Standard Quantum Phase Estimation Detects All Eigenvalues via Randomized Initial States

• URL: http://arxiv.org/abs/2604.00475v1
• Date: Wed, 01 Apr 2026 04:38:41 GMT
• Title: Standard Quantum Phase Estimation Detects All Eigenvalues via Randomized Initial States
• Abstract summary: The output distribution of standard QPE can be written as a superposition of Fejér kernels weighted by the squared overlaps with the eigenmodes.<n>We establish a rigorous peak-detection theory and derive a sufficient shot-count estimate for detecting all peaks.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Standard quantum phase estimation (QPE) has often been regarded as unsuitable for simultaneous detection of all eigenvalues, because it requires initial states with sufficient overlap with the target eigenstates. In this paper, we show that this limitation is not inherent to the QPE circuit itself. The output distribution of standard QPE can be written as a superposition of Fejér kernels weighted by the squared overlaps with the eigenmodes. We prove that, if the initial state is independently drawn at each shot from a 1-design (in particular, by random selection of computational basis states), these mode weights are equalized in expectation, yielding a state-averaged QPE distribution that exhibits peaks at every eigenphase location. In this sense, all eigenvalues become accessible without any modification of the standard QPE circuit; repeated eigenvalues appear through the aggregated weight of their eigenspaces. For distinct eigenphases satisfying a separation condition, we further establish a rigorous peak-detection theory and derive a sufficient shot-count estimate for detecting all peaks. We validate the theory through numerical experiments on a finite element method (FEM) matrix with 1,008 degrees of freedom arising from computer-aided engineering (CAE).

Related papers

• Effects of Trotter Error, Digitization Error, and Initial State Overlap on Tapered Quantum Phase Estimation for Minimum Eigenvalue Computation [3.953304476953445]
  We numerically implement full quantum circuits of optimal tapered Quantum Phase Estimation.<n>We show how tapered QPE performs with respect to optimal phase sampling rate, absolute error, Shannon entropy, when the tQPE algorithm parameters are changed.
  arXiv  Detail & Related papers  (2026-09-05T20:25:20Z)
• Eigenstate Preparation Through Near-Optimal Eigenprobability Filtering [3.2651468573861524]
  We introduce the Dominant Eigenstate Filtering via Eigenprobability Amplification and Thresholding (DEFEAT) algorithm.<n>DEFEAT identifies and filters the eigenstate with the largest overlap with the supplied initial state.<n>Our results provide a general eigenvalue-agnostic primitive for dominant eigenstate filtering and preparation, and for estimating properties of dominant eigenstates.
  arXiv  Detail & Related papers  (2026-08-12T17:39:15Z)
• Robust CHSH Self-Testing with Finite-Energy GKP States [42.71287663143178]
  We present a full-oscillator analysis of a finite-energy GKP CHSH test.<n>The observed score yields robust Bell-pair self-testing.
  arXiv  Detail & Related papers  (2026-08-11T16:33:28Z)
• Adiabatic Quantum Phase Estimation [47.3103723337301]
  Quantum phase estimation (QPE) is a central algorithmic primitive that estimates eigenvalues of a Hamiltonian up to precision $$ in Heisenberg-limited time $T= (1/)$.<n>Standard gate-based implementations of QPE require deep controlled time-evolution circuits and are not native to analog hardware.<n>We present a simple adiabatic protocol for QPE that achieves the optimal Heisenberg-limited scaling $T = Oleft( frac1 logleft(-1right)right)$ in both the precision $$
  arXiv  Detail & Related papers  (2026-05-21T17:31:36Z)
• Operational interpretation of the reverse sandwiched Renyi divergences in composite quantum hypothesis testing [40.82628972269358]
  We study the Hoeffding regime of composite quantum hypothesis testing, in which each hypothesis is specified by a sequence of sets of quantum states.<n>We find that passing from simple to composite hypotheses can fundamentally change which quantum divergence determines the operational limits of discrimination.
  arXiv  Detail & Related papers  (2026-05-04T04:02:55Z)
• Filtered Spectral Projection for Quantum Principal Component Analysis [1.2318267573115809]
  Filtered Spectral Projection Algorithm (FSPA)<n>For amplitude-encoded centered data, the ensemble density matrix $=sum_i p_i|_iranglelangle_i|$ coincides with the covariance matrix.<n>For uncentered data, $$ corresponds to PCA without centering, and we derive eigenvalue interlacing bounds quantifying the deviation from standard PCA.
  arXiv  Detail & Related papers  (2026-03-13T11:55:39Z)
• Fisher information based lower bounds on the cost of quantum phase estimation [0.0]
  Quantum phase estimation (QPE) is a cornerstone of quantum algorithms designed to estimate the eigenvalues of a unitary operator.<n>Existing performance assessments fail to separate the statistical information inherent in the quantum circuit from the efficiency of classical post-processing.<n>We employ Fisher information and the Cramer-Rao lower bound to formulate the performance limits of circuit designs.
  arXiv  Detail & Related papers  (2026-03-13T06:40:12Z)
• Eigenstate thermalization in thermal first-order phase transitions [39.146761527401424]
  The eigenstate thermalization hypothesis (ETH) posits how isolated quantum many-body systems thermalize.<n>We show that it requires generalization in the presence of thermal first-order phase transitions.
  arXiv  Detail & Related papers  (2026-01-13T09:07:46Z)
• Uniformity Bias in Ground-State Sampling Induced by Replica Alignment in Quantum Monte Carlo for Quantum Annealing [0.688204255655161]
  Quantum Monte Carlo (QMC) is widely used to simulate quantum systems.<n>We show that QMC produces uniform ground-state probabilities, unlike QA's biased distribution.<n>This bias originates from replica alignment, caused by the energetic suppression and entropic reduction of kink configurations.
  arXiv  Detail & Related papers  (2025-10-12T12:23:12Z)
• Quantum Sequential Universal Hypothesis Testing [62.751483592497806]
  Quantum hypothesis testing (QHT) concerns the statistical inference of unknown quantum states.<n>We introduce the quantum sequential universal test (QSUT), a novel framework for sequential QHT in the general case of composite hypotheses.<n> QSUT builds on universal inference, and it alternates between adaptive local measurements aimed at exploring the hypothesis space and joint measurements optimized for maximal discrimination.
  arXiv  Detail & Related papers  (2025-08-29T12:50:04Z)
• Channel-based framework for phase esimation of multiple eigenvalues [2.3814052021083354]
  We develop a theoretical framework based on sequential quantum channels for iterative QPE. We find that QPE of multiple eigenvalues can be efficiently realized for arbitrary initial target system state.
  arXiv  Detail & Related papers  (2023-08-04T13:18:21Z)
• Quantum State Tomography for Matrix Product Density Operators [28.799576051288888]
  Reconstruction of quantum states from experimental measurements is crucial for the verification and benchmarking of quantum devices. Many physical quantum states, such as states generated by noisy, intermediate-scale quantum computers, are usually structured. We establish theoretical guarantees for the stable recovery of MPOs using tools from compressive sensing and the theory of empirical processes.
  arXiv  Detail & Related papers  (2023-06-15T18:23:55Z)
• Statistical Approach to Quantum Phase Estimation [62.92678804023415]
  We introduce a new statistical and variational approach to the phase estimation algorithm (PEA) Unlike the traditional and iterative PEAs which return only an eigenphase estimate, the proposed method can determine any unknown eigenstate-eigenphase pair. We show the simulation results of the method with the Qiskit package on the IBM Q platform and on a local computer.
  arXiv  Detail & Related papers  (2021-04-21T00:02:00Z)
• Generalized Measure of Quantum Fisher Information [0.0]
  We present a lower bound on the quantum Fisher information (QFI) which is efficiently computable on near-term quantum devices. We show that it satisfies the canonical criteria of a QFI measure.
  arXiv  Detail & Related papers  (2020-10-06T17:36:30Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.