October 9, 2026. This is the first in a series of (hopefully regular/monthly) posts where I go over new arXiv/journal articles from September that have been posted that are of interest, as well as past papers/notes I have been reading the last month.

September arXiv postings

  • A nonabelian anyon violates Haag duality 2609.01267 by Daniel Wallick, Henrik Wilming.
    • Haag duality is a concept taken from (formal) quantum field theory, which relates the commutant of an algebra of observables in one region with the algebra of a disconnected region, and has been shown (e.g.) in free scalar field theories (2108.01257 gives a review for the hep-th setting). In the quantum information setting, the duality is equivalent to the uniqueness of purifications of a state. This paper has a very nice argument that a single non-abelian anyon is sufficient to violate the duality/uniqueness of purifications; by splitting a non-abelion \(b\) is split into \(a + b\) (and then moving the \(a\) anyon to a different region), one can find that the \(a+b\) and \(b\) state look the same on the \(B\) region but any unitary in the \(A\) region has zero overlap. As an aside, I appreciate greatly the structure of this paper, wherein the physical argument of the main text is exceptionally digestable, and the formal proof (which goes over my head) can be relegated to the appendix for the experts. This argument then implies that this nice algebraic property can be violated in entire gapped phases of matter (those supporting non-abelions). There is also an interesting point in the outlook about a conjectured equivalence between the entanglement bootstrap axiom(s) and this duality.
  • Computing with qLDPC Codes by Climbing the Chain Map Hierarchy 2609.02999 by Rahul Sahay, David M. Long, Vedika Khemani.
    • A nice paper advancing our understanding of the hot topic of qLDPC codes (on which so much literature is being produced that I feel that it may be impossible for me to catch up). Instead of taking the “quantum engineering” approach to qLDPC (finding particular instances and exploring their properties), the qLDPCrew here explores a very general connection between the homological structure of qLDPC and encoded Clifford gates one can perform (and as a concrete example, they use their formalism to find new gates for even the 2D toric code! The code that keeps on giving). The paper is fairly long but the techniques/formalism presented seems interesting to understand for the QEC minded.
  • Fractalizing spacetime: Floquet codes with fractonic excitations that are immobile in space and time 2609.03703 by Juliette Soule, Dominic J. Williamson.
    • Fractionalization is a procedure in which a lower-dimensional model is mapped to a higher dimensional one via embuing it with a cellular automaton rule - for example, Haah’s cubic code (the prototypical example of a type-II fracton order, possessing immobile fracton quasiparticles and partial self-correction properties) is the fractalization of the 2D toric code! In this work the authors apply this procedure to spacetime codes, in particular considering the fractalization of the 3D RHG cluster state (the canonical resource for 3D fault tolerant measurement-based quantum computation). This results in a model with fracton excitations that are immobile in spacetime, not just space (in addition to CMT interest, their model also has nice scaling of fault-distance, and generically this procedure may yield good fault-tolerant resources). An interesting mash-up of ideas from topological phases of matter, QEC, and MBQC.
  • On the geometry and typicality of quantum magic 2609.03944 by Zhenhuan Liu, Zi-Wen Liu.
    • Quantum magic is one of the necessary components for a quantum state to be non-simulable; states without magic have efficeint representations in terms of the stabilizer tableau and hence can be efficiently classically simulated (this is the celebrated Gottesman-Knill theorem)! The characterization of such states are thus of both applied and theoretical interest. For a single qubit, the stabilizer polytope has the easy interpretation of being the convex hull (octahedron) formed by the Pauli eigenstates, but for multi-qubit states the geometry has been not well understood. The authors show that every state below a purity threshold is within the multi-qubit stabilizer polytope, and also prove other results establishing that magic is typically robust (moreso than entanglement!), owing to the extremal geometry of the stabilizer polytope. The article is consice but technical - it seems unclear if the used techniques may be generically useful for the condensed matter theorist, but the geometric intuition about magic seems perhaps useful and the results fundamental and impressive. I wonder if long-range magic may be embued with a similar geometric interpretation.
  • Matrix Product Belief Propagation 2609.05598 by Gabriel Woolls, Shahin Jahanbani, Adarsh Pashikanti, Matthew T. Fishman, Joseph Tindall, Michael P. Zaletel.
    • Although many of my current projects center around tensor networks/MPS, I’m generally fairly unfamiliar with the algorithm-design side of the subfield. That said, the MP-BP algorithm described here sounds like quite a promising approach, both in its improved convergence and gauge equivariant properties, but also intuition in the sense that it can be viewed as the generalization of familiar techniques (e.g. corner transfer matrix methods, boundary MPS, standard BP). Hopefully we may see it implemented in iTensor in the near future!
  • Ginzburg-Landau Theory for Non-Invertible Symmetry-Breaking Transitions 2609.06751 by Vibhu Ravindran, Luisa Eck, Xie Chen.
    • The SymTFT/sandwich formalism presents a nice language for discussing the “Generalized Landau Paradigm”, in which both conventional (global) and generalized symmetry-breaking transitions can be naturally described (this paradigm is a reflection of our contemporary understanding of phase transitions which may not look like SSB on their face, but can be interpreted such upon more careful analysis - e.g. the transition between the toric code phase and paramagnetic phase can be interpreted as the \(\mathbb{Z}_2\) 1-form symmetry breaking transition). An open question in this area (see PRL-tmvy-vsqd for an accessible essay by Xie Chen about this new paradigm, where I saw this question get presented) is whether (like for global, group-based symmetries) one can describe such phase transitions using field theory (by considering a fluctuating order parameter field). This new preprint answers this in the affirmative, and lays out the structure of the generalized Landau-Ginzberg theory for Rep(\(S_3\))-symmetry breaking transitions. The paper is written very pedagogically, and reviews both Landau-Ginzberg and SymTFT for \(S_3\)-SSB transitions (already a helpful example to have worked out explicitly in the literature, as the level of complexity is above the standard illustration of the \(\mathbb{Z}_2\) case) before moving onto Rep(\(S_3\)).
  • Subsystem self-correction of the GKP qubit 2609.07702 by Brian Chung Hang Cheung, Lasse Bjørn Kristensen, Frederik Nathan, Michael Kastoryano.
    • Thermally stable/passively self-correcting quantum memories (the 4D toric code being the prototypical example, and a 3D construction arising just recently 2605.10943) are interesting and highly desirable classes of many-body quantum systems. In optical systems, a well-studied and targeted CV error correcting code is the Gottesman-Kitaev-Preskill (GKP) code, wherein qubit degrees of freedom are encoded in infinite comb-like states. Such states are robust to quadrature errors, but an interesting problem is whether they are thermally stable, which this paper studies. The authors find that the ideal Hamiltonian is self-correcting, and finite-energy approximations (necessary as the exact eigenstates are infinite energy and hence not realizable) carry over an Arrhenius-like scaling of the logical lifetime. The authors also draw a nice physical picture - GKP qubits have an “error string tension” which suppresses the growth of a logical error (in contrast to the 2D toric code, where extending error string operators costs no energy - this is why it is not a thermally stable memory). On the other hand, unlike the toric code which can be scaled to the thermodynamic limit, GKP codes have a fixed decoding cell/critical error length, and thus there is no sense in which there is a phase transition/threshold below which the GKP qubit displays self correction (rather, there is some smooth crossover into a regime with exponentially long lifetimes).
  • Fermionic quantum cellular automata in 2d are trivial 2609.09317 by Jeffrey Kwan, David M. Long, Jeongwan Haah.
    • A very technical and algebraic article, but an important result! All 1D QCA 0910.3675 and all 2D bosonic QCA 1902.10285 have been proven to be trivial (the former proof by Gross–Nesme–Vogts–Werner, the latter by Freedman–Hastings), in the sense that all can be written as a combination of a finite depth circuit + a shift/translation. Haah-Fidkowski-Hastings have also previously constructed a 3D QCA 1812.01625 which disentangles 3D Walker-Wang, with a result that either this QCA was nontrivial or there exists some nontrivial fermionic QCA. This new preprint shows the first case is the correct one by showing that 2D fermionic QCA are also trivial (though they note that there are technical details to be worked out in a forthcoming article to make this implication complete). QCA “feel” like very general and natural structures in terms of physically reasonable maps, and we now have an even better understanding of the landscape!
  • Local decoders for fault-tolerant quantum computation and translation-invariant stabilizer codes 2609.11457 by Nathaniel Selub, Aditya Bhardwaj, Ethan Lake.
    • On the note of cellular automaton, this monumental work uses them to construct local decoders for repetition and surface codes as well as a general proof of local decodability. The very rough idea is that for a given cluster of errors in a region of size \(W\), the decoders/CA are designed such that all errors in such clusters are erased in \(O(W)\) (linear cluster erosion) and so are all messages/auxiliary bits in that region. If the clusters are designed to eliminate before they ever intersect, the only way for a logical error to occur is to have some order system-size error, which is suprressed below threshold in the system size. They also give a very nice intuition for how a repetition code decoder (and in 2D, the toric code decoder) satisfies this property; a defect creates messages to the right at speed \(1/q \leq 1/2\), moving to the left whenever it sees a message to its left, until it meets another defect and annihilates. In the absence of defects, messages erode from the left at speed 1. Under these dynamics, defects in a block size \(W\) annilhilate in \(O(W)\) time, and messages also erase themselves in \(O(W)\) time, giving the linear cluster erosion property. Beyond the technical advancements/insights of the work (of which there are probably many in the 100+ pages…), this seems like a really nice work towards proving fault tolerance under realistic physical assumptions, as well as presenting new avenues to think about non-equilibrium quantum matter.
  • Remarks on invertible phases with non-onsite symmetry 2609.12042 by Ryohei Kobayashi, Kansei Inamura, Ken Shiozaki.
    • Invertible phases are phases which are gapped and admits an inverse under stacking (i.e. given representative of the phase \(A\), there exists \(A^{-1}\) such that \(A \oplus A^{-1}\) is deformable to the trivial Hamiltonian). They are usually classified in the presence of an onsite symmetry (which has a symmetric product state as the canonical choice of the trivial gapped phase/parent Hamiltonian \(H_0\) in the above). How then do we consider such phases in the presence of a non-onsite (and on-onsiteable, i.e. anomalous) symmetry? Such symmetries usually forbid SRE states, but here they show that by considering a model with a fermionic \(\mathbb{Z}_4^F\) symmetry that not only prevents SRE but also shifts the preserved invertible phases to oen with half-odd-integer chiral central charge (instead of integer). The paper is a bit technical and beyond my field of expertise, but getting a grip on anomalous symmetries and their implications on the lattice seems like an interesting discussion (see also “Disentangling the Toric Code” later down this list).
  • QMA has perfect completeness 2609.13032 by Sabee Grewal, Dorian Rudolph.
    • A resolution of a big open problem in quantum complexity theory! The setting is as follows - one considers a prover (Merlin) and verifier (Arthur). Merlin sends arthur a proof, of either a YES or NO instance. There are two parameters to the setup - completeness \(c\), wherein Arthur accepts proofs of YES instances with probability at least \(c\), and soundness \(s\) wherein Arthur rejects proofs of NO instances with probability at most \(s\). Computational systems are intuitively more powerful with \(c < 1\), as this allows for protocols to be inexact/have errors. For many cases, it has been shown that proof systems can be made perfectly complete by taking \(c = 1\) without loss of power, e.g. MA \(=\) MA\(_1\) (for classical proofs and randomized classical verifiers) and QCMA \(=\) QCMA\(_1\) (for classical proofs and a quantum verifier). The quantum proof/quantum verifier case was open, but now resolved! Since complexity is outside of my field, I don’t understand the full suite of implications (mainly seems to be connected to implying different problems are QMA-complete, such as quantum 3-SAT), but this seems like a nice hole to close and yet another sign that AI is playing a large role in the fall of many open conjectures in math/computer science/mathematical physics.
  • Universal computation with magic Hamiltonians 2609.14757 by Marius Junge, Jason Pollack, Luke Visser.
    • A nice more “physics” way of thinking about quantum computation in the Hamiltonian evolution picture (rather than the gate-based picture as it is often conceptualized - of course in experiment, any gate is generally realized by the suitable application of Hamiltonian evolution for some time, e.g. evolving with \(H = gX\) for some appropriate time to realize an \(X\)-rotation). The authors consider magic Hamiltonians which (in conjunction with standard/easy to implement Hamiltonians) give rise to universality, and consider approximation algorithms (ala Solovay-Kitaev) in this picture. What is unclear to me is how realistic their assumptions are with regards to actual physical setups - their setting is where global (Ising type) Hamiltonians are expensive (these are the “magic” Hamiltonians/resources) while low weight Paulis are cheap; but this seems somewhat unrealistic; if we imagine an analogue system I don’t really see why such a global Hamiltonian would be expensive (this could just be the natural system dynamics) and even in a highly controlled system the source of magic could just be some single-qubit rotations via an arbitrary angle, which is not hard for experimental setups. Phrased another way, quantum magic is something that is hard for classical computers, but often in experiment is not the driving/expensive resource - it can be very easy to inject magic via suitable single-qubit gates/Hamiltonian evolution. So (modulo my misunderstanding of their setting) this could be a fun paper with confusing assumptions.
  • Fermionic quantum error correction is never free 2609.15059 by Yifan Tang, Ingo Roth, Philippe Faist, Zi-Wen Liu, Jens Eisert, Zhenhuan Liu.
    • The most common framework of quantum error correction on qubits is in the form of stabilizer codes - this formalism is very useful for many reasons, one of which is that it is amenable to classical simulation; the codewords are stabilizer states (and preparation of the codewords only involves the measurement and correction of the stabilizers). The analogous classically simulable set of states/operations in the fermionic case are Gaussian states and Gaussian operations (that map from Gaussians to Gaussians) - here, the authors show a hard departure of fermionic QEC from the qubit case, as any fermionic quantum error correction operation requires non-Gaussian operations (both in the sense that any fermionic QEC code cannot have a pure Gaussian codeword, and that the codewords require many non-Gaussian operations to prepare). Thus fermionic QEC (which is relevant, e.g., for Majorana fermion based architectures) appears to have a level of complexity (both in simulation and implementation) absent in the qubit case.
  • Emergent classicality and wavefunction branching in an isolated quantum many-body system 2609.19254 by Saúl Pilatowsky-Cameo, Jordan Cotler, Daniel Ranard, C. Jess Riedel.
    • The central setting is very interesting (and something I have been asked about/wondered about occasionally) - on macroscopic scales systems look classical, even though the microscopic theory is quantum mechanical. One proposed mechanism for this is decoherence from system-environment induced interactions; but a similar crossover should occur also for isolated quantum many-body systems. Here the authors consider a 3-local, all-to-all model of kicked spins, finding that the internal degrees of freedom act as a bath such that the collective spin of the system exhibits classical (Fokker-Planck) dynamics. In some sense this is a very toy model (the all-to-all part especially - as the authors note in the outlook, it would be curious to see if the same could be observed in a system with local interactions), but it is a very neat toy/example of emergent classicality!
  • Non-Abelian Anyon Condensation: a Path-Integral Monte Carlo Approach 2609.19282 by Rafael Flores-Calderón, Frank Pollmann, Michael Knap.
    • A nice new formalism/technique for exploring non-abelian topological order under decoherence! I’m not quite sure what older techniques covered (for example I am aware of prior works looking at decoherence of \(\mathcal{D}(D_4)\) topological order) but this seems like a fairly general technique for looking at \(G\)-topological orders (the central idea being a map to a sign-free 2+1D classical Gauge theory, which is amenable to Monte Carlo). Perhaps a nice addition to the toolkit of thinking about TO and generalized symmetry-breaking transitions.
  • Lee-Yang theorem for fermions 2609.23942 by Chaithanya Rayudu, Takahiro Misawa, Andrew Zhao, Jun Takahashi.
    • Lee-Yang zeroes of partition functions are tractable mathematical probes of many-body systems - their absence coincides with the lack of a phase transition in a given system, and they can also be used to design classical and quantum simulation algorithms (e.g. for estimating energy gaps and correlations). The authors extend the analysis (previously done on many-body spin models) to free fermion and a natural class of interacting fermion models (including attractive Hubbard and repulsive bipartite Hubbard), proving that such models are free of Lee-Yang zeroes. This gives both some nice analytical guarantees of simulation algorithms of such system, as well as resolving some ambiguity about the existence of phase transitions in fermionic systems (excluding TO with stable GSD).
  • Kitaev spin liquid in superconducting networks 2609.25210 by Guilherme Delfino, Mehmet Dede, Dmitry Green, Michael J. Manfra, Charles M. Marcus, Claudio Chamon.
    • A neat experimental architecture proposal for realizing the prototypical Kitaev honeycomb model (an exactly solvable model which can describe gapless spin-liquids, as well as non-Abelian phases/anyons!). There has been a lot of development recently in the trapped ion and neutral atom spheres towards quantum simualtion (one example is recent work on realizing a Dirac spin liquid (candidate) on Rydbergs, 2602.14323) but also neat to see developments on the superconductor side of things! Also see 2605.28942 for simulating classical models on hyperbolic space using superconducting networks!
  • Non-Abelian sheaf quantum LDPC codes: good and magical 2609.30159 by Zimu Li, Fuchuan Wei, Zhengyi Han, Zi-Wen Liu.
    • One of two closely appearing works on sheaf codes, towards a nice body of works both (a) constructing interesting/good families of such codes and (b) developing physical understanding. Here, the authors construct a family of codes that is good (linear distance) but also with the long-range magic property (non-stabilizerness that cannot be removed in finite depth), towards the NLTM conjecture (resolved in a preprint by the same authors a few days later - see below)!
  • Deep thermalization and Hilbert space ergodicity 2609.30248 by Daniel K. Mark, Manuel Endres, Matteo Ippoliti, Wen Wei Ho, Soonwon Choi.
    • A consice review on some exciting emerging topics at the interface of quantum information science, statistical mechanics, and complexity! Deep (as opposed to standard) thermalization is the notion that maximal randomness in all moments of the (projected/temporal) ensemble of quantum states (in standard thermalization, one only strudies the first moment), with a simple and well-studied instance arising from Haar random ensembles (quantum states that are uniformly sampled from the Hilbert space). The authors also discuss a new structure - the Scrooge ensemble (a deformed Haar ensemble) and its relation to thermalization. The landscape they present is quite rich and interesting! - I personally would like to better understand phase transitions in entropy/information content and their physical interpretation.
  • Disentangling the Toric Code 2609.30363 by Lei Gioia, Salvatore D. Pace, Ruben Verresen, Shu-Heng Shao, Ryan Thorngren.
    • Anomalous symmetries were born in the high-energy/continuum setting but have recently spurred a lot of interesting work in the lattice setting. By definition, such symmetries are not onsitable (this is often, but not always, equivalent to the notion that there is an obstruction to finite-depth disentangler to these states). A known result in hep-th is that there exists no \(U(1)\) anomalous systems in 2+1D. What about on the lattice? Here, the authors consider the 1+1D Ising ferromagnet (with generator \(Q = H_{SSB} = \sum \frac{1}{4}(1- Z_iZ_j)\)) and 2+1D toric code (with generator \(Q = H_{TC} = \sum_v \frac{1}{4}(1 - A_v) + \sum_p \frac{1}{4}(1 - B_p)\)), both of which have long-range order in their ground states. They show that with bounded ancillas the symmetry is not onsitable, but with unbounded (quantum rotor) ancillas the symmetry is onsitable (appears non-anomalous!) Since the presence of such ancillas means the Hamiltonian is unbounded from below, this is consistent with the LRO of the ground states (i.e. this protocol does not give you a way to prepare the cat state or toric code with FDLU). Neat that the introduction of infinite dimensional ancilla brings you closer to the continuum result!
  • Sipser-Spielman meets Dijkgraaf-Witten: non-Abelian qLDPC codes via twisted sheaf gauge theory and almost-constant-overhead magic state fountain 2609.31541 by Guanyu Zhu, Shi Jie Samuel Tan, Ryohei Kobayashi, Po-Shen Hsin.
    • The other work on sheaf codes, this one places a greater emphasis on magic state generation in such codes, as well as connections to (Dijkgraaf-Witten) gauge theories/topological field theoretic analysis. As is the case with many related works about qLDPC from these authors, the results are quite dense and technical. Since I am personally quite interested in understanding the physics interpretations (e.g. non-local phases of matter) of qLDPC codes, this would be a body of work I want to dedicate a bit more time to.
  • Probing the classical complexity of quantum dynamics experiments 2609.31830 by Thomas Schuster, Andreas Elben.
    • Various techniques have been put forwards to classically simulate quantum dynamics, such as Pauli path propagation (tracking Pauli weights through a circuit) or tensor network methods (storing some finite bond-dimension approximation of a state and evolving it in time). A generic measure of classical simulability is quite nontrivial (this is related to the fact that there are many necessary conditions for quantum advantage, but it is hard to pin down sufficent ones). Here, a reactivity function is defined as the contribution of the total contribution from Pauli paths with a given weight - high reactivity thus corresponds to high complexity. Further, the authors establish a Pauli spectroscopy protocol which allows for an efficient measurement of the reactivity - this seems to be quite a useful probe for quantifying what experiments are classically nontrivial as hardware continues to improve.
  • Theory of criticality-enabled U(1) symmetry breaking in a class of 1+1D systems 2609.38581 by E. S. Andriyakhina, A. S. Shankar, T. Senthil, Z. D. Shi
    • I didn’t know about this, but the fate of LRO of continuous symmetries in 1D systems has been contested! In 2+1D, SSB of continuous symmetries is forbidden by the celebrated Mermin-Wagner, and I thought the theorem also applied to 1+1D, but apparently there exists a loophole. Specifically, the argument relies on mapping the quantum 1+1D system to a classical 2+1D system. Since quantum systems can possess Berry phase terms that can induce structure that modifies fluctuations of the Goldstone mode. This combined with a softening of the \(U(1)\) density can lead to LRO at quantum criticality. Previously Adam Nahum had proposed a field theory with this feature in 2506.21540, but this was not amenable to verifying the \(U(1)\) order parameter had LRO. The current authors present a large-\(N\) analysis of the proposed 1+1D Lifschitz field theory and also present some accompanying DMRG/numerical analysis of a fermionic lattice model, confirming and elucidating the nature of \(U(1)\) LRO.
  • Measurement and feedforward circuits from quantum error correcting codes 2609.39764 by Georgios Styliaris, Rahul Trivedi.
    • I have been thinking about measurement-and-feedback protocols for a while (both in the context of MBQC and for measurement-based state preparation of long-range entangled states), and whenever talking about them casually have always referred to the step of cleaning up the measurement errors as “error-correction”. Here the authors nicely formalize this intuition, casting the FDLU as an encoder, and the measurements projectors as detectable errors (in the case of deterministic MBSP). Being able to trade the MBSP problem for a code design problem seems like a generally useful perspective! I have also been thinking a bit about whether there exist MBSP protocols which require some non-linear (or even more complicated) processing of the measurement outcomes, and this work seems to give a nice picture for why known protocols look linear (and perhaps where/how to look for more complicated cases).
  • Fault Tolerant Quantum Phases of Matter 2609.39879 by Colin V. Coane, Shouzhen Gu, Aleksander Kubica.
    • A work with lots of insights I want to digest. The classification of mixed state phases of matter remains still elusive/contested in the community. Here the equivalence is introduced (though I think related ideas have been discussed) as a full-stack fault tolerance equivalence, in the sense that two states are in the same phase if they have a nonzero error threshiold and can be releated by a finite depth local channel (presumably two way). I like this kind of operational thinking of quantum phases, and would be nice to see where it fits in with previous conceptions of mixed state phases of matter. They also touch on the fault-tolerance of preparing states via single-shot measurement and feedback protocols, building on ideas from 2208.11136.
  • NLTM Hamiltonians from gauged sheaf quantum locally testable codes 2609.40220 by Fuchuan Wei, Zhengyi Han, Zimu Li, Zi-Wen Liu.
    • A few years ago, Anshu-Breuckmann-Nirkhe proved the NLTS theorem, by showing good qLDPC codes have the property that all of their low-energy states are non-trivial (not preparable by a constant depth circuit). This work strengthens this theorem by considering another family of quantum error correcting codes such that all states in the low-energy subspace have no trivial magic (i.e. they are non-stabilizer states whose magic cannot be removed by a constant depth circuit). This presents another step towards one of the holy grails of quantum complexity theory, the quantum analogue of the PCP theorem.
  • All Unitaries Have Constant Depth Quantum Circuit 2609.40351 by Barak Nehoran, Joseph Slote, Henry Yuen.
    • A very cool result on the structure of unitaries, essentially a rigorous proof that depth can be traded for time in quantum computation; given any \(n\)-qubit unitary, the unitary can be constructed in constant circuit depth using only one/two qubit gates and \(O^{2(n)}\) ancilla qubits (as well as unbounded fan-out, alternatively realizable by local measurement and feedback). Somewhat surprisingly, any unitary (and hence any form of quantum dynamics…) is highly parallelizable. A very cool result to end off the month, and would be nice to understand the techniques, which appear to mix insights from error correction/encoding and continuous variable quantum mechanics.

Past Papers/Articles

  • Topological phases and quantum computation 0904.2771 by Alexei Kitaev, Chris Laumann.
    • A consice set of lecture notes centering on three exactly solvable models (the 1D Kitaev chain, the toric code, and the Kitaev honeycomb model), presenting an accessible digest version of some results from Kitaev’s cond-mat/0010440, quant-ph/9707021, and cond-mat/0506438 (each of which are striking and insightful papers)!
  • Lecture notes on condensed matter theory Website by Xie Chen.
    • A nicely pedagogical set of lecture notes that span many key topics of interest in modern condensed matter theory (SPTs, fractionalization, topological and fracton order, topological holography). Particularly, I found helpful the explicit worked out example of deriving the toric code from gauging the \(\mathbb{Z}_2\) symmetry of the transverse field Ising model. Although “gauging” is often thrown around in the modern CMT literature, it certainly was quite mysterious to me (and I can imagine to students that have only seen gauge theories discussed in the context of electromagnetism or quantum field theory courses), so it was helpful to see it in the lattice context explicitly. Going in the opposite direction, I found the construction of the 1+1D TFIM in the SymTFT framework (arising from the 2+1D toric code “sandwich”) to also be a useful worked out example.
  • Long-lived memory in sliding spin chains 2607.14383 by Charles Stahl, Ethan Lake.
    • 1D equilibrium systems with short range interactions are known to not exhibit order (the classic entropic argument is due to Landau, consicely presented by Thouless for the case of the Ising chain in PhysRev.187.732). Thus, they are incompatible as candidates for retaining memory for thermodynamically long times. Out of equilibrium, a construction by Gács math/0003117 is known (I am also interested in understanding this paper, but it is advertised as notoriously complicated), but simple models for 1D systems with memory have long remained evasive. This paper presents a delightfully simple model (the kind of mechanism you wish you would have thought of!) that achieves a parametrically longer lifetime than any equilibrium model, and practically a stable memory (in the sense that it is finite in the thermodynamic limit, but astronomically large for reasonable parameters). Surprisingly, two 1D Ising chains stacked together and sliding in opposite directions does the trick! The central physical insight is as follows - in 1D, there is no energetic cost to growing a minority domain (hence no LRO), but with two sliding chains, the inter-chain coupling penalizes the presence of any minority domain on a single chain, causing it to erode ballistically, and hence for the initial magnetization to survive for long times.

On the to-read list

  • Almost-idempotent quantum channels and approximate C*-algebras 2405.02434 by Alexei Kitaev.
    • Marcus Bintz reminded me of this semi-recent preprint by Kitaev and pointed out that it seems to be not particularly well-understood by the community (it only has 4 citations on Google Scholar). Given that Kitaev’s papers tend to be full of inspiring ideas, it might be useful to see what insights could be gleamed out of this (and the presented motivation of understanding encoded quantum systems appears to be quite broadly useful, though the mathematical content of the paper is exceptionally technical).
  • A passive self-correcting quantum memory in three dimensions 2605.10943 by Shankar Balasubramanian, Margarita Davydova, Ting-Chun Lin.
    • A beautiful result and solution to a longstanding problem of whether a self-correcting memory can exist in 3D! A bit of a behemoth of a construction, so it would be nice to understand. I am also curious (inspired by some discussion in an earlier paper about cored product codes 2510.05479, which presented numerical evidence but not a proof for a 3D self-correcting system) as to how generic/common this feature of self-correction is once one abandons “nice” notions like translation invariance.
  • Perturbatively Stable Self-Correcting Classical Memory from Gauge Averaging 2607.20605 by Ryan Thorngren.
    • Going back to the classical realm for more fun systems exhibiting self-correction! The \(\mathbb{Z}_2\) 2D Ising model is the canonical example (minority domains are energetically costly, and so the initial order survives for thermodynamically long times so long as \(T < T_c\)/one is in the low-T ordered phase), but this is not robust to symmetry-breaking perturbations (e.g. an exponentially small external field). Ryan proves that the 3D Wegner \(\mathbb{Z}_2\) gauge theory’s property of self-correction is stable to arbitrary small perturbations, and it would be nice to understand why! (The main insight appears to be a rewriting of a symmetry breaking perturbation to a symmetry preserving one via an averaging of the state over the symmetry, and counterintuitively the state is more stable the higher the temperature is, so long as \(T < T_c\)!)
  • Neutral atom quantum computing 2608.30783 by Mark Saffman.
    • With some of the exciting developments coming out of the neutral atom community (e.g. this Nature-s41586-025-09848-5 paper from the Lukin group and striking resource estimates from Oratomic 2603.28627), it would be nice to understand some of the fundamental physics of these highly controllable AMO systems a bit better.