2024 Simons Collaboration on Ultra Quantum Matter Annual Meeting

The fifth annual meeting of the Simons Collaboration on Ultra-Quantum Matter (UQM) was held January 18–19, 2024, with over 90 in-person participants. In addition to the speakers, UQM PIs and postdoctoral fellows, and other students and postdocs, the meeting was attended by nearly 20 other faculty members working on various aspects of UQM.

The meeting began with a pair of talks from UQM PI Xie Chen (Caltech) and former UQM postdoctoral fellow Shu-Heng Shao (Stony Brook). Chen described recent work showing how sequential quantum circuits can be used to understand a variety of defects in topological phases — especially Cheshire string defects in the toric code. Shao discussed non-invertible symmetries realized exactly in lattice models, focusing in particular on the Kramers-Wannier symmetry of the 1+1d Ising model, and its realization as a sequential circuit. The close connections between these talks were a nice example of the benefits of bringing together different sub-disciplines of theoretical physics within the UQM Collaboration.

Andrea Young (UC Santa Barbara) gave a comprehensive review of the rapid recent progress in realizing the quantum Hall effect in the Chern bands of two-dimensional materials. He emphasized the important role spatially-resolved measurements play in twisted structures. Finally, he reviewed the Quantum Hall effect in graphene, and contrasted the observation of anyon statistics in this new setup with related measurements in GaAs platforms. He ended with the tantalizing possibility of similar studies of non-Abelian states.

Henrik Dreyer (Quantinuum) laid out the dramatic recent improvements in the ion trap computers at Quantinuum that allow for mid-circuit measurement and feedforward. He gave a broad overview of the motivation for preparing complex quantum states and described in detail the realization of the long sought non-Abelian topological order and its smoking gun signatures including Borromean braiding on their H2 platform. These experiments and related theory emerged in collaboration with UQM PIs and postdocs.

The meeting’s first day concluded with a talk from Yin-Chen He (Perimeter Institute) who described surprising and exciting numerical results on 2+1d conformal field theories (CFTs) using regularization on the fuzzy sphere. These new methods are providing a wealth of information on CFTs of interest as effective theories of UQM and promise to become a powerful new tool in studying gapless phases and quantum critical points.

The second day began with a talk from UQM PI Ana Maria Rey (CU Boulder), who discussed theory and experiments on dynamical phases of BCS superfluids in ultra-cold atomic systems, including progress toward studying p-wave superfluids and realizing the non-trivial topological phase. She also covered the tension between scalability and quantum control in quantum sensors, and connections to ultra-quantum matter.

Next, UQM Postdoc Ruben Verresen (Harvard) explained how Higgs phases of gauge theories can be interpreted as symmetry protected topological phases. This gives a new perspective on basic issues in gauge theories, and Verresen’s talk stimulated lively discussions among participants.

UQM PI Senthil Todari (MIT) then turned to exciting theoretical developments stimulated by recent experiments on moiré materials. In particular, he outlined scenarios for continuous transitions between fractional Hall states in Chern bands and conventional CDW insulators. He also outlined a recent theory explaining the zero magnetic field observation of the fractional Hall effect in pentalayer graphene, tying into the themes discussed by Andrea Young in his overview of experiments in 2D materials.

The meeting was marked by a highly interactive and stimulating atmosphere, including lively discussions during poster sessions in which students and postdocs presented recent results from within the Collaboration. Many attendees stayed behind after the last talk brainstorming new directions and discussing recent developments.

Xie Chen
California Institute of Technology

Sequential Quantum Circuit as String Operator for Topological Defects
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Bosonic point charge excitations in 3+1D topological phases can condense along a line and form a descendant defect called the Cheshire string. Unlike the elementary flux loop excitations in the system, Cheshire strings do not have to appear as the boundary of a 2D disc and can exist on open-line segments. On the other hand, Cheshire strings are different from trivial excitations that can be created with either local unitaries in 0D or finite depth quantum circuits in 1D and higher. In this talk, Xie Chen will show that to create a Cheshire string, one needs the sequential quantum circuit — a linear depth circuit that acts sequentially along the length of the string. Once a Cheshire string is created, its deformation, movement and fusion can be realized by finite-depth circuits. Quantum circuits hence provide a way to define equivalence classes of gapped topological defects, potentially giving rise to an operational meaning of the higher category description of topological orders in 3+1D or higher.
 

Henrik Dreyer
Quantinuum

Long-Range Entangled States in Trapped Ions from Measurement and Feed-Forward
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Quantum devices have matured to the point where multipartite entanglement can be created on 30+ qubits. One important capability of these devices is the creation of long-range entangled states, both as initial states for quantum simulation and for error correction within the same devices. Unfortunately, by definition, topologically ordered states require extensive unitary circuit depths for their preparation, which places constraints on the coherence times of near-term devices. Henrik Dreyer will discuss how constant-depth protocols based on measurement and feed-forward have recently been used to prepare toric code and non-Abelian topological order on Quantinuum’s H-series trapped-ion computers.
 

Yin-Chen He
Perimeter Institute

Physics Meets Geometry: A Fuzzy Sphere Odyssey in Critical Phenomena
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Historically, the synergy between physics and geometry has consistently catalyzed pivotal breakthroughs in both fields. In this talk, He will explain how non-commutative geometry, a concept that emerged from physics, offers new ways to understand critical phenomena, including the 3D Ising transition. Specifically, He will introduce our recently proposed ‘fuzzy (non-commutative) sphere regularization’ scheme, inspired by quantum Hall effect. He will showcase that this method is powerful, revealing universal data of 3D conformal field theories (CFTs) that were previously inaccessible, and it is efficient, with computations that can be done on a laptop within an hour. The scheme not only heralds a new era for the study of CFTs but also hints at a profound connection between non-commutative geometry and both CFTs and QFTs more broadly.
 

Ana Maria Rey
University of Colorado Boulder / NIST

Manipulating Propagation and Growth of Emergent Collective Correlations

In this talk Ana Maria Rey will illustrate a pathway for harnessing large-scale entanglement in systems featuring short range interactions. Rey will show these systems can emulate many features of the one-axis-twisting (OAT) model, an iconic fully connected model known to generate scalable entanglement and GHZ-like states. The collective nature of the state manifests itself in the preservation of the total transverse magnetization, the reduced growth of the structure factor, i.e., spin-wave excitations, at finite momenta, the generation of spin squeezing comparable to OAT and the development of non-Gaussian states in the form of atomic multi-headed cat states in the Q-distribution. The simplicity of the underlying mechanisms enables scalability to large arrays with minimal overhead and opens the door to advances in timekeeping as well as new methods for preserving coherence in quantum simulation and computation.
 

Shu-Heng Shao
Stony Brook University

Exact Non-Invertible Symmetries on a Tensor Product Hilbert Space
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Shu-Heng Shao will discuss the exact non-invertible Kramers-Wannier symmetry of 1+1d lattice models on a tensor product Hilbert space of qubits. This symmetry mixes with lattice translations, and obeys a different algebra compared to the continuum one. Shao will present a clear notion of an anomaly involving this non-invertible symmetry, parity/time-reversal symmetries, and lattice translations. The non-invertible symmetry leads to a constraint similar to that of Lieb-Schultz-Mattis, implying that the system cannot have a unique gapped ground state. It is either in a gapless phase or in a gapped phase with three (or a multiple of three) ground states, associated with the spontaneous breaking of the non-invertible symmetry.
 

Senthil Todadri
Massachusetts Institute of Technology

Fractional Quantum Hall without Magnetic Fields: Realizations, Proximate Phases and Phase Transitions

An exciting recent development is the discovery of fractional quantum Hall physics in the absence of external magnetic fields in 2D moiré materials. Senthil Todadri will discuss the physics enabling this realization, and the opportunities provided for exploration of proximate ultra-quantum phases and phase transitions.
 

Ruben Verresen
Harvard University

Gauss’ Law as SPT-Stabilizer: From Superconductors to Intrinsically Gapless Topological Matter
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In this talk, Ruben Verresen will explore how Gauss’ laws for gauge fields coupled to matter provide a pathway to symmetry-protected topological (SPT) phases of matter. Firstly, when such Gauss’ laws are only energetically enforced, we use them to create gapless SPT states in 2+1D which do not have any gapped analogue. This generalizes previous work on intrinsically gapless SPT phases in 1+1D and highlights the importance of considering higher-form symmetries. Secondly, when Gauss laws are exact, the SPT phenomena can still manifest themselves and end up explaining the rich phenomenology of superconductors. For instance, supercurrents are argued to be topological Thouless pumps arising from SPT physics.
 

Andrea Young
University of California, Santa Barbara

Anyons in Graphene

Recent advances in the fabrication of graphene heterostructures now allow devices to be created that incorporate both nanoscale electrostatic control and ultra-high mobility. Andrea Young will describe the application of these methods to probing anyonic statistics, focusing on transport in mesoscopic devices. First, single quantum point contacts are used to connect =1 and =1/3 edge to probe the properties of the chiral Luttinger liquid. In addition to observing the theoretically expected universal T2, V2 power law for single electron tunneling, experiments at strong coupling reveal nearly-perfect Andreev-like reflection of fractional quasiparticles. Young uses this regime to demonstrate a direct current voltage step-up transformer operating with 97% power efficiency. Armed with a complete understanding of single point contacts, Young then concatenates point contacts to form a Fabry-Pérot interferometer. Experiments at filling =1/3 show robust, nearly-quantized phase slips associated with the motion of single abelian anyons into the interferometer loop.