The spin-1/2 $J_1$-$J_2$ Heisenberg model on square lattices are investigated via the finite projected entangled pair states (PEPS) method. Using recently developed gradient optimization method combining with Monte Carlo sampling techniques, we able to obtain ground energies that competitive best results. calculations show there is no N\'eel order, dimer order and plaquette in region of 0.42 $\lesssim J_2/J_1\lesssim$ 0.6, suggesting a single spin liquid phase intermediate region....

Projected entangled pair states (PEPS) methods have been proven to be powerful tools solve strongly correlated quantum many-body problems in two dimensions. However, due the high computational scaling with virtual bond dimension $D$, a practical application, PEPS are often limited rather small dimensions, which may not large enough for some highly systems, instance, frustrated systems. Optimization of ground state using imaginary time evolution method simple update scheme go larger...

Neural networks have been used as variational wave functions for quantum many-particle problems. It has shown that the correct sign structure is crucial to obtain highly-accurate ground state energies. In this paper, we propose a hybrid function combining convolutional neural network (CNN) and projected entangled pair states (PEPS), in which structures are determined by PEPS, amplitudes of provided CNN. We benchmark ansatz on highly frustrated spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$...

Noise-enhanced applications in open quantum walk (QW) have recently seen a surge due to their ability improve performance. However, verifying the success of QW is challenging, as mixed-state tomography resource-intensive process, and implementing all required measurements almost impossible various physical constraints. To address this challenge, we present neural-network-based method for reconstructing mixed states with high fidelity (~97.5%) while costing only 50% number typically...

Diverse advanced logic circuits are fabricated to implement arithmetic functions based on a simple and single molecular beacon platform, including half adder, subtractor, full digital comparator. Dual fluorescence outputs generated in parallel constant threshold value is set build all the circuits. The developed enzyme-free DNA system provides novel prototype for design of high-level biomolecular platform. Looking through history humanity with respect count computing, electronic computers...

The study of strongly frustrated magnetic systems has drawn great attentions from both theoretical and experimental physics. Efficient simulations these models are essential for understanding their exotic properties. Here we present PEPS++, a novel computational paradigm simulating other correlated quantum many-body systems. PEPS++ can accurately solve at the extreme scale with low cost high scalability on modern heterogeneous supercomputers. We implement Sunway TaihuLight based carefully...

The recently developed stochastic gradient method combined with Monte Carlo sampling techniques [W. Y. Liu et al., Phys. Rev. B 95, 195154 (2017)] offers a low scaling and accurate to optimize the projected entangled pair states (PEPS). We extended this fermionic PEPS (fPEPS). To simplify implementation, we introduce Fermi arrow notation specify order of fermion operators in virtual EPR pairs. By defining some local operation rules associated arrows, one can implement fPEPS algorithms very...

By using a state-of-the-art tensor network state method, we study the ground-state phase diagram of an extended Bose-Hubbard model on square lattice with frustrated next-nearest-neighbor tunneling. In hard-core limit, tunneling frustration stabilizes peculiar half-supersolid one sublattice being superfluid and other Mott insulator away from half filling. soft-core case, shows very rich diagrams above filling, including three different types supersolid phases depending interaction parameters....

The anisotropic-exchange spin-1/2 model on the triangular lattice has been used to describe rare-earth chalcogenides, which may have exotic ground states. We investigate quantum phase diagram of by using projected entangled pair state method, and compare it classical diagram. Besides two stripe-ordered phases, ${120}^{\ensuremath{\circ}}$ phase, there is also a multi-Q phase. identify as ${Z}_{2}$ vortex state. No spin liquid found in diagram, contrary previous density matrix renormalization...

Abstract We investigate the two-dimensional t – J model at a hole doping of $${\bar{n}}_{{\rm{h}}}=1/8$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mover> <mml:mi>n</mml:mi> </mml:mrow> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>h</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>8</mml:mn> </mml:math> using recently developed high accuracy fermionic projected entangled pair states method. By applying stochastic...

Quantum computing offers potential solutions for finding ground states in condensed-matter physics and chemistry. However, achieving effective state preparation is also computationally hard arbitrary Hamiltonians. It necessary to propose certain assumptions make this problem efficiently solvable, including preparing a trial of non-trivial overlap with the genuine state. Here, we classical-assisted quantum method many-body systems, combining Tensor Network States (TNS) Monte Carlo (MC)...

Whether noisy quantum devices without error correction can provide advantage over classical computers is a critical issue of current computation. In this work, the random circuits, which are used as paradigm model to demonstrate advantage, simulated with depolarizing noise on experiment-relevant two-dimensional architecture. With comprehensive numerical simulation and theoretical analysis, we find that maximum achievable operator entanglement entropy, indicates maximal cost, has area law...

Projected Entangled Pair States (PEPS) are recognized as a potent tool for exploring two-dimensional quantum many-body systems. However, significant challenge emerges when applying conventional PEPS methodologies to systems with periodic boundary conditions (PBC), attributed the prohibitive computational scaling bond dimension. This has notably restricted study of complex conditions. To address this challenge, we have developed strategy that involves superposition open (OBC) treat PBC....

Tensor-network (TN) states supply one of the most powerful variational tools to simulate quantum many-body systems. Though classical simulation TN (with approximation) is efficient, required computational (classical) resources are still beyond our current capability when size system and bond dimension becomes large (which necessary for studying complicated systems). The contraction, which dominant cost in algorithms, can be replaced by measuring corresponding physical observables directly...

The study of strongly frustrated magnetic systems has drawn great attentions from both theoretical and experimental physics. Efficient simulations these models are essential for understanding their exotic properties. Here we present PEPS++, a novel computational paradigm simulating other correlated quantum many-body systems. PEPS++ can accurately solve at the extreme scale with low cost high scalability on modern heterogeneous supercomputers. We implement Sunway TaihuLight based carefully...

Algorithms to simulate the ring-exchange models using projected entangled pair states (PEPS) are developed. We generalize imaginary time evolution (ITE) method optimize PEPS wave functions for with interactions. compare effects of different approximations environment. To understand numerical instability during optimization, we introduce ``singularity'' a and develop regulation procedure that can effectively reduce singularity PEPS. benchmark our toric code model, obtain extremely accurate...

The non-Markovianity is a prominent concept of the dynamics open quantum systems, which fundamental importance in mechanics and information. Despite lots efforts, experimental measurement an system still limited to very small systems. Presently, it impossible experimentally quantify high-dimensional systems with widely used Breuer-Laine-Piilo trace distance measure. In this paper, we propose method, combining measurements numerical calculations, that allow quantifying $N$-dimensional only...

In a recent comments [arXiv:1909.12788 (2019)], Zhao et al. argue that the definition of dimer orders used in our paper [Phys. Rev. B 98, 241109 (2018)] may not rule out valence bond solid (VBS) $J_1$-$J_2$ model on open boundary conditions (OBC). this reply, we show their argument does apply to case.