arXiv subjects

Andi Gu

Publications and source records attributed to Andi Gu.

24 records · Page 2Linked to original sources

arXiv2024

Pseudomagic Quantum States

Notions of nonstabilizerness, or "magic", quantify how non-classical quantum states are in a precise sense: states exhibiting low nonstabilizerness preclude quantum advantage. We introduce 'pseudomagic' ensembles of quantum states that, despite low nonstabilizerness, are computationally indistinguishable from those with high nonstabilizerness. Previously, such computational indistinguishability has been studied with respect to entanglement, introducing the concept of pseudoentanglement. However, we demonstrate that pseudomagic neither follows from pseudoentanglement nor implies it. In terms of applications, the study of pseudomagic offers fresh insights into the theory of quantum scrambling: it uncovers states that, even though they originate from non-scrambling unitaries, remain indistinguishable from scrambled states to any physical observer. Additional applications include new lower bounds on state synthesis problems, property testing protocols, and implications for quantum cryptography. Our work is driven by the observation that only quantities measurable by a computationally bounded observer - intrinsically limited by finite-time computational constraints - hold physical significance. Ultimately, our findings suggest that nonstabilizerness is a 'hide-able' characteristic of quantum states: some states are much more magical than is apparent to a computationally bounded observer.

quant-ph↗

arXiv2024

Magic-induced computational separation in entanglement theory

Entanglement serves as a foundational pillar in quantum information theory, delineating the boundary between what is classical and what is quantum. The common assumption is that higher entanglement corresponds to a greater degree of `quantumness'. However, this folk belief is challenged by the fact that classically simulable operations, such as Clifford circuits, can create highly entangled states. The simulability of these states raises a question: what are the differences between `low-magic' entanglement, and `high-magic' entanglement? We answer this question in this work with a rigorous investigation into the role of magic in entanglement theory. We take an operational approach to understanding this relationship by studying tasks such as entanglement estimation, distillation and dilution. This approach reveals that magic has notable implications for entanglement. Specifically, we find an operational separation that divides Hilbert space into two distinct regimes: the entanglement-dominated (ED) phase and magic-dominated (MD) phase. Roughly speaking, ED states have entanglement that significantly surpasses their magic, while MD states have magic that dominates their entanglement. The competition between the two resources in these two phases induces a computational phase separation between them: there are {sample- and time-efficient} quantum algorithms for almost any entanglement task on ED states, while these tasks are {provably computationally intractable} in the MD phase. Our results find applications in diverse areas such as quantum error correction, many-body physics, and the study of quantum chaos, providing a unifying framework for understanding the behavior of quantum systems. We also offer theoretical explanations for previous numerical observations, highlighting the broad implications of the ED-MD distinction across various subfields of physics.

quant-ph↗

arXiv2023

Exploiting Inductive Biases in Video Modeling through Neural CDEs

We introduce a novel approach to video modeling that leverages controlled differential equations (CDEs) to address key challenges in video tasks, notably video interpolation and mask propagation. We apply CDEs at varying resolutions leading to a continuous-time U-Net architecture. Unlike traditional methods, our approach does not require explicit optical flow learning, and instead makes use of the inherent continuous-time features of CDEs to produce a highly expressive video model. We demonstrate competitive performance against state-of-the-art models for video interpolation and mask propagation tasks.

cs.CV↗

arXiv2023

Variable Length Embeddings

In this work, we introduce a novel deep learning architecture, Variable Length Embeddings (VLEs), an autoregressive model that can produce a latent representation composed of an arbitrary number of tokens. As a proof of concept, we demonstrate the capabilities of VLEs on tasks that involve reconstruction and image decomposition. We evaluate our experiments on a mix of the iNaturalist and ImageNet datasets and find that VLEs achieve comparable reconstruction results to a state of the art VAE, using less than a tenth of the parameters.

cs.CV↗

arXiv2022

Practical Black Box Hamiltonian Learning

We study the problem of learning the parameters for the Hamiltonian of a quantum many-body system, given limited access to the system. In this work, we build upon recent approaches to Hamiltonian learning via derivative estimation. We propose a protocol that improves the scaling dependence of prior works, particularly with respect to parameters relating to the structure of the Hamiltonian (e.g., its locality $k$). Furthermore, by deriving exact bounds on the performance of our protocol, we are able to provide a precise numerical prescription for theoretically optimal settings of hyperparameters in our learning protocol, such as the maximum evolution time (when learning with unitary dynamics) or minimum temperature (when learning with Gibbs states). Thanks to these improvements, our protocol is practical for large problems: we demonstrate this with a numerical simulation of our protocol on an 80-qubit system.

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arXiv2021

Adaptive shot allocation for fast convergence in variational quantum algorithms

Variational Quantum Algorithms (VQAs) are a promising approach for practical applications like chemistry and materials science on near-term quantum computers as they typically reduce quantum resource requirements. However, in order to implement VQAs, an efficient classical optimization strategy is required. Here we present a new stochastic gradient descent method using an adaptive number of shots at each step, called the global Coupled Adaptive Number of Shots (gCANS) method, which improves on prior art in both the number of iterations as well as the number of shots required. These improvements reduce both the time and money required to run VQAs on current cloud platforms. We analytically prove that in a convex setting gCANS achieves geometric convergence to the optimum. Further, we numerically investigate the performance of gCANS on some chemical configuration problems. We also consider finding the ground state for an Ising model with different numbers of spins to examine the scaling of the method. We find that for these problems, gCANS compares favorably to all of the other optimizers we consider.

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