Search results in Quantum Physics from PIRSA
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Universal quantum computation in two dimensions by converting between the toric code and a nonabelian quantum double
Margarita Davydova Massachusetts Institute of Technology (MIT)



Unraveling quantum manybody scars: Insights from collective spin models
Meenu Kumari National Research Council Canada (NRC)

Typical eigenstate entanglement entropy as a diagnostic of quantum chaos and integrability
Marcos Rigol Pennsylvania State University

Approximate Quantum Codes From Long Wormholes
Brian Swingle Brandeis University

Defining stable steadystate phases of open systems
Sarang Gopalakrishnan Princeton University

Certifying almost all quantum states with few singlequbit measurements
HsinYuan Huang California Institute of Technology (Caltech)

Entanglementbased probes of topological phases of matter
Michael Levin University of Chicago

How much entanglement is needed for quantum error correction?
Zhi Li Perimeter Institute for Theoretical Physics


Emergent symmetries and their application to logical gates in quantum LDPC codes
In this talk, I’ll discuss the deep connection between emergent kform symmetries and transversal logical gates in quantum lowdensity paritycheck (LDPC) codes. I’ll then present a parallel faulttolerant quantum computing scheme for families of homological quantum LDPC codes defined on 3manifolds with constant or almostconstant encoding rate using the underlying higher symmetries in our recent work. We derive a generic formula for a transversal T gate on color codes defined on general 3manifolds, which acts as collective nonClifford logical CCZ gates on any triplet of logical qubits with their logicalX membranes having a Z2 triple intersection at a single point. The triple intersection number is a topological invariant, which also arises in the path integral of the emergent higher symmetry operator in a topological quantum field theory (TQFT): the (Z2) 3 gauge theory. Moreover, the transversal S gate of the color code corresponds to a higherform symmetry supported on a codimension1 submanifold, giving rise to exponentially many addressable and parallelizable logical CZ gates. Both symmetries are related to gauged SPT defects in the (Z2) 3 gauge theory. We have then developed a generic formalism to compute the triple intersection invariants for general 3 manifolds. We further develop three types of LDPC codes supporting such logical gates with constant or almostconstant encoding rate and logarithmic distance. Finally, I’ll point out a connection between the gauged SPT defects in the 6D color code and a recently discovered nonAbelian selfcorrecting quantum memory in 5D. Reference: arXiv:2310.16982, arXiv:2208.07367, arXiv:2405.11719. 
Universal quantum computation in two dimensions by converting between the toric code and a nonabelian quantum double
Margarita Davydova Massachusetts Institute of Technology (MIT)
In this talk, I will explain how to implement faulttolerant nonClifford gates in copies of toric code in two dimensions achieved by transiently switching to a nonAbelian topologically ordered phase by expanding earlier results by Bombin [arXiv.1810.09571] and Brown [SciAdv.aay4929]. This addresses the challenge of performing universal faulttolerant quantum computation in purely two spatial dimensions and shows a new approach to quantum computation using nonAbelian phases. This talk is based on upcoming work in collaboration with A. Bauer, B.Brown, J. Magdalena de la Fuente, M. Webster and D. Williamson. 
Fault tolerance with the ZXcalculus and fusion complexes
Naomi Nickerson PSI Quantum
Quantum error correction methods for qubit technologies such as ions, photons, or superconducting qubits can appear very different at first glance. Moreover, as more detailed error models are accounted for, the relationship to the abstract models of fault tolerance can appear to become more distant. In this talk I will discuss two unifying frameworks which connect hardware specific models more closely to the underlying code structures, which can help enable QEC development. First I will introduce a unifying framework for fault tolerance based on the ZX calculus (arXiv:2303.08829) and show how it allows us to view circuitbased, measurementbased, fusionbased quantum computation, and Floquet codes as different flavors of the same underlying stabilizer faulttolerance structure. Secondly I will introduce fusion complexes (arXiv:2308.07844) which allows a topological interpretation of fault tolerance even under circuit level error models. Both of these frameworks are tools that can aid in the design of quantum error correction methods under hardwarefocussed models, and I will give some examples of this applied to the design of photonic architectures. 
Landscape of MeasurementPrepared Tensor Networks and Decohered NonAbelian Topological Order
Ruben Verresen Harvard University
What is the structure of manybody quantum phases and transitions in the presence of nonunitary elements, such as decoherence or measurements? In this talk we explore two new directions. First, recent works have shown that even if one starts with an ideal preparation of topological order such as the toric code, decoherence can lead to interesting mixed states with subtle phase transitions [e.g., Fan et al, arXiv:2301.05689]. Motivated by a recent experimental realization of nonAbelian topological order [Iqbal et al, Nature 626 (2024)], we generalize this to decohered nonAbelian states, based on work with Pablo Sala and Jason Alicea [to appear]. Second, we study whether and how one can prepare pure states which are already detuned from ideal fixedpoint caseswith tunable correlation lengths. This turns out to be possible for large classes of tensor network states which can be deterministically prepared using finitedepth measurement protocols. This is based on two recent works with Rahul Sahay [arXiv:2404.17087; arXiv:2404.16753]. 
Unraveling quantum manybody scars: Insights from collective spin models
Meenu Kumari National Research Council Canada (NRC)
Quantum manybody scars (QMBS) are atypical eigenstates of chaotic systems that are characterized by subvolume or area law entanglement as opposed to the volume law present in the bulk of the eigenstates. The term, QMBS, was coined using heuristic correlations with quantum scars  eigenstates with high probability density around unstable classical periodic orbits in quantum systems with a semiclassical description. Through the study of entanglement in a multiqubit system with a semiclassical description, quantum kicked top (QKT), we show that the properties of QMBS states strongly correlate with the eigenstates corresponding to the very few stable periodic orbits in a chaotic system as opposed to quantum scars in such systems. Specifically, we find that eigenstates associated with stable periodic orbits of small periodicity in chaotic regime exhibit markedly different entanglement scaling compared to chaotic quantum states, while quantum scar eigenstates demonstrate entanglement scaling resembling that of chaotic quantum states. Our findings reveal that quantum manybody scars and quantum scars are distinct. This work is in collaboration with ChengJu Lin and Amirreza Negari. 
Typical eigenstate entanglement entropy as a diagnostic of quantum chaos and integrability
Marcos Rigol Pennsylvania State University
Quantumchaotic systems are known to exhibit eigenstate thermalization and to generically thermalize under unitary dynamics. In contrast, quantumintegrable systems exhibit a generalized form of eigenstate thermalization and need to be described using generalized Gibbs ensembles after equilibration. I will discuss evidence that the entanglement properties of highly excited eigenstates of quantumchaotic and quantumintegrable systems are fundamentally different. They both exhibit a typical bipartite entanglement entropy whose leading term scales with the volume of the subsystem. However, while the coefficient is constant and maximal in quantum chaotic models, in integrable models it depends on the fraction of the system that is traced out. The latter is typical in random Gaussian pure states. I will also discuss the nature of the subleading corrections that emerge as a consequence of the presence of abelian and nonabelian symmetries in such models. 
Approximate Quantum Codes From Long Wormholes
Brian Swingle Brandeis University
We discuss families of approximate quantum error correcting codes which arise as the nearlydegenerate ground states of certain quantum manybody Hamiltonians composed of noncommuting terms. For exact codes, the conditions for error correction can be formulated in terms of the vanishing of a twosided mutual information in a lowtemperature thermofield double state. We consider a notion of distance for approximate codes obtained by demanding that this mutual information instead be small, and we evaluate this mutual information for the SachdevYeKitaev (SYK) model and for a family of lowrank SYK models. After an extrapolation to nearly zero temperature, we find that both kinds of models produce fermionic codes with constant rate as the number, N, of fermions goes to infinity. For SYK, the distance scales as N^1/2, and for lowrank SYK, the distance can be arbitrarily close to linear scaling, e.g. N^.99, while maintaining a constant rate. We also consider an analog of the no lowenergy trivial states property and show that these models do have trivial lowenergy states in the sense of adiabatic continuity. We discuss a holographic model of these codes in which the large code distance is a consequence of the emergence of a long wormhole geometry in a simple model of quantum gravity 
Defining stable steadystate phases of open systems
Sarang Gopalakrishnan Princeton University
The steady states of dynamical processes can exhibit stable nontrivial phases, which can also serve as faulttolerant classical or quantum memories. For Markovian quantum (classical) dynamics, these steady states are extremal eigenvectors of the nonHermitian operators that generate the dynamics, i.e., quantum channels (Markov chains). However, since these operators are nonHermitian, their spectra are an unreliable guide to dynamical relaxation timescales or to stability against perturbations. We propose an alternative dynamical criterion for a steady state to be in a stable phase, which we name uniformity: informally, our criterion amounts to requiring that, under sufficiently small local perturbations of the dynamics, the unperturbed and perturbed steady states are related to one another by a finitetime dissipative evolution. We show that this criterion implies many of the properties one would want from any reasonable definition of a phase. We prove that uniformity is satisfied in a canonical classical cellular automaton, and provide numerical evidence that the gap determines the relaxation rate between nearby steady states in the same phase, a situation we conjecture holds generically whenever uniformity is satisfied. We further conjecture some sufficient conditions for a channel to exhibit uniformity and therefore stability. 
Certifying almost all quantum states with few singlequbit measurements
HsinYuan Huang California Institute of Technology (Caltech)
Certifying that an nqubit state synthesized in the lab is close to the target state is a fundamental task in quantum information science. However, existing rigorous protocols either require deep quantum circuits or exponentially many singlequbit measurements. In this work, we prove that almost all nqubit target states, including those with exponential circuit complexity, can be certified from only O(n^2) singlequbit measurements. This result is established by a new technique that relates certification to the mixing time of a random walk. Our protocol has applications for benchmarking quantum systems, for optimizing quantum circuits to generate a desired target state, and for learning and verifying neural networks, tensor networks, and various other representations of quantum states using only singlequbit measurements. We show that such verified representations can be used to efficiently predict highly nonlocal properties that would otherwise require an exponential number of measurements. We demonstrate these applications in numerical experiments with up to 120 qubits, and observe advantage over existing methods such as crossentropy benchmarking (XEB). 
Entanglementbased probes of topological phases of matter
Michael Levin University of Chicago
I will discuss recent progress in understanding entanglementbased probes of 2D topological phases of matter. These probes are supposed to extract universal topological information from a manybody ground state. Specifically, I will discuss (1) the topological entanglement entropy, which is supposed to give information about the number of anyon excitations, and (2) the modular commutator, which is supposed to tell us the chiral central charge. 
How much entanglement is needed for quantum error correction?
Zhi Li Perimeter Institute for Theoretical Physics
It is commonly believed that logical states of quantum errorcorrecting codes have to be highly entangled such that codes capable of correcting more errors require more entanglement to encode a qubit. Here we show that this belief may or may not be true depending on a particular code. To this end, we characterize a tradeoff between the code distance d quantifying the number of correctable errors, and geometric entanglement of logical states quantifying their maximal overlap with product states or more general ``topologically trivial" states. The maximum overlap is shown to be exponentially small in d for three families of codes: (1) lowdensity parity check (LDPC) codes with commuting check operators, (2) stabilizer codes, and (3) codes with a constant encoding rate. Equivalently, the geometric entanglement of any logical state of these codes grows at least linearly with d. On the opposite side, we also show that this distanceentanglement tradeoff does not hold in general. For any constant d and k (number of logical qubits), we show there exists a family of codes such that the geometric entanglement of some logical states approaches zero in the limit of large code length.