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arxiv: 2507.22562 · v3 · submitted 2025-07-30 · 🪐 quant-ph

Minimizing entanglement entropy for enhanced quantum state preparation

Oskari Kerppo , William Steadman , Ossi Niemim\"aki , Valtteri Lahtinen This is my paper

Pith reviewed 2026-05-19 02:54 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum state preparationentanglement entropymatrix product statesNISQ devicesquantum algorithmsstate preparation methodsentanglement minimization
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The pith

Minimizing entanglement entropy of a target quantum state enables more accurate preparation using matrix product states on near-term devices.

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

The authors introduce a two-step approach to quantum state preparation aimed at overcoming the exponential scaling of gates needed for arbitrary states. They first minimize the entanglement entropy to create a simpler version of the state that is easier to prepare on quantum hardware. This simplified state is then encoded using a matrix product state representation, which efficiently handles states with limited entanglement. The method includes rigorous lower bounds on the preparation accuracy expressed in terms of the remaining entanglement entropy. Benchmarks on states representing 2D normal distributions and Ricker wavelets demonstrate high accuracy for systems with 6 to 20 qubits, making it practical for current noisy quantum devices.

Core claim

The paper establishes that transforming a target quantum state to one with minimized entanglement entropy and then preparing it via a matrix product state representation achieves high accuracy preparation, with accuracy lower bounds directly related to the entanglement entropy of the transformed state. This two-step process addresses the challenge of preparing arbitrary states that would otherwise require an exponential number of two-qubit gates.

What carries the argument

The entanglement entropy minimization step that transforms the target state into a lower-entanglement version suitable for efficient matrix product state representation.

Load-bearing premise

A target quantum state can be transformed into one with reduced entanglement entropy while still allowing high-accuracy recovery of the original state through matrix product state preparation.

What would settle it

A calculation showing that for some target states the accuracy bound from the entanglement entropy is too loose to achieve the claimed high accuracy, or an experiment where the prepared state deviates significantly from the target despite low entropy.

Figures

Figures reproduced from arXiv: 2507.22562 by Oskari Kerppo, Ossi Niemim\"aki, Valtteri Lahtinen, William Steadman.

Figure 1
Figure 1. Figure 1: FIG. 1. A single truncated MPS disentangling layer followed by a PQC that minimizes entanglement entropy. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Two-step VDSP method for QSP. MPD stands for matrix [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. A PQC with 4 qubits and two layers. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Scaling of accuracy and infidelity with respect to number [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. A PQC trained for 10000 rounds with [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. A 1D normal distribution transformed into a state with low entanglement entropy by a trained PQC. [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. A 1D normal distribution prepared with single layer MPD with [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
read the original abstract

Quantum state preparation is an important subroutine in many quantum algorithms. The goal is to encode classical information directly to the quantum state so that it is possible to leverage quantum algorithms for data processing. However, quantum state preparation of arbitrary states scales exponentially in the number of two-qubit gates, and this makes quantum state preparation a very difficult task on quantum computers, especially on near-term noisy devices. This represents a major challenge in achieving quantum advantage. We present and analyze a novel two-step state preparation method where we first minimize the entanglement entropy of the target quantum state, thus transforming the state to one that is easier to prepare. The state with reduced entanglement entropy is then represented as a matrix product state, resulting in a high accuracy preparation of the target state. Our method is suitable for NISQ devices and we give rigorous lower bounds on the accuracy of the prepared state in terms of the entanglement entropy. We benchmark our method with 2D normal distribution and Ricker wavelet states with 6--20 qubits.

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

1 major / 2 minor

Summary. The manuscript proposes a two-step quantum state preparation protocol for NISQ devices. First, a transformation is applied to the target state |ψ⟩ to produce |φ⟩ = T|ψ⟩ with minimized entanglement entropy S(φ). The low-entropy state is then approximated by a matrix product state |φ_MPS⟩, after which the inverse transformation is applied to recover an approximation to the original state. The authors assert that this yields high-accuracy preparation and provide rigorous lower bounds on the final fidelity expressed in terms of the reduced entanglement entropy. Benchmarks are reported for 2D normal-distribution and Ricker-wavelet target states on 6–20 qubits.

Significance. If the accuracy bounds are shown to be rigorous and to account for all error sources, the approach could meaningfully reduce the resource cost of state preparation by exploiting entanglement minimization before MPS truncation. The explicit benchmarks on concrete states and the claim of NISQ suitability constitute a practical contribution, though the method’s advantage over direct MPS preparation of the original state remains to be quantified.

major comments (1)
  1. [Section on rigorous lower bounds] § on rigorous lower bounds (abstract and main text): The claimed lower bounds on prepared-state accuracy are stated solely in terms of the reduced entanglement entropy S(φ). It is unclear whether these bounds incorporate the MPS truncation error after the approximation of |φ⟩ or the error amplification that occurs when the inverse map T† is applied to the truncated |φ_MPS⟩. If the derivation treats the MPS step as exact or assumes T is exactly invertible without error propagation analysis, the guarantee for fidelity to the original |ψ⟩ does not follow. A concrete error-propagation lemma or numerical bound that includes both sources of error is required for the central claim.
minor comments (2)
  1. [Abstract] The abstract and introduction would benefit from an explicit statement of the fidelity metric (e.g., 1−|⟨ψ|ψ_prep⟩|) and the precise definition of the transformation T used to minimize entanglement entropy.
  2. [Benchmark section] Figure captions for the benchmark results should include the bond dimension chosen for the MPS representation and the resulting truncation error for each qubit number.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback. We address the single major comment below and will revise the manuscript accordingly to strengthen the rigor of our error bounds.

read point-by-point responses

  1. Referee: [Section on rigorous lower bounds] § on rigorous lower bounds (abstract and main text): The claimed lower bounds on prepared-state accuracy are stated solely in terms of the reduced entanglement entropy S(φ). It is unclear whether these bounds incorporate the MPS truncation error after the approximation of |φ⟩ or the error amplification that occurs when the inverse map T† is applied to the truncated |φ_MPS⟩. If the derivation treats the MPS step as exact or assumes T is exactly invertible without error propagation analysis, the guarantee for fidelity to the original |ψ⟩ does not follow. A concrete error-propagation lemma or numerical bound that includes both sources of error is required for the central claim.

    Authors: We agree that the presentation of the bounds requires clarification to be fully rigorous. The current derivation provides a lower bound on fidelity expressed in terms of the reduced entanglement entropy S(φ) after the transformation, treating the subsequent MPS step as achieving a controllable approximation error that is separately bounded by the bond dimension. However, the explicit propagation of this truncation error through the inverse map T† and any potential amplification was not stated as a separate lemma. In the revised manuscript we will add a concise error-propagation result (new Lemma in Section III) that combines both contributions: the total infidelity is bounded by a term linear in S(φ) plus the MPS truncation error scaled by the operator norm of T. We will also include a short numerical check confirming that the composite bound remains tight for the reported 2D-normal and Ricker-wavelet examples. This addition directly addresses the referee’s concern without altering the central claims. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on standard quantum information quantities

full rationale

The paper describes a two-step procedure: transform the target state to minimize entanglement entropy S, represent the result as an MPS, then (implicitly) invert. The abstract and description state that rigorous lower bounds on prepared-state accuracy are given in terms of the (reduced) entanglement entropy. These bounds are presented as following from standard entanglement measures and MPS approximation properties rather than from any fitted parameter, self-referential definition, or self-citation chain that collapses the claim back onto the input data. No equations or steps are shown that equate a derived accuracy bound directly to a fitted quantity or to a prior result whose only justification is the present authors' own unverified ansatz. The method therefore remains self-contained against external benchmarks and does not reduce by construction to its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper builds on standard quantum information concepts such as entanglement entropy and matrix product states. No new free parameters, invented entities, or ad-hoc axioms are apparent from the abstract.

axioms (1)
  • domain assumption Quantum state preparation of arbitrary states scales exponentially in the number of two-qubit gates.
    Stated directly in the abstract as background motivation.

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