Talks

Tensor Processing Units are application specific integrated circuits (ASICs) built by Google to run large-scale machine learning (ML) workloads (e.g. AlphaFold). They excel at matrix multiplications, and hence can be repurposed for applications beyond ML. In this talk I will explain how TPUs can be leveraged to run large-scale density matrix renormalization group (DMRG) calculations at unprecedented size and accuracy. DMRG is a powerful tensor network algorithm originally applied to computing ground-states and low-lying excited states of strongly correlated, low-dimensional quantum systems. For certain systems, like one-dimensional gapped or quantum critical Hamiltonians, or small, strongly correlated molecules, it has today become the gold standard method for computing e.g. ground-state properties. Using a TPUv3-pod, we ran large-scale DMRG simulations for a system of 100 spinless fermions, and optimized matrix product state wave functions with a bond dimension of more than 65000 (a parameter space with more than 600 billion parameters). Our results clearly indicate that hardware accelerator platforms like Google's latest TPU versions or NVIDIAs DGX systems are ideally suited to scale tensor network algorithms to sizes that are beyond capabilities of traditional HPC architectures.

Zoom link:  https://pitp.zoom.us/j/99337818378?pwd=SGZvdFFValJQaDNMQ0U1YnJ6NU1FQT09

Soon after the discovery of high temperature superconductivity in the cuprates, Anderson proposed a connection to quantum spin liquids. But observations since then have shown that the low temperature phase diagram is dominated by conventional states, with a competition between superconductivity and charge-ordered states which break translational symmetry. We employ the "pseudogap metal" phase, found at intermediate temperatures and low hole doping, as the parent to the phases found at lower temperatures. The pseudogap metal is described as a fractionalized phase of a single-band model, with small pocket Fermi surfaces of electron-like quasiparticles whose enclosed area is not equal to the free electron value, and an underlying pi-flux spin liquid with an emergent SU(2) gauge field. This pi-flux spin liquid is now known to be unstable to confinement at sufficiently low energies. We develop a theory of the different routes to confinement of the pi-flux spin liquid, and show that d-wave superconductivity, antiferromagnetism, and charge order are natural outcomes. We are argue that this theory provides routes to resolving a number of open puzzles on the cuprate phase diagram.

As a side result, at half-filling, we propose a deconfined quantum critical point between an antiferromagnet and a d-wave superconductor described by a conformal gauge theory of 2 flavors of massless Dirac fermions and 2 flavors of complex scalars coupled as fundamentals to a SU(2) gauge field.

This talk is based on Maine Christos, Zhu-Xi Luo, Henry Shackleton, Ya-Hui Zhang, Mathias S. Scheurer, and S. S., arXiv:2302.07885

Zoom link:  https://pitp.zoom.us/j/97370076705?pwd=Q1MwQmNaSFkxaWFEdUl5NFZDS0E4Zz09

Schrodinger's thought experiment famously illustrates the dramatic effect of measuring a quantum state. The resulting wave function collapse is often thought to make states more classical and familiar. However, in this colloquium, we explore how measurements can be used as a chisel to efficiently build exotic forms of quantum entanglement. We focus on topological states of matter, whose quasiparticles exhibit generalized 'anyonic' exchange statistics with potential relevance to quantum computation. We use these ideas to experimentally realize the first controlled realization of non-Abelian anyons, which can remember the sequence in which they are exchanged. The smoking gun signature of this experiment is inspired by the coat of arms of the House of Borromeo.

Zoom Link: https://pitp.zoom.us/j/98167813390?pwd=aG5vcklVZzBWT1BRSjI4RVRtbDhBUT09

We investigate the evolution of quantum information under Pauli measurement circuits. We focus on the case of one- and two-dimensional systems, which are relevant to the recently introduced Floquet topological codes. We define local reversibility in context of measurement circuits, which allows us to treat finite depth measurement circuits on a similar footing to finite depth unitary circuits. In contrast to the unitary case, a finite depth locally reversible measurement sequence can implement a translation in one dimension. A locally reversible measurement sequence in two dimensions may also induce a flow of logical information along the boundary. We introduce "measurement quantum cellular automata" which unifies these ideas and define an index in one dimension to characterize the flow of logical operators. We find a Z_2 bulk invariant for Floquet topological codes which indicates an obstruction to having a trivial boundary. We prove that the Hastings-Haah honeycomb code belong to a class with such obstruction, which means that any boundary must have either non-local dynamics, period doubled, or admits boundary flow of quantum information.

Zoom Link: https://pitp.zoom.us/j/96083249406?pwd=MnhYbTEyU05ybVdyUlE3UGZrdEhPdz09

We construct two-dimensional quantum states associated to four-dimensional linearized rotating self-dual black holes in (2,2) signature Klein space. The states are comprised of global conformal primaries circulating on the celestial torus, the Kleinian analog of the celestial sphere. By introducing a generalized tower of Goldstone operators we identify the states as coherent exponentiations carrying an infinite tower of w1+inf charges or soft hair. We relate our results to recent approaches to black hole scattering, including a connection to Wilson lines, S-matrix results, and celestial holography in curved backgrounds.

Zoom link:  https://pitp.zoom.us/j/94163164577?pwd=RHFVZU5XUEN0T3c3Zm1VR3VhZnNsZz09

Despite first observing cosmic rays with energies above an EeV (10^18 eV) in the 1960s, the source of these particles remains an open question. Modern observatories, in particular the Pierre Auger Observatory and Telescope Array, have firmly established that the cosmic ray spectrum continues up to ~10^20.3 eV and have significantly advanced our understanding of these particles. However, limited statistics, uncertainties in particle physics, and significant deflections in the Galactic magnetic field have made progress towards discovering their astrophysical source extremely challenging. One key astrophysical input needed to understand ultrahigh energy cosmic ray data is the distribution of their sources, or the source evolution. In this talk, I will focus on multimessenger observations which have the potential to pin down the source evolution for the very first time.

Zoom Link:  https://pitp.zoom.us/j/94054513261?pwd=aHRNWE04VDI2cDA2RmRYQmtNRnd3dz09

Cosmology presents some puzzling aspects: the cosmological constant, the nature of the big bang, the source of inflation, and perhaps the tension in Hubble constant values. One normally uses standard effective field theory to study cosmology. But we know that such an approach fails in black holes due to the information paradox. We will draw on lessons on black holes to see how quantum gravity effects can modify evolution on macroscopic scales, and that such effects may be important is resolving puzzles in cosmology.

Zoom link:  https://pitp.zoom.us/j/98085421952?pwd=NFBCWXNBNkhrTVpaRkRlOWRtSkczdz09

We explore how measurements and unitary feedback can generate distinct phases of matter from a given resource state, with a specific focus on the toric code in two dimensions. First, we map random Pauli measurements on the toric code to a classical loop model with crossings, and we show how measurement-induced entanglement exactly maps to watermelon correlators of the loop model.  Then, we consider measuring all but a 1d boundary of qubits, and we map this setup to hybrid circuits in 1+1 dimensions.  In particular, we find that varying the probabilities of different Pauli measurements can drive phase transitions in the unmeasured boundary between phases with different orders and entanglement scaling, corresponding to short and long loop phases in the classical model.  Finally, by utilizing single-site boundary unitaries conditioned on the bulk measurement outcomes, we generate mixed state ordered phases and transitions that can be experimentally diagnosed with linear observables. Our findings showcase the potential of measurement-based quantum computing setups in producing and manipulating phases of matter.

Zoom Link: https://pitp.zoom.us/j/99159680593?pwd=V29wRit6T3NlSjZGTDEvTnRFcTlrUT09

EMRIs are one of the primary targets of spaceborne gravitational wave (GW) detectors and will be ideal GW sources for testing fundamental laws of gravity. In a generic non-Kerr spacetime,  the EMRI system  is non-integrable due to the lack of the Carter constant. As a result,  chaos along with resonance islands arise in these systems leaving a non-Kerr signature in the EMRI waveform as proposed in many previous studies. In this work, we systematically analyze the dynamics of an EMRI system near orbital resonances and we have derived an effective resonant Hamiltonian that describes the dynamics of the resonant degree of freedom  with the action-angle formalism. We have two major findings: (1) the chaotic orbits in general produce unique commensurate jumps in actions and (2) the EMRI orbits driven by radiation-reaction in general do not cross the resonance islands.

Zoom Link: https://pitp.zoom.us/j/95975225333?pwd=V05NZzQ3cE9neUZpN3RIOCt0UE5mZz09

I will describe a correspondence between hyperkähler/quaternion-Kähler geometry and two dimensional chiral algebras that arises from twistor theory. As an application, I will explain how to use correlators of these chiral algebras to compute gravitational scattering amplitudes in four dimensional general relativity.

Zoom Link: https://pitp.zoom.us/j/98706048161?pwd=a3k1U3l2UXJlUjlqUElkOEZhZGwwUT09