Multivariate quantum state preparation with optimized tensor networks

Abstract

Quantics tensor trains are attracting intense interest for quantum-inspired computing and quantum state preparation. These methods, which approximate continuum functions by representing their amplitude encoding as a matrix product state (MPS), are exceedingly powerful for univariate functions but rapidly become challenging when handling multivariate functions, since the linear chain topology leads to a large distance between highly-entangled qubits. We overcome this limitation by introducing SCENT (Spectral Clustering for Entanglement miNimizing Trees). SCENT is a protocol that utilizes efficiently-computable pairwise entanglement metrics to determine a suitable tree tensor network (TTN) structure, which can then be efficiently approximated using tensor cross-interpolation (TCI); we find that it substantially outperforms MPS methods and improves upon previous TTN methods. We then apply these optimized TTNs to state preparation, introducing an approximate circuit compilation method based on environment-tensor methods without significantly conceding overall accuracy. Importantly, the inherent gauge freedom of TTNs can be directly exploited in this method, resulting in higher fidelity at a given circuit depth. We demonstrate this quantum state-preparation pipeline on archetypal state-preparation problems in quantum chemistry and financial portfolio optimization. In our flagship demonstration, we encode a 20-variable probability distribution with long-ranged, non-nearest neighbor inter-variable correlations in a 200-qubit state-preparation circuit with infidelity 7.44× 10⁻⁹ using only 43284 CNOTs; depth and fidelity can be traded, allowing the same distribution to be prepared to infidelity 10⁻³ with as few as 5584 CNOTs.

Optimized Tensor-Network Renormalization for Quantum Dynamics: Resolving the Spectral Function of K₂Co(SeO₃)₂
Jiahang Hu, Runze Chi, B. Normand +2
arXiv13 Sep 2026PreprintarXiv licenceFull textCondensed matter Quantum physics & quantum informationarXiv
Quantum power iterations via tensor networks
V. Akshay, A. Berezutskii, Ar. Melnikov +2
Physical Review Research1 Nov 2026Peer-reviewedPublisher termsAtomic, molecular & optical physicsCrossref
Dynamics of disordered quantum systems with two- and three-dimensional tensor networks
Joseph Tindall, Antonio Francesco Mello, Matthew Fishman +2
Science21 May 2026Peer-reviewedLicence not statedFull text67 citedAtomic, molecular & optical physicsOpenAlex
Simulating and sampling from quantum circuits with 2D tensor networks
Manuel S. Rudolph, Joseph Tindall
npj Quantum Information24 Sep 2026Peer-reviewedCC BY-NC-NDFull text30 citedAtomic, molecular & optical physicsOpenAlex
Emergent de Sitter Space and Non-Unitary Tensor Networks from Non-Hermitian Quantum Criticality
Kuang-Hung Chou, Po-Yao Chang
arXiv30 Sep 2026PreprintCC BY 4.0Full textHigh-energy & particle physics Quantum physics & quantum informationarXiv

Cite

BibTeX RIS

BibTeX

@misc{simsgoh2026multivariate,
  title = {{Multivariate quantum state preparation with optimized tensor networks}},
  author = {Matthew L. Sims-Goh and Lukasz Cincio and Annina Z. Lieberherr and Mekena McGrew and Thomas R. Bromley},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09304},
  eprint = {2609.09304},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09304},
}

RIS

TY  - UNPB
TI  - Multivariate quantum state preparation with optimized tensor networks
AU  - Matthew L. Sims-Goh
AU  - Lukasz Cincio
AU  - Annina Z. Lieberherr
AU  - Mekena McGrew
AU  - Thomas R. Bromley
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.09304
UR  - https://arxiv.org/abs/2609.09304
AB  - Quantics tensor trains are attracting intense interest for quantum-inspired computing and quantum state preparation. These methods, which approximate continuum functions by representing their amplitude encoding as a matrix product state (MPS), are exceedingly powerful for univariate functions but rapidly become challenging when handling multivariate functions, since the linear chain topology leads to a large distance between highly-entangled qubits. We overcome this limitation by introducing SCENT (Spectral Clustering for Entanglement miNimizing Trees). SCENT is a protocol that utilizes efficiently-computable pairwise entanglement metrics to determine a suitable tree tensor network (TTN) structure, which can then be efficiently approximated using tensor cross-interpolation (TCI); we find that it substantially outperforms MPS methods and improves upon previous TTN methods. We then apply these optimized TTNs to state preparation, introducing an approximate circuit compilation method based on environment-tensor methods without significantly conceding overall accuracy. Importantly, the inherent gauge freedom of TTNs can be directly exploited in this method, resulting in higher fidelity at a given circuit depth. We demonstrate this quantum state-preparation pipeline on archetypal state-preparation problems in quantum chemistry and financial portfolio optimization. In our flagship demonstration, we encode a 20-variable probability distribution with long-ranged, non-nearest neighbor inter-variable correlations in a 200-qubit state-preparation circuit with infidelity 7.44× 10^−9 using only 43284 CNOTs; depth and fidelity can be traded, allowing the same distribution to be prepared to infidelity 10^−3 with as few as 5584 CNOTs.
ER  -

Abstract

Related

Cite