Zhou-Quan Wan

Variational Monte Carlo (VMC) is a powerful and fast-growing method for optimizing and evolving parametrized many-body wave functions, especially with modern neural-network quantum states. In practice, however, the stochastic estimators that form the backbone of the method can become unstable or biased due to the presence of nodes, a ubiquitous feature of quantum wave functions. In the continuum, this results in heavy-tailed estimators with potentially divergent variances, while in discrete Hilbert spaces the sampling distribution can miss parts of the support needed to form unbiased estimators. These statistical pathologies lead to unreliable optimization trajectories in stochastic reconfiguration or incorrect variational dynamics in time-dependent variational Monte Carlo (t-VMC) and severely limit the power of the numerical simulations. We introduce blurred sampling to address these difficulties. The method has a number of rigorous properties that make it well behaved, effective, and computationally efficient. Additionally, it is a postprocessing approach that can be used without modifying the underlying sampler and incurs only minimal overhead. We demonstrate its effectiveness in a broad range of problems—including ground-state optimization in both continuum and discrete settings as well as in time-dependent variational Monte Carlo, where it resolves previously identified failure modes—and further apply it to large-scale problems in spin dynamics. This work establishes a broadly applicable framework for robust VMC and t-VMC calculations.

While experimental evidence for spacetime supersymmetry (SUSY) in particle physics remains elusive, condensed matter systems offer a promising arena for its emergence at quantum critical points (QCPs). Although there have been a variety of proposals for emergent SUSY at symmetry-breaking QCPs, the emergence of SUSY at fractionalized QCPs remains largely unexplored. Here, we demonstrate emergent spacetime SUSY at a fractionalized QCP in the Kitaev honeycomb model with Su-Schrieffer-Heeger (SSH) spin-phonon coupling. Specifically, through numerical computations and analytical analysis, we show that the anisotropic SSH-Kitaev model hosts a fractionalized QCP between a Dirac spin liquid and an incommensurate or commensurate valence-bond-solid phase coexisting with Z 2 topological order. A low-energy field theory incorporating phonon quantum fluctuations reveals that this fractionalized QCP features an emergent N = 2 spacetime SUSY. We further discuss their universal experimental signatures in thermal transport and viscosity, highlighting the concrete lattice realization of emergent SUSY at a fractionalized QCP in 2D.

The quantum error correction threshold is closely related to the Nishimori physics of random statistical models. We extend quantum information measures such as coherent information beyond the Nishimori line and establish them as sharp indicators of phase transitions over the full p − T plane. These generalized measures admit a natural operational interpretation as diagnostics of inference mismatch for decoders operating at an effective temperature. We derive exact inequalities for several generalized measures, demonstrating that each attains its extremum along the Nishimori line. As a direct application, we study these measures in the 2d ± J random-bond Ising model—corresponding to a surface code under bit-flip noise—and revisit the Nishimori multicritical point. Among all indicators, coherent information exhibits the weakest finite-size effects, enabling a high-precision estimate p c = 0.109 2212 ( 4 ) and the associated critical exponents.

We revisit the infinite variance problem in fermionic Monte Carlo simulations, which is widely encountered in areas ranging from condensed matter to nuclear and high-energy physics. The different algorithms, which we broadly refer to as determinantal quantum Monte Carlo (DQMC), are applied in many situations and differ in details, but they share a foundation in field theory, and often involve fermion determinants whose symmetry properties make the algorithm sign-problem-free. We show that the infinite variance problem arises as the observables computed in DQMC tend to form heavy-tailed distributions. To remedy this issue retrospectively, we introduce a tail-aware error estimation method to correct the otherwise unreliable estimates of confidence intervals. Furthermore, we demonstrate how to perform DQMC calculations that eliminate the infinite variance problem for a broad class of observables. Our approach is an exact bridge link method, which involves a simple and efficient modification to the standard DQMC algorithm. The method introduces no systematic bias and is straightforward to implement with minimal computational overhead. Our results establish a practical and robust solution to the infinite variance problem, with broad implications for improving the reliability of a variety of fundamental fermion simulations.