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arXiv:2508.20770 · Physica Scripta

Equally entangled multiqubit states

F. Albarrán-Arriagada, Guillermo Romero, J. C. Retamal

Published Mar 3, 2026• 1 citation
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Abstract

Abstract We present a protocol for generating multiqubit quantum states with translationally invariant pairwise entanglement, addressing the challenge posed by restricted qubit connectivity in current digital quantum computing platforms Our method relies on sequences of local single-qubit rotations and controlled operations, and we analyze two distinct configurations: a star topology, which produces cyclic permutation invariant entanglement patterns, and a linear topology, which enables translationally invariant entanglement across the chain. Using a variant of the time-dependent density matrix renormalization group (tDMRG) algorithm, we show that in the linear configuration the resulting bulk entanglement is independent of the number of qubits, demonstrating the scalability of the approach. Moreover, by alternating local unitaries along the chain, we uncover a periodic regime in which nearest-neighbor entanglement exhibits a dimerized structure. These results provide a practical and experimentally feasible pathway for realizing highly symmetric entangled states in near-term quantum devices.

DOI
10.1088/1402-4896/ae4cd2

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Abstract We present a protocol for generating multiqubit quantum states with translationally invariant pairwise entanglement, addressing the challenge posed by restricted qubit connectivity in current digital quantum computing platforms Our method relies on sequences of local single-qubit rotations and controlled operations, and we analyze two distinct configurations: a star topology, which produces cyclic permutation invariant entanglement patterns, and a linear topology, which enables translationally invariant entanglement across the chain. Using a variant of the time-dependent density matrix renormalization group (tDMRG) algorithm, we show that in the linear configuration the resulting bulk entanglement is independent of the number of qubits, demonstrating the scalability of the approach. Moreover, by alternating local unitaries along the chain, we uncover a periodic regime in which nearest-neighbor entanglement exhibits a dimerized structure. These results provide a practical and experimentally feasible pathway for realizing highly symmetric entangled states in near-term quantum devices.
We refine recent local unitary entanglement classification for symmetric pure states of nnn qubits (that is, states invariant under permutations of qubits) using local unitary stabilizer subgroups and Majorana configurations. Stabilizer subgroups carry more entanglement distinguishing power than do the stabilizer subalgebras used in our previous work. We extend to mixed states recent results about local operations on pure symmetric states by showing that if two symmetric density operators are equivalent by a local unitary operation, then they are equivalent via a local unitary operation that is the {\em same} in each qubit. A geometric consequence, used in our entanglement classification, is that two symmetric pure states are local unitary equivalent if and only if their Majorana configurations can be interchanged by a rotation of the Bloch sphere.
The study of entanglement properties of multiqubit states that are invariant under permutations of qubits is motivated by potential applications in quantum computing, quantum communication, and quantum metrology. In this work we generalize the notions of symmetrization, Dicke states, and the Majorana representation to the alternating, cyclic, and dihedral subgroups of the full group of permutations. We use these tools to characterize states that are invariant under these subgroups and analyze their entanglement properties.
As quantum information technologies advance, challenges in scaling and connectivity persist, particularly the need for long-range qubit connectivity and efficient entanglement generation. Perfect State Transfer enables time-optimal state transfer between distant qubits using only nearest-neighbor couplings, enhancing device connectivity. Moreover, the transfer protocol results in effective parity-dependent non-local interactions, extending its utility to entanglement generation. Here, we experimentally demonstrate Perfect State Transfer and multi-qubit entanglement generation on a chain of six superconducting transmon qubits with tunable couplers, controlled via parametric drives. By simultaneously activating and engineering all couplings, we implement the transfer for up to six qubits, verifying single-excitation dynamics for different initial states. Extending the protocol to multiple excitations, we confirm its parity-dependent nature, where excitation number controls the phase of the transferred state. Finally, leveraging this property, we prepare a Greenberger-Horne-Zeilinger state using a single transfer operation, showcasing potential of Perfect State Transfer for efficient entanglement generation.
Classical computation relies heavily on information manipulation. Each component of a hardware needs to communicate with others, and this is done by encoding information into strings of bits and application of logical operations. When dealing with quantum technologies, there arises a new set of paradigms and devices, based on manipulations of qubits, the quantum analogues of conventional bits. This work investigates the generation and distribution of quantum entanglement, a uniquely non-classical correlation, across spin chains, which serve as promising platforms for quantum information processing. We systematically compare two distinct entanglement generation protocols: Protocol 1 (P1), based on alternating weak and strong couplings that create a band structure enabling an effective trimer-model approximation, and Protocol 2 (P2), which employs symmetric boundary couplings and virtual excitations to establish a direct effective interaction between the chain ends. Our results demonstrate that a protocol based on virtual excitations and optimized boundary couplings consistently outperforms its counterpart in speed, achieved entanglement, and robustness against fabrication imperfections and noise. Furthermore, by employing effective model reductions and open quantum systems techniques we provide a comprehensive framework for understanding the resilience of distributed entanglement in solid-state quantum devices. The characteristics of the virtual-coupling protocol highlight its potential for experimental implementation in scalable quantum technologies.
Quantum entanglement reflects itself through non-local correlations among the subsystems of a quantum system. This thesis focuses on constructing a complete set of local invariants characterizing symmetric two qubit systems and analyzing the pairwise entanglement properties like collective spin squeezing - exhibited by multiqubits - in terms of two qubit entanglement invariants. Further, the collective pairwise entanglement properties of symmetric multiqubit states are shown to be captured entirely by the off diagonal block of the covariance matrix.
A construction of genuinely entangled multipartite quantum states based on the group theory is presented. Analyzed states resemble the Dicke states, whereas the interactions occur only between specific subsystems related by the action of the selected group. The states constructed by this technique exhibit desired symmetry properties and form a natural resource for less-symmetric quantum informational tasks. We propose quantum circuits efficiently generating such states, which in general have smaller complexity than the circuits necessary to create fully symmetric entangled states. Exemplary five-qubit quantum states are simulated on quantum computers.