Entanglement asymmetry, which serves as a diagnostic tool for symmetry breaking and proxy thermalization, has recently been proposed studied in the context of restoration quantum many-body systems undergoing quench. In this Letter, we investigate various symmetric random circuits, particularly focusing on U(1) case. contrast to nonsymmetric circuits where small subsystem can always be restored at late times, reveal that fail U(1)-symmetric certain weak symmetry-broken initial states...

Ground state preparation is classically intractable for general Hamiltonians. On quantum devices, shallow parametrized circuits can be effectively trained to obtain short-range entangled states under the paradigm of variational eigensolver, while deep are generally untrainable due barren plateau phenomenon. In this Letter, we give a lower bound on variance circuit gradients arbitrary composed local 2-designs. Based our unified framework, prove absence plateaus in training finite local-depth...

The recent discovery of high-temperature superconductivity in La_{3}Ni_{2}O_{7} offers a fresh platform for exploring unconventional pairing mechanisms. Starting with the basic argument that electrons d_{z^{2}} orbitals nearly form local moments, we examine effect Hubbard interaction U on binding strength Cooper pairs based single-orbital bilayer model intralayer hopping t_{∥} and interlayer superexchange J_{⊥}. By extensive density matrix renormalization group calculations, observe...

The recent discovery of high-temperature superconductivity in $\mathrm{La}_3 \mathrm{Ni}_2 \mathrm{O}_7$ offers a fresh platform for exploring unconventional pairing mechanisms. Based on single-orbital bilayer model with intralayer hopping $t_{\|}$ and interlayer super-exchange $J_{\perp}$, we investigate the impact on-site Hubbard interaction $U$ Ni-3d orbital binding strength Cooper pairs. By extensive density matrix renormalization group calculations, observe remarkable enhancement energy...

A composite pairing structure of the superconducting state is revealed by a density matrix renormalization group study in two-leg $t\text{\ensuremath{-}}J$ model. The order parameter composed amplitude and phase factor, which latter explicitly depends on spin background with an analytic form. Such stringlike factor responsible for pair wave (PDW) induced polarization $m$ vector ${Q}_{\mathrm{PDW}}=2\ensuremath{\pi}m$. By contrast, remains smooth, unchanged PDW. Moreover, local can give rise...

The tradeoff between trainability and expressibility is a central challenge faced by today's variational quantum computing. Recent studies indicate that resolving this dilemma necessitates designing specific parametrized circuits (PQC) tailored for problems, which urgently needs general efficient method to assess the learnability of PQCs regarding given target. In Letter, we demonstrate simple metric comparing fluctuations training landscape with standard learnable landscapes. This shows...

The pairing mechanism in an antiferromagnetic (AFM) bosonic $t$-$J$ model is investigated via large-scale density matrix renormalization group calculations. In contrast to the competing orders fermionic model, we discover that a pair wave (PDW) of tightly bound hole pairs coexists with AFM order forming ``supersolid'' at small doping model. collapses larger superfluid single-boson condensation spin background polarized ferromagnetic (FM) simultaneously. This phase will disappear once hidden...

Ground state preparation is classically intractable for general Hamiltonians. On quantum devices, shallow parameterized circuits can be effectively trained to obtain short-range entangled states under the paradigm of variational eigensolver, while deep are generally untrainable due barren plateau phenomenon. In this Letter, we give a lower bound on variance circuit gradients arbitrary composed local 2-designs. Based our unified framework, prove absence plateaus in training finite local-depth...

A composite pairing structure of superconducting state is revealed by density matrix renormalization group study in a two-leg $t$-$J$ model. The order parameter composed amplitude and phase factor, which the latter explicitly depends on spin background with an analytic form identified anisotropic limit as interchain hopping integral $t_{\perp}\rightarrow 0$. Such string-like factor responsible for pair wave (PDW) induced polarization wavevector $Q_{\mathrm {PDW}}=2πm$ ($m$ magnetization). By...