arXiv subjects

Nic Shannon

Publications and source records attributed to Nic Shannon.

At least 19 recordsLinked to original sources

arXiv2026

Such stuff as magic is made on: compact operator algebra, stabilizer polytope and the structure of reduced density matrices in a Kitaev spin liquid

Quantum many-body systems exhibit rich and complex behaviour. Magic has recently emerged as a powerful new diagnostic for probing such systems, complementing other key features such as many-body entanglement. Here, starting from an investigation of the onset of magic within subsystems of a larger many-body quantum system, we show that intricate structures emerge which shed important light on the underlying many-body physics. Focusing on the Kitaev honeycomb model, we first identify the temperature below which local subsystems acquire magic. Remarkably, we find that the optimal magic witnesses active at the onset of magic reveal compact operator spaces that continue to capture the local thermal states throughout their subsequent evolution. For the six-site hexagonal marginal, this connection can be made stronger: the same operator space emerges independently from the symmetries of the local marginal and forms the symmetry-resolved plaquette algebra. When these symmetries are realized exactly, the local state lies entirely within this algebra and the reduced robustness of magic is equal to the full robustness of magic. The same reduced description can also be applied to other local quantum resources, which we illustrate using genuine multipartite entanglement. Furthermore, the operator spaces possess a rich algebraic structure in the form of finite-dimensional Euclidean Jordan algebras, with a natural interpretation in terms of bond and bond-cycle operators. Our general methodology therefore show how the onset of local magic can reveal a compact, physically meaningful operator structure underlying the finite-temperature Kitaev spin liquid, and opens up a new avenue towards reduced descriptions of quantum resources in many-body systems.

cond-mat.str-el↗

arXiv2025

Characterizing entanglement at finite temperature: how does a "classical" paramagnet become a quantum spin liquid?

Quantum spin liquids (QSL) are phases of matter which are distinguished not by the symmetries they break, but rather by the patterns of entanglement within them. Although these entanglement properties have been widely discussed for ground states, the way in which QSL form at finite temperature remains an open question. Here we introduce a method of characterizing both the depth and spatial structure of entanglement, and use this to explore how patterns of entanglement form as temperature is reduced in two widely studied models of QSL, the Kitaev honeycomb model, and the spin-1/2 Heisenberg antiferromagnet on a Kagome lattice. These results enable us to evaluate both the temperature at which spins within the high-temperature paramagnet first become entangled, and the temperature at which the system first develops the structured, multipartite entanglement characteristic of its QSL ground state.

cond-mat.str-el↗

arXiv2025

Can experimentally-accessible measures of entanglement distinguish quantum spin liquids from disorder-driven "random singlet" phases ?

At the theoretical level, quantum spin liquids are distinguished from other phases of matter by their entanglement properties. However, since the usual measure of entanglement, entanglement entropy, cannot accessed in experiment, indentifying quantum spin liquids in candidate materials remains an acute problem. Here we show other, experimentally-accessible, measures of entanglement can be used to distinguish a quantum spin liquid from a competing disorder-driven "random singlet" phase, in a model of a disordered antiferromagnet on a triangular lattice. The application of these results to the triangular-lattice systems YbZnGaO$_4$, YbZn$_2$GaO$_5$ and KYbSe$_2$ is discussed.

cond-mat.str-el↗

arXiv2025

Warm Start Adaptive-Bias Quantum Approximate Optimization Algorithm

In the search for quantum advantage in real--world problems, one promising avenue is to use a quantum algorithm to improve on the solution found using an efficient classical algorithm. The quantum approximate optimization algorithm (QAOA) is particularly well adapted for such a "warm start" approach, and can be combined with the powerful classical Goemans-Williamson (GW) algorithms based on semi-definite programming. Nonetheless, the best way to leverage the power of the QAOA remains an open question. Here we propose a general model that describes a class of QAOA variants, and use it to explore routes to quantum advantages in a canonical optimization problem, MaxCut. For these algorithms we derive analytic expectation values of the cost Hamiltonian for the MaxCut problem in the level-1 case. Using these analytic results we obtain reliable averages over many instances for fairly large numbers of qubits. We find that the warm start adaptive-bias QAOA (WS-ab-QAOA) initialized by the GW algorithm outperforms previously proposed warm start variants on problems with $40$ to $180$ qubits. To assess whether a quantum advantage exists with this algorithm, we did numerical simulations with up to $1000$ qubits to see whether the level-1 WS-ab-QAOA can improve the GW solution for 3-regular graphs. In fact the improvement in the $1000$-qubit case even in level 1 can only be matched by the GW algorithm after about $10^{5.5}$ random projections performed after the semi-definite program stage. This work gives evidence that the final stage of optimization after an efficient classical algorithm has produced an approximate solution may be a place where quantum advantages can be realized.

quant-ph↗

arXiv2025

Nematic spin liquid in a spin-1 pyrochlore magnet and its realization in $\mathrm{NaCaNi}_2\mathrm{F}_7$

The search for spin liquids, magnetic phases which lie outside the Landau paradigm, remains one of the central challenges for modern condensed matter physics. For a long time, the prime candidates were thought to be spin-1/2 magnets, but recently examples have been identified in many spin-1 materials, including the pyrochlore NaCaNi$_2$F$_7$. Here we use numerical simulation to explore the spin liquid phases which arise in a minimal model of a spin-1 magnet on the pyrochlore lattice. We find this model supports seven distinct spin liquid phases, including one with nematic correlations. Through quantitative comparison with inelastic neutron scattering, we show that this nematic spin liquid provides a compelling scenario for NaCaNi$_2$F$_7$. These results suggest that the behaviour of spin liquids found in spin-1 pyrochlore magnets may be even richer than in materials with spin-1/2 moments.

cond-mat.str-el↗

arXiv2024

Eight-color chiral spin liquid in the $S=1$ bilinear-biquadratic model with Kitaev interactions

Multipolar spin systems provide a rich ground for the emergence of unexpected states of matter due to their enlarged spin degree of freedom. In this study, with a specific emphasis on $S=1$ magnets, we explore the interplay between spin nematic states and spin liquids. Based on the foundations laid in the prior work [R. Pohle et al., Phys. Rev. B 107, L140403 (2023)], we investigate the $S=1$ Kitaev model with bilinear-biquadratic interactions, which stabilizes, next to Kitaev spin liquid, spin nematic and triple-$q$ phases, also an exotic chiral spin liquid. Through a systematic reduction of the spin degree of freedom -- from $\mathbb{CP}^{2}$ to $\mathbb{CP}^{1}$ and ultimately to a discrete eight-color model -- we provide an intuitive understanding of the nature and origin of this chiral spin liquid. We find that the chiral spin liquid is characterized by an extensive ground-state degeneracy, bound by a residual entropy, extremely short-ranged correlations, a nonzero scalar spin chirality marked by $\mathbb{Z}_{2}$ flux order, and a gapped continuum of excitations. Our work contributes not only to the specific exploration of $S=1$ Kitaev magnets but also to the broader understanding of the importance of multipolar spin degree of freedom on the ground state and excitation properties in quantum magnets.

cond-mat.str-el↗

arXiv2024

Witnessing Disorder in Quantum Magnets

There are no clean samples in nature. Therefore, when we come to discuss the entanglement properties of quantum materials, the effects of disorder must be taken into account. This question is of particular interest for high-entangled phases, such as quantum spin liquids, which lie outside the Landau paradigm for classifying phases of matter. In this work, we explore what experimentally-accessible measures, in the form of concurrence, residual tangle and quantum Fisher information, can teach us about the entanglement in the presence of disorder. As a representative example, we consider the Tomonaga-Luttinger liquids (TLL) and disorder-driven random singlet (RS) phases found in antiferromagnetic quantum spin chains. Using quantum Fisher information and residual tangle, we demonstrate that both TLL and RS phases exhibit multi-partite entanglement. In the case of the RS phase, we attribute this to entanglement localized below a crossover length scale. We further show that the order of disorder average matters in calculating measures like concurrence, and that this can lead to false inferences when interpreting experiment. Nonetheless, correctly interpreted, these witnesses provide useful information about the effects of disorder. We explore how information about the central charge of the TLL can be extracted from the low-temperature behavior of concurrence, and conjecture that this analysis can be extended to the effective central charge of the RS phase. Finally, we establish how RS and TLL phases can be distinguished through the growth of multi-partite entanglement, as witnessed by the equal-time structure factor. These results establish that, used carefully, experiments based on entanglement witnesses can provide important information about quantum spin systems in the presence of disorder.

cond-mat.str-el↗

arXiv2024

Magnon Spectra of Cuprates beyond Spin Wave Theory

The usual starting point for understanding magnons in cuprate antiferromagnets such as La$_2$CuO$_4$ is a spin model incorporating cyclic exchange, which descends from a one-band Hubbard model, and has parameters taken from fits based on non-interacting spin wave theory. Here we explore whether this provides a reliable description of experiment, using matrix product states (MPS) to calculate magnon spectra beyond spin wave theory. We find that analysis based on low orders of spin wave theory leads to systematic overestimates of exchange parameters, with corresponding errors in estimates of Hubbard $t/U$. Once these are corrected, the ''standard'' model provides a good account of magnon dispersion and lineshape in La$_2$CuO$_4$, but fails to fully capture the continuum observed at high energies. The extension of this analysis to CaCuO$_2$ and Sr$_2$IrO$_4$ is also discussed.

cond-mat.str-el↗

arXiv2024

Exploiting many-body localization for scalable variational quantum simulation

Variational quantum algorithms (VQAs) represent a promising pathway toward achieving practical quantum advantage on near-term hardware. Despite this promise, for generic, expressive ans\"atze, their scalability is critically hindered by barren plateaus--regimes of exponentially vanishing gradients. We demonstrate that initializing a hardware-efficient, Floquet-structured ansatz within the many-body localized (MBL) phase mitigates barren plateaus and enhances algorithmic trainability. Through analysis of the inverse participation ratio, entanglement entropy, and a novel low-weight stabilizer R\'enyi entropy, we characterize a distinct MBL-thermalization transition. Below a critical kick strength, the circuit avoids forming a unitary 2-design, exhibits robust area-law entanglement, and maintains non-vanishing gradients. Leveraging this MBL regime facilitates the efficient variational preparation of ground states for several model Hamiltonians with significantly reduced computational resources. Crucially, experiments on a 127-qubit superconducting processor provide evidence for the preservation of trainable gradients in the MBL phase for a kicked Heisenberg chain, validating our approach on contemporary noisy hardware. Our findings position MBL-based initialization as a viable strategy for developing scalable VQAs and motivate broader integration of localization into quantum algorithm design.

quant-ph↗

arXiv2024

Quantum size effects on Andreev transport in Nb/Au/Nb Josephson junctions: A combined ab-initio and experimental study

We have measured the critical current density, superconducting coherence length, and superconducting transition temperature of single-domain, epitaxially-grown Nb(110)/Au(111)/Nb(110) trilayers, all of which show a non-monotonic dependence on the thickness of the Au layer. These results are compared with the predictions of a relativistic, ab-initio theory, which incorporates superconducting correlations. We find good agreement with experiment, coming from a rich interplay between superconducting proximity - and quantum size effects, mediated by Andreev bound states. These results suggest that quantum size effects could provide a systematic method of controlling the transport properties of superconducting multilayers.

cond-mat.supr-con↗

arXiv2024

Human-machine collaboration: ordering mechanism of rank-2 spin liquid on breathing pyrochlore lattice

Machine learning algorithms thrive on large data sets of good quality. Here we show that they can also excel in a typical research setting with little data of limited quality, through an interplay of insights coming from machine, and human researchers. The question we address is the unsolved problem of ordering out of a spin-liquid phase described by an emergent rank-2 U(1) gauge theory, as described by [H. Yan et al., Phys. Rev. Lett. 124, 127203 (2020)]. Published Monte Carlo simulations for this problem are consistent with a strong first-order phase transition, but were too noisy for the form of low-temperature order to be identified. Using a highly-interpretable machine learning approach based on a support vector machine with a tensorial kernel (TKSVM), we re-analyze this Monte Carlo data, gaining new information about the form of order that could in turn be interpreted by traditionally-trained physicists. We find that the low-temperature ordered phase is a form of magnetic order analogous to a smectic liquid crystal. This arises due to a subtle thermal order-by-disorder mechanism, that can be understood from the fluctuations of the tensor electric field of the parent rank-2 gauge theory. These results were obtained by a back-and-forth process which closely resembles a collaboration between human researchers and machines. We argue that this "collaborative" approach may provide a blueprint for solving other problems that have not yielded to human insights alone.

cond-mat.str-el↗

arXiv2023

Gravitational wave analogues in spin nematics and cold atoms

Many large-scale phenomena in our Universe, such as gravitational waves, are challenging to reproduce in laboratory settings. However, parallels with condensed matter systems can provide alternative routes for experimental accessibility. Here we show how spin nematic phases provide a low-energy avenue for accessing the physics of linearized gravity, and in particular that their Goldstone modes are relativistically-dispersing massless spin-2 excitations, analogous to gravitational waves. We show at the level of the action that the low-energy effective field theory describing a spin nematic is in correspondence with that of linearized gravity. We then explicitly identify a microscopic model of a spin-1 magnet whose excitations in the low energy limit are relativistically dispersing, massless spin-2 Bosons which are in one-to-one correspondence with gravitational waves and, supported by simulation, outline a procedure for directly observing these analogue waves in a cold gas of $^{23}$Na atoms.

cond-mat.str-el↗

arXiv2023

Solution of SAT Problems with the Adaptive-Bias Quantum Approximate Optimization Algorithm

The quantum approximate optimization algorithm (QAOA) is a promising method for solving certain classical combinatorial optimization problems on near-term quantum devices. When employing the QAOA to 3-SAT and Max-3-SAT problems, the quantum cost exhibits an easy-hard-easy or easy-hard pattern respectively as the clause density is changed. The quantum resources needed in the hard-region problems are out of reach for current NISQ devices. We show by numerical simulations with up to 14 variables and analytical arguments that the adaptive-bias QAOA (ab-QAOA) greatly improves performance in the hard region of the 3-SAT problems and hard region of the Max-3-SAT problems. For similar accuracy, on average, ab-QAOA needs 3 levels for 10-variable 3-SAT problems as compared to 22 for QAOA. For 10-variable Max-3-SAT problems, the numbers are 7 levels and 62 levels. The improvement comes from a more targeted and more limited generation of entanglement during the evolution. We demonstrate that classical optimization is not strictly necessary in the ab-QAOA since local fields are used to guide the evolution. This leads us to propose an optimization-free ab-QAOA that can solve the hard-region 3-SAT and Max-3-SAT problems effectively with significantly fewer quantum gates as compared to the original ab-QAOA. Our work paves the way for realizing quantum advantages for optimization problems on NISQ devices.

quant-ph↗

arXiv2023

Spin Nematics Meet Spin Liquids: Exotic Quantum Phases in the Spin-$1$ Bilinear-Biquadratic Model with Kitaev Interactions

Spin liquid crystals are magnetic analogs of liquid crystals, possessing properties of both liquids and solids, a typical example of which are spin nematics. Spin nematics share many features with spin liquids, and the interplay between them is a promising, but little explored, route to uncovering new phases of matter. Here, we address this question in the context of a spin-$1$ magnet on the honeycomb lattice, by considering a model with both biquadratic interactions, favouring spin-nematic states, and Kitaev-like interactions, supporting spin liquids. Accompanying these, where dipole and quadrupole moments compete, we find a plethora of exotic phases, including multiple-$q$ states with nonzero scalar spin chirality; a quasi-one-dimensional coplanar phase; a twisted conical phase; and a noncoplanar order state which gives way to a chiral spin liquid at finite temperature. The implication of these results for experiment is discussed.

cond-mat.str-el↗

arXiv2023

Pinch points and half moons encode Berry curvature

"Half moons", distinctive crescent patterns in the dynamical structure factor, have been identified in inelastic neutron scattering experiments for a wide range of frustrated magnets. In an earlier paper [H. Yan et al., Phys. Rev. B 98, 140402(R) (2018)] we have shown how these features are linked to the local constraints realized in classical spin liquids. Here we explore their implication for the topology of magnon bands. The presence of half moons indicates a separation of magnetic degrees of freedom into irrotational and incompressible components. Where bands satisfying these constraints meet, it is at a singular point encoding Berry curvature of $\pm 2\pi$. Interactions which mix the bands open a gap, resolving the singularity, and leading to bands with finite Berry curvature, accompanied by characteristic changes to half--moon motifs. These results imply that inelastic neutron scattering can, in some cases, be used to make rigorous inference about the topological nature of magnon bands.

cond-mat.str-el↗

arXiv2022

Mitigating algorithmic errors in quantum optimization through energy extrapolation

Quantum optimization algorithms offer a promising route to finding the ground states of target Hamiltonians on near-term quantum devices. None the less, it remains necessary to limit the evolution time and circuit depth as much as possible, since otherwise decoherence will degrade the computation. And even where this is done, there always exists a non-negligible error in estimates of the ground state energy. Here we present a scalable extrapolation approach to mitigating this error, which significantly improves estimates obtained using three of the most popular optimization algorithms: quantum annealing (QA), the variational quantum eigensolver (VQE), and quantum imaginary time evolution (QITE), at fixed evolution time or circuit depth. The approach is based on extrapolating the annealing time to infinity, or the variance of estimates to zero. The method is reasonably robust against noise, and for Hamiltonians which only involve few-body interactions, the additional computational overhead is an increase in the number of measurements by a constant factor. Analytic derivations are provided for the quadratic convergence of estimates of energy as a function of time in QA, and the linear convergence of estimates as a function of variance in all three algorithms. We have verified the validity of these approaches through both numerical simulation and experiments on an IBM quantum computer. This work suggests a promising new way to enhance near-term quantum computing through classical post-processing.

quant-ph↗

arXiv2022

Quantum Approximate Optimization Algorithm with Adaptive Bias Fields

The quantum approximate optimization algorithm (QAOA) transforms a simple many-qubit wavefunction into one which encodes a solution to a difficult classical optimization problem. It does this by optimizing the schedule according to which two unitary operators are alternately applied to the qubits. In this paper, the QAOA is modified by updating the operators themselves to include local fields, using information from the measured wavefunction at the end of one iteration step to improve the operators at later steps. It is shown by numerical simulation on MaxCut problems that, for a fixed accuracy, this procedure decreases the runtime of QAOA very substantially. This improvement appears to increase with the problem size. Our method requires essentially the same number of quantum gates per optimization step as the standard QAOA, and no additional measurements. This modified algorithm enhances the prospects for quantum advantage for certain optimization problems.

quant-ph↗

arXiv2022

Semi-classical simulation of spin-1 magnets

Theoretical studies of magnets have traditionally concentrated on either classical spins, or the extreme quantum limit of spin-1/2. However, magnets built of spin-1 moments are also intrinsically interesting, not least because they can support quadrupole, as well as dipole moments, on a single site. For this reason, spin-1 models have been extensively studied as prototypes for quadrupolar (spin-nematic) order in magnetic insulators, and Fe-based superconductors. At the same time, because of the presence of quadrupoles, the classical limit of a spin-1 moment is not an $O(3)$ vector, a fact which must be taken into account in describing their properties. In this Article we develop a method to simulate spin-1 magnets based on a $u(3)$ algebra which treats both dipole and quadrupole moments on equal footing. This approach is amenable to both classical and quantum calculations, and we develop the techniques needed to calculate thermodynamic properties through Monte Carlo simulations and classical low-temperature expansion, and dynamical properties, through "molecular dynamics" simulations and a multiple-boson expansion. As a case study, we present detailed analytic and numerical results for the thermodynamic properties of ferroquadrupolar order on the triangular lattice, and its associated dynamics. At low temperatures, we show that it is possible to "correct" for the effects of classical statistics in simulations, and extrapolate to the zero-temperature quantum results found in flavour-wave theory.

cond-mat.str-el↗