Universal Pairing Symmetry

Ilias Magoulas, Muhan Zhang, Francesco A. Evangelista

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.

Hong-Ming Cui, Zhong-Ying Fan

A bstract The symmetry of Ising model questions any single crossover scenario for supercritical fluids. In this work, we firstly study a pair of thermodynamic crossovers L ± analytically for the Van der Waals class fluids. We uncover an emergent Z 2 symmetry in addition to the universal scalings in the scaling regime for this class fluids. By using the self-reciprocal property between coexistenct phases, we further establish that under suitable conditions, the Ising symmetry generally emerges in the scaling regime for a general universality class. As a consequence, the thermodynamic crossovers L ± generally exhibit an emergent Z 2 symmetry in the scaling regime. This partly resolves the symmetry puzzle raised by the Ising model. The results also imply that the physical importance of the Ising model in critical phenomenon is far beyond the scope of magentic transitions.

Mahir Saleh Hussein, Mauricio Porto Pato

It is shown that the maximum entropy principle provides a natural basis for construction of an interpolating ensemble between any pair of the universality classes of random matrix theory. As an application, the Gaussian unitary ensemble to Gaussian orthogonal ensemble transition is worked out in detail. Transitions from these two ensembles to a Poisson distribution, of relevance to the metal-insulator transition in disordered metals, is also discussed in detail and the ``universal critical ensemble'' was found to depend on the time-reversal symmetry.

K. Tamvakis