For more information, please visit: https://scgp.stonybrook.edu/archives/43118

Title:   Decoherence and dissipation induced topological phenomenon in open quantum system
Speaker:   Yizhi You
Abstract:   In this talk, I will explore decoherence effects in open quantum systems through a holographic lens. While decoherence and dissipation intuitively seem to trivialize quantum states and reduce long-range mutual information, they can, in fact, give rise to intriguing mixed quantum states far from equilibrium. I will begin by discussing the holographic duality between a d-dimensional mixed-state symmetry-protected topological phase and a $d+1$-dimensional subsystem symmetry-protected topological state. This duality links the mixed ensemble in the lower dimension to the entanglement properties of the higher-dimensional wavefunction, offering a practical approach for analyzing nonlinear quantities and quantum information metrics in mixed-state ensembles.

Title:   Letting the tiger out of its cage: homological bosonic coding without concatenation
Speaker:   Victor Albert
Abstract:   Continuous-variable cat codes are encodings into a single photonic or phononic mode that offer a promising avenue for hardware-efficient fault-tolerant quantum computation. Protecting information in a cat code requires measuring the mode's occupation modulo two, but this can be relaxed to a linear occupation-number constraint using the alternative two-mode pair-cat encoding. We construct multi-mode codes with similar linear constraints using any two integer matrices satisfying the homological constraint of a quantum rotor code. Just like the pair-cat code, syndrome extraction can be performed in tandem for both types of stabilizers using current superconducting-circuit designs. The framework includes codes with various finite- or infinite-dimensional codespaces, and codes with finite or infinite Fock-state support. It encompasses two-component cat, pair-cat, two-mode binomial, and aspects of chi-squared encodings while also yielding bosonic codes from homological products, lattices, and algebraic varieties. Among our examples are analogues of repetition codes, the Shor code, and a surface-like code that is not obtained by concatenating a bosonic code with the qubit surface code.

Title:   Spin glass order in classical and quantum LDPC codes
Speaker:   Vedika Khemani
Abstract:   Spin glasses constitute an important family of problems in statistical physics, as they go beyond the usual paradigm of symmetry breaking order, with important connections to computer science. However, despite intense study, exact results and a clear physical picture are hard to come by, away from the limit of all-to-all interactions. Here, we revisit the problem of glassiness in low-density parity check (LDPC), also generalizing it to quantum LDPC codes, which are at the center of much recent activity. For classical LDPC codes, we show how so-called code expansion can be used to establish properties of their energy landscapes that lead to finite-temperature spin glass order and we provide an intriguing physical interpretation in terms of the spontaneous breaking of emergent symmetries. Generalizing these ideas to the quantum setting, we argue that certain families of qLDPC codes realize a new state of matter that we term topological quantum spin glass, which combines features of spin glass and topological order. We discuss interpretations of this topological glassiness in terms of the separability of Gibbs states and passive quantum memories.

Title:   Spin glass order in classical and quantum LDPC codes
Speaker:   Tibor Rakovszky
Abstract:   Spin glasses constitute an important family of problems in statistical physics, as they go beyond the usual paradigm of symmetry breaking order, with important connections to computer science. However, despite intense study, exact results and a clear physical picture are hard to come by, away from the limit of all-to-all interactions. Here, we revisit the problem of glassiness in low-density parity check (LDPC), also generalizing it to quantum LDPC codes, which are at the center of much recent activity. For classical LDPC codes, we show how so-called code expansion can be used to establish properties of their energy landscapes that lead to finite-temperature spin glass order and we provide an intriguing physical interpretation in terms of the spontaneous breaking of emergent symmetries. Generalizing these ideas to the quantum setting, we argue that certain families of qLDPC codes realize a new state of matter that we term topological quantum spin glass, which combines features of spin glass and topological order. We discuss interpretations of this topological glassiness in terms of the separability of Gibbs states and passive quantum memories.

Title:   Monitored Kitaev models: Quantum circuits, entanglement dynamics, and synthetic fractionalization
Speaker:   Simon Trebst
Abstract:   Quantum circuits offer a versatile platform for simulating digital quantum dynamics and uncovering novel states of non-equilibrium quantum matter. In this talk, I will present monitored circuit analogs of the Kitaev honeycomb model and discuss how the non-unitary dynamics induced by mid-circuit measurements can give rise to robust phases of dynamic, entangled states of matter, which – akin to Hamiltonian ground-state phases – can be categorized based on circuit symmetries and spatial dimensionality. Imprinting a Floquet dynamics and tunable, weak measurements allows to realize qubit fractionalization in a synthetic variant of the finite-temperature physics of the Hamiltonian Kitaev model, pointing a way to realizing this physics in current quantum processors.

Title:   Concomitant Entanglement and Control Criticality Driven by Collective Measurements
Speaker:   Thomas Iadecola
Abstract:   Adaptive quantum circuits -- where a quantum many-body state is controlled using measurements and conditional unitary operations -- are a powerful paradigm for state preparation and quantum error correction tasks. They can support two types of nonequilibrium quantum phase transitions: measurement-induced transitions between volume- and area-law-entangled steady states and control-induced transitions where the system falls into an absorbing state or, more generally, an orbit visiting several absorbing states. Within this context, nonlocal conditional operations can alter the critical properties of the two transitions and the topology of the phase diagram. Here, we consider the scenario where the measurements are nonlocal, in order to engineer efficient control onto dynamical trajectories. Motivated by Rydberg-atom arrays, we consider a locally constrained model with global sublattice magnetization measurements to steer the system's dynamics onto a many-body orbit with finite recurrence time. With the aid of a suitable classical limit, we diagnose the control transition to be in a nonequilibrium universality class with dynamical exponent z<1 that persists upon reintroducing quantum fluctuations. In the quantum limit, an entanglement transition additionally emerges that coincides with the control transition -- to within our numerical resolution. Both transitions exhibit a dynamical criticality consistent with recent results on measurement-induced phase transitions in power-law interacting circuits. We attribute this feature and the apparent coincidence of the control and entanglement transitions to the global nature of the control.

Title:   Positive scalar curvature with point singularities
Speaker:   Simone Cecchini [Texas A & M]

Abstract:   Abstract:   I will discuss obstructions to metrics of positive scalar curvature with uniformly Euclidean point singularities. This provides counterexamples to a conjecture by Schoen. I will also discuss the existence of metrics with uniformly Euclidean point singularities which cannot be smoothed by a geometric flow while preserving nonnegativity of the scalar curvature.
This is based on joint work with Georg Frenck and Rudi Zeidler.
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Title:   The "Choi-Spin Liquids" in Steady States
Speaker:   Cenke Xu
Abstract:   We propose a new approach of constructing spin liquid physics. We demonstrate that the steady states of a class of Lindbladians can be mapped to the "Gutzwiller projected" wave functions in the doubled Hilbert space, i.e. the representation of the density matrix through the Choi-Jamiolkowski isomorphism. A Gutzwiller projection is a standard approach of constructing spin liquid states. For example, if one starts with a gapless free fermion pure quantum state, the steady state of the Lindbladian evolution in the doubled Hilbert space is an analog of an algebraic spin liquid, which is dubbed the "Choi-spin liquid". The Choi-spin liquid can also be produced through strong measurement without post-selection. Predictions of the Choi-spin liquids can be made based on the understanding on spin liquids, and we will design the experimental protocol to test these predictions. If one starts with a Chern insulator, theory predicts that the steady state of the Lindbladian evolution is expected to have a spontaneous "strong-to-weak" U(1) symmetry breaking, which corresponds to a superconductor in the doubled Hilbert space.

Title:   TBD
Speaker:   Ehud Altman
Abstract:   TBD

Title:   Intrinsic mixed-state topological states from a symmetry perspective
Speaker:   Zhu-Xi Luo
Abstract:   Pure state topological phases in 2d exhibit spontaneous symmetry breaking (SSB) of 1-form symmetries. In mixed states, the notion of symmetry is enriched to include both strong and weak symmetries, therefore allowing for multiple symmetry breaking patterns. This talk focuses on the strong-to-weak SSB of 1-form symmetries, leading to topological states that are intrinsically mixed-state, i.e. do not arise in pure states. Two states are defined to be in the same phase if they are connected by finite Lindbladian evolution that maintains analytically varying, finite Rényi-2 Markov length. This definition is finer than that of the two-way channel connectivity; the latter would label our target states as trivial. We illustrate these concepts using the toric code model subject to various quenched disorders. Time permitting, I will also discuss the tensor network representations of these mixed-state topological states at fixed points.

Title:   TBD
Speaker:   Sagar Vijay
Abstract:   TBD

Title:   On classification of threefolds of general type
Speaker:   Jungkai Alfred Chen [National Taiwan University]

Abstract:   In higher dimensional algebraic geometry, the following three types of varieties are considered to be the building blocks: Fano varieties, Calabi-Yau varieties, and varieties of general type. In the study of varieties of general type, one usually works on \"good models\" inside birtationally equivalent classes. Minimal models and canonical models are natural choices of good models.\r\nIn the first part of the talk, we will try to introduce some aspects of the geography problem for threefolds of general type, which aim to study the distribution of birational invariants of threefolds of general type. In the second part of the talk, we will explore more geometric properties of those threefolds on or near the boundary. Some explicit examples will be described and we will compare various different models explicitly. If time permits, we also try to talk about their moduli spaces from different points of view.
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Title:   Universal measurement-based quantum computation in a one-dimensional architecture enabled by dual-unitary circuits
Speaker:   David Stephen
Abstract:   We use dual-unitary circuits, which are unitary even when read 'sideways', as the basis of a new framework for measurement-based quantum computation (MBQC). In particular, applying a dual-unitary circuit to a many-body state followed by appropriate measurements effectively implements quantum computation in the spatial direction. We study the dual-unitary dynamics of the 1D kicked Ising chain and find that after k time-steps, equivalent to a depth-k quantum circuit, we obtain a resource state for universal MBQC on ∼3k/4 logical qubits. This removes the usual requirement of going to 2D to achieve universality, thereby reducing the demands imposed on potential experimental platforms. We also show that our resource states belong to a new class of symmetry-protected topological phases with spatially modulated symmetries, and that our protocol is robust to symmetric deformations.

Title:   TBD
Speaker:   Fiona Burnell
Abstract:   TBD

Title:   Unstable cohomology and point counting on moduli spaces of curves
Speaker:   Sam Payne [University of Texas and IAS]

Abstract:   I will survey recent advances in understanding the unstable cohomology groups of moduli spaces of curves. The approach is fundamentally rooted in motivic structures, such as mixed Hodge theory. It draws inspiration from predictions about l-adic Galois representations of conductor one from the automorphic side of the Langlands correspondence. Many of the resulting predictions for the cohomology of moduli spaces of curves are now proved unconditionally, and a graph complex governs the appearances of each such representation. By studying these graph complexes, we have described many new infinite families of unstable cohomology groups and obtained arithmetic consequences regarding the nature of the function counting geometric isomorphism classes of curves of fixed genus over varying finite fields.
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Title:   SPTO, MBQC, & SSQEC: Quantum error-correction from Walker-Wang models
Speaker:   Tyler Ellison
Abstract:   Recent developments in quantum error correction have shown that there is significant value in viewing the process from a spacetime perspective. This has enabled, in particular, the development of new quantum error-correcting codes and the establishment of unifying frameworks for seemingly different quantum error correction schemes. This perspective has also made transparent the emergence of 1-form symmetries in spacetime, suggesting tantalizing connections to symmetry-protected topological orders (SPTOs). In this talk, we strengthen the relation between 1-form SPTOs and fault-tolerant quantum error correction. We first formally establish that Walker-Wang models -- 3D lattice models based on 2D anyon theories -- provide fixed-point models for 1-form SPTOs. We then argue that fault-tolerant measurement-based quantum computation (MBQC) is a universal property of the entire SPTO phase. Finally, we show that MBQC using a 1-form SPTO as a resource defines a subsystem code with single-shot quantum error correction (SSQEC). This allows us to tie known examples of SSQEC codes, such as the 3D subsystem toric code and the gauge color code, to 1-form SPTOs. This is based on various works in progress with Lawrence Cohen, Sam Roberts, Dominic Williamson, Yaodong Li, Charles Stahl, and Dongjin Lee.

Title:   Decohering Topological Order
Speaker:   Ruben Verresen
Abstract:   Topological order (TO) is characterized by the emergence of anyonic quasiparticles, with potential applications for quantum computation. An open question of conceptual and practical importance is the effect of decoherence on TO. Thus far, the resulting mixed states have mostly been studied for the simplest TO, such as the toric code with its celebrated error threshold. In this talk, we will generalize to the broader landscape of TO, which is generically non-Abelian. Remarkably, despite being richer, we find that decohering with non-Abelian anyons leads to enhanced stability, compared to the Abelian counterpart. Our general framework is based on effective stat-mech loop models involving the quantum dimension of the anyons. Specific examples include decoherence of the Kitaev honeycomb model, as well as D4 TO which has recently been experimentally realized in quantum processors. Based on works with Pablo Sala and Jason Alicea [arXiv:2409.12948 and arXiv:2409.12230].

Title:   Matrix Product Operator Algebras and their use to study topological order
Speaker:   David Perez-Garcia
Abstract:   I will show how a detailed study of Matrix Product Operator Algebras lead to new results in the study of topological order, both in and out of equilibrium.

Title:   Topological invariants for pure and mixed state phases
Speaker:   Isaac Kim
Abstract:   We present a framework for constructing topological invariants for pure and mixed-state phases of matter. For pure states, this approach yields a circuit-invariant definition of topological entanglement entropy. For mixed states, we establish necessary and sufficient conditions for an analogous quantity to be an invariant.

Title:   The measurement-induced phase transition on dynamical quantum trees
Speaker:   Brian Skinner
Abstract:   Two difficulties that have impeded the study of the measurement-induced entanglement phase transition are (1) the difficulty of finding an exact analytical solution for the transition and its critical properties, and (2) the need for postselection in experimental realizations. Here we find a way to circumvent these two difficulties in the setting of tree-shaped tensor networks. The tree structure allows the problem to be treated by recursion, which yields an exact solution for the critical measurement strength and critical vanishing of the entanglement between the root and leaves of the tree. The recursive structure also enables an efficient experimental realization, where an entanglement witness reveals the entanglement entropy by means of a classical calculation whose complexity scales only linearly with the number of qubits in the system. I show experimental data for this postselection-free observation of the transition using trapped-ion quantum computers at Quantinuum.

Title:   Observable-sharpening transitions in monitored quantum circuits
Speaker:   Andrew Potter
Abstract:   For microscopic quantum systems, there is a smooth crossover between weak measurements that give partial information about an observable while weakly disturbing the quantum state, and strong projective measurements that fully collapse the quantum state into one with definite value of the observable. For a macroscopic quantum many-body system undergoing its own internal dynamics while interacting with a measurement apparatus, this crossover sharpens into an abrupt phase transition that sharply distinguishes the weak- and strong- measurement phases. This talk will describe how this phase transition can be observed as a change in whether or not an observer learns enough information from the measurement record to accurately predict the observable, and present data from recent experimental demonstrations in a trapped-ion quantum processor. Unlike measurement-induced entanglement phase transitions, observable-sharpening transitions can be efficiently observed in regimes where the circuit dynamics cannot be efficiently simulated classically.

Title:   A tale of two Lie groups
Speaker:   Spiro Karigiannis [ University of Waterloo, Ontario, Canada]

Abstract:   The classical Lie group SO(4) is well-known to possess a very rich structure, relating in several ways to complex Euclidean spaces. This structure can be used to construct the classical twistor space Z over an oriented Riemannian 4-manifold M, which is a 6-dimensional almost Hermitian manifold. Special geometric properties of Z are then related to the curvature of M, an example of which is the celebrated Atiyah-Hitchin-Singer Theorem. The Lie group Spin(7) is a particular subgroup of SO(8) determined by a special 4-form. Inriguingly, Spin(7) has several properties relating to complex Euclidean spaces which are direct analogues of SO(4) properties, but sadly (or intrestingly, depending on your point of view) not all of them. I will give a leisurely introduction to both groups in parallel, emphasizing the similarities and differences, and show how we can nevertheless at least partially succeed in constructing a "twistor space" over an 8-dimensional manifold equipped with a torsion-free Spin(7)-structure. (I will define what those are.) This is joint work with Michael Albanese, Lucia Martin-Merchan, and Aleksandar Milivojevic. (Michael and Aleks are recent Stony Brook PhDs.) The talk will be accessible to a broad audience.
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Title:   Quantum cellular automata and quantum phases of matter
Speaker:   Lukasz Fidkowski
Abstract:   We will show how quantum cellular automata (QCA), which originated in quantum information theory, appear naturally in the study of symmetry protected topological (SPT) phases of matter. Specifically, they appear when one studies these phases in the "condensed matter" or "many-qubit model" context, i.e. in a Hamiltonian formalism with a tensor product Hilbert space of finite dimensional site Hilbert spaces. We will make connections between QCA and the field theoretic methods for classifying these phases. We will also give a very simple explicit form for a non-trivial three dimensional QCA which was found previously via a computer assisted method, and relate this form to discrete Chern Simons theory.

Title:   Preparing many-body quantum states with quantum circuits and measurements
Speaker:   Lorenzo Piroli
Abstract:   Quantum-state preparation is a well established branch of quantum information theory, with immediate implications for quantum simulation. However, while several existing algorithms rely on the assumption of disposing of a perfect quantum computer, current noisy intermediate-scale quantum (NISQ) devices are limited in the number of qubits and the coherence time. Therefore, it is very important to devise efficient preparation schemes making use of the minimum amount of resources. Following early ideas, an emerging theme is that preparation protocols using unitary circuits can be improved making use of additional ancillas, measurements, and feedforward operations. Understanding which states or phases of matter can be realised efficiently by these operations is a non-trivial problem: while much progress has been made in the past few years, especially in the context of topological order, many questions remain open. In this talk, I will discuss how many-body quantum-state preparation can be further enhanced by lifting the requirement that the propocols are exact and deterministic, realising simple states that eluded previous protocols. I will show in particular how the so-called W and Dicke states can be prepared by shallow quantum circuits whose depth and number of ancillas per site that are independent of the system size. This is made possible by the introduction of an efficient scheme to implement certain non-local, non-Clifford unitary operators. I will argue that similar ideas may be applied in the preparation of eigenstates of well-known spin models, both free and interacting.

Title:   Dynamically generated concatenated codes and their phase diagrams
Speaker:   Michael Gullans
Abstract:   We formulate code concatenation as the action of a unitary quantum circuit on an expanding tree geometry and find that for certain classes of gates, applied identically at each node, a binary tree circuit encodes a single logical qubit with code distance that grows exponentially in the depth of the tree. When there is noise in the bulk or at the end of this encoding circuit, the system undergoes a phase transition between a coding phase, where an optimal decoder can successfully recover logical information, and non-coding phase. Leveraging the tree structure, we combine the formalism of “tensor enumerators” from quantum coding theory with standard recursive techniques for classical spin models on the Bethe lattice to explore these phases. In the presence of bulk errors, the coding phase is a type of spin glass, characterized by a distribution of failure probabilities. When the errors are heralded, the recursion relation is exactly solvable, giving us an analytic handle on the phase diagram.

Title:   A local automaton for the 2D toric code
Speaker:   Shankar Balasubramanian
Abstract:   We construct a local decoder for the 2D toric code using ideas from the hierarchical classical cellular automata of Tsirelson and Gács. Such a decoder is realized as a circuit of strictly local quantum channels that preserves the logical subspace of the toric code for exponential time in the presence of (below threshold) circuit-level noise without the need for non-local classical computation or communication. Our 2D construction is not translation invariant in spacetime, but can be made time-translation invariant in 3D.

Title:   Chaotic almost minimal systems
Speaker:   Scott Schmieding [Penn State University.]

Abstract:   A classical theorem of Furstenberg states that the only proper closed subsets of the circle which are invariant under multiplication by both two and three are finite. Several generalizations of this result have been proven since then. First I will give some background, and then discuss a class of systems motivated by this, called chaotic almost minimal systems. I'll present some results joint with Kra and Cyr about such systems, including the existence of Z^d-actions which are chaotic almost minimal and possess multiple non-atomic ergodic measures for d>=1. Time permitting, I will list some more recent work, joint with Kra, about some related results.
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Last day to take a leave of absence or withdraw from the University. Students can process via SOLAR. Requests must be processed by 4:00 PM.

Title:   Geometric Manin\'s Conjecture for Coindex Three Fano Varieties
Speaker:   Eric Jovinelly [ Brown University]

Abstract:   Manin’s Conjecture predicts an asymptotic formula for the number of rational points of bounded height on a smooth Fano variety defined over a number field. This formula emerged from heuristic arguments by Batyrev; however, these heuristics erroneously assumed certain moduli spaces of embedded rational curves are irreducible.\r\n\r\nGeometric Manin’s Conjecture (GMC) refines Batyrev’s heuristics into a conjecture about free rational curves on Fano varieties. In this talk, I will first review this refinement and motivate the framework of GMC with concrete examples. I will then describe a recent proof of GMC for smooth coindex 3 Fano varieties over the complex numbers.
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Title:   Strongly Overtwisted Contact 3-Manifolds
Speaker:   Eduardo Fernandez [University of Georgia]

Abstract:   Overtwisted contact structures in 3 dimensions were introduced by Y. Eliashberg in his seminal 1989 paper. A key property of these structures is that two overtwisted contact structures are homotopic as contact structures if and only if they are homotopic as plane fields. However, this equivalence does not hold for the classification of families of overtwisted contact structures up to homotopy: T. Vogel (2018) demonstrated the existence of a non-contractible loop of overtwisted contact structures on the 3-sphere that is contractible as a loop of plane fields.

In this talk, I will introduce a new subclass of overtwisted contact structures in dimension 3, termed strongly overtwisted, for which the classification of families can indeed be reduced to the classification of families of plane fields. In the first part of the talk, I will discuss the classification problem for families of contact structures and motivate the notion of strongly overtwisted. In the second part, I will prove the key property that strongly overtwisted contact structures satisfy the parametric h-principle.
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