In recent years,variational Monte Carlo(VMC)calculations of projected entangled pair states(PEPS)have emerged as a competitive method for computing the ground states of many-body quantum systems.This approach is parti...In recent years,variational Monte Carlo(VMC)calculations of projected entangled pair states(PEPS)have emerged as a competitive method for computing the ground states of many-body quantum systems.This approach is particularly important for fermionic systems,where sign problems are prevalent.We derive and explain the algorithms for VMC calculations of fermionic PEPS within the swap-gates formulation.As a separate key result,we prove the detailed balance for sequential sampling of tensor networks.展开更多
We propose the realization of Majorana fermions （MFs） on the edges of a two-dimensional topological insulator in the proximity with s-wave superconductors and in the presence of transverse exchange field h. It is sh...We propose the realization of Majorana fermions （MFs） on the edges of a two-dimensional topological insulator in the proximity with s-wave superconductors and in the presence of transverse exchange field h. It is shown that there appear a pair of MFs localized at two junctions and that a reverse in the direction of h can lead to permutation of two MFs. With decreasing h, the MF states can either be fused or form one Dirac fermion on the π-junctions, exhibiting a topological phase transition. This characteristic can be used to detect physical states of MFs when they are transformed into Dirac fermions MFs is also given. localized on the π-junction. A condition of decoupling two展开更多
Using a quantum computer to simulate fermionic systems requires fermion-to-qubit transformations.Usually,lower Pauli weight of transformations means shallower quantum circuits.Therefore,most existing transformations a...Using a quantum computer to simulate fermionic systems requires fermion-to-qubit transformations.Usually,lower Pauli weight of transformations means shallower quantum circuits.Therefore,most existing transformations aim for lower Pauli weight.However,in some cases,the circuit depth depends not only on the Pauli weight but also on the coefficients of the Hamiltonian terms.In order to characterize the circuit depth of these algorithms,we propose a new metric called weighted Pauli weight,which depends on Pauli weight and coefficients of Hamiltonian terms.To achieve smaller weighted Pauli weight,we introduce a novel transformation,Huffman-code-based ternary tree(HTT)transformation,which is built upon the classical Huffman code and tailored to different Hamiltonians.We tested various molecular Hamiltonians and the results show that the weighted Pauli weight of the HTT transformation is smaller than that of commonly used mappings.At the same time,the HTT transformation also maintains a relatively small Pauli weight.The mapping we designed reduces the circuit depth of certain Hamiltonian simulation algorithms,facilitating faster simulation of fermionic systems.展开更多
The phenomenon of pseudogap and Fermi arcs has been a long-standing puzzle in the field of unconventional superconductivity(SC).Since first discovered in underdoped cuprates[1],the pseudogap has been generally identif...The phenomenon of pseudogap and Fermi arcs has been a long-standing puzzle in the field of unconventional superconductivity(SC).Since first discovered in underdoped cuprates[1],the pseudogap has been generally identified in various(quasi)two-dimensional(2D)contexts,including thin-film FeSe[2],layered heavy fermion systems[3],magic angle twisted bilayer graphene[4],and recently even ultra-cold atoms[5].One prominent explanation for the pseudogap is hence to treat it as a precursor of pairing due to phase decoherence.展开更多
文摘In recent years,variational Monte Carlo(VMC)calculations of projected entangled pair states(PEPS)have emerged as a competitive method for computing the ground states of many-body quantum systems.This approach is particularly important for fermionic systems,where sign problems are prevalent.We derive and explain the algorithms for VMC calculations of fermionic PEPS within the swap-gates formulation.As a separate key result,we prove the detailed balance for sequential sampling of tensor networks.
基金Supported by the Natural Science Foundation of Jiangsu Province under Grant No BK20140588the Research Grant Council of Hongkong under Grant No HKU7058/11P+1 种基金the CRF of the Research Grant Council of Hongkong under Grant No HKU-8/11Gthe National Basic Research Program of China under Grant No 2011CB922103
文摘We propose the realization of Majorana fermions （MFs） on the edges of a two-dimensional topological insulator in the proximity with s-wave superconductors and in the presence of transverse exchange field h. It is shown that there appear a pair of MFs localized at two junctions and that a reverse in the direction of h can lead to permutation of two MFs. With decreasing h, the MF states can either be fused or form one Dirac fermion on the π-junctions, exhibiting a topological phase transition. This characteristic can be used to detect physical states of MFs when they are transformed into Dirac fermions MFs is also given. localized on the π-junction. A condition of decoupling two
基金supported by the National Key Research and Development Program of China(Grant No.2024YFB4504101)the National Nat-ural Science Foundation of China(Grant No.22303022)the Anhui Province Innovation Plan for Science and Technology(Grant No.202423r06050002).
文摘Using a quantum computer to simulate fermionic systems requires fermion-to-qubit transformations.Usually,lower Pauli weight of transformations means shallower quantum circuits.Therefore,most existing transformations aim for lower Pauli weight.However,in some cases,the circuit depth depends not only on the Pauli weight but also on the coefficients of the Hamiltonian terms.In order to characterize the circuit depth of these algorithms,we propose a new metric called weighted Pauli weight,which depends on Pauli weight and coefficients of Hamiltonian terms.To achieve smaller weighted Pauli weight,we introduce a novel transformation,Huffman-code-based ternary tree(HTT)transformation,which is built upon the classical Huffman code and tailored to different Hamiltonians.We tested various molecular Hamiltonians and the results show that the weighted Pauli weight of the HTT transformation is smaller than that of commonly used mappings.At the same time,the HTT transformation also maintains a relatively small Pauli weight.The mapping we designed reduces the circuit depth of certain Hamiltonian simulation algorithms,facilitating faster simulation of fermionic systems.
基金supported by the National Key R&D Program of China(2022YFA1402702,2021YFA1401400,and 2022YFA1403402)the National Natural Science Foundation of China(12447103,12274289,12174068,and 12374144)+3 种基金the Innovation Program for Quantum Science and Technology(2021ZD0301902)the Science and Technology Commission of Shanghai Municipality(24LZ1400100,23JC1400600)support of Yangyang Development Fund,Shanghai Jiao Tong University 2030 Initiative,and startup funds from SJTUsupport of Shuguang Program of Shanghai Education Development Foundation and Shanghai Municipal Education Commission。
文摘The phenomenon of pseudogap and Fermi arcs has been a long-standing puzzle in the field of unconventional superconductivity(SC).Since first discovered in underdoped cuprates[1],the pseudogap has been generally identified in various(quasi)two-dimensional(2D)contexts,including thin-film FeSe[2],layered heavy fermion systems[3],magic angle twisted bilayer graphene[4],and recently even ultra-cold atoms[5].One prominent explanation for the pseudogap is hence to treat it as a precursor of pairing due to phase decoherence.
