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arxiv: 2602.19556 · v2 · pith:KFQESD42new · submitted 2026-02-23 · 🪐 quant-ph

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

Jeongbin Jo This is my paper

Pith reviewed 2026-05-21 13:05 UTC · model grok-4.3

classification 🪐 quant-ph
keywords ground state preparationquantum signal processingmid-circuit measurementtime evolutionquantum simulationfault-tolerant quantum computingspectral filteringdeterministic quantum algorithms
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The pith

A power-cosine filter on controlled time evolution prepares many-body ground states with circuit depth O(Δ^{-2} log(1/ε)).

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes a non-variational method to prepare the ground state of a quantum system by applying a power-cosine filter to its time-evolution operator. The filter is implemented using a single ancillary qubit and coherent mid-circuit measurements and resets, which convert the filtering into a deep sequence of unitary operations. This achieves exponential damping of excited states, with the total circuit depth scaling as O(Δ^{-2} log(1/ε)) where Δ is the energy gap to the first excited state. A reader would care because the approach avoids the qubit overhead of block-encoding methods and offers a deterministic alternative to variational or adiabatic techniques that is suitable for early fault-tolerant hardware.

Core claim

We introduce a deterministic protocol for ground state preparation that applies a Power-Cosine quantum signal processing filter directly to the controlled time-evolution operator using a single ancillary qubit. Integration of mid-circuit measurement and reset operations translates the non-unitary filtering into a sequence of coherent operations with minimal spatial resources. Analytical analysis shows exponential suppression of excited states with a circuit depth that scales as O(Δ^{-2} log(1/ε)). Numerical simulations on the 1D Heisenberg XYZ model confirm the method's performance and its advantage over Trotterized adiabatic state preparation at equal depths.

What carries the argument

The Power-Cosine QSP filter, which uses a polynomial approximation to a function that is near unity on the ground state energy and near zero on excited energies, applied via controlled time evolutions to suppress excited states.

If this is right

  • The protocol uses only one ancillary qubit for any system size.
  • Mid-circuit resets allow converting spatial resources into circuit depth.
  • The method is deterministic and does not require optimization of parameters.
  • It provides exponential suppression of excited states.
  • It shows advantage over adiabatic methods in circuit depth.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This filtering technique might be adapted to target excited states or other energy windows by changing the filter polynomial.
  • The scaling prioritizes simplicity, so constant factors in the depth may matter more for near-term implementations than asymptotic optimality.
  • Testing the coherent MCMR assumption on actual hardware would be a key next step for validation.

Load-bearing premise

The protocol assumes that mid-circuit measurement and reset can be performed coherently with negligible error on the hardware.

What would settle it

Run the protocol on a small spin chain with a known exact ground state and measure whether the achieved fidelity scales as predicted when the spectral gap is varied artificially.

Figures

Figures reproduced from arXiv: 2602.19556 by Jeongbin Jo.

Figure 1
Figure 1. Figure 1: FIG. 1. Deterministic Ground State Preparation via Power [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Quantum circuit representation of the Power-Cosine [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Advantage analysis comparing the state infidelity [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Energy convergence and theoretical state fidelity of [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Energy convergence of the Power-Cosine filter under [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
read the original 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 $\mathcal{O}(\Delta^{-2}\log(1/\epsilon))$, where $\Delta$ 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes a deterministic, non-variational protocol for preparing quantum many-body ground states via Power-Cosine quantum signal processing (QSP) filtering applied directly to controlled time-evolution operators on a single ancilla. Mid-circuit measurement and reset (MCMR) is used to realize iterative non-unitary filtering in the time domain. The central analytic claim is exponential suppression of excited-state weight with circuit depth scaling O(Δ^{-2} log(1/ε)), where Δ is the spectral gap; this is supported by numerical simulations on the 1D Heisenberg XYZ model and an advantage comparison against Trotterized adiabatic state preparation (TASP).

Significance. If the scaling and error-resilience claims hold, the protocol offers a practical route to ground-state preparation on early fault-tolerant hardware that trades optimal asymptotic complexity for implementational simplicity and single-ancilla spatial overhead. The numerical validation on the Heisenberg model and the explicit TASP comparison constitute concrete, falsifiable evidence of performance.

major comments (2)
  1. [Abstract and analytic derivation] Abstract (paragraph on MCMR integration) and the analytic derivation of the scaling: the claimed O(Δ^{-2} log(1/ε)) depth and exponential suppression treat each mid-circuit measurement and reset as an ideal coherent projector. No bounds are derived on the accumulation of reset infidelity or measurement error over the Θ(Δ^{-2} log(1/ε)) iterations; even small per-step errors can reintroduce excited-state weight at a rate that invalidates the suppression guarantee.
  2. [Numerical validation section] Numerical validation section: the manuscript states that simulations on the 1D Heisenberg XYZ model confirm theoretical soundness and shot-noise resilience, yet provides no explicit system sizes, Trotter steps, number of shots, or quantitative metric (e.g., final infidelity vs. shot count) that would allow independent verification of the resilience claim.
minor comments (2)
  1. [Method description] Clarify the precise definition of the Power-Cosine filter polynomial and its relation to standard QSP phase functions; the current notation leaves the mapping from filter degree to circuit depth implicit.
  2. [Advantage analysis] Add a short table comparing resource counts (ancillae, depth, gate count) against at least one other single-ancilla ground-state method (e.g., variational or QSP-based) at fixed Δ and ε.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable feedback on our work. We address each of the major comments in detail below and have made revisions to the manuscript to incorporate the suggested improvements.

read point-by-point responses

  1. Referee: [Abstract and analytic derivation] Abstract (paragraph on MCMR integration) and the analytic derivation of the scaling: the claimed O(Δ^{-2} log(1/ε)) depth and exponential suppression treat each mid-circuit measurement and reset as an ideal coherent projector. No bounds are derived on the accumulation of reset infidelity or measurement error over the Θ(Δ^{-2} log(1/ε)) iterations; even small per-step errors can reintroduce excited-state weight at a rate that invalidates the suppression guarantee.

    Authors: The referee correctly identifies that our analytic claims assume ideal MCMR operations. We will revise the manuscript to include a new subsection analyzing the effects of realistic measurement and reset errors. Under the assumption of independent per-iteration error rate ε_m, we derive that the excited state suppression remains exponential provided ε_m << Δ^2, with the depth scaling modified by a logarithmic factor in 1/ε_m. This bound ensures the protocol's robustness on early fault-tolerant hardware. revision: yes

  2. Referee: [Numerical validation section] Numerical validation section: the manuscript states that simulations on the 1D Heisenberg XYZ model confirm theoretical soundness and shot-noise resilience, yet provides no explicit system sizes, Trotter steps, number of shots, or quantitative metric (e.g., final infidelity vs. shot count) that would allow independent verification of the resilience claim.

    Authors: We agree that additional details are necessary for reproducibility. In the revised manuscript, we will expand the numerical validation section to explicitly state the system sizes (N = 4 to 12 spins), the number of Trotter steps (O(Δ^{-1})), the number of shots (10^4 to 10^6), and include a figure showing the final infidelity as a function of shot count to quantitatively demonstrate shot-noise resilience. revision: yes

Circularity Check

0 steps flagged

No circularity detected in derivation chain

full rationale

The paper claims an analytical derivation of exponential excited-state suppression with O(Δ^{-2} log(1/ε)) depth scaling via Power-Cosine QSP filtering applied to controlled time-evolution operators, integrated with MCMR. This scaling is presented as following from QSP filter properties and iterative application, without reduction to fitted parameters, self-definitional loops, or load-bearing self-citations. The protocol is self-contained as a first-principles construction from standard QSP and time-evolution primitives under the stated MCMR coherence assumption; no equations or steps equate the output scaling directly to inputs by construction. External validation via numerical simulations on the Heisenberg model further supports independence from circular elements.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The protocol rests on standard quantum mechanics and the existence of a spectral gap; no free parameters or new entities are introduced in the abstract.

axioms (2)
  • domain assumption The Hamiltonian possesses a finite spectral gap Δ separating the ground state from the first excited state.
    Invoked when stating the circuit depth scaling depends on Δ.
  • domain assumption Controlled time-evolution operators can be implemented coherently on the target hardware.
    Required for the single-ancilla filtering construction.

pith-pipeline@v0.9.0 · 5738 in / 1240 out tokens · 34036 ms · 2026-05-21T13:05:20.759405+00:00 · methodology

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