arXiv subjects

Yijia Xu

Publications and source records attributed to Yijia Xu.

27 records · Page 2Linked to original sources

arXiv2025

Clifford operations and homological codes for rotors and oscillators

We develop quantum information processing primitives for the planar rotor, the state space of a particle on a circle. By interpreting rotor wavefunctions as periodically identified wavefunctions of a harmonic oscillator, we determine the group of bosonic Gaussian operations inherited by the rotor. This $n$-rotor Clifford group, $\text{U}(1)^{n(n+1)/2} \rtimes \text{GL}_n(\mathbb{Z})$, is represented by continuous $\text{U}(1)$ gates generated by polynomials quadratic in angular momenta, as well as discrete $\text{GL}_n(\mathbb Z)$ momentum sign-flip and sum gates. We classify homological rotor error-correcting codes [arXiv:2303.13723] and various rotor states based on equivalence under Clifford operations. Reversing direction, we map homological rotor codes and rotor Clifford operations back into oscillators by interpreting occupation-number states as rotor states of non-negative angular momentum. This yields new multimode homological bosonic codes protecting against dephasing and changes in occupation number, along with their corresponding encoding and decoding circuits. In particular, we show how to non-destructively measure the oscillator phase using conditional occupation-number addition and post selection. We also outline several rotor and oscillator varieties of the GKP-stabilizer codes [arXiv:1903.12615].

quant-ph↗

arXiv2024

SpearBot: Leveraging Large Language Models in a Generative-Critique Framework for Spear-Phishing Email Generation

Large Language Models (LLMs) are increasingly capable, aiding in tasks such as content generation, yet they also pose risks, particularly in generating harmful spear-phishing emails. These emails, crafted to entice clicks on malicious URLs, threaten personal information security. This paper proposes an adversarial framework, SpearBot, which utilizes LLMs to generate spear-phishing emails with various phishing strategies. Through specifically crafted jailbreak prompts, SpearBot circumvents security policies and introduces other LLM instances as critics. When a phishing email is identified by the critic, SpearBot refines the generated email based on the critique feedback until it can no longer be recognized as phishing, thereby enhancing its deceptive quality. To evaluate the effectiveness of SpearBot, we implement various machine-based defenders and assess how well the phishing emails generated could deceive them. Results show these emails often evade detection to a large extent, underscoring their deceptive quality. Additionally, human evaluations of the emails' readability and deception are conducted through questionnaires, confirming their convincing nature and the significant potential harm of the generated phishing emails.

cs.CR↗

arXiv2023

Error-correcting codes for fermionic quantum simulation

Utilizing the framework of $\mathbb{Z}_2$ lattice gauge theories in the context of Pauli stabilizer codes, we present methodologies for simulating fermions via qubit systems on a two-dimensional square lattice. We investigate the symplectic automorphisms of the Pauli module over the Laurent polynomial ring. This enables us to systematically increase the code distances of stabilizer codes while fixing the rate between encoded logical fermions and physical qubits. We identify a family of stabilizer codes suitable for fermion simulation, achieving code distances of $d=2,3,4,5,6,7$, allowing correction of any $\lfloor \frac{d-1}{2} \rfloor$-qubit error. In contrast to the traditional code concatenation approach, our method can increase the code distances without decreasing the (fermionic) code rate. In particular, we explicitly show all stabilizers and logical operators for codes with code distances of $d=3,4,5$. We provide syndromes for all Pauli errors and invent a syndrome-matching algorithm to compute code distances numerically.

quant-ph↗

arXiv2023

Fine-Grained Extraction of Road Networks via Joint Learning of Connectivity and Segmentation

Road network extraction from satellite images is widely applicated in intelligent traffic management and autonomous driving fields. The high-resolution remote sensing images contain complex road areas and distracted background, which make it a challenge for road extraction. In this study, we present a stacked multitask network for end-to-end segmenting roads while preserving connectivity correctness. In the network, a global-aware module is introduced to enhance pixel-level road feature representation and eliminate background distraction from overhead images; a road-direction-related connectivity task is added to ensure that the network preserves the graph-level relationships of the road segments. We also develop a stacked multihead structure to jointly learn and effectively utilize the mutual information between connectivity learning and segmentation learning. We evaluate the performance of the proposed network on three public remote sensing datasets. The experimental results demonstrate that the network outperforms the state-of-the-art methods in terms of road segmentation accuracy and connectivity maintenance.

cs.CV↗

arXiv2023

Qubit-oscillator concatenated codes: decoding formalism & code comparison

Concatenating bosonic error-correcting codes with qubit codes can substantially boost the error-correcting power of the original qubit codes. It is not clear how to concatenate optimally, given there are several bosonic codes and concatenation schemes to choose from, including the recently discovered GKP-stabilizer codes [Phys. Rev. Lett. 125, 080503 (2020)}] that allow protection of a logical bosonic mode from fluctuations of the mode's conjugate variables. We develop efficient maximum-likelihood decoders for and analyze the performance of three different concatenations of codes taken from the following set: qubit stabilizer codes, analog/Gaussian stabilizer codes, GKP codes, and GKP-stabilizer codes. We benchmark decoder performance against additive Gaussian white noise, corroborating our numerics with analytical calculations. We observe that the concatenation involving GKP-stabilizer codes outperforms the more conventional concatenation of a qubit stabilizer code with a GKP code in some cases. We also propose a GKP-stabilizer code that suppresses fluctuations in both conjugate variables without extra quadrature squeezing, and formulate qudit versions of GKP-stabilizer codes.

quant-ph↗

arXiv2022

Boson Sampling for Generalized Bosons

We introduce the notion of "generalized bosons" whose exchange statistics resemble those of bosons, but the local bosonic commutator $[a_i,a_i^\dagger]=1$ is replaced by an arbitrary single-mode operator that is diagonal in the generalized Fock basis. Examples of generalized bosons include boson pairs and spins. We consider the analogue of the boson sampling task for these particles and observe that its output probabilities are still given by permanents, so that the results regarding hardness of sampling directly carry over. Finally, we propose implementations of generalized boson sampling in circuit-QED and ion-trap platforms.

quant-ph↗

arXiv2022

Path sampling of recurrent neural networks by incorporating known physics

Recurrent neural networks have seen widespread use in modeling dynamical systems in varied domains such as weather prediction, text prediction and several others. Often one wishes to supplement the experimentally observed dynamics with prior knowledge or intuition about the system. While the recurrent nature of these networks allows them to model arbitrarily long memories in the time series used in training, it makes it harder to impose prior knowledge or intuition through generic constraints. In this work, we present a path sampling approach based on principle of Maximum Caliber that allows us to include generic thermodynamic or kinetic constraints into recurrent neural networks. We show the method here for a widely used type of recurrent neural network known as long short-term memory network in the context of supplementing time series collected from different application domains. These include classical Molecular Dynamics of a protein and Monte Carlo simulations of an open quantum system continuously losing photons to the environment and displaying Rabi oscillations. Our method can be easily generalized to other generative artificial intelligence models and to generic time series in different areas of physical and social sciences, where one wishes to supplement limited data with intuition or theory based corrections.

cond-mat.dis-nn↗

arXiv2022

Equivalence between fermion-to-qubit mappings in two spatial dimensions

We argue that all locality-preserving mappings between fermionic observables and Pauli matrices on a two-dimensional lattice can be generated from the exact bosonization in Ref. [1], whose gauge constraints project onto the subspace of the toric code with emergent fermions. Starting from the exact bosonization and applying Clifford finite-depth generalized local unitary (gLU) transformation, we can achieve all possible fermion-to-qubit mappings (up to the re-pairing of Majorana fermions). In particular, we discover a new super-compact encoding using 1.25 qubits per fermion on the square lattice, which is lower than any method in the literature. We prove the existence of fermion-to-qubit mappings with qubit-fermion ratios $r=1+ \frac{1}{2k}$ for positive integers $k$, where the proof utilizes the trivialness of quantum cellular automata (QCA) in two spatial dimensions. When the ratio approaches 1, the fermion-to-qubit mapping reduces to the 1d Jordan-Wigner transformation along a certain path in the two-dimensional lattice. Finally, we explicitly demonstrate that the Bravyi-Kitaev superfast simulation, the Verstraete-Cirac auxiliary method, Kitaev's exactly solved model, the Majorana loop stabilizer codes, and the compact fermion-to-qubit mapping can all be obtained from the exact bosonization.

quant-ph↗

arXiv2021

Efficient Product Formulas for Commutators and Applications to Quantum Simulation

We construct product formulas for exponentials of commutators and explore their applications. First, we directly construct a third-order product formula with six exponentials by solving polynomial equations obtained using the operator differential method. We then derive higher-order product formulas recursively from the third-order formula. We improve over previous recursive constructions, reducing the number of gates required to achieve the same accuracy. In addition, we demonstrate that the constituent linear terms in the commutator can be included at no extra cost. As an application, we show how to use the product formulas in a digital protocol for counterdiabatic driving, which increases the fidelity for quantum state preparation. We also discuss applications to quantum simulation of one-dimensional fermion chains with nearest- and next-nearest-neighbor hopping terms, and two-dimensional fractional quantum Hall phases.

quant-ph↗