A hardware-efficient binary-tree ansatz has a closed-form diagonal Fubini–Study metric, enabling metric-aware VQE and time evolution without auxiliary circuits, with linear-in-k pruning for sparse sectors.
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Introduces an efficient SSE QMC algorithm with global updates and parallel tempering for mixed-dimensional models and applies it to map angle-dependent correlated insulators and Wigner-Mott states in M-point twisted AA-stacked SnSe2.
Equilibrium quantum many-body methods are encoders from admissible states to represented variables, with exact decoders existing precisely when tasks are constant on encoder fibers.
MPS energy landscapes lack poor local minima because gauge freedom induces overparametrization that concentrates local minima near the global minimum, with the local minimum distribution proven invariant under orthogonality center moves.
Tensor networks enable tunable, objective compression of 1D fluid data with lossless reconstruction at high bond dimension and efficient in-compressed-space operations like periodic convolution.
A convergent SDP hierarchy certifies upper bounds on the thermodynamic-limit bulk spectral gap, making the bulk gap semi-decidable and producing the first certified bounds for the kagome Heisenberg model.
A zero-mode gauge fixing technique truncates bonds in loopy tensor networks by exploiting linear dependencies in the metric tensor of cut-bond states, applied to iPEPS representations of the finite-temperature 2D Z2 lattice gauge theory.
The paper introduces compositional interpretability as a category-theoretic framework that casts mechanistic explanations as commuting syntactic-semantic mappings optimized under faithfulness and complexity constraints derived from minimum description length.
Dynamical correlations in a dissipative XXZ spin chain preserve early-time transport universality classes (ballistic, KPZ, diffusive) with magnon ballistic features at finite magnetization, but acquire exponential damping at long times under Lindblad evolution.
AI coding agents evolve simple ground-state protocols into improved versions for VQE, DMRG, and AFQMC on spin models and molecules by using executable energy scores under fixed compute budgets.
Computational constraints exponentially suppress accessible entanglement for some highly entangled quantum states and can make mixed-state min-entropy appear maximal when the information-theoretic version is negative.
Alternating cross interpolation performs elementwise operations on tensor trains in O(χ³) time with error control, improving on the standard O(χ⁴) scaling when output ranks are controlled.
An adaptive patching method exploits block-sparse QTT structures to reduce computational costs for tensor contractions and enables efficient evaluation of bubble diagrams and Bethe-Salpeter equations.
All embedding quantum kernels can be understood as entangled tensor kernels, yielding new insights into their inductive bias and potential dequantization.
k-local quantum Hamiltonians admit system-size-independent spectral gap for Gibbs samplers at high temperature, enabling FPT quantum approximation algorithms for partition functions.
Presents MPI-based parallelization using inverse canonical and site-canonical gauges plus randomized projections to accelerate MPO-MPO contractions via the fit algorithm.
Tensor network scans reveal that the stationary spin entanglement entropy ridge follows population phase boundaries at small s but lacks the two-branch structure at large s in the sub-Ohmic spin-boson model.
Derives combinatorial expression for degrees of tensor train varieties via integral geometry and releases Julia package TTVarietyDegree.jl.
A communication-aware multi-GPU distribution approach for tensor network contraction reports 7-173x extra speedup over slicing on 8 H100 GPUs and 42x to 67,869x on 1024 GPUs.
DMFT on the 2D Hubbard-Holstein model produces two Fermi-resonance peaks in electronic friction missed by MFT, with EF-LD simulations revealing substantial differences in electron population dynamics.
COO co-optimizes orbitals with TrimCI to absorb many-body correlations into the basis, cutting determinant count by orders of magnitude for iron-sulfur clusters versus localized bases or DMRG.
A quantum prototype learning scheme encodes class representatives as generative matrix product states and performs classification and clustering via geometric measures in Hilbert space, outperforming classical prototypes on Fashion-MNIST and ECG data.
A tensor train method computes the Koopman generator via operator logarithm while preserving low-rank structure for scalable identification of high-dimensional nonlinear dynamics.
A tensor-network solver extended with jump-counting computes electron currents in up to 50 quantum dots, matching traditional solvers for small systems but with orders of magnitude less memory and time.
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A hardware-efficient variational ansatz with an exact diagonal metric for real- and imaginary-time evolution and Haar sampling
A hardware-efficient binary-tree ansatz has a closed-form diagonal Fubini–Study metric, enabling metric-aware VQE and time evolution without auxiliary circuits, with linear-in-k pruning for sparse sectors.
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Mixed-dimensional quantum Monte Carlo studies of M-point moir\'e materials
Introduces an efficient SSE QMC algorithm with global updates and parallel tempering for mixed-dimensional models and applies it to map angle-dependent correlated insulators and Wigner-Mott states in M-point twisted AA-stacked SnSe2.
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Full-State and Reduced-Moment Encodings: A Representation-Level View of Equilibrium Quantum Many-Body Theory
Equilibrium quantum many-body methods are encoders from admissible states to represented variables, with exact decoders existing precisely when tasks are constant on encoder fibers.
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Absence of poor local minima in matrix product states
MPS energy landscapes lack poor local minima because gauge freedom induces overparametrization that concentrates local minima near the global minimum, with the local minimum distribution proven invariant under orthogonality center moves.
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Tensor network compression using fluid dynamics as a testbed: Analytical foundations in one dimension
Tensor networks enable tunable, objective compression of 1D fluid data with lossless reconstruction at high bond dimension and efficient in-compressed-space operations like periodic convolution.
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The bulk spectral gap is semi-decidable: a convergent family of certified upper bounds
A convergent SDP hierarchy certifies upper bounds on the thermodynamic-limit bulk spectral gap, making the bulk gap semi-decidable and producing the first certified bounds for the kagome Heisenberg model.
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Truncating loopy tensor networks by zero-mode gauge fixing: the $Z_2$ lattice gauge theory at finite temperature
A zero-mode gauge fixing technique truncates bonds in loopy tensor networks by exploiting linear dependencies in the metric tensor of cut-bond states, applied to iPEPS representations of the finite-temperature 2D Z2 lattice gauge theory.
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From Mechanistic to Compositional Interpretability
The paper introduces compositional interpretability as a category-theoretic framework that casts mechanistic explanations as commuting syntactic-semantic mappings optimized under faithfulness and complexity constraints derived from minimum description length.
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Dynamical correlations in a dissipative XXZ spin chain
Dynamical correlations in a dissipative XXZ spin chain preserve early-time transport universality classes (ballistic, KPZ, diffusive) with magnon ballistic features at finite magnetization, but acquire exponential damping at long times under Lindblad evolution.
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Optimizing ground state preparation protocols with autoresearch
AI coding agents evolve simple ground-state protocols into improved versions for VQE, DMRG, and AFQMC on spin models and molecules by using executable energy scores under fixed compute budgets.
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Accessible Quantum Correlations Under Complexity Constraints
Computational constraints exponentially suppress accessible entanglement for some highly entangled quantum states and can make mixed-state min-entropy appear maximal when the information-theoretic version is negative.
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Fast elementwise operations on tensor trains with alternating cross interpolation
Alternating cross interpolation performs elementwise operations on tensor trains in O(χ³) time with error control, improving on the standard O(χ⁴) scaling when output ranks are controlled.
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Adaptive Patching for Tensor Train Computations
An adaptive patching method exploits block-sparse QTT structures to reduce computational costs for tensor contractions and enables efficient evaluation of bubble diagrams and Bethe-Salpeter equations.
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New perspectives on quantum kernels through the lens of entangled tensor kernels
All embedding quantum kernels can be understood as entangled tensor kernels, yielding new insights into their inductive bias and potential dequantization.
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Fast mixing of all-to-all quantum systems at high temperatures
k-local quantum Hamiltonians admit system-size-independent spectral gap for Gibbs samplers at high temperature, enabling FPT quantum approximation algorithms for partition functions.
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Parallelized contraction of tensor trains or matrix product operators
Presents MPI-based parallelization using inverse canonical and site-canonical gauges plus randomized projections to accelerate MPO-MPO contractions via the fit algorithm.
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Entanglement structure of the dynamical phases in the sub-Ohmic spin-boson model
Tensor network scans reveal that the stationary spin entanglement entropy ridge follows population phase boundaries at small s but lacks the two-branch structure at large s in the sub-Ohmic spin-boson model.
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Degree of tensor train varieties via integral geometry
Derives combinatorial expression for degrees of tensor train varieties via integral geometry and releases Julia package TTVarietyDegree.jl.
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Parallelizing Large-Scale Tensor Network Contraction on Multiple GPUs
A communication-aware multi-GPU distribution approach for tensor network contraction reports 7-173x extra speedup over slicing on 8 H100 GPUs and 42x to 67,869x on 1024 GPUs.
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A DMFT approach to evaluate electronic frictional effects near solid surfaces of strongly correlated systems
DMFT on the 2D Hubbard-Holstein model produces two Fermi-resonance peaks in electronic friction missed by MFT, with EF-LD simulations revealing substantial differences in electron population dynamics.
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Absorbing Many-Body Correlations into Core-Optimized Orbitals
COO co-optimizes orbitals with TrimCI to absorb many-body correlations into the basis, cutting determinant count by orders of magnitude for iron-sulfur clusters versus localized bases or DMRG.
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Geometric Prototype Learning in Quantum Hilbert Space with Matrix Product States
A quantum prototype learning scheme encodes class representatives as generative matrix product states and performs classification and clustering via geometric measures in Hilbert space, outperforming classical prototypes on Fashion-MNIST and ECG data.
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Tensor-based computation of the Koopman generator via operator logarithm
A tensor train method computes the Koopman generator via operator logarithm while preserving low-rank structure for scalable identification of high-dimensional nonlinear dynamics.
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Tensor-network simulation of quantum transport in many-quantum-dot systems
A tensor-network solver extended with jump-counting computes electron currents in up to 50 quantum dots, matching traditional solvers for small systems but with orders of magnitude less memory and time.
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QCommute: a tool for symbolic computation of nested commutators in quantum many-body spin-1/2 systems
A new open-source C++ package computes nested commutators [H,[H,...A]] exactly and symbolically in the thermodynamic limit for spin-1/2 hypercubic lattices.
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Tensor-Parallel Emulation of Quantum Circuits with Block-Cyclic Distributed Matrix Product States
Presents a tensor-parallel distributed MPS method with block-cyclic partitioning and pivoted QR that emulates Google's RCS benchmark at bond dimension 16384 on 32 nodes, claiming three orders of magnitude better accuracy than prior methods.
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Spectral and transmission properties of multiple correlated quantum dots made simple
i-DFT computes spectral and transmission properties of correlated quantum dots from Coulomb blockade to Kondo regimes, matching many-body results at reduced cost.
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Shuttling of $\mathbb{Z}_4$ parafermions in an electronic ladder model
Numerical study demonstrates controlled transport of Z4 parafermion edge states in a ladder model and quantifies the adiabatic speed limit under realistic conditions.
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Revisiting semiclassical scalar QED in 1+1 dimensions
Backreaction in semiclassical scalar QED in 1+1D avoids instabilities and produces over-screening at high external charges.
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Completely Positive and Trace Preserving Schemes with Tensor Train Compression for the Lindblad Equation
A two-level low-rank method using tall-skinny factorization plus tensor-train compression enables completely positive trace-preserving integration of the Lindblad equation for systems with up to 10^19 degrees of freedom.
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Pair binding and Hund's rule breaking in high-symmetry fullerenes
DMRG simulations of the Hubbard model on fullerenes find a lower Mott transition in C20 than prior estimates, repulsive pair binding, and Hund's rule breaking in C40 and C60 consistent with an electronic superconductivity mechanism.
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Comparison of MPS based real time evolution algorithms for Anderson Impurity Models
Adapted TEBD in star geometry is the most efficient MPS method for real-time evolution of Anderson impurity models among the tested combinations.
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Quantum-Inspired Hamiltonian Optimization, Stochastic Tensor Networks and Adaptive Congestion Routing for Large-Scale QKD Networks
A quantum-inspired framework using effective Hamiltonians, Metropolis annealing and stochastic tensor-network compression is proposed for adaptive multi-demand routing in large-scale QKD networks.
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PEPSKit.jl: A Julia package for projected entangled-pair state simulations
PEPSKit.jl is a Julia package that supplies high-level algorithms for ground-state, time-evolution and finite-temperature iPEPS simulations with symmetry support on various lattices.
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Quantum Optimization Algorithms for Strongly Correlated Many-Body Systems
Perspective review comparing variational and feedback quantum algorithms for simulating phase transitions in quantum many-body systems, highlighting barren plateaus and advocating physics-informed hybridization.
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Lecture Notes on Replica Tensor Networks for Random Quantum Circuits
Lecture notes and accompanying library teach replica tensor network methods to compute circuit-averaged observables in random quantum circuits by mapping them to classical statistical mechanics models.
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Benchmarking a restricted Boltzmann machine on the $\mathbb{Z}_2$ Bose-Hubbard chain in the adiabatic hard-core regime
A shallow restricted Boltzmann machine variational Monte Carlo ansatz reproduces the main features of the adiabatic phase diagram and selected symmetry-broken insulating states for the one-dimensional Z2 Bose-Hubbard chain at half filling.
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Quantum-inspired tensor networks in machine learning models
Tensor networks developed for quantum states are reviewed as tools for machine learning models, with assessment of their potential computational, explanatory, and privacy advantages alongside remaining challenges.
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Introduction to matrix-product states and tensor networks
Introductory lecture notes on tensor networks with emphasis on matrix-product states, their algorithms, higher-dimensional generalizations, and applications to mixed states and open quantum systems, accompanied by Julia code.
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