Hansen S. Wu | Searcharxiv

arXiv2026

Qubit discretizations of d=3 conformal field theories

We propose that scaling dimensions of d=3 conformal field theories can be studied on a system of qubits with near term quantum simulation platforms. Our proposal chooses couplings of quantum many-body problems on a polyhedral lattice at which the conformal state-operator correspondence can be observed most accurately in the spectrum. We validate our protocol on the Ising model where we extract the scaling dimensions of a number of scaling operators with a few percent accuracy from the spectrum of a system of just 20 qubits. The procedure makes only minor assumptions beyond general conformal invariance -- it may hence be applied widely. Requirements and challenges to realize this proposal on quantum computers are discussed. Our results demonstrate that for current or near term qubit platforms, three dimensional conformal field theories present a unique opportunity -- a forefront problem that is difficult on classical computers but may be solved through quantum simulation.

cond-mat.str-el↗

arXiv2025

Projected Density Matrix Sampling for Lattice Hamiltonians

Quantum Monte Carlo methods are powerful tools for studying quantum many-body systems but face difficulties in accessing excited states and in treating sign problems. We present a continuous-time path-integral Monte Carlo method for computing the low-lying spectrum of generic quantum Hamiltonians within a projection subspace. The method projects the thermal density matrix onto a subspace spanned by a chosen set of linearly independent states. It is free of Trotter discretization errors and systematically converges to the low-energy states which have finite overlap with the projection subspace as the $β$ parameter increases. While most effective for systems without a sign problem, the method also yields information about low-energy spectra when sign problems are present. We illustrate the approach on two problems. For the sign-free case, we compute the first four low-energy levels in the scaling limit of the one-dimensional Ising model with both transverse and longitudinal fields, demonstrating the flow from the conformal limit to the massive $E_8$ quantum field theory. For the sign-problem case, we apply the method to the frustrated Shastry-Sutherland model and benchmark it against exact diagonalization on small lattices. We also present results for larger systems beyond the lattice sizes accessible to exact diagonalization, while limited to small $β$ where sign problems occur. Our method provides a general route toward quantum Monte Carlo spectroscopy for lattice Hamiltonians.

cond-mat.str-el↗