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It is believed that active quantum error correction will be an essential ingredient to build a scalable quantum computer. The currently favored scheme is the surface code due to its high decoding threshold and efficient decoding algorithm. However, it suffers from large overheads which are even more severe when parity check measurements are subject to errors and have to be repeated. Furthermore, the number of encoded qubits in the surface code does not grow with system size, leading to a sub-optimal use of the physical qubits.

Finally, the decoding algorithm, while efficient, has non-trivial complexity and it is not clear whether it can be implemented in hardware that can keep up with the classical processing.

We present a class of low-density-parity check (LDPC) quantum codes which fix all three of the concerns mentioned above. They were first proposed in [1] and called 4D hyperbolic codes, as their definition is based on four-dimensional, curved geometries. They have the remarkable property that the number of encoded qubits grows linearly with system size, while their distance grows polynomially with system size, i.e. d~n a with 0.1 < a < 0.3. This is remarkable since it was previously conjectured that such codes could not exist [1]. Their structure allows for decoders which can deal with erroneous syndrome measurements, a property called single-shot error correction [2] as well as local decoding schemes [3].

Although [1] analyzed the encoding rate and distance of this code family abstractly, it is a non-trivial task to actually construct them. There is no known efficient deterministic procedure for obtaining small examples. Only single examples of reasonable size had been obtained previously [4]. These previous examples were part of different code families, so that it was not possible to determine a threshold. We succeeded to construct several small examples by utilizing a combination of randomized search and algebraic tools. We analyze the performance of these codes under several different local decoding procedures via Monte Carlo simulations. The decoders all share the property that they can be executed in parallel in O(1) time. Under the phenomenological noise model and including syndrome errors we obtain a threshold of ~5% which to our knowledge is the highest threshold among all local decoding schemes.

[1] A. Lubotzky, A. Guth, Journal Of Mathematical Physics 55, 082202 (2014).
[2] H. Bombin, Physical Review X 5 (3), 031043 (2015).
[3] M. Hastings, QIC 14, 1187 (2014).
[4] V. Londe, A. Leverrier, arXiv:1712.08578 (2017).

The area law for entanglement provides one of the most important connections between information theory and quantum many-body physics. It is not only related to the universality of quantum phases, but also to efficient numerical simulations in the ground state (i.e., the lowest energy state).  Various numerical observations have led to a strong belief that the area law is true for every non-critical phase in short-range interacting systems [1]. The so-called area-law conjecture states that the entanglement entropy is proportional to the surface region of subsystem if the ground state is non-critical (or gapped). 

However, the area law for long-range interacting systems is still elusive as the long-range interaction results in correlation patterns similar to the ones in critical phases. Here, we show that for generic non-critical one-dimensional ground states, the area law robustly holds without any corrections even under long-range interactions [2]. Our result guarantees an efficient description of ground states by the matrix-product state in experimentally relevant long-range systems, which justifies the density-matrix renormalization algorithm. In the present talk, I will give an overview of the results, and show ideas of the proof if the time allows. 

[1] J. Eisert, M. Cramer, and M. B. Plenio, ``Colloquium: Area laws for the entanglement entropy,'' Rev. Mod. Phys. 82, 277–306 (2010).

[2] T. Kuwahara and K. Saito, ``Area law of non-critical ground states in 1d long-range interacting systems,'' arXiv preprint arXiv:1908.11547 (2019),

As our understanding of the universe and its fundamental building blocks extends to shorter and shorter distances, experiments capable of probing these scales are becoming increasingly difficult to construct. Fundamental particle physics faces a potential crisis: an absence of data at the shortest possible scales. Yet remarkably, even in the absence of experimental data, the requirement of theoretical consistency puts stringent constraints on viable models of fundamental particles and their interactions. In this talk I’ll discuss a variety of criteria that constrain theories of particles in flat spacetime and de Sitter. Such criteria have the possibility to address questions such as: What low energy theories admit consistent UV completions? Which massive particles are allowed in an interacting theory? Is string theory the unique weakly coupled UV completion of General Relativity?

In our four-dimensional world supersymmetry is the only extension of the classical Poincaré invariance which laid the foundation of modern physics in the beginning of the 20th century. Supersymmetry, a new geometric symmetry extending Poincaré, was discovered in 1970 –– it was overlooked for decades because of its quantum nature. In the next 10 years or so supersymmetry 

assumed the role of a universal framework in which new models for natural phenomena and regularities (e.g. the concept of naturalness) have been developed. It gave rise to a powerful stream of theoretical phenomenology.

The fact that LHC at CERN produced no evidence for low-energy supersymmetry (and naturalness as well) was a powerful blow. However, despite its absence in experiments the less known second mission of supersymmetry is highly successful, with remarkable advances occurring on a regular basis. Supersymmetry proved its power and uniqueness for those who address hard questions in strongly coupled field theories, including Yang-Mills. Some supersymmetry-based exact results obtained in four dimensions are the main topics of my talk. In the past one could hardly dream that such results are possible.

The average entanglement entropy of subsystems of random pure states is (nearly) maximal. In this talk, we discuss the average entanglement entropy of subsystems of highly excited eigenstates of integrable and nonintegrable many-body lattice Hamiltonians. For translationally invariant quadratic models (or spin models mappable to them) we prove that, when the subsystem size is not a vanishing fraction of the entire system, the average eigenstate entanglement entropy exhibits a leading volume-law term that is different from that of random pure states. We argue that such a leading term is likely universal for translationally invariant (noninteracting and interacting) integrable models. For random pure states with a fixed particle number (random canonical states) away from half filling and normally distributed real coefficients, we prove that the deviation from the maximal value grows with the square root of the system's volume when the size of the subsystem is one half of that of the system. We then show that the average entanglement entropy of highly excited eigenstates of a particle number conserving quantum chaotic model is the same as that of random canonical states.

Beginning with the landmark gravitational wave detections by LIGO/Virgo, we have been gaining an unprecedented view of the dynamics of strongly curved spacetime originally predicted by Einstein. Enabling and motivated by these observations, there has been rapid development in the theoretical and computational tools we use to understand and interpret the nature of gravity and matter in this regime. This is essential to fulfilling the promise of gravitational wave astronomy to not only be a new window on the astrophysics of black hole and neutron star mergers, but also to be a unique probe of fundamental physics. I will illustrate this, highlighting the example of how black holes can be used to search for new particles. The same theoretical tools also allow us to push Einstein's theory to the extreme in search of the limits of its predictability, for example testing cosmic censorship, the idea that the breakdown in Einstein's equations associated with unhalted collapse is always hidden behind a black hole horizon. I will describe some recent work resolving a long-standing putative counterexample to this conjecture.