Constant-Depth Unitary Preparation of Dicke States

Francisca Vasconcelos; Malvika Raj Joshi

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Constant-Depth Unitary Preparation of Dicke States

Malvika Raj Joshi, Francisca Vasconcelos

Quantum Physics · Submitted 15 Jan 2026

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this work, we present the first unitary, constant-depth protocols for exact Dicke state preparation.

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What the abstract itself states, as probabilities: claims first 0.96 · states limitation 0.56 · human participants 0.01 · controlled comparison 0.09 · randomized assignment 0.01 · states quantitative result 0.72 · compares with prior results 0.95 · mentions code or data availability 0.02.

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arXiv listing abstract v3. Results and the main claim are underlined; show every role.

Dicke states serve as a critical resource in quantum metrology, communication, and computation. However, unitary preparation of Dicke states is limited to logarithmic depth in standard circuit models and existing constant-depth protocols require measurement and feed-forward. In this work, we present the first unitary, constant-depth protocols for exact Dicke state preparation. We overcome the logarithmic-depth barrier by moving beyond the standard circuit model and leveraging global interactions (native to architectures such as neutral atoms and trapped ions). Specifically, utilizing unbounded CZ gates (i.e. within the QAC$^0$ circuit class), we offer circuits for exact computation of constant-weight Dicke states, using polynomial ancillae, and approximation of weight-1 Dicke states (i.e. $W$ states), using only constant ancillae. Granted additional access to the quantum FAN-OUT operation (i.e. upgrading to the QAC$_f^0$ circuit class), we also achieve exact and clean preparation of arbitrary-weight Dicke states, with polynomial ancillae. These protocols distinguish the constant-depth capabilities of quantum architectures based on connectivity and offer a novel path toward resolving a long-standing quantum complexity conjecture.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Dicke states serve as a critical resource in quantum metrology, communication, and computation.	background 1.00	0.04	0.02	asserted 1.00
s1	However, unitary preparation of Dicke states is limited to logarithmic depth in standard circuit models and existing constant-depth protocols require measurement and feed-forward.	gap 0.86	0.05	0.03	asserted 1.00
s2	In this work, we present the first unitary, constant-depth protocols for exact Dicke state preparation.	contribution 1.00	0.96	0.84	asserted 1.00
s3	We overcome the logarithmic-depth barrier by moving beyond the standard circuit model and leveraging global interactions (native to architectures such as neutral atoms and trapped ions).	method 0.86	0.78	0.14	asserted 1.00
s4	Specifically, utilizing unbounded CZ gates (i.e. within the QAC$^0$ circuit class), we offer circuits for exact computation of constant-weight Dicke states, using polynomial ancillae, and approximation of weight-1 Dicke states (i.e. $W$ states), using only constant ancillae.	contribution 0.47	0.93	0.18	asserted 1.00
s5	Granted additional access to the quantum FAN-OUT operation (i.e. upgrading to the QAC$_f^0$ circuit class), we also achieve exact and clean preparation of arbitrary-weight Dicke states, with polynomial ancillae.	contribution 0.70	0.94	0.18	asserted 0.99
s6	These protocols distinguish the constant-depth capabilities of quantum architectures based on connectivity and offer a novel path toward resolving a long-standing quantum complexity conjecture.	interpretation 1.00	0.66	0.46	asserted 0.97

What kind of paper the classifier reports this is: method or tool 0.74 · evidence from proof or derivation 0.99.

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The paper

Original abstract

Dicke states serve as a critical resource in quantum metrology, communication, and computation. However, unitary preparation of Dicke states is limited to logarithmic depth in standard circuit models and existing constant-depth protocols require measurement and feed-forward. In this work, we present the first unitary, constant-depth protocols for exact Dicke state preparation. We overcome the logarithmic-depth barrier by moving beyond the standard circuit model and leveraging global interactions (native to architectures such as neutral atoms and trapped ions). Specifically, utilizing unbounded CZ gates (i.e. within the QAC$^0$ circuit class), we offer circuits for exact computation of constant-weight Dicke states, using polynomial ancillae, and approximation of weight-1 Dicke states (i.e. $W$ states), using only constant ancillae. Granted additional access to the quantum FAN-OUT operation (i.e. upgrading to the QAC$_f^0$ circuit class), we also achieve exact and clean preparation of arbitrary-weight Dicke states, with polynomial ancillae. These protocols distinguish the constant-depth capabilities of quantum architectures based on connectivity and offer a novel path toward resolving a long-standing quantum complexity conjecture.

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References

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5 arXiv papers cite this in 27 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 17 sentences without a confident label

Uses its method or tool 2 papers

Although known constructions of $$ require $_n$, we can apply them to prepare $|D^k^3_k⟩$ using $_k$ [ref] .

Polylogarithmic-Weight Dicke States in QAC$^0$ and Arbitrary Symmetric States in QAC$^0_f$ · Constructing a state with constant fidelity with . · 0.88
Therefore, we use a clean unitary circuit that exactly prepares $|D_k^n⟩$ for every $0≤k≤n$ constructed recently [ref] .

Constant-depth adaptive preparation of Dicke and symmetric states · From Dicke-State Preparation to Arbitrary Symmetric States · 0.94

Compares with it 2 papers

Our constructions require substantially different techniques than the constant-weight Dicke state construction of [ref] , as we elaborate upon in <Ref>.

Polylogarithmic-Weight Dicke States in QAC$^0$ and Arbitrary Symmetric States in QAC$^0_f$ · Our results · 1.00
More recently, Ref. [ref] obtained a constant-depth unitary construction for arbitrary excitation number using $O(n^2√(logn))$ ancillary qubits.

Constant-depth adaptive preparation of Dicke and symmetric states · A Constant-Depth Preparation Scheme for Dicke States · 0.86

Cites it as background 4 papers

In the $$ model where light-cone arguments also break down, Dicke states have recently been of interest for both upper bounds [ref] and for understanding the power of Toffoli gates vs $$ ($$ vs $$) [ref] .

Polylogarithmic-Weight Dicke States in QAC$^0$ and Arbitrary Symmetric States in QAC$^0_f$ · Prior work · 0.98
Since its introduction, $$ has been studied extensively [ref] .

On the Computational Power of Geometrically Local QAC circuits · Introduction · 0.99
In addition, [ref] show that $$ can prepare constant-weight $n$-qubit Dicke states.

Parity $\notin$ QAC0 $\iff$ QAC0 is Fourier-Concentrated · Prior work · 0.92

What it cites · 13 sentences without a confident label

Builds on 1 paper

First, while [ref] focuses on just the $k=1$ case in , we offer circuits for exact preparation of any constant-weight, i.e. $k=(1)$, Dicke state.

2601.03243 · Comparison to Prior Work · 0.99

Compares with 3 papers

Relaxing to all-to-all connectivity resulted in significantly improved logarithmic-depth scaling [ref] .

Low-depth quantum symmetrization · Comparison to Prior Work · 0.94
Relaxing to all-to-all connectivity resulted in significantly improved logarithmic-depth scaling [ref] .

Depth-Efficient Quantum Circuit Synthesis for Deterministic Dicke State Preparation · Comparison to Prior Work · 0.94
Finally, we acknowledge concurrent and independent work by [ref] , who similarly established constant-depth preparation of $W$ states via global gates (i.e. in ).

2601.03243 · Comparison to Prior Work · 0.94

Cites as background 2 papers

Nearly 30 years since Moore's original proposal [ref] , it still remains open as to whether = .

Quantum Circuits: Fanout, Parity, and Counting · Preliminaries · 0.99
Since the gate can straightforwardly be used to compute the GHZ/CAT state, most of the literature on versus has focused on synthesis of GHZ states and its variants [ref] .

Improved Lower Bounds for QAC0 · Introduction · 0.92

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