Lie group diffusion models combine a discrete circuit skeleton selector with continuous diffusion on SU(2) ≃ S³ to synthesize hardware-aware quantum circuits, outperforming baselines on three-qubit Hamiltonian simulation targets.
An Introduction to Cartan's KAK Decomposition for QC Programmers
9 Pith papers cite this work, alongside 47 external citations. Polarity classification is still indexing.
9
Pith papers citing it
47
external citations · Pith
abstract
This paper presents no new results; its goals are purely pedagogical. A special case of the Cartan Decomposition has found much utility in the field of quantum computing, especially in its sub-field of quantum compiling. This special case allows one to factor a general 2-qubit operation (i.e., an element of U(4)) into local operations applied before and after a three parameter, non-local operation. In this paper, we give a complete and rigorous proof of this special case of Cartan's Decomposition. From the point of view of QC programmers who might not be familiar with the subtleties of Lie Group Theory, the proof given here has the virtues, that it is constructive in nature, and that it uses only Linear Algebra. The constructive proof presented in this paper is implemented in some Octave/Matlab m-files that are included with the paper. Thus, this paper serves as documentation for the attached m-files.
representative citing papers
GULPS partitions two-qubit unitary synthesis into depth-2 segments solved via linear programming over Littlewood-Richardson inequalities followed by least-squares optimization, yielding faster and lower-cost decompositions than prior synthesizers on heterogeneous ISAs.
Introduces a parallelizable hybrid tensor network algorithm for time-evolving matrix product states that combines classical BUG integration with quantum methods without synchronization barriers.
Conveyor-mode electron shuttling enables high-fidelity single-qubit rotations via EDSR and tunable two-qubit interactions via diabatic gates in semiconductor spin qubits.
A co-design method for frequency allocation and noise-aware transpilation in tunable-coupler quantum systems yields 8.9% lower log-infidelity cost and 6.8% shorter circuits than SABRE on SNAIL architectures.
An algorithm is presented for estimating distribution complexity of electronic structure Hamiltonians, with O(N^3) entanglement estimation per fragment and quadratic/exponential reductions in distribution cost for quantum and classical interconnects.
Presents a universal parametrized quantum circuit ansatz based on Euler-Cartan decompositions, benchmarked on energy spectra of lattice QFT models with short- and long-range interactions.
citing papers explorer
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Lie Group Diffusion Models for Hardware-Aware Quantum Circuit Synthesis
Lie group diffusion models combine a discrete circuit skeleton selector with continuous diffusion on SU(2) ≃ S³ to synthesize hardware-aware quantum circuits, outperforming baselines on three-qubit Hamiltonian simulation targets.
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GULPS: Two-Qubit Gate Synthesis via Linear Programming for Heterogeneous Instruction Sets
GULPS partitions two-qubit unitary synthesis into depth-2 segments solved via linear programming over Littlewood-Richardson inequalities followed by least-squares optimization, yielding faster and lower-cost decompositions than prior synthesizers on heterogeneous ISAs.
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Time Evolution on Hybrid Tensor Networks -- A Novel and Parallelizable Algorithm
Introduces a parallelizable hybrid tensor network algorithm for time-evolving matrix product states that combines classical BUG integration with quantum methods without synchronization barriers.
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Spin qubit operations by conveyor-mode shuttling
Conveyor-mode electron shuttling enables high-fidelity single-qubit rotations via EDSR and tunable two-qubit interactions via diabatic gates in semiconductor spin qubits.
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Fidelity-Aware Frequency Allocation and Transpilation Co-Design for Tunable Coupler Quantum Systems
A co-design method for frequency allocation and noise-aware transpilation in tunable-coupler quantum systems yields 8.9% lower log-infidelity cost and 6.8% shorter circuits than SABRE on SNAIL architectures.
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Distribution Complexity of Electronic Structure Simulations on Quantum Supercomputers
An algorithm is presented for estimating distribution complexity of electronic structure Hamiltonians, with O(N^3) entanglement estimation per fragment and quadratic/exponential reductions in distribution cost for quantum and classical interconnects.
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Universal Euler-Cartan Circuits for Quantum Field Theories
Presents a universal parametrized quantum circuit ansatz based on Euler-Cartan decompositions, benchmarked on energy spectra of lattice QFT models with short- and long-range interactions.
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