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arXiv:2602.19556 · Physics Letters A

Deterministic Ground State Preparation via Power-Cosine Filtering of Time Evolution Operators

Jeongbin Jo

quant-phSubmitted Feb 23, 2026• Announced Feb 24, 2026• 0 citations• Revised May 20, 2026 (v2)
v1 · Feb 23, 2026v2 · May 20, 2026
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Abstract

The deterministic preparation of quantum many-body ground states is essential for advanced quantum simulation, yet optimal algorithms often require prohibitive hardware resources. Here, we propose a highly efficient, non-variational protocol for ground state preparation using a Power-Cosine quantum signal processing (QSP) filter. By eschewing complex block-encoding techniques, our method directly utilizes coherent time-evolution operators controlled by a single ancillary qubit. The integration of mid-circuit measurement and reset (MCMR) drastically minimizes spatial overhead, translating iterative non-unitary filtering into deep temporal coherence. We analytically demonstrate that this approach achieves exponential suppression of excited states with a circuit depth scaling of $\mathcal{O}(Δ^{-2}\log(1/ε))$, where $Δ$ denotes the spectral gap, prioritizing implementational simplicity over optimal asymptotic complexity. Numerical simulations on the 1D Heisenberg XYZ model validate the theoretical soundness and shot-noise resilience of our method. Furthermore, an advantage analysis reveals that our protocol exponentially outperforms standard Trotterized Adiabatic State Preparation (TASP) at equivalent circuit depths. This single-ancilla framework provides a highly practical and deterministic pathway for many-body ground state preparation on Early Fault-Tolerant (EFT) quantum architectures.

Journal reference
Physics Letters A (2026)
DOI
10.1016/j.physleta.2026.131813
Comments
Accepted for publication in Physics Letters A

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The deterministic preparation of quantum many-body ground states is essential for advanced quantum simulation, yet optimal algorithms often require prohibitive hardware resources. Here, we propose a highly efficient, non-variational protocol for ground state preparation using a Power-Cosine quantum signal processing (QSP) filter. By eschewing complex block-encoding techniques, our method directly utilizes coherent time-evolution operators controlled by a single ancillary qubit. The integration of mid-circuit measurement and reset (MCMR) drastically minimizes spatial overhead, translating iterative non-unitary filtering into deep temporal coherence. We analytically demonstrate that this approach achieves exponential suppression of excited states with a circuit depth scaling of O(Δ−2log⁡(1/ε))\mathcal{O}(Δ^{-2}\log(1/ε))O(Δ−2log(1/ε)), where ΔΔΔ denotes the spectral gap, prioritizing implementational simplicity over optimal asymptotic complexity. Numerical simulations on the 1D Heisenberg XYZ model validate the theoretical soundness and shot-noise resilience of our method. Furthermore, an advantage analysis reveals that our protocol exponentially outperforms standard Trotterized Adiabatic State Preparation (TASP) at equivalent circuit depths. This single-ancilla framework provides a highly practical and deterministic pathway for many-body ground state preparation on Early Fault-Tolerant (EFT) quantum architectures.
Despite rapid advances in quantum hardware, noise remains a central obstacle to deploying quantum algorithms on near-term devices. In particular, random coherent errors that accumulate during circuit execution constitute a dominant and fundamentally challenging noise source. We introduce a noise-resilient framework for Quantum Signal Processing (QSP) that mitigates such coherent errors without increasing circuit depth or ancillary qubit requirements. Our approach uses ensembles of noisy QSP circuits combined with measurement-level averaging to suppress random phase errors in Z rotations. Building on this framework, we develop robust QSP algorithms for implementing polynomial functions of Hermitian matrices and for estimating observables, with applications to Hamiltonian simulation, quantum linear systems, and ground-state preparation. We analyze the trade-off between approximation error and hardware noise, which is essential for practical implementation under the stringent depth and coherence constraints of current quantum hardware. Our results establish a practical pathway for integrating error mitigation seamlessly into algorithmic design, advancing the development of robust quantum computing, and enabling the discovery of scientific applications with near- and mid-term quantum devices.
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Efficient low-energy state preparation is a key objective in quantum computation and quantum simulation. Quantum imaginary-time evolution replaces real-time dynamics with imaginary-time dynamics, exponentially suppressing higher-energy eigenstates. We introduce deterministic unitary protocols that approximate imaginary-time evolution for ground state preparation. The protocols require multiple copies of the system, real-time evolution under the system Hamiltonian, and controlled-SWAP operations (or more general SWAP-generated unitaries). Our analysis focuses on two concrete circuit families: a tree architecture with provable polynomial-in-depth convergence but rapidly growing width, and a compact "hedge" architecture that achieves comparable accuracy with only polynomial width in a heuristic construction supported by numerics. Numerical evidence indicates that mid-circuit post-selection can accelerate convergence with practical success probabilities. Separately, we demonstrate that circuit volume can be traded for the shot complexity of post-circuit observable estimation in the ground state preparation setting. Finally, we outline concrete platform-specific implementations in which multi-copy registers and SWAP-mediated couplings are natural, illustrating how these hybrid analog-digital circuits can complement existing state-preparation methods in the near term.
Preparation and verification of specific quantum states is an important capability for quantum devices to realise advantages over classical computations and algorithms. In this work, we have demonstrated an end-to-end framework that combines resource-efficient quantum state preparation with rapid, robust fidelity verification on near-term quantum hardware. By experimentally preparing and validating a structured complex quantum state encoding a digitized acoustic signal on the Quantinuum H2-1 trapped-ion platform, we achieved a high hardware fidelity of Fhw=0.929F_{\mathrm{hw}} = 0.929Fhw​=0.929. Crucially, this milestone was realized without relying on idealized assumptions or deep fault-tolerant overhead, but rather through resource-minimal circuits optimized for NISQ-era and early fault-tolerant devices. Furthermore, we addressed a key limitation in current quantum state certification. While validation methods like shadow overlap work well for random states, their sample complexity can become prohibitively high for the structured states used in practical algorithms. We mitigate this by introducing a pre-measurement basis-change technique that reduces the verification parameter, τττ, by over 10 orders of magnitude for structured targets. This approach tightens the theoretical certification guarantees of the shadow overlap method and integrates tensor-network preparation and shadow validation into a unified workflow. These results shift the paradigm of how structured classical data can be mapped to and verified on quantum hardware under realistic noise and measurement budgets. By compressing a robust verification procedure to just 1,000 measurement shots, this framework offers an immediate, scalable benchmarking standard.
The preparation of the ground state of a Hamiltonian HHH with a large spectral radius has applications in many areas such as electronic structure theory and quantum field theory. Given an initial state with a constant overlap with the ground state, and assuming that the Hamiltonian HHH can be efficiently simulated with an ideal fast-forwarding protocol, we first demonstrate that employing a linear combination of unitaries (LCU) approach can prepare the ground state at a cost of O(log⁡2(∥H∥Δ−1))\mathcal{O}(\log^2(\|H\| Δ^{-1}))O(log2(∥H∥Δ−1)) queries to controlled Hamiltonian evolution. Here ∥H∥\|H\|∥H∥ is the spectral radius of HHH and ΔΔΔ the spectral gap. However, traditional Quantum Signal Processing (QSP)-based methods fail to capitalize on this efficient protocol, and its cost scales as O(∥H∥Δ−1)\mathcal{O}(\|H\| Δ^{-1})O(∥H∥Δ−1). To bridge this gap, we develop a multi-level QSP-based algorithm that exploits the fast-forwarding feature. This novel algorithm not only matches the efficiency of the LCU approach when an ideal fast-forwarding protocol is available, but also exceeds it with a reduced cost that scales as O(log⁡(∥H∥Δ−1))\mathcal{O}(\log(\|H\| Δ^{-1}))O(log(∥H∥Δ−1)). Additionally, our multi-level QSP method requires only O(log⁡(∥H∥Δ−1))\mathcal{O}(\log(\|H\| Δ^{-1}))O(log(∥H∥Δ−1)) coefficients for implementing single qubit rotations. This eliminates the need for constructing the PREPARE oracle in LCU, which prepares a state encoding O(∥H∥Δ−1)\mathcal{O}(\|H\| Δ^{-1})O(∥H∥Δ−1) coefficients regardless of whether the Hamiltonian can be fast-forwarded.
We introduce a quantum algorithm to efficiently prepare states with a small energy variance at the target energy. We achieve it by filtering a product state at the given energy with a Lorentzian filter of width δ . Given a local Hamiltonian on N qubits, we construct a parent Hamiltonian whose ground state corresponds to the filtered product state with variable energy variance proportional to δN . We prove that the parent Hamiltonian is gapped and its ground state can be efficiently implemented in poly(N,1/δ) time via adiabatic evolution. We numerically benchmark the algorithm for a particular non-integrable model and find that the adiabatic evolution time to prepare the filtered state with a width δ is independent of the system size N . Furthermore, the adiabatic evolution can be implemented with circuit depth O(N2δ−4) . Our algorithm provides a way to study the finite energy regime of many body systems in quantum simulators by directly preparing a finite energy state, providing access to an approximation of the microcanonical properties at an arbitrary energy.