arXiv subjects

Enji Xiong

Publications and source records attributed to Enji Xiong.

3 recordsLinked to original sources

arXiv2026

Learning Quantum Matter through Attention in Complex Space

Magnetic many-electron wavefunctions require amplitude and phase to be optimized together. Whether a complex internal representation improves this variational search is a practical question for neural wavefunction design. We introduce Complex Psiformer for interacting electrons in a magnetic moir\'e continuum, combining complex hidden features and Hermitian-magnitude attention with magnetic boundary conditions and fermionic antisymmetry. After the same number of optimization steps, Complex Psiformer reaches lower energies than Real Psiformer in two finite supercells. Both Psiformers also improve on their respective neural Hartree-Fock references. Across five training seeds in the 25-cell system, the mean Complex advantage is 1.458 meV per electron, with a smaller observed spread. A separately trained two-electron Complex state has a smaller energy gap to a finite configuration interaction reference than its Real counterpart. In the Complex states, flux scans show nonmonotonic density correlations and weaker honeycomb mean-density modulation at higher flux, while connected fluctuations persist. Gauge invariant current maps provide a qualitative comparison of local circulation in the optimized states. These benchmarks support the combined architecture as a variational ansatz for studying energies and charge arrangements in finite magnetic systems.

cond-mat.str-el↗

arXiv2026

Realified tensor networks: quantum circuit simulation on real-valued matrix accelerators

Tensor-network contraction simulates quantum circuits, but modern matrix accelerators (NPUs, TPUs) expose only real GEMM pipelines, so the complex networks of quantum simulation must be reconstructed in software. We resolve the mismatch by a realification rewrite that maps any complex tensor network to a real one. At each merge of two complex tensors, a rank-3 structure tensor realizes Gauss's three-multiplication (3M) formula; contractions with one or no complex operand need only two or one real products. We prove a tight cost law: overhead $1 + 2m + r$ in real multiplications, where $m$ and $r$ are the volume fractions of two- and one-complex-operand contractions, never exceeding $3\times$ relative to real contraction, with every intermediate at most doubled in size. On 67 circuits (random, Clifford+$T$, QAOA, VQE), the law holds across the real-to-complex range and complex-gate placement, not count, governs cost. Contraction orders transfer from the complex network with a relative arithmetic-cost gap below $5\times 10^{-4}$ on 66 of 67 circuits; the exception closes under a few steps of low-temperature simulated annealing. On an Ascend 910 NPU the rewrite beat both the four-real-GEMM baseline and a per-GEMM Gauss lowering on all twelve random circuits and on 52 of 55 structured cells (three cells slower by at most 12\%); the four-GEMM baseline was slower by a median $1.7\times$ (random) and $1.4\times$ (structured). Realification makes complex tensor-network contraction native to real-only matrix engines.

quant-ph↗

arXiv2026

A Nonstabilizerness Resource Law for Universal Quantum State Purification

Quantum state purification aims to recover higher-fidelity quantum states from multiple noisy copies and is a fundamental primitive for quantum information processing. Magic resources enable operations beyond classically simulable dynamics and are central to universal fault-tolerant quantum computation. Recent no-go results show that classically simulable operations cannot achieve a nontrivial universal fidelity gain. This motivates a quantitative theory of the magic required for purification at prescribed success probability and target fidelity. For universal purification with two input copies, we prove an exact linear mana law in odd dimensions and a two-sided linear robustness law for multi-qubit systems, which becomes exact for a single qubit. We also identify an explicit successful purification map that makes the tradeoff transparent. These results establish universal purification as a task obeying a quantitative magic-fidelity law and link magic resources to error mitigation and fault-tolerant quantum information processing.

quant-ph↗