a new measurement density matrix. The components of the measurement density matrix are then plotted as a function of the pulse time intervals of the periodic multipulse sequence. The changing curve yields the time interval of the central pulse. In the case of a sine wave (i.e., noise) coupled to ions, the measurement density matrix components are subjected to pulse time intervals as a periodic multipulse sequence. A changing curve.

[0043] carrier The loading of pulsed and periodic multi-pulse sequences is based on the following steps: an radio frequency (RF) signal is generated by an arbitrary waveform generator and applied to an acousto-optic modulator controlling the laser. The acousto-optic modulator can control the frequency, intensity, and phase of the laser passing through it by modulating the applied RF signal. The laser, after passing through the acousto-optic modulator, is then incident on an ion trap via an optical fiber, completing the carrier wave. Loading of pulse and periodic multi-pulse sequences.

[0044] Step 6: Perform theoretical calculations based on the center pulse time interval of the periodic multi-pulse sequence selected in Step 1. And the amplitude calculation of the theoretical density matrix of the set reference sinusoidal signal, with each component varying with the pulse time interval of the periodic multipulse sequence. A changing curve.

[0045] The calculation method is as follows: A reference sinusoidal signal is set, and the Schrödinger equation is used to solve for the theoretical density matrix corresponding to the final quantum state after each repetition of steps 2 to 4. The initial state is set to the GHZ state, i.e., the maximally entangled state explained in step 1, with the Hamiltonian... for:

[0046] ;

[0047] in, To reference the angular frequency of the sinusoidal signal, The gyromagnetic ratio of electrons. For time, To reference the phase of the sinusoidal signal, it is generally set to 0. , The half-cycle of the sinusoidal signal to be measured As a reference, the effective value of the sinusoidal signal coupled to the qubit, This represents the coupling strength between the laser (a time-varying laser) and ions corresponding to a periodic multi-pulse sequence, used to describe the interaction strength between the periodic multi-pulse sequence and the qubit. For the overall Pauli z operator, i.e. , , It is the identity matrix. , For the overall Pauli Operator, i.e. , , It is the identity matrix. .

[0048] The frequency of the reference sine signal is obtained. and amplitude measurement accuracy :

[0049]

[0050]

[0051] in, The angular frequency of the pulse time interval in a periodic multi-pulse sequence. , The total evolution time, In this embodiment, the number of qubits is... .

[0052] The components of the theoretical density matrix generated on the qubit by the operations described in steps 2 to 4, with varying pulse time intervals, represent the amplitudes of different reference sinusoidal signals. The theoretical curves for the changes are different. Center pulse time. The purpose is to make half-cycle The sinusoidal signal is extracted from the noisy environment; that is, steps 2 to 4 enhance the half-cycle. The effect of sinusoidal signals on qubits.

[0053] Step 7: Assign each component of the measurement density matrix from Step 5 to the pulse time interval of the periodic multipulse sequence. The changing curves and the components of the theoretical density matrix in step 6 change with the pulse time interval of the periodic multipulse sequence. Compare the changing curves to see if they overlap.

[0054] Step 8: If they coincide, then the half-cycle of the sine wave to be measured is... That is, the center pulse time interval The amplitude of the reference sine wave is the amplitude of the sine wave to be measured.

[0055] If they cannot coincide, change the amplitude of the reference sinusoidal signal in step 6 and recalculate the pulse time interval of each component of the theoretical density matrix with respect to the periodic multipulse sequence. The curve changes, and the process returns to step 7. If, after iterating through and changing the amplitude of all reference sinusoidal signals, they still cannot coincide, then the pulse time interval of the periodic multipulse sequence at the center of step 1 is changed. Then return to step 1.

[0056] Coincidence refers to the phenomenon where the components of the theoretical density matrix vary with the pulse time interval of a periodic multipulse sequence. The changing curves all fall within the measurement density matrix corresponding to the pulse time interval of the periodic multipulse sequence. The error range of the points on the changing curve is within the range of the bar. Once they coincide, the amplitude of the reference sinusoidal signal is considered to be the amplitude of the sinusoidal signal actually coupled to the quantum bit extracted in the noisy environment, representing half a period of the sinusoidal signal. That is, the pulse time interval of a central periodic multipulse sequence. In this way, the amplitude of the sinusoidal signal coupled to the qubit is obtained, and the frequency of the sinusoidal signal in the noisy environment is extracted through a periodic multi-pulse sequence. Therefore, it can be considered that quantum lock-in detection (QLID) has been completed and the required sinusoidal signal has been measured.

[0057] Example 2:

[0058] Verification experiment:

[0059] The second channel of the arbitrary waveform generator is activated to generate a 10kHz loading sine wave signal. This signal is then amplified approximately 30 times by an RF power amplifier (OPA549 module) and input to the compensation electrode of the ion trap. The electromagnetic wave signal emitted by the compensation electrode of the ion trap interacts with... 40 Ca + Ions are coupled to generate an equivalent loading sinusoidal signal on the qubit. Following steps 1-8 of Example 1, it can be observed that the matched reference sinusoidal signal and the loading sinusoidal signal are identical, and the measurement accuracy meets the amplitude measurement accuracy requirements. See attached Figure 3This indicates that quantum phase-locked detection has been completed, and the measurement accuracy has reached the Heisenberg limit.

[0060] The initial quantum state initialized in step 1 as a maximally entangled state is adjusted to prepare the initial state into a non-entangled state (such as a product state). Repeat steps 1-5 of step 1 to verify whether the measurement accuracy is close to the standard quantum limit. Compare with the case where the initial state is prepared as a maximally entangled state to verify whether preparing the maximally entangled state improves the measurement accuracy.

[0061] It should be noted that the embodiments described in this invention are merely illustrative of the spirit of the invention. Those skilled in the art to which this invention pertains can make various modifications or additions to the described embodiments or use similar methods to substitute them, without departing from the spirit of the invention or exceeding the scope defined by the appended claims.

Claims

1. A quantum phase-locked detection method based on entanglement enhancement, characterized in that, Includes the following steps: Step 1: During the center pulse time interval The pulse time interval of a periodic multipulse sequence is selected within the upper and lower fluctuation range. ; Step 2: Encode the qubit in the ground state and excited state to prepare the qubit into an initialized quantum state; Step 3: Apply a periodic multi-pulse sequence to the qubit; Step 4: Load a carrier wave that resonates with the ground and excited states. The pulse is used to detect the final quantum state of the qubit and obtain the corresponding measurement density matrix. Step 5: During the pulse time interval The pulse time interval traverses the upper and lower fluctuation range. Repeat steps 2-4 until all pulse time intervals have been traversed. The pulse time intervals of each component of the measurement density matrix as a function of a periodic multipulse sequence are obtained. A changing curve; Step 6: Set a reference sinusoidal signal and use the Schrödinger equation to solve for the theoretical density matrix corresponding to the final quantum state after each repetition of steps 2 to 4; Step 7: Compare the components of the measured density matrix and the theoretical density matrix with the pulse time interval of the periodic multipulse sequence. Do the changing curves overlap? Step 8: If they coincide, then the half-cycle of the sine wave to be measured is... The center pulse time interval The amplitude of the reference sine wave is the amplitude of the sine wave to be measured; If they cannot coincide, change the amplitude of the reference sinusoidal signal and recalculate the pulse time interval of each component of the theoretical density matrix with respect to the periodic multipulse sequence. The curve changes, and the process returns to step 7. If, after iterating through and changing the amplitude of all reference sinusoidal signals, they still cannot coincide, then the pulse time interval of the periodic multipulse sequence at the center of step 1 is changed. Then return to step 1.

2. The quantum phase-locked detection method based on entanglement enhancement according to claim 1, characterized in that, The center pulse time interval The range of fluctuation is .

3. The quantum phase-locked detection method based on entanglement enhancement according to claim 1, characterized in that, The initial quantum state is either a maximally entangled state or a product state.

4. The quantum phase-locked detection method based on entanglement enhancement according to claim 1, characterized in that, In the periodic multi-pulse sequence, each pulse represents the ground state of the qubit. and excited state resonant carrier pulse.

5. The quantum phase-locked detection method based on entanglement enhancement according to claim 4, characterized in that, The carrier Pulses flip qubits between the ground state and the excited state.

6. The quantum phase-locked detection method based on entanglement enhancement according to claim 1, characterized in that, The carrier The pulse flips the qubit from its ground state to its final state. , It is the ground state. It is an excited state.

7. The quantum phase-locked detection method based on entanglement enhancement according to claim 1, characterized in that, carrier The loading of pulse and periodic multi-pulse sequences is based on the following steps: An arbitrary waveform generator produces a radio frequency (RF) signal, which is then applied to an acousto-optic modulator. The acousto-optic modulator controls the frequency, intensity, and phase of the laser light passing through it by modulating the RF signal. The laser light then passes through an optical fiber and is incident on an ion trap, completing the carrier wave. Loading of pulse and periodic multi-pulse sequences.

8. The quantum phase-locked detection method based on entanglement enhancement according to claim 1, characterized in that, The preparation of the qubit into an initialized quantum state includes the following steps: using a resonant laser between the ground state and the excited state, the qubit is prepared into an initialized quantum state by controlling the phase, intensity, and duration of the resonant laser.

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