Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2608.22892

Deterministic Preparation of Arbitrary Spin Eigenfunctions

Wenxuan Tao, Jianan Wang, Fen Zuo

quant-phcond-mat.str-elcs.DSphysics.chem-phSubmitted Aug 24, 2026• Announced Aug 25, 2026• 0 citations
arXivHTMLPDF

Abstract

Quantum states with conserved total spins, or spin eigenfunctions, are important for studying quantum chemistry and quantum manybody physics problems. A typical class of spin eigenfunctions are Dicke states, which attain maximal spins. While we already have many efficient quantum algorithms to prepare Dicke states, it is not yet clear if we could do so for arbitrary spin eigenfunctions deterministically. Generalizing Bärtschi and Eidenbenz's elegant algorithms for Dicke state preparation, we successfully prepare arbitrary spin eigenfunctions characterized by branching paths and binary spin trees. As a byproduct, we also develop the corresponding classical algorithms to reconstruct all these spin states.

Comments
38 pages, 14 figures

Related papers

Quantum state preparation of spin eigenstates including the Dicke states with generalized all-coupled interaction in a spintronic quantum computing architecture

Amritesh Sharma, Ashwin A. Tulapurkar

There has been an extensive development in the use of multi-partite entanglement as a resource for various quantum information processing tasks. In this paper we focus on preparing arbitrary spin eigenstates whose subset contain important entangled resources like Dicke states as well as some other sub-radiant states that are difficult to prepare. Leveraging on the symmetry of these states we consider uniform pairwise exchange coupling between every pair of qubits. Starting from a product state of a given spin eigenstate with a single qubit state, another spin eigenstate can be prepared using simple time evolutions. This expansion paves a deterministic approach to prepare arbitrary Dicke states in linear steps. We discuss an improvement in this cost building up on a previous work for W states deterministic preparation in logarithmic circuit depth. The modified algorithm requires several iterations of pumping spin angular momentum into the system and is akin to the amplitude amplification in Grover search. As a use case to demonstrate the proposed scheme, we choose a system of non-interacting static spin qubits connected to a ferromagnetic reservoir. The flying qubits emerging from the reservoir locally interact with static qubits successively, mediating an in-direct exchange interaction between all the pairs.

arXiv:2008.06705•Aug 15, 2020•1 citation

Spin-$s$ $U(1)$-eigenstate preparation

Nabi Zare Harofteh, Rafael I. Nepomechie

We formulate a deterministic algorithm for preparing a general $U(1)$-eigenstate of a spin-$s$ chain of length $n$. These states consist of linear combinations of computational basis states $|\vec{m}\rangle$ of $n$ qudits, each with $(2s+1)$ levels and $s= 1/2, 1, 3/2, \ldots$, whose ditstrings $\vec{m}$ have a fixed digit sum. Exploiting a Gray code for bounded integer compositions, whose consecutive ditstrings obey the Gray property, the quantum state is prepared by applying corresponding ``Gray gates.'' We use this algorithm to prepare exact eigenstates of integrable spin-$s$ XXX Hamiltonians. We also consider the preparation of AKLT states and spin-$s$ Dicke states.

quant-pharXiv:2601.14513•Annalen der Physik•Jan 22, 2026•0 citations

Spin‐ssss Dicke States and Their Preparation

Rafael I. Nepomechie, Francesco Ravanini, David Raveh

Abstract The notion of spin‐ Dicke states is introduced, which are higher‐spin generalizations of usual (spin‐1/2) Dicke states. These multi‐qudit states can be expressed as superpositions of qudit Dicke states. They satisfy a recursion formula, which is used to formulate an efficient quantum circuit for their preparation, whose size scales as , where is the number of qudits and is the number of times the total spin‐lowering operator is applied to the highest‐weight state. The algorithm is deterministic and does not require ancillary qudits.

arXiv:2402.03233•Advanced Quantum Technologies•Sep 9, 2024•8 citations

Constant-depth adaptive preparation of Dicke and symmetric states

Rui Luo, Junjie Chen, Xiongfeng Ma

Efficient preparation of Dicke states and, more generally, permutation-symmetric states is important for quantum metrology, quantum networking, and collective quantum information processing. Measurements and classical feedforward enable low-depth preparations of these states, with a cost of ancillary qubits. In this work, we introduce an exact constant-depth adaptive preparation protocol for arbitrary Dicke-$(n,k)$ states and further symmetric states. We first provide a protocol preparing the uniform subset superposition state, as a primitive, using constant-depth adaptive circuit with $O(k^2\log^2 n)$ ancillary qubits and success probability at least $1/k$. This yields an exact, probabilistic, constant-depth Dicke-state preparation protocol using $O\left(n^2+k^2\log^2 n+kn\log n\log\log n\right)$ ancillary qubits. Parallel repetition suppresses the failure probability exponentially without increasing the quantum depth. Moreover, the uniform subset superposition state is also of independent interest as the uniform vertex state of the Johnson graph and as the compact uniform subset state appearing in quantum-walk and topological-data-analysis algorithms. We further establish a general lifting framework that coherently combines clean unitary Dicke-state preparation circuits to prepare arbitrary symmetric states with only polynomial ancillary overhead. Combined with recent constant-depth unitary Dicke-state constructions, this gives an exact constant-depth preparation protocol for arbitrary $n$-qubit symmetric states using $O(n^3\sqrt{\log n})$ ancillary qubits.

quant-pharXiv:2608.01144•Aug 4, 2026•0 citations

Quantum Circuits for the Preparation of Spin Eigenfunctions on Quantum Computers

Alessandro Carbone, Davide Emilio Galli, Mário Motta +1 more

The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wave functions that are relevant in the behavior of the system under study. Hamiltonian symmetries are important instruments used to classify relevant many-particle wave functions and to improve the efficiency of numerical simulations. In this work, quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers are presented. Two different strategies are discussed and compared: exact recursive construction of total spin eigenfunctions based on the addition theorem of angular momentum, and heuristic approximation of total spin eigenfunctions based on the variational optimization of a suitable cost function. The construction of these quantum circuits is illustrated in detail, and the preparation of total spin eigenfunctions is demonstrated on IBM quantum devices, focusing on three- and five-spin systems on graphs with triangle connectivity.

arXiv:2202.09479•Symmetry•Mar 21, 2022•17 citations

Dicke states as matrix product states

David Raveh, Rafael I. Nepomechie

We derive an exact canonical matrix product state (MPS) representation for Dicke states $|{D}_{k}^{n}\ensuremath{\rangle}$ with a minimal bond dimension $\ensuremath{\chi}=k+1$, for general values of $n$ and $k$, for which the $W$ state is the simplest case $k=1$. We use this MPS to formulate a quantum circuit for sequentially preparing Dicke states deterministically, relating it to the recursive algorithm of B\"artschi and Eidenbenz. We also find exact canonical MPS representations with a minimal bond dimension for higher-spin and qudit Dicke states.

arXiv:2408.04729•Physical Review A•Nov 26, 2024•7 citations
Quantum states with conserved total spins, or spin eigenfunctions, are important for studying quantum chemistry and quantum manybody physics problems. A typical class of spin eigenfunctions are Dicke states, which attain maximal spins. While we already have many efficient quantum algorithms to prepare Dicke states, it is not yet clear if we could do so for arbitrary spin eigenfunctions deterministically. Generalizing Bärtschi and Eidenbenz's elegant algorithms for Dicke state preparation, we successfully prepare arbitrary spin eigenfunctions characterized by branching paths and binary spin trees. As a byproduct, we also develop the corresponding classical algorithms to reconstruct all these spin states.
There has been an extensive development in the use of multi-partite entanglement as a resource for various quantum information processing tasks. In this paper we focus on preparing arbitrary spin eigenstates whose subset contain important entangled resources like Dicke states as well as some other sub-radiant states that are difficult to prepare. Leveraging on the symmetry of these states we consider uniform pairwise exchange coupling between every pair of qubits. Starting from a product state of a given spin eigenstate with a single qubit state, another spin eigenstate can be prepared using simple time evolutions. This expansion paves a deterministic approach to prepare arbitrary Dicke states in linear steps. We discuss an improvement in this cost building up on a previous work for W states deterministic preparation in logarithmic circuit depth. The modified algorithm requires several iterations of pumping spin angular momentum into the system and is akin to the amplitude amplification in Grover search. As a use case to demonstrate the proposed scheme, we choose a system of non-interacting static spin qubits connected to a ferromagnetic reservoir. The flying qubits emerging from the reservoir locally interact with static qubits successively, mediating an in-direct exchange interaction between all the pairs.
Spin-sss U(1)U(1)U(1)-eigenstate preparation
We formulate a deterministic algorithm for preparing a general U(1)U(1)U(1)-eigenstate of a spin-sss chain of length nnn. These states consist of linear combinations of computational basis states ∣m⃗⟩|\vec{m}\rangle∣m⟩ of nnn qudits, each with (2s+1)(2s+1)(2s+1) levels and s=1/2,1,3/2,…s= 1/2, 1, 3/2, \ldotss=1/2,1,3/2,…, whose ditstrings m⃗\vec{m}m have a fixed digit sum. Exploiting a Gray code for bounded integer compositions, whose consecutive ditstrings obey the Gray property, the quantum state is prepared by applying corresponding ``Gray gates.'' We use this algorithm to prepare exact eigenstates of integrable spin-sss XXX Hamiltonians. We also consider the preparation of AKLT states and spin-sss Dicke states.
Abstract The notion of spin‐ Dicke states is introduced, which are higher‐spin generalizations of usual (spin‐1/2) Dicke states. These multi‐qudit states can be expressed as superpositions of qudit Dicke states. They satisfy a recursion formula, which is used to formulate an efficient quantum circuit for their preparation, whose size scales as , where is the number of qudits and is the number of times the total spin‐lowering operator is applied to the highest‐weight state. The algorithm is deterministic and does not require ancillary qudits.
Efficient preparation of Dicke states and, more generally, permutation-symmetric states is important for quantum metrology, quantum networking, and collective quantum information processing. Measurements and classical feedforward enable low-depth preparations of these states, with a cost of ancillary qubits. In this work, we introduce an exact constant-depth adaptive preparation protocol for arbitrary Dicke-(n,k)(n,k)(n,k) states and further symmetric states. We first provide a protocol preparing the uniform subset superposition state, as a primitive, using constant-depth adaptive circuit with O(k2log⁡2n)O(k^2\log^2 n)O(k2log2n) ancillary qubits and success probability at least 1/k1/k1/k. This yields an exact, probabilistic, constant-depth Dicke-state preparation protocol using O(n2+k2log⁡2n+knlog⁡nlog⁡log⁡n)O\left(n^2+k^2\log^2 n+kn\log n\log\log n\right)O(n2+k2log2n+knlognloglogn) ancillary qubits. Parallel repetition suppresses the failure probability exponentially without increasing the quantum depth. Moreover, the uniform subset superposition state is also of independent interest as the uniform vertex state of the Johnson graph and as the compact uniform subset state appearing in quantum-walk and topological-data-analysis algorithms. We further establish a general lifting framework that coherently combines clean unitary Dicke-state preparation circuits to prepare arbitrary symmetric states with only polynomial ancillary overhead. Combined with recent constant-depth unitary Dicke-state constructions, this gives an exact constant-depth preparation protocol for arbitrary nnn-qubit symmetric states using O(n3log⁡n)O(n^3\sqrt{\log n})O(n3logn​) ancillary qubits.
The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wave functions that are relevant in the behavior of the system under study. Hamiltonian symmetries are important instruments used to classify relevant many-particle wave functions and to improve the efficiency of numerical simulations. In this work, quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers are presented. Two different strategies are discussed and compared: exact recursive construction of total spin eigenfunctions based on the addition theorem of angular momentum, and heuristic approximation of total spin eigenfunctions based on the variational optimization of a suitable cost function. The construction of these quantum circuits is illustrated in detail, and the preparation of total spin eigenfunctions is demonstrated on IBM quantum devices, focusing on three- and five-spin systems on graphs with triangle connectivity.
We derive an exact canonical matrix product state (MPS) representation for Dicke states $|{D}_{k}^{n}\ensuremath{\rangle}$ with a minimal bond dimension $\ensuremath{\chi}=k+1$, for general values of nnn and kkk, for which the WWW state is the simplest case k=1k=1k=1. We use this MPS to formulate a quantum circuit for sequentially preparing Dicke states deterministically, relating it to the recursive algorithm of B\"artschi and Eidenbenz. We also find exact canonical MPS representations with a minimal bond dimension for higher-spin and qudit Dicke states.