Gauss law codes identify the full gauge-invariant sector as the code space while vacuum codes restrict to the matter vacuum, with the two shown to be unitarily equivalent for finite gauge groups.
Hamiltonian Simulation by Qubitization
6 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We present the problem of approximating the time-evolution operator $e^{-i\hat{H}t}$ to error $\epsilon$, where the Hamiltonian $\hat{H}=(\langle G|\otimes\hat{\mathcal{I}})\hat{U}(|G\rangle\otimes\hat{\mathcal{I}})$ is the projection of a unitary oracle $\hat{U}$ onto the state $|G\rangle$ created by another unitary oracle. Our algorithm solves this with a query complexity $\mathcal{O}\big(t+\log({1/\epsilon})\big)$ to both oracles that is optimal with respect to all parameters in both the asymptotic and non-asymptotic regime, and also with low overhead, using at most two additional ancilla qubits. This approach to Hamiltonian simulation subsumes important prior art considering Hamiltonians which are $d$-sparse or a linear combination of unitaries, leading to significant improvements in space and gate complexity, such as a quadratic speed-up for precision simulations. It also motivates useful new instances, such as where $\hat{H}$ is a density matrix. A key technical result is `qubitization', which uses the controlled version of these oracles to embed any $\hat{H}$ in an invariant $\text{SU}(2)$ subspace. A large class of operator functions of $\hat{H}$ can then be computed with optimal query complexity, of which $e^{-i\hat{H}t}$ is a special case.
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2026 6representative citing papers
A Monte Carlo-assisted analytic method tightens energy-based bounds on boson truncation errors, substantially reducing the volume dependence of the required cutoff in scalar and gauge theories.
Non-invertible symmetries define quantum gates with generalized complexity distances, and simple objects in symmetry categories turn out to be computationally complex in concrete 4D and 2D QFT examples.
Qudit encodings for quadratic diagonal evolutions require exponentially stronger synthesis advantages than qubits to win asymptotically in product formulas but can yield constant-factor savings in LCU at low d.
Quantum simulation methods for Thirring and Gross-Neveu fermionic models with arbitrary flavors, including gate complexity bounds and ground-state preparation up to 20 qubits.
Unitaria is a new open-source Python library that provides a high-level, composable interface for block encodings in quantum computing, enabling automatic circuit generation and classical simulation-based verification.
citing papers explorer
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Gauss law codes and vacuum codes from lattice gauge theories
Gauss law codes identify the full gauge-invariant sector as the code space while vacuum codes restrict to the matter vacuum, with the two shown to be unitarily equivalent for finite gauge groups.
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Tightening energy-based boson truncation bound using Monte Carlo-assisted methods
A Monte Carlo-assisted analytic method tightens energy-based bounds on boson truncation errors, substantially reducing the volume dependence of the required cutoff in scalar and gauge theories.
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Generalized Complexity Distances and Non-Invertible Symmetries
Non-invertible symmetries define quantum gates with generalized complexity distances, and simple objects in symmetry categories turn out to be computationally complex in concrete 4D and 2D QFT examples.
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Fault-Tolerant Resource Comparison of Qudit and Qubit Encodings for Diagonal Quadratic Operators
Qudit encodings for quadratic diagonal evolutions require exponentially stronger synthesis advantages than qubits to win asymptotically in product formulas but can yield constant-factor savings in LCU at low d.
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Quantum simulation of massive Thirring and Gross--Neveu models for arbitrary number of flavors
Quantum simulation methods for Thirring and Gross-Neveu fermionic models with arbitrary flavors, including gate complexity bounds and ground-state preparation up to 20 qubits.
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Unitaria: Quantum Linear Algebra via Block Encodings
Unitaria is a new open-source Python library that provides a high-level, composable interface for block encodings in quantum computing, enabling automatic circuit generation and classical simulation-based verification.