Symmetry Dilemmas in Quantum Computing for Chemistry: A Comprehensive Analysis

• URL: http://arxiv.org/abs/2512.12097v1
• Date: Sat, 13 Dec 2025 00:08:55 GMT
• Title: Symmetry Dilemmas in Quantum Computing for Chemistry: A Comprehensive Analysis
• Authors: Ilias Magoulas, Muhan Zhang, Francesco A. Evangelista,
• Abstract summary: Gate-efficient fully symmetry-adapted operator pools may not be universal.<n>We show that the popular, gate-efficient operator pool consisting of singlet spin-adapted singles and perfect-pairing doubles is not universal when spatial symmetry is enforced.<n>Our results show when symmetry-breaking but universal pools can be used safely, when enforcing at least one distinguishing symmetry suffices, and when a particular symmetry must be rigorously preserved.
• Score: 31.99154889590184
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Symmetry adaptation, universality, and gate efficiency are central but often competing requirements in quantum algorithms for electronic structure and many-body physics. For example, fully symmetry-adapted universal operator pools typically generate long and deep quantum circuits, gate-efficient universal operator pools generally break symmetries, and gate-efficient fully symmetry-adapted operator pools may not be universal. In this work, we analyze such symmetry dilemmas both theoretically and numerically. On the theory side, we prove that the popular, gate-efficient operator pool consisting of singlet spin-adapted singles and perfect-pairing doubles is not universal when spatial symmetry is enforced. To demonstrate the strengths and weaknesses of the three types of pools, we perform numerical simulations using an adaptive algorithm paired with operator pools that are (i) fully symmetry-adapted and universal, (ii) fully symmetry-adapted and non-universal, and (iii) breaking a single symmetry and are universal. Our numerical simulations encompass three physically relevant scenarios in which the target state is (i) the global ground state, (ii) the ground state crossed by a state differing in multiple symmetry properties, and (iii) the ground state crossed by a state differing in a single symmetry property. Our results show when symmetry-breaking but universal pools can be used safely, when enforcing at least one distinguishing symmetry suffices, and when a particular symmetry must be rigorously preserved to avoid variational collapse. Together, the formal and numerical analysis provides a practical guide for designing and benchmarking symmetry-adapted operator pools that balance universality, resource requirements, and robust state targeting in quantum simulations for chemistry.

Related papers

• Resource-Theoretic Quantifiers of Weak and Strong Symmetry Breaking: Strong Entanglement Asymmetry and Beyond [0.0]
  We provide a framework to track how weak symmetry breaking is irreversibly converted into strong symmetry breaking in open quantum systems.<n>We propose extensions to generalized symmetries and illustrate the qualitative impact of strong symmetry breaking in analytically tractable QFT examples and applications.
  arXiv  Detail & Related papers  (2026-01-28T19:00:00Z)
• Anomalies on the Lattice, Homotopy of Quantum Cellular Automata, and a Spectrum of Invertible States [41.99844472131922]
  We develop a rigorous theory of anomalies on the lattice, which are obstructions to gauging global symmetries and the existence of trivial symmetric states.<n>We also construct $$-spectra of a class of invertible states and quantum cellular automata, which allows us to classify both anomalies and symmetry protected topological phases up to blend equivalence.
  arXiv  Detail & Related papers  (2025-12-01T19:00:01Z)
• Spin-Adapted Fermionic Unitaries: From Lie Algebras to Compact Quantum Circuits [0.013714053458441644]
  We introduce a minimum universal symmetry-adapted operator pool to further reduce the required quantum resources.<n>Conservation of symmetries plays a crucial role in both classical and quantum simulations of many-body systems.
  arXiv  Detail & Related papers  (2025-11-17T15:21:22Z)
• Predicting symmetries of quantum dynamics with optimal samples [41.42817348756889]
  Identifying symmetries in quantum dynamics is a crucial challenge with profound implications for quantum technologies.<n>We introduce a unified framework combining group representation theory and subgroup hypothesis testing to predict these symmetries with optimal efficiency.<n>We prove that parallel strategies achieve the same performance as adaptive or indefinite-causal-order protocols.
  arXiv  Detail & Related papers  (2025-02-03T15:57:50Z)
• Diagnosing Strong-to-Weak Symmetry Breaking via Wightman Correlators [20.572965801171225]
  Recent developments have extended the discussion of symmetry and its breaking to mixed states. We propose the Wightman correlator as an alternative diagnostic tool.
  arXiv  Detail & Related papers  (2024-10-12T02:04:40Z)
• Spontaneous symmetry breaking in open quantum systems: strong, weak, and strong-to-weak [4.41737598556146]
  We show that strong symmetry always spontaneously breaks into the corresponding weak symmetry. We conjecture that this relation among strong-to-weak symmetry breaking, gapless modes, and symmetry-charge diffusion is general for continuous symmetries.
  arXiv  Detail & Related papers  (2024-06-27T17:55:36Z)
• How much symmetry do symmetric measurements need for efficient operational applications? [0.0]
  For informationally complete sets, we propose construction methods from orthonormal Hermitian operator bases. Some of the symmetry properties, lost in the process of generalization, can be recovered without fixing the same number of elements for all POVMs.
  arXiv  Detail & Related papers  (2024-04-02T15:23:08Z)
• Symmetry-restricted quantum circuits are still well-behaved [45.89137831674385]
  We show that quantum circuits restricted by a symmetry inherit the properties of the whole special unitary group $SU(2n)$. It extends prior work on symmetric states to the operators and shows that the operator space follows the same structure as the state space.
  arXiv  Detail & Related papers  (2024-02-26T06:23:39Z)
• Operational interpretation and estimation of quantum trace-norm asymmetry based on weak value measurement and some bounds [0.0]
  An important and geometrically intuitive measure of translational asymmetry of a state is given by the trace-norm asymmetry. We show that the trace-norm asymmetry is equal to the average absolute imaginary part of the weak value of the generator of the translation group optimized over all possible orthonormal bases of the Hilbert space. We then use the link between the trace-norm asymmetry and the nonreal weak value to derive the relation between the trace-norm asymmetry with other basic concepts in quantum statistics.
  arXiv  Detail & Related papers  (2023-09-17T05:12:13Z)
• Theory of Quantum Circuits with Abelian Symmetries [0.0]
  Generic unitaries respecting a global symmetry cannot be realized, even approximately, using gates that respect the same symmetry.<n>We show that while the locality of interactions still imposes additional constraints on realizable unitaries, certain restrictions do not apply to circuits with Abelian symmetries.<n>This result suggests that global non-Abelian symmetries may affect the thermalization of quantum systems in ways not possible under Abelian symmetries.
  arXiv  Detail & Related papers  (2023-02-24T05:47:13Z)
• On discrete symmetries of robotics systems: A group-theoretic and data-driven analysis [38.92081817503126]
  We study discrete morphological symmetries of dynamical systems. These symmetries arise from the presence of one or more planes/axis of symmetry in the system's morphology. We exploit these symmetries using data augmentation and $G$-equivariant neural networks.
  arXiv  Detail & Related papers  (2023-02-21T04:10:16Z)
• General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory [44.99833362998488]
  We introduce quantum algorithms that can efficiently simulate certain classes of interactions consisting of correlated changes in multiple quantum numbers. The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions. The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories.
  arXiv  Detail & Related papers  (2022-12-28T18:56:25Z)
• Quantum Mechanics as a Theory of Incompatible Symmetries [77.34726150561087]
  We show how classical probability theory can be extended to include any system with incompatible variables. We show that any probabilistic system (classical or quantal) that possesses incompatible variables will show not only uncertainty, but also interference in its probability patterns.
  arXiv  Detail & Related papers  (2022-05-31T16:04:59Z)
• Approximately Equivariant Networks for Imperfectly Symmetric Dynamics [24.363954435050264]
  We find that our models can outperform both baselines with no symmetry bias and baselines with overly strict symmetry in both simulated turbulence domains and real-world multi-stream jet flow.
  arXiv  Detail & Related papers  (2022-01-28T07:31:28Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.