DMRG Preprints

We introduce group surface codes, which are a natural generalization of the $ℤ_2$ surface code, and equivalent to quantum double models of finite groups with specific boundary conditions. We show that group surface codes can be leveraged to perform non-Clifford gates in $ℤ_2$ surface codes, thus enabling universal computation with well-established means of performing logical Clifford gates. Moreover, for suitably chosen groups, we demonstrate that arbitrary reversible classical gates can be implemented transversally in the group surface code. We present the logical operations in terms of a set of elementary logical operations, which include transversal logical gates, a means of transferring encoded information into and out of group surface codes, and preparation and readout. By composing these elementary operations, we implement a wide variety of logical gates and provide a unified perspective on recent constructions in the literature for sliding group surface codes and preparing magic states. We furthermore use tensor networks inspired by ZX-calculus to construct spacetime implementations of the elementary operations. This spacetime perspective also allows us to establish explicit correspondences with topological gauge theories. Our work extends recent efforts in performing universal quantum computation in topological orders without the braiding of anyons, and shows how certain group surface codes allow us to bypass the restrictions set by the Bravyi-K{ö}nig theorem, which limits the computational power of topological Pauli stabilizer models.

Correlated noise is a critical failure mode in quantum error correction (QEC), as temporal memory and spatial structure concentrate faults into error bursts that undermine standard threshold assumptions. Yet, a fundamental gap persists between the stochastic Pauli models ubiquitous in QEC and the microscopic, non-Markovian descriptions of physical device dynamics. We close this gap by introducing \emph{Spatiotemporal Pauli Processes} (SPPs). By applying a multi-time Pauli twirl -- operationally realised by Pauli-frame randomisation -- to a general process tensor, we map arbitrary multi-time, non-Markovian dynamics to a multi-time Pauli process. This process is represented by a process-separable comb, or equivalently, a well-defined joint probability distribution over Pauli trajectories in spacetime. We show that SPPs inherit efficient tensor network representations whose bond dimensions are bounded by the environment's Liouville-space dimension. To interpret these structures, we develop transfer operator diagnostics linking spectra to correlation decay, and exact hidden Markov representations for suitable classes of SPPs. We demonstrate the framework via surface code memory and stability simulations of up to distance \(19\) for (i) a temporally correlated ``storm'' model that tunes correlation length at fixed marginal error rates, and (ii) a genuinely spatiotemporal 2D quantum cellular automaton bath that maps exactly to a nonlinear probabilistic cellular automaton under twirling. Tuning coherent bath interactions drives the system into a pseudo-critical regime, exhibiting critical slowing down and macroscopic error avalanches that cause a complete breakdown of surface code distance scaling. Together, these results justify SPPs as an operationally grounded, scalable toolkit for modelling, diagnosing, and benchmarking correlated noise in QEC.

In this work, we numerically study the effect of weak measurement on deconfined quantum critical point(DQCP). Particularly, we consider the ground state of an one-dimensional spin $1/2$ system with long range exchange interactions($K$), which shows analogues phase transition to DQCP in the thermodynamic limit. This system is in the ferromagnetic phase below the critical exchange interaction $K_c$ and in the valance bond solid phase above $K_c$. The weak measurement is carried out by coupling a secondary ancilla system to the critical system via unitary interactions and later measuring the ancilla spins projectively. We numerically calculate entanglement entropy,correlation length, and order parameters of leading post-measurement states using uniform matrix product state representation of the quantum many-body state in the thermodynamic limit. We report asymmetric restructuring of entanglement of the post measurement states across the phase boundary under weak measurements. Especially, the trajectory $\left(\downarrow \downarrow\right)$ describing a uniform measurement outcome given the all ancilla spins initiated in the same $\left(\downarrow \right)$ state, shows anomalous entanglement when increasing the strength of weak measurement. The bipartite entanglement entropy strongly increases when $K<K_c$ whereas it weakly decreases when $K>K_c$. We argue with numerical evidences that observed asymmetry in entanglement would lead to a weak first order phase boundary in the thermodynamic limit. We also discuss important aspects in experimental observation of measurement induced effects linked to the strength of weak measurement and probability of post-measurement states.

We train machine learning algorithms to infer the entanglement structure of disordered long-range interacting quantum spin chains by learning from the strong disorder renormalisation group (SDRG) method. The system consists of $S=1/2$-quantum spins coupled by antiferromagnetic power-law interactions with decay exponent $α$ at random positions on a one-dimensional chain. Using SDRG as a physics-informed teacher, we compare a Random Forest classifier as a classical baseline with a graph neural network (GNN) that operates directly on the interaction graph and learns a bond-ranking rule mirroring the SDRG decimation policy. The GNN achieves a disorder-averaged pairing accuracy close to one and reproduces the entanglement entropy $S(\ell)$ in excellent quantitative agreement with SDRG across all subsystem sizes and interaction exponents. RG flow heat maps confirm that the GNN learns the sequential decimation hierarchy rather than merely fitting final-state observables. Finite-temperature entanglement properties are incorporated via the SDRGX framework through a two-stage strategy, using the zero-temperature GNN to generate the RG flow and sampling thermal occupations from the canonical ensemble, yielding results in agreement with both numerical SDRGX and analytical predictions without retraining.

Classical tensor network and hybrid quantum-classical algorithms are promising candidates for the investigation of real-time properties of lattice gauge theories. We develop here a novel framework which enforces gauge symmetry via a quantum-link virtual rishon representation applied at intermediate steps. Crucially, the gauge and matter degrees of freedom are dynamical variables encoded in terms of qubits, enabling analysis of gauge theories in $d+1$ spacetime dimensions. We benchmark this framework in a U(1) gauge theory with and without matter fields. For $d = 1$, the multi-flavor Schwinger model with $1\leq N_f\leq3$ flavors is analyzed for arbitrary boundary conditions and nonzero topological angle, capturing signatures of the underlying Wess-Zumino-Witten conformal field theory. For $d = 2$, we extract the confining string tension in close agreement with continuum expectations. These results establish the virtual rishon framework as a scalable and robust approach for the simulation of lattice gauge theories using both classical tensor networks as well as near-term quantum hardware.

Integrated sensing and communication (ISAC) systems promise efficient spectrum utilization by jointly supporting radar sensing and wireless communication. This paper presents a deep learning-driven framework for enhancing physical-layer security in multicarrier ISAC systems under imperfect channel state information (CSI) and in the presence of unknown eavesdropper (Eve) locations. Unlike conventional ISAC-based friendly jamming (FJ) approaches that require Eve's CSI or precise angle-of-arrival (AoA) estimates, our method exploits radar echo feedback to guide directional jamming without explicit Eve's information. To enhance robustness to radar sensing uncertainty, we propose a radar-aware neural network that jointly optimizes beamforming and jamming by integrating a novel nonparametric Fisher Information Matrix (FIM) estimator based on f-divergence. The jamming design satisfies the Cramer-Rao lower bound (CRLB) constraints even in the presence of noisy AoA. For efficient implementation, we introduce a quantized tensor train-based encoder that reduces the model size by more than 100 times with negligible performance loss. We also integrate a non-overlapping secure scheme into the proposed framework, in which specific sub-bands can be dedicated solely to communication. Extensive simulations demonstrate that the proposed solution achieves significant improvements in secrecy rate, reduced block error rate (BLER), and strong robustness against CSI uncertainty and angular estimation errors, underscoring the effectiveness of the proposed deep learning-driven friendly jamming framework under practical ISAC impairments.

Physical instantiations of a bit of information are subject to thermal noise that can trigger unintended bit-flip errors. Bits implemented with CMOS technology typically operate in regimes that reliably suppress these errors with a large bias voltage, but miniaturization and circuit design for implantable biomedical devices motivate error suppression via alternative low-voltage strategies. We present and analyze an error-suppression technique that involves coupling multiple CMOS units into chains, introducing a natural error correction arising from inter-unit correlations. Using tensor networks to numerically solve a stochastic master equation for the CMOS chain, we quantify the reliability-dissipation tradeoff across system sizes that would be intractable with conventional sparse-matrix methods. The calculations show that the typical time for bit-flip errors scales exponentially with the bias voltage but subexponentially with the chain length. While a CMOS chain adds stability compared to a single CMOS unit for a fixed low bias voltage, increasing the bias voltage is a lower-dissipation route to equivalent stability.

Combining tensor network techniques with quantum autoregressive moving average models, we quantify the effects of time-correlated noise on quantum algorithms and predict their performance at scale. As a paradigmatic test case, we examine the quantum Fourier transformation. Building on our first technical result, which shows how stochastic tensor network calculations capture frequency correlations, our second result is the revelation that infidelity exponents (scaling from diffuse, to superdiffuse) are determined by the spectral features of the noise. This numerical result rigorously quantifies the common belief that the temporal correlation scale is a key predictive feature of noise's deleterious impact on multi-qubit circuits. To highlight prospects for predicting algorithmic performance, our third result quantifies how infidelity scaling exponents -- which are fits determined by training data at moderate scales (40-80 qubits) -- can be used to predict more computationally expensive simulation at larger scales (100-128 qubits). Aside from highlighting the scalability of our methods, this workflow feeds into our last result, which is the proposal of predictive benchmarking protocols connecting simulations to experiments. Our work paves the way for large-scale algorithmic simulations and performance prediction under hardware-relevant noise conditions informed by realistic device characteristics.

We propose a concrete realization of a triangular ladder for ultracold atoms, which simultaneously hosts geometric frustration and unusual two-body interactions, and in particular controllable pair hopping and density-induced tunneling. This is done by means of a spin-dependent Kronig-Penney lattice created using a spatially-dependent tripod-type atom-light coupling. We apply density matrix renormalization group (DMRG) calculations to derive the quantum phase diagram. We find that pair tunneling stabilizes a robust pair superfluid, characterized by power-law decay of pair correlations. Additionally, a chiral superfluid arises from frustration induced by competing nearest neighbor (NN) and next-nearest neighbor (NNN) tunnelings. Finally, in the high barrier regime, we map our system onto the XXZ spin model and find the exact phase transition points.

Computing the vacuum and energy spectrum in non-Abelian, interacting lattice gauge theories remains an open challenge, in part because approximating the continuum limit requires large lattices and huge Hilbert spaces. To address this difficulty with near-term quantum computing devices, we adapt the variational quantum eigensolver to non-Abelian gauge theories. We outline scaling advantages when using a spin-network basis to simulate the gauge-invariant Hilbert space and develop a systematic state preparation ansatz that creates gauge-invariant excitations while alleviating the barren plateau problem. We illustrate our method in the context of SU(2) Yang-Mills theory by testing it on a minimal toy model consisting of a single vertex in 3+1 dimensions. In this toy model, simulations allow us to investigate the impact of noise expected in current quantum devices.