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Physical Review Letters

Ultrahigh-Precision Hamiltonian Parameter Estimation in a Superconducting Circuit

Sai Li, De-Jian Pan, Yuan-Ke Zhu, Jia-Lang Zhou, Wen-Cui Liao, Wei-Xin Zhang, Zhen-Tao Liang, Qing-Xian Lv, Haifeng Yu, Zheng‐Yuan Xue, Hui Yan, Shi-Liang Zhu

Published Jun 18, 2024• 7 citations
Publisher

Abstract

The Hamiltonian, which determines the evolution of a quantum system, is fundamental in quantum physics. Therefore, it is crucial to implement high-precision generation and measurement of the Hamiltonian in a practical quantum system. Here, we experimentally demonstrate ultrahigh-precision Hamiltonian parameter estimation with a significant quantum advantage in a superconducting circuit via sequential control. We first observe the commutation relation for noncommuting operations determined by the system Hamiltonian, both with and without adding quantum control, verifying the commuting property of controlled noncommuting operations. Based on this control-induced commuting property, we further demonstrate Hamiltonian parameter estimation for polar and azimuth angles in superconducting circuits, achieving ultrahigh metrological gains in measurement precision exceeding the standard quantum limit by up to 16.0 and 16.1 dB at N=100, respectively.

DOI
10.1103/physrevlett.132.250204

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The Hamiltonian, which determines the evolution of a quantum system, is fundamental in quantum physics. Therefore, it is crucial to implement high-precision generation and measurement of the Hamiltonian in a practical quantum system. Here, we experimentally demonstrate ultrahigh-precision Hamiltonian parameter estimation with a significant quantum advantage in a superconducting circuit via sequential control. We first observe the commutation relation for noncommuting operations determined by the system Hamiltonian, both with and without adding quantum control, verifying the commuting property of controlled noncommuting operations. Based on this control-induced commuting property, we further demonstrate Hamiltonian parameter estimation for polar and azimuth angles in superconducting circuits, achieving ultrahigh metrological gains in measurement precision exceeding the standard quantum limit by up to 16.0 and 16.1 dB at N=100, respectively.
The advantage of quantum metrology has been experimentally demonstrated for phase estimations where the dynamics are commuting. General noncommuting dynamics, however, can have distinct features. For example, the direct sequential scheme, which can achieve the Heisenberg scaling for the phase estimation under commuting dynamics, can have even worse performances than the classical scheme when the dynamics are noncommuting. Here we realize a scalable optimally controlled sequential scheme, which can achieve the Heisenberg precision under general noncommuting dynamics. We also present an intuitive geometrical framework for the controlled scheme and identify sweet spots in time at which the optimal controls used in the scheme can be prefixed without adaptation, which simplifies the experimental protocols significantly. We successfully implement the scheme up to eight controls in an optical platform and demonstrate a precision near the Heisenberg limit. Our work opens the avenue for harvesting the power of quantum control in quantum metrology, and provides a control-enhanced recipe to achieve the Heisenberg precision under general noncommuting dynamics.
Precision measurements of frequency are critical to accurate time keeping and are fundamentally limited by quantum measurement uncertainties. While for time-independent quantum Hamiltonians the uncertainty of any parameter scales at best as 1/T, where T is the duration of the experiment, recent theoretical works have predicted that explicitly time-dependent Hamiltonians can yield a 1/T^{2} scaling of the uncertainty for an oscillation frequency. This quantum acceleration in precision requires coherent control, which is generally adaptive. We experimentally realize this quantum improvement in frequency sensitivity with superconducting circuits, using a single transmon qubit. With optimal control pulses, the theoretically ideal frequency precision scaling is reached for times shorter than the decoherence time. This result demonstrates a fundamental quantum advantage for frequency estimation.
Quantum metrology has emerged as a powerful tool for timekeeping, field sensing, and precision measurements in fundamental physics. With the advent of distributed quantum metrology, its capabilities have extended to probing spatially distributed parameters across networked quantum systems. However, scalable implementations of distributed quantum metrology with multiparameter estimation remain limited, particularly due to the challenges of generating and distributing entanglement across a quantum network and dealing with incompatibilities in multiparameter quantum metrology. Here we demonstrate distributed multiparameter quantum metrology on a modular superconducting quantum network with low-loss microwave interconnects, a platform that uniquely combines fast gate operations, adaptive control, and deterministic non-local entanglement generation. Using a control-enhanced sequential protocol, we estimate all three components of a remote vector field, achieving up to 13.72 dB improvement in precision over the individual strategy. We further perform direct estimation of vector field gradients along two directions across spatially separated nodes, realizing a 3.44 dB gain over local entanglement strategies. These results establish superconducting quantum networks as a competitive and reconfigurable platform for scalable multiparameter distributed quantum metrology.
The ability to characterise a Hamiltonian with high precision is crucial for the implementation of quantum technologies. In addition to the well-developed approaches utilising optimal probe states and optimal measurements, the method of optimal control can be used to identify time-dependent pulses applied to the system to achieve higher precision in the estimation of Hamiltonian parameters, especially in the presence of noise. Here, we extend optimally controlled estimation schemes for single qubits to non-commuting dynamics as well as two interacting qubits, demonstrating improvements in terms of maximal precision, time-stability, as well as robustness over uncontrolled protocols.
Abstract Two-mode interferometers lay the foundations for quantum metrology. Instead of exploring quantum entanglement in the two-mode interferometers, a single bosonic mode also promises a measurement precision beyond the shot-noise limit (SNL) by taking advantage of the infinite-dimensional Hilbert space of Fock states. Here, we demonstrate a single-mode phase estimation that approaches the Heisenberg limit (HL) unconditionally. Due to the strong dispersive nonlinearity and long coherence time of a microwave cavity, quantum states of the form (∣0⟩+∣N⟩)/2\left( {\left| 0 \right\rangle + \left| N \right\rangle } \right)/\sqrt 2(∣0⟩+∣N⟩)/2​ 0 + N ∕ 2 can be generated, manipulated and detected with high fidelities, leading to an experimental phase estimation precision scaling as ∼N−0.94. A 9.1 dB enhancement of the precision over the SNL at N = 12 is achieved, which is only 1.7 dB away from the HL. Our experimental architecture is hardware efficient and can be combined with quantum error correction techniques to fight against decoherence, and thus promises quantum-enhanced sensing in practical applications.
Abstract Two-mode interferometers lay the foundations for quantum metrology. Instead of exploring quantum entanglement in the two-mode interferometers, a single bosonic mode also promises a measurement precision beyond the shot-noise limit (SNL) by taking advantage of the infinite-dimensional Hilbert space of Fock states. Here, we demonstrate a single-mode phase estimation that approaches the Heisenberg limit (HL) unconditionally. Due to the strong dispersive nonlinearity and long coherence time of a microwave cavity, quantum states of the form (∣0⟩+∣N⟩)/2\left( {\left| 0 \right\rangle + \left| N \right\rangle } \right)/\sqrt 2(∣0⟩+∣N⟩)/2​ 0 + N ∕ 2 can be generated, manipulated and detected with high fidelities, leading to an experimental phase estimation precision scaling as ∼ N −0.94 . A 9.1 dB enhancement of the precision over the SNL at N = 12 is achieved, which is only 1.7 dB away from the HL. Our experimental architecture is hardware efficient and can be combined with quantum error correction techniques to fight against decoherence, and thus promises quantum-enhanced sensing in practical applications.