A first-moment operator diagnostic reveals exponentially many inequivalent initialization distributions avoid barren plateaus in variational quantum algorithms, with numerics indicating distinct attained minima.
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Pauli propagation: A computational framework for simulating quantum systems
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abstract
Classical methods to simulate quantum systems are not only a key element of the physicist's toolkit for studying many-body models but are also increasingly important for verifying and challenging upcoming quantum computers. Pauli propagation has recently emerged as a promising new family of classical algorithms for simulating digital quantum systems. Here we provide a comprehensive account of Pauli propagation, tracing its algorithmic structure from its bit-level implementation and formulation as a tree-search problem, all the way to its high-level user applications for simulating quantum circuits and dynamics. Utilising these observations, we present PauliPropagation.jl, a Julia software package that can perform rapid Pauli propagation simulation straight out-of-the-box and can be used more generally as a building block for novel simulation algorithms.
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Above a critical noise strength, operator scrambling in random circuits is suppressed leading to classical simulability; below it, simulation stays exponentially hard.
Local quenches in chaotic quantum systems produce a Renyi-index-tuned hierarchy of entanglement transitions, with S_alpha>1 obeying area law while S_alpha<=1 is volume-law, carried by an O(1)-dimensional dominant Schmidt sector that itself exhibits similar transitions at lower critical indices.
Symmetry-adapted Pauli-orbit and modified Gell-Mann bases make polynomial-dimensional dynamical Lie algebras practically simulable beyond free fermions.
fTDHF extends time-dependent Hartree-Fock to fermionized spin-1/2 Hamiltonians, remaining exact for free fermions while handling non-local strings via non-orthogonal Slater determinant transitions and reproducing qualitative dynamics in three benchmark models.
A new sparse Pauli-frame method shows coherent noise thresholds are overestimated by a factor of ~4 under Pauli-twirling and revises the T-to-S gate error rate factor to as high as 7 at distance d=5.
cTJM combines local TDVP MPS gate evolution with variance-aware Pauli-Lindblad jump sampling, cutting trajectory variance and bond growth on noisy circuits up to 127 qubits.
Diameter truncation of operators provides an efficient approximation for simulating local dynamics and transport in out-of-equilibrium quantum many-body systems.
Develops an invariant-based framework connecting Pauli Lie algebras to transvection-generated Clifford subgroups for quantum reachability and dynamics analysis.
A hybrid method uses fixed quantum annealing states as boundary resources for classical MERA tensor networks to improve ground-state approximations without deeper quantum circuits.
Fourier-based LCU decomposes diagonal and non-diagonal unitaries into hardware-friendly forms for QAOA-style optimization, trading circuit depth for sampling overhead with performance guarantees.
A recipe for initial points in variational compression of quantum time-evolution operators that provably converges to near-optimal O(N t polylog(N t/ε)) gate complexity for local translationally invariant Hamiltonians.
A 120-qubit digital simulation of 1D Fermi-Hubbard dynamics on IBM hardware matches TDVP tensor-network results to ~1% RMSE up to t≈5.2, with a large wall-clock speedup at the point of divergence.
Randomized Subsystem Descent reduces weighted Pauli weight in fermion-to-qubit mappings for Hubbard models up to 16x16 sites and molecular Hamiltonians with 54 modes.
Local operators in quantum chaotic systems cascade toward non-local fractal structures whose dimension is tied by unitarity to the decay rate of local correlations, demonstrated exactly in dual-unitary circuits and numerically in others.
New techniques for error-independent unified path variation, non-degenerate batched sampling, and flexible contraction accelerate tensor network quantum trajectory simulations by more than 10^8 times.
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.
The paper proposes variational decision diagrams (VDDs) for quantum state representation in QML and reports successful training without barren plateaus on transverse-field Ising and Heisenberg Hamiltonians.
Hybrid framework combines Pauli propagation with noise-canceling channels to compute observables more accurately on quantum hardware with lower classical and quantum resource costs.
Statistical interference sampling using a Chemical Abstract Machine model prunes nearly 50% of endpoint interference reactions while retaining over 90% output accuracy on Deutsch-Jozsa, Grover, Simon, and small Shor instances.
PauLIB implements a compact bit-packed symplectic representation and SoA layout for Pauli strings, delivering 14x–21,000x speedups and 7.3x memory reduction versus existing Python frameworks at 500 qubits.
Quantum computers may enable more natural manipulation of Fourier spectra in ML models via the Quantum Fourier Transform, potentially leading to resource-efficient spectral methods.
PauliEngine delivers a high-performance C++ backend for Pauli string multiplication, commutators, and symbolic tracking that outperforms existing tools in benchmarks.
Systematic numerical study of QAOA parameter transfer on heavy-hex Ising models with local cubic terms shows transferred angles from small instances yield improving expectation values up to 49 layers on instances up to 156 qubits, with hardware runs confirming gains up to p=10.
citing papers explorer
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Exponentially many initializations to avoid barren plateaus
A first-moment operator diagnostic reveals exponentially many inequivalent initialization distributions avoid barren plateaus in variational quantum algorithms, with numerics indicating distinct attained minima.
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Noise-induced Simulability Transition from Operator Scrambling
Above a critical noise strength, operator scrambling in random circuits is suppressed leading to classical simulability; below it, simulation stays exponentially hard.
-
Hierarchical entanglement transitions and hidden area-law sectors in quantum many-body dynamics
Local quenches in chaotic quantum systems produce a Renyi-index-tuned hierarchy of entanglement transitions, with S_alpha>1 obeying area law while S_alpha<=1 is volume-law, carried by an O(1)-dimensional dominant Schmidt sector that itself exhibits similar transitions at lower critical indices.
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Enabling Lie-Algebraic Classical Simulation beyond Free Fermions
Symmetry-adapted Pauli-orbit and modified Gell-Mann bases make polynomial-dimensional dynamical Lie algebras practically simulable beyond free fermions.
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Fermionic mean-field dynamics for spin systems beyond free fermions
fTDHF extends time-dependent Hartree-Fock to fermionized spin-1/2 Hamiltonians, remaining exact for free fermions while handling non-local strings via non-orthogonal Slater determinant transitions and reproducing qualitative dynamics in three benchmark models.
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Computing logical error thresholds with the Pauli Frame Sparse Representation
A new sparse Pauli-frame method shows coherent noise thresholds are overestimated by a factor of ~4 under Pauli-twirling and revises the T-to-S gate error rate factor to as high as 7 at distance d=5.
-
Noisy quantum circuit simulation with the tensor jump method
cTJM combines local TDVP MPS gate evolution with variance-aware Pauli-Lindblad jump sampling, cutting trajectory variance and bond growth on noisy circuits up to 127 qubits.
-
Diameter truncated operator evolution
Diameter truncation of operators provides an efficient approximation for simulating local dynamics and transport in out-of-equilibrium quantum many-body systems.
-
From Pauli Strings to Quantum Dynamics: A Unified Characterization
Develops an invariant-based framework connecting Pauli Lie algebras to transvection-generated Clifford subgroups for quantum reachability and dynamics analysis.
-
Combining non-parametric quantum states and MERA tensor networks for ground-state optimization
A hybrid method uses fixed quantum annealing states as boundary resources for classical MERA tensor networks to improve ground-state approximations without deeper quantum circuits.
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Efficient Fourier-Based Linear Combination of Unitaries and Applications in Quantum Optimization
Fourier-based LCU decomposes diagonal and non-diagonal unitaries into hardware-friendly forms for QAOA-style optimization, trading circuit depth for sampling overhead with performance guarantees.
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Near-Optimal Quantum Time Evolution Circuits via Provably Convergent Compression
A recipe for initial points in variational compression of quantum time-evolution operators that provably converges to near-optimal O(N t polylog(N t/ε)) gate complexity for local translationally invariant Hamiltonians.
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Fast, accurate, high-resolution simulation of large-scale Fermi-Hubbard models on a digital quantum processor
A 120-qubit digital simulation of 1D Fermi-Hubbard dynamics on IBM hardware matches TDVP tensor-network results to ~1% RMSE up to t≈5.2, with a large wall-clock speedup at the point of divergence.
-
Randomized Subsystem Descent for Fermion-to-Qubit Mapping
Randomized Subsystem Descent reduces weighted Pauli weight in fermion-to-qubit mappings for Hubbard models up to 16x16 sites and molecular Hamiltonians with 54 modes.
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Quantum many-body operator cascade as a route to chaos
Local operators in quantum chaotic systems cascade toward non-local fractal structures whose dimension is tied by unitarity to the decay rate of local correlations, demonstrated exactly in dual-unitary circuits and numerically in others.
-
Accelerating Quantum Tensor Network Simulations with Unified Path Variations and Non-Degenerate Batched Sampling
New techniques for error-independent unified path variation, non-degenerate batched sampling, and flexible contraction accelerate tensor network quantum trajectory simulations by more than 10^8 times.
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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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Variational decision diagrams for quantum-inspired machine learning applications
The paper proposes variational decision diagrams (VDDs) for quantum state representation in QML and reports successful training without barren plateaus on transverse-field Ising and Heisenberg Hamiltonians.
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Computing noise-canceling observables via Pauli propagation
Hybrid framework combines Pauli propagation with noise-canceling channels to compute observables more accurately on quantum hardware with lower classical and quantum resource costs.
-
Half the Interference, Most of the Answer: Approximate Quantum Simulation via Path-Sum Pruning
Statistical interference sampling using a Chemical Abstract Machine model prunes nearly 50% of endpoint interference reactions while retaining over 90% output accuracy on Deutsch-Jozsa, Grover, Simon, and small Shor instances.
-
PauLIB: A High-Performance Library for Processing Pauli Strings
PauLIB implements a compact bit-packed symplectic representation and SoA layout for Pauli strings, delivering 14x–21,000x speedups and 7.3x memory reduction versus existing Python frameworks at 500 qubits.
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Spectral methods: crucial for machine learning, natural for quantum computers?
Quantum computers may enable more natural manipulation of Fourier spectra in ML models via the Quantum Fourier Transform, potentially leading to resource-efficient spectral methods.
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PauliEngine: High-Performant Symbolic Arithmetic for Quantum Operations
PauliEngine delivers a high-performance C++ backend for Pauli string multiplication, commutators, and symbolic tracking that outperforms existing tools in benchmarks.
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Evaluating the Limits of QAOA Parameter Transfer at High-Rounds on Sparse Ising Models With Geometrically Local Cubic Terms
Systematic numerical study of QAOA parameter transfer on heavy-hex Ising models with local cubic terms shows transferred angles from small instances yield improving expectation values up to 49 layers on instances up to 156 qubits, with hardware runs confirming gains up to p=10.
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SAFE ma-QAOA: Surrogate-Assisted and Fine-Tuning Enhanced Multi-Angle QAOA with Parameter Distillation
Combining a truncated classical surrogate, angle pruning, and exact fine-tuning cuts the number of active angles and estimated fine-tuning cost of ma-QAOA on small spin-glass and Max-Cut instances while preserving near-optimal approximation ratios.
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How to Build a Quantum Supercomputer: Scaling from Hundreds to Millions of Qubits
A comprehensive review of scaling paths for superconducting quantum computers, with resource and sensitivity analyses for utility-scale applications under realistic error distributions.
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Setting angles in quantum approximate optimization at utility-scale
The paper benchmarks approximation techniques and transfer learning for setting QAOA angles at utility scale and extracts operational guidance from hardware-validated results.
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- Non-Local Magic Resources for Fermionic Gaussian States
- Recursion method for quench dynamics: strengths and limitations