DMRG Preprints

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.

Measures on Fraïssé classes are a key input in the Harman--Snowden (2022) construction of tensor categories. Treelike Fraïssé classes provide a particularly tractable source of examples. In this paper, we complete the classification of measures on Cameron's elementary treelike classes. In particular, for the class $\partial \mathfrak{T}_3(n)$ of node-colored rooted binary tree structures with $n$ colors, we classify measures by an explicit bijection with directed rooted trees edge-labeled by $\{1, \dots, n\}$ with a distinguished vertex, yielding $(2n+2)^n$ distinct $\ZZ\left[\frac 12\right]$-valued measures. For each $n \geq 1$, we use a family of measures $μ_n^I$ and their supports $\partial \mathfrak{T}_3(n)^{\mathrm{ord}}_I$ (where $I \subseteq \{1, \dots n\}$) to construct the Karoubi envelopes $\mathbf{Rep}(\partial \mathfrak{T}_3(n)^{\mathrm{ord}}_I;μ^I_n)$, producing infinite families of semisimple tensor categories with superexponential growth that cannot be obtained via Deligne's interpolation of representation categories. We also prove the nonexistence of measures on the $n$-colored tree class $C_n\mathfrak{T}$ for $n \geq 2$ and the labeled tree class $L \mathfrak{T}$, extending Snowden's results for uncolored trees.

Quantum crosstalk poses a major challenge to scaling up quantum computations as its strength is typically unknown and its effect accumulates exponentially as system size grows. Here, we show that many-body robust control can be utilized to suppress unwanted couplings during multi-qubit gate operations and state preparation. By combining tensor network simulations with the GRAPE algorithm, and leveraging an efficient random sampling over noise ensembles, our method overcomes the exponential scaling of the Hilbert space. We demonstrate its effectiveness for designing control solutions for high-fidelity implementations of parallel X gates and parallel CNOT on a chain of 50 qubits, and for realizing a 30-qubit GHZ state and the ground state of a 20-qubit Heisenberg model. In the presence of many-body quantum crosstalk due to parasitic interaction between neighboring qubits, robust control results in order-of magnitude improvement in fidelity for large system sizes. These findings pave the way for more reliable operations on near-term quantum processors.

Transversal gates are the simplest form of fault-tolerant gates and are relatively easy to implement in practice. Yet designing codes that support useful transversal operations -- especially non-Clifford or addressable gates -- remains difficult within the stabilizer formalism or CSS constructions alone. We show that these limitations can be overcome using tensor-network frameworks such as the quantum lego formalism, where transversal gates naturally appear as global or localized symmetries. Within the quantum lego formalism, small codes carrying desirable symmetries can be "glued" into larger ones, with operator-flow rules guiding how logical symmetries are preserved. This approach enables the systematic construction of codes with addressable transversal single- and multi-qubit gates targeting specific logical qubits regardless of whether the gate is Clifford or not. As a proof of principle, we build new finite-rate code families that support strongly transversal $T$, $CCZ$, $SH$, and Gottesman's $K_3$ gates, structures that are challenging to realize with conventional methods. We further construct holographic and fractal-like codes that admit addressable transversal inter-, meso-, and intra-block $T$, $CS$, and $C^\ell Z$ gates. As a corollary, we demonstrate that the heterogeneous holographic Steane-Reed-Muller black hole code also supports fully addressable transversal inter- and intra-block $CZ$ gates, significantly lowering the overhead for universal fault-tolerant computation.

We review recent developments in tensor network approaches, focusing on renormalization group methods. Since they are free from the negative sign and complex action problems, there is growing interest in their application to lattice field theories, particularly with a view toward future studies of quantum chromodynamics (QCD) at finite temperature and density. They are also of broad interest in quantum field theory, with recent advances in approaches that allow one to directly investigate universal aspects of critical behavior by making use of theoretical insights from conformal field theory. We highlight several recently explored topics that are expected to play important roles in forthcoming tensor-network studies of QCD.

We investigate critical phenomena in the $O(2)$ models using symmetry-twisted partition functions that can be efficiently computed within the tensor renormalization group framework. We first demonstrate, taking the three-dimensional model as an example, that symmetry-twisted partition functions detect the spontaneous breaking of global continuous symmetry. We then consider the same model in two dimensions, where the Berezinskii--Kosterlitz--Thouless (BKT) transition occurs. Since symmetry-twisted partition functions directly provide the helicity modulus at a finite twist angle, we determine the BKT transition point. These results are presented based on Ref.~&icedil;te{Akiyama:2026dzg}. Finally, in addition to the original paper~&icedil;te{Akiyama:2026dzg}, we apply this approach to the two-dimensional generalized $O(2)$ model and confirm that it successfully identifies the phase transitions between the ferromagnetic and nematic phases, as well as between the nematic and paramagnetic phases.

We study the problem of recovering a low-tubal-rank tensor $\mathcal{X}\_\star\in ℝ^{n \times n \times k}$ from noisy linear measurements under the t-product framework. A widely adopted strategy involves factorizing the optimization variable as $\mathcal{U} * \mathcal{U}^\top$, where $\mathcal{U} \in ℝ^{n \times R \times k}$, followed by applying factorized gradient descent (FGD) to solve the resulting optimization problem. Since the tubal-rank $r$ of the underlying tensor $\mathcal{X}_\star$ is typically unknown, this method often assumes $r < R \le n$, a regime known as over-parameterization. However, when the measurements are corrupted by some dense noise (e.g., Gaussian noise), FGD with the commonly used spectral initialization yields a recovery error that grows linearly with the over-estimated tubal-rank $R$. To address this issue, we show that using a small initialization enables FGD to achieve a nearly minimax optimal recovery error, even when the tubal-rank $R$ is significantly overestimated. Using a four-stage analytic framework, we analyze this phenomenon and establish the sharpest known error bound to date, which is independent of the overestimated tubal-rank $R$. Furthermore, we provide a theoretical guarantee showing that an easy-to-use early stopping strategy can achieve the best known result in practice. All these theoretical findings are validated through a series of simulations and real-data experiments.

With the advent of quantum simulators, exploring exotic collective phenomena in lattice models with local symmetries and unconventional geometries is at reach of near-term experiments. Motivated by recent progress in this direction, we study a $ℤ_2$ lattice gauge theory defined on a multi-graph with links that can be visualized as great circles of a spherical shell hosting the $ℤ_2$ gauge fields. Elementary Wilson loops along pairs of these bonds allow to identify a dynamical gauge-invariant flux, responsible for Aharonov-Bohm-like interference effects in the tunneling dynamics of charged matter residing on the vertices. Focusing on an odd number of links, we show that this leads to state-dependent tunneling amplitudes underlying a phenomenon analogous to the Peierls instability. We find inhomogeneous phases in which an ordered pattern of the gauge fluxes spontaneously breaks translational invariance, and intertwines with a bond order wave for the gauge-invariant kinetic matter operators. Long-range order is shown to coexist with symmetry protected topological order, which survives the quantum fluctuations of the gauge flux induced by an external electric field. Doping the system above half filling leads to the formation of topological soliton/anti-soliton pairs interpolating between different inhomogeneous orderings of the gauge fluxes. By performining a detailed analysis based on matrix product states, we prove that charge deconfinement emerges as a consequence of charge-fractionalization. Quasiparticles carrying fractional charge and bound at the soliton centers can be arbitrarily separated without feeling a confining force, in spite of the long-range attractive interactions set by the small electric field on the individual integer charges.

Entanglement asymmetry provides a quantitative measure of symmetry breaking in many-body quantum states. Focusing on inhomogeneous $U(1)$ charges, such as dipole and multipole moments, we show that the typical asymmetry is bounded by a specific fraction of its maximal value, and verify this behavior in several settings, including random matrix product states. Within the latter ensemble, by identifying the bond dimension with an effective time, we qualitatively reproduce recent findings on the entanglement asymmetry dynamics in random quantum circuits, thereby suggesting a universal dynamical structure of the asymmetry of $U(1)$ charges in local ergodic systems. Multipole charges naturally arise in systems with Hilbert-space fragmentation, where the dynamics splits into exponentially many disconnected sectors. Using the commutant algebra formalism, we generalize entanglement asymmetry to account for fragmentation. We derive general upper bounds for both conventional and fragmented symmetries and identify states that saturate them. While the asymmetry grows logarithmically for conventional symmetries, it can scale extensively in fragmented systems, providing a probe that distinguishes classical from genuinely quantum fragmentation.

We study the formation of a trion liquid in doped low-dimensional semiconductors with strong electron-hole interactions and analyze its signatures in angle-resolved photoemission spectroscopy (ARPES). We show that this strongly correlated state of matter forms naturally in the vicinity of the phase boundary between a normal band insulator and an excitonic insulator upon doping. By studying the photoemission spectrum, we show that a partially occupied trion band gives rise to an in-gap feature in the ARPES spectrum with vanishing spectral weight at the Fermi energy. We demonstrate our findings using a 1D microscopic model employing exact, unbiased, matrix product state (MPS)-based calculations.