arXiv subjects

Jan Behrends

Publications and source records attributed to Jan Behrends.

At least 19 recordsLinked to original sources

arXiv2026

Projected logical ensembles in surface codes via the random-matrix theory of quantum dots

Measurements underpin active quantum error correction (QEC) and have been recognized as a source of novel measurement-induced many-body phenomena. Here, we study the statistical properties of post-measurement logical states arising in QEC on topological codes subject to deterministic transversal unitary gates. Upon syndrome extraction followed by maximum-likelihood decoding, a Born-weighted ensemble arises which we dub the "projected logical ensemble" (PLE). Focusing on surface codes subject to uniform single-qubit Pauli-$X$ rotations, we characterize the measurement-induced randomness of the PLE. To this end, we show that for a code with a single logical qubit, the PLE is isomorphic to an ensemble of scattering matrices describing mesoscopic quantum dots obtained from a 2D Majorana network model with suitable boundary conditions. We uncover regimes where these quantum dots are chaotic such that their scattering matrices are well-described by random matrix theory. In these regimes, the PLE approaches a universal ensemble that is maximally random up to symmetry and decoder-induced constraints. The symmetry constraints, set by stabilizer and logical operator weights, realize Altland-Zirnbauer classes D or DIII, which we both illustrate. Our results establish a fundamental connection between emergent universality concepts in mesoscopic physics, quantum many-body systems, and QEC.

quant-ph↗

arXiv2026

Computing with many encoded logical qubits beyond break-even

High-rate quantum error correcting (QEC) codes encode many logical qubits in a given number of physical qubits, making them promising candidates for quantum computation. Implementing high-rate codes at a scale that both frustrates classical computing and improves performance by encoding requires both high fidelity gates and long-range qubit connectivity -- both of which are offered by trapped-ion quantum computers. Here, we demonstrate computations that outperform their unencoded counterparts in the high-rate $[[ k+2,\, k,\, 2 ]]$ iceberg quantum error detecting (QED) and $[[ (k_2 + 2)(k_1 + 2),\, k_2k_1,\, 4 ]]$ two-level concatenated iceberg QEC codes, using the 98-qubit Quantinuum Helios trapped-ion quantum processor. Utilizing new gadgets for encoded operations, we realize this "beyond break-even" performance with reasonable postselection rates across a range of fault-tolerant (FT) and partially-fault-tolerant (pFT) component and application benchmarks with between $48$ and $94$ logical qubits. These benchmarks include FT state preparation and measurement, QEC cycle benchmarking, logical gate benchmarking, GHZ state preparation, and a pFT quantum simulation of the three-dimensional $XY$ model of quantum magnetism. Additionally, we illustrate that postselection rates can be suppressed by increasing the code distance via concatenation. Our results represent state-of-the-art logical component and state fidelities and provide evidence that high-rate QED/QEC codes are viable on contemporary quantum computers for near-term beyond-classical-scale computation.

quant-ph↗

arXiv2026

Critical non-equilibrium phases from noisy topological memories

We demonstrate the existence of an extended non-equilibrium critical phase, characterized by sub-exponential decay of conditional mutual information (CMI), in the surface code subject to heralded random Pauli measurement channels. By mapping the resulting mixed state to the ensemble of completely packed loops on a square lattice, we relate the extended phase to the Goldstone phase of the loop model. In particular, CMI is controlled by the characteristic length scale of loops, and we use analytic results of the latter to establish polylogarithmic decay of CMI in the critical phase. We find that the critical phase retains partial logical information that can be recovered by a global decoder, but not by any quasi-local decoder. To demonstrate this, we introduce a diagnostic called punctured coherent information which provides a necessary condition for quasi-local decoding.

quant-ph↗

arXiv2025

Quantum Geometric Bounds in Non-Hermitian Systems

We identify quantum geometric bounds for observables in non-Hermitian systems. We find unique bounds on non-Hermitian quantum geometric tensors, generalized two-point response correlators, conductivity tensors, and optical weights. We showcase these findings in topological systems with non-Hermitian Chern numbers. We demonstrate that the non-Hermitian geometric constraints on response functions naturally arise in open quantum systems governed by out-of-equilibrium Lindbladian dynamics. Our findings are relevant to experimental observables and responses under the realistic setups that fall beyond the idealized closed-system descriptions.

quant-ph↗

arXiv2025

Quantum geometry of non-Hermitian systems

The Berry curvature characterizes one aspect of the geometry of quantum states. It materializes, among other consequences, as an anomalous velocity of wave packets. In non-Hermitian systems, wave packet dynamics is enriched by additional terms that can be expressed as generalizations of the Berry connection to non-orthogonal eigenstates. Here, we contextualize these anomalous non-Hermitian contributions by showing that they directly arise from the geometry of the underlying quantum states as corrections to the distance between left and perturbed right eigenstates. By calculating the electric susceptibility for a single-band wave packet and comparing it with the wave packet's localization, we demonstrate that these terms can, in some circumstances, lead to a violation of fluctuation-dissipation relations in non-Hermitian systems. We discuss experimental signatures in terms of response functions and transport signatures.

quant-ph↗

arXiv2024

The surface code beyond Pauli channels: Logical noise coherence, information-theoretic measures, and errorfield-double phenomenology

We consider the surface code under errors featuring both coherent and incoherent components and study the coherence of the corresponding logical noise channel and how this impacts information-theoretic measures of code performance, namely coherent information and quantum relative entropy. Using numerical simulations and developing a phenomenological field theory, focusing on the most general single-qubit X-error channel, we show that, for any nonzero incoherent noise component, the coherence of the logical noise is exponentially suppressed with the code distance. We also find that the information-theoretic measures require this suppression to detect optimal thresholds for Pauli recovery; for this they thus require increasingly large distances for increasing error coherence and ultimately break down for fully coherent errors. To obtain our results, we develop a statistical mechanics mapping and a corresponding matrix-product-state algorithm for approximate syndrome sampling. These methods enable the large scale simulation of these non-Pauli errors, including their maximum-likelihood thresholds, away from the limits captured by previous approaches.

quant-ph↗

arXiv2024

Statistical mechanical mapping and maximum-likelihood thresholds for the surface code under generic single-qubit coherent errors

The surface code, one of the leading candidates for quantum error correction, is known to protect encoded quantum information against stochastic, i.e., incoherent errors. The protection against coherent errors, such as from unwanted gate rotations, is however understood only for special cases, such as rotations about the $X$ or $Z$ axes. Here we consider generic single-qubit coherent errors in the surface code, i.e., rotations by angle $\alpha$ about an axis that can be chosen arbitrarily. We develop a statistical mechanical mapping for such errors and perform entanglement analysis in transfer matrix space to numerically establish the existence of an error-correcting phase, which we chart in a subspace of rotation axes to estimate the corresponding maximum-likelihood thresholds $\alpha_\mathrm{th}$. The classical statistical mechanics model we derive is a random-bond Ising model with complex couplings and four-spin interactions (i.e., a complex-coupled Ashkin-Teller model). The error correcting phase, $\alpha<\alpha_\mathrm{th}$, where the logical error rate decreases exponentially with code distance, is shown to correspond in transfer matrix space to a gapped one-dimensional quantum Hamiltonian exhibiting spontaneous breaking of a $\mathbb{Z}_2$ symmetry. Our numerical results rest on two key ingredients: (i) we show that the state evolution under the transfer matrix -- a non-unitary (1+1)-dimensional quantum circuit -- can be efficiently numerically simulated using matrix product states. Based on this approach, (ii) we also develop an algorithm to (approximately) sample syndromes based on their Born probability. The $\alpha_\mathrm{th}$ values we find show that the maximum likelihood thresholds for coherent errors are larger than those for the corresponding incoherent errors (from the Pauli twirl), and significantly exceed the values found using minimum weight perfect matching.

quant-ph↗

arXiv2024

High-Spin State Dynamics and Quintet-Mediated Emission in Intramolecular Singlet Fission

High-spin states in molecular systems hold significant interest for a wide range of applications ranging from optoelectronics to quantum information and singlet fission (SF). Quintet and triplet states play crucial roles, particularly in SF systems, necessitating a precise monitoring and control of their spin dynamics. Spin states in intramolecular SF (iSF) are of particular interest, but tuning these systems to control triplet multiplication pathways has not been extensively studied. Additionally, whilst studies in this context focus on participation of triplet pathways leading to photoluminescence, emission pathways via quintet states remain largely unexplored. Here, we employ a set of unique spin-sensitive techniques to investigate high-spin state formation and emission in dimers and trimers comprising multiple diphenylhexatriene (DPH) units. We demonstrate the formation of pure quintet states in all these oligomers, with high-spin state optical emission via quintet states dominating delayed fluorescence up to room temperature. For triplet formation, we distinguish between the ability to form weakly exchange-coupled triplet pairs and the efficiency-reducing pathway of intersystem crossing (ISC), identifying the trimer Me-(DPH)$_3$ as the only oligomer exhibiting exclusively the desired SF pathways. Conversely, linear (DPH)$_3$ and (DPH)$_2$ show additional or exclusive triplet pathways via ISC. Our comprehensive analysis provides a detailed investigation into high-spin state formation, control, and emission in intramolecular singlet fission systems.

cond-mat.mtrl-sci↗

arXiv2024

Optical read and write of spin states in organic diradicals

Optical control and read-out of the ground state spin structure has been demonstrated for defect states in crystalline semiconductors, including the diamond NV- center, and these are promising systems for quantum technologies. Molecular organic semiconductors offer synthetic control of spin placement, in contrast to current limitations in these crystalline systems. Here we report the discovery of spin-optical addressability in a diradical molecule that comprises two trityl radical groups coupled via a fluorene bridge. We demonstrate the three important properties that enable operation as a spin-photon interface: (i) triplet and singlet spin states show photoluminescence peaked at 640 and 700 nm respectively; this allows easy optical measurement of ground state spin. (ii) the ground state spin exchange is small (~60 {\mu}eV) that allows preparation of ground state spin population. This can be achieved by spin-selective excited state intersystem crossing, and we report up to 8% microwave-driven contrast in photoluminescence. (iii) both singlet and triplet manifolds have near-unity photoluminescence quantum yield, which is in contrast to the near-zero quantum yields in prior reports of molecular diradicals. Our results establish these tuneable open-shell organic molecules as a platform to engineer tailor-made spin-optical interfaces.

cond-mat.mtrl-sci↗

arXiv2024

Controllable bipolaron formation unveiling structural features of trap states in organic charge transport

Magnetic resonance methods offer a unique chance for in-depth study of conductive organic material systems, not only accounts for number of charge carriers, but also allows manipulations of spin dynamics of particles. Here we present a study of continuous-wave electrically detected magnetic resonance on a range of organic conjugate polymers under transistor architecture, with tunability in both carrier concentration and drifting electric field. We demonstrate the general existence of bipolaron between mobile and trapped charges at the magnetic resonance condition, then estimates the wavefunction expansion of charge carriers on their hopping sites along conductive pathways. This finding allows direct observation of energetically disordered trap sites under the charge hopping picture, linking-up the microscopic structural properties to the bulk electronic performances.

physics.app-ph↗

arXiv2024

Conductivity scaling and absence of localization in disordered nodal line semimetals

Transport plays a key role in characterizing topological insulators and semimetals. Understanding the effect of disorder is crucial to assess the robustness of experimental signatures for topology. In this work, we find the absence of localization in nodal line semimetals for long-range scalar disorder and a large range of disorder strengths. Using a continuum transfer matrix approach, we find that the conductivity in the plane and out of the plane of the nodal line increases with system size and disorder strength. We substantiate these findings by a perturbative calculation and show that the conductivity increases with disorder strength using the Kubo formula in the self-consistent Born approximation. We also find that the system remains metallic for vector disorder and that vector disorder can drive a transition from an insulating to a metallic regime. Our results demonstrate the absence of localization in a three-dimensional bulk system.

cond-mat.dis-nn↗

arXiv2022

Surface codes, quantum circuits, and entanglement phases

Surface codes$\unicode{x2014}$leading candidates for quantum error correction (QEC)$\unicode{x2014}$and entanglement phases$\unicode{x2014}$a key notion for many-body quantum dynamics$\unicode{x2014}$have heretofore been unrelated. Here, we establish a link between the two. We map two-dimensional (2D) surface codes under a class of incoherent or coherent errors (bit flips or uniaxial rotations) to $(1+1)$D free-fermion quantum circuits via Ising models. We show that the error-correcting phase implies a topologically nontrivial area law for the circuit's 1D long-time state $|\Psi_\infty\rangle$. Above the error threshold, we find a topologically trivial area law for incoherent errors and logarithmic entanglement in the coherent case. In establishing our results, we formulate 1D parent Hamiltonians for $|\Psi_\infty\rangle$ via linking Ising models and 2D scattering networks, the latter displaying respective insulating and metallic phases and setting the 1D fermion gap and topology via their localization length and topological invariant. We expect our results to generalize to a duality between the error-correcting phase of ($d+1$)D topological codes and $d$-dimensional area laws; this can facilitate assessing code performance under various errors. The approach of combining Ising models, scattering networks, and parent Hamiltonians can be generalized to other fermionic circuits and may be of independent interest.

quant-ph↗

arXiv2022

Room Temperature Optically and Magnetically Active Edges in Phosphorene Nanoribbons

Nanoribbons - nanometer wide strips of a two-dimensional material - are a unique system in condensed matter physics. They combine the exotic electronic structures of low-dimensional materials with an enhanced number of exposed edges, where phenomena including ultralong spin coherence times, quantum confinement and topologically protected states can emerge. An exciting prospect for this new material concept is the potential for both a tunable semiconducting electronic structure and magnetism along the nanoribbon edge. This combination of magnetism and semiconducting properties is the first step in unlocking spin-based electronics such as non-volatile transistors, a route to low-energy computing, and has thus far typically only been observed in doped semiconductor systems and/or at low temperatures. Here, we report the magnetic and semiconducting properties of phosphorene nanoribbons (PNRs). Static (SQUID) and dynamic (EPR) magnetization probes demonstrate that at room temperature, films of PNRs exhibit macroscopic magnetic properties, arising from their edge, with internal fields of ~ 250 to 800 mT. In solution, a giant magnetic anisotropy enables the alignment of PNRs at modest sub-1T fields. By leveraging this alignment effect, we discover that upon photoexcitation, energy is rapidly funneled to a dark-exciton state that is localized to the magnetic edge and coupled to a symmetry-forbidden edge phonon mode. Our results establish PNRs as a unique candidate system for studying the interplay of magnetism and semiconducting ground states at room temperature and provide a stepping-stone towards using low-dimensional nanomaterials in quantum electronics.

cond-mat.mes-hall↗

arXiv2022

Coherent error threshold for surface codes from Majorana delocalization

Statistical mechanics mappings provide key insights on quantum error correction. However, existing mappings assume incoherent noise, thus ignoring coherent errors due to, e.g., spurious gate rotations. We map the surface code with coherent errors, taken as $X$- or $Z$-rotations (replacing bit or phase flips), to a two-dimensional (2D) Ising model with complex couplings, and further to a 2D Majorana scattering network. Our mappings reveal both commonalities and qualitative differences in correcting coherent and incoherent errors. For both, the error-correcting phase maps, as we explicitly show by linking 2D networks to 1D fermions, to a $\mathbb{Z}_2$-nontrivial 2D insulator. However, beyond a rotation angle $\phi_\text{th}$, instead of a $\mathbb{Z}_2$-trivial insulator as for incoherent errors, coherent errors map to a Majorana metal. This $\phi_\text{th}$ is the theoretically achievable storage threshold. We numerically find $\phi_\text{th}\approx0.14\pi$. The corresponding bit-flip rate $\sin^2(\phi_\text{th})\approx 0.18$ exceeds the known incoherent threshold $p_\text{th}\approx0.11$.

quant-ph↗

arXiv2021

Quantum tunneling in the presence of a topology-changing fermionic bath

Coupling a quantum particle to a fermionic bath suppresses the particle's amplitude to tunnel, even at zero temperature. While this effect can generally be neglected for gapped baths -- a key feature for superconducting qubits -- , it is possible for the bath to be gapped near the potential minima between which the particle tunnels, but different minima to correspond to different bath topologies. This enforces the bath to undergo gap closing along the tunneling path. In this work, we investigate quantum tunneling in the presence of such a topology-changing fermionic bath. We develop a field theory for this problem, linking the instantons describing tunneling in a bath of $d$ space dimensions to topological boundary modes of systems in $d+1$ dimensions, thus stepping a level higher in a dimensional hierarchy. We study in detail a $d=1$ example, inspired by planar Josephson junctions where the particle coordinate is the superconducting phase whose value sets the electronic topology. We find that the topology change suppresses tunneling by a factor scaling exponentially with the system size. This translates to a correspondingly enhanced suppression of the energy splitting for the lowest-lying states, despite these being linear combinations of states near potential minima where the bath is gapped. Our results help to estimate the influence of charging energy on topological phases arising due to the Josephson effect and, conversely, to assess the potential utility of such topological systems as superconducting qubits. For moderate-sized baths, the incomplete suppression of tunneling opens the prospects of quantum-mechanical superpositions of many-body states of different topology, including superpositions of states with and without Majorana fermions.

cond-mat.mes-hall↗

arXiv2020

Sachdev-Ye-Kitaev circuits for braiding and charging Majorana zero modes

The Sachdev-Ye-Kitaev (SYK) model is an all-to-all interacting Majorana fermion model for many-body quantum chaos and the holographic correspondence. Here we construct fermionic all-to-all Floquet quantum circuits of random four-body gates designed to capture key features of SYK dynamics. Our circuits can be built using local ingredients in Majorana devices, namely charging-mediated interactions and braiding Majorana zero modes. This offers an analog-digital route to SYK quantum simulations that reconciles all-to-all interactions with the topological protection of Majorana zero modes, a key feature missing in existing proposals for analog SYK simulation. We also describe how dynamical, including out-of-time-ordered, correlation functions can be measured in such analog-digital implementations by employing foreseen capabilities in Majorana devices.

cond-mat.dis-nn↗

arXiv2020

Berry connection induced anomalous wave-packet dynamics in non-Hermitian systems

Berry phases strongly affect the properties of crystalline materials, giving rise to modifications of the semiclassical equations of motion that govern wave-packet dynamics. In non-Hermitian systems, generalizations of the Berry connection have been analyzed to characterize the topology of these systems. While the topological classification of non-Hermitian systems is being developed, little attention has been paid to the impact of the new geometric phases on dynamics and transport. In this work, we derive the full set of semiclassical equations of motion for wave-packet dynamics in a system governed by a non-Hermitian Hamiltonian, including corrections induced by the Berry connection. We show that non-Hermiticity is manifested in anomalous weight rate and velocity terms that are present already in one-dimensional systems, in marked distinction from the Hermitian case. We express the anomalous weight and velocity in terms of the Berry connections defined in the space of left and right eigenstates and compare the analytical results with numerical lattice simulations. Our work specifies the conditions for observing the anomalous contributions to the semiclassical dynamics and thereby paves the way to their experimental detection, which should be within immediate reach in currently available metamaterials.

cond-mat.mes-hall↗

arXiv2019

Symmetry classes, many-body zero modes, and supersymmetry in the complex Sachdev-Ye-Kitaev model

The complex Sachdev-Ye-Kitaev (cSYK) model is a charge-conserving model of randomly interacting fermions. The interaction term can be chosen such that the model exhibits chiral symmetry. Then, depending on the charge sector and the number of interacting fermions, level spacing statistics suggests a fourfold categorization of the model into the three Wigner-Dyson symmetry classes. In this work, inspired by previous findings for the Majorana Sachdev-Ye-Kitaev model, we embed the symmetry classes of the cSYK model in the Altland-Zirnbauer framework and identify consequences of chiral symmetry originating from correlations across different charge sectors. In particular, we show that for an odd number of fermions, the model hosts exact many-body zero modes that can be combined into a generalized fermion that does not affect the system's energy. This fermion directly leads to quantum-mechanical supersymmetry that, unlike explicitly supersymmetric cSYK constructions, does not require fine-tuned couplings, but only chiral symmetry. Signatures of the generalized fermion, and thus supersymmetry, include the long-time plateau in time-dependent correlation functions of fermion-parity-odd observables: The plateau may take nonzero value only for certain combinations of the fermion structure of the observable and the system's symmetry class. We illustrate our findings through exact diagonalization simulations of the system's dynamics.

hep-th↗