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Hardware-Efficient Quantum Phase Estimation via Local Control

Benjamin F. Schiffer1,2,*, Dominik S. Wild1,2, Nishad Maskara3, Mikhail D. Lukin3, and J. Ignacio Cirac1,2

  • *Contact author: benjamin.schiffer@mpq.mpg.de
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PRX Quantum 6, 040348 – Published 1 December, 2025

DOI: https://doi.org/10.1103/zlp8-rz9n

Abstract

Quantum phase estimation plays a central role in quantum simulation as it enables the study of spectral properties of many-body quantum systems. Most variants of the phase estimation algorithm require the application of the global unitary evolution conditioned on the state of one or more auxiliary qubits, posing a significant challenge for current quantum devices. In this work, we present an approach to quantum phase estimation that uses only locally controlled operations, resulting in a significantly reduced circuit depth. At the heart of our approach are efficient routines to measure the complex phase of the expectation value of the time-evolution operator, the so-called Loschmidt echo, for both circuit dynamics and Hamiltonian dynamics. By tracking changes in the phase during the dynamics, the routines trade circuit depth for increased sampling cost and classical postprocessing. Our approach does not rely on reference states and is applicable to any efficiently preparable state, regardless of its correlations. We provide a comprehensive analysis of the sample complexity and illustrate the results with numerical simulations. Our methods offer a practical pathway for measuring spectral properties in large many-body quantum systems using current quantum devices.

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Popular Summary

Quantum phase estimation is a cornerstone algorithm in quantum computing, allowing us to find the spectral fingerprints of quantum systems with applications in quantum chemistry, materials science, and beyond. However, implementing quantum phase estimation requires very deep circuits, which is a challenging demand for today’s quantum devices, which are still prone to errors.

We introduce a family of phase-estimation techniques that avoid deep quantum circuits. The approach relies on the time series of the complex expectation value of the time-evolution operator, also referred to as the “Loschmidt echo.” To obtain the necessary phase information, our methods track how the Loschmidt echo’s phase changes over time—we show that this information can be obtained without global control operations. This enables phase estimation with a (near-)optimal circuit depth.

We present three complementary methods: a digital method is suitable for arbitrary circuit dynamics, while a second method and a third method can also be executed on hardware platforms that implement both analog time evolution and gate operations. All our techniques trade circuit depth for increased sampling cost and classical postprocessing. We rigorously analyze the sample complexity and include a numerical case study. Our simulations indicate robustness of phase extraction with realistic noise parameters.

Looking ahead, deploying these hardware-efficient protocols opens a practical route to realize spectroscopy on current quantum hardware for large quantum many-body models, with exciting applications for probing systems at criticality and strongly correlated quantum matter.

Article Text

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PRX Quantum 6, 040348– Published 1 December, 2025
  • Received 27 June 2025
  • Revised 22 September 2025
  • Accepted 15 October 2025
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