Other

We present a quantum architecture based on a linear chain of trapped 171Yb+ ions with individual laser beam addressing and readout. The collective modes of motion in the chain are used to efficiently produce entangling gates between any qubit pair. In combination with a classical software stack, this becomes in effect an arbitrarily programmable and fully connected quantum computer. The system compares favorably to commercially available alternatives [2].
We use this versatile setup to perform a quantum walk algorithm that realizes a simulation of the free Dirac equation where the quantum coin determines the particle mass [3]. We are also pursuing digital simulations towards models relevant in high-energy physics among other applications. Recent results from these efforts, and concepts for expanding and scaling up the architecture will be discussed.
[1] S. Debnath et al., Nature 563:63 (2016); P. Murali et al., IEEE Micro, 40:3 (2020); [3] C. Huerta Alderete et al., Nat. Communs. 11:3720 (2020).

The idea that structure in the Universe was created from quantum mechanical vacuum fluctuations during inflation is very compelling, but unproven. Finding a test of this proposal has been challenging because the universe we observe is effectively classical. I will explain how quantum fluctuations can give rise to the density fluctuations we observe and will show that we can test this hypothesis using the statistical properties of maps of the universe.

One of the major themes of the modern condensed matter physics is the study of materials with nontrivial electronic structure topology. Particularly significant progress in this field has happened within the last decade, due to the discovery of topologically nontrivial states of matter, that have a gap in their energy spectrum, namely Topological Insulators and Topological Superconductors. In this talk I will describe the most recent work, partly my own, extending the notions of the nontrivial electronic structure topology to gapless states of matter as well, namely to semimetals and even metals. I will discuss both the theoretical concepts, and the recent experimental work, realizing these novel states of condensed matter.

In most materials, electrons fill bands, starting from the lowest kinetic energy states. The Fermi level is the boundary between filled states below and empty states above. This is the basis for our very successful understanding of how metals and semiconductors work. But what if all the electrons within a band had the same kinetic energy (this situation is called a "flat band")? Then electrons could arrange themselves so as to minimize their Coulomb repulsion, giving rise to a wide variety of possible states including superconductors and magnets. Until recently, flat bands were achieved only by applying large magnetic fields perpendicular to a 2D electron system; in this context they are known as Landau levels. Fractional quantum hall effects result from Coulomb-driven electron arrangement within a Landau level. Recently, Pablo Jarillo-Herrero of MIT and coworkers demonstrated flat minibands in graphene-based superlattices, discovering correlated insulators and superconductors at different fillings of these minibands. We have now discovered dramatic magnetic states in such superlattice systems. Specifically, in magic-angle twisted bilayer graphene which is also aligned with a hexagonal boron nitride (hBN) cladding layer, we observe a giant anomalous Hall effect as large as 10.4 kΩ, and signs of chiral edge states. This all occurs at zero magnetic field, in a narrow density range around an apparent insulating state at 3 electrons (1 hole) per moiré cell in the conduction miniband [1]. Remarkably, the magnetization of the sample can be reversed by applying a small DC current. Although the anomalous Hall resistance is not quantized, and dissipation is significant, we suggest that the system is essentially a "Chern insulator", a type of topological insulator similar to an integer quantum Hall state. In a quite different superlattice system, ABC-trilayer graphene aligned with hBN, again near 3 electrons (1 hole) per moiré cell a Chern insulator emerges [2]. This time the flat band is a valence miniband, and a magnetic field of order 100 mT is needed to quantize the anomalous hall signal. This trilayer system can be tuned in-situ to display superconductivity instead of magnetism [3]. We will discuss possible magnetic states, complementary probes to examine which state actually emerges as the ground state in each system, and what one might do with such states.

[1] A.L. Sharpe et al., “Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene”, Science 365, 6453 (2019).
[2] G. Chen et al., “Tunable Correlated Chern Insulator and Ferromagnetism in Trilayer Graphene/Boron Nitride Moire Superlattice”, Nature 579, 56 (2020)
[3] G. Chen et al., “Signatures of tunable superconductivity in a trilayer graphene moiré superlattice”, Nature 572, 215 (2019).

What factors drive the growth and decay of a pandemic? Can a study of community differences (in demographics, settlement, mobility, weather, and epidemic history) allow these factors to be identified? Has “herd immunity” to COVID-19 been reached anywhere? What are the best steps to manage/avoid future outbreaks in each community?  We analyzed the entire set of local COVID-19 epidemics in the United States; a broad selection of demographic, population density, climate factors, and local mobility data, in order to address these questions. What we found will surprise you! (based on arXiv:2007.00159)

We propose a reinforcement learning (RL) scheme for feedback quantum control within the quantum approximate optimization algorithm (QAOA). QAOA requires a variational minimization for states constructed by applying a sequence of unitary operators, depending on parameters living in a highly dimensional space. We reformulate such a minimum search as a learning task, where a RL agent chooses the control parameters for the unitaries, given partial information on the system. We show that our RL scheme learns a policy converging to the optimal adiabatic solution for QAOA found by Mbeng et al. arXiv:1906.08948 for the translationally invariant quantum Ising chain. In presence of disorder, we show that our RL scheme allows the training part to be performed on small samples, and transferred successfully on larger systems. Finally, we discuss QAOA on the p-spsin model and how its robustness is enhanced by reinforce learning. Despite the possibility of finding the ground state with polynomial resources even in the presence of a first order phase transition, local optimizations in the p-spsin model suffer from the presence of many minima in the energy landscape. RL helps to find regular solutions that can be generalized to larger systems and make the optimization less sensitive to noise.

References

https://arxiv.org/abs/2003.07419

https://arxiv.org/abs/2004.12323

Many quantum information protocols require the implementation of random unitaries. Because it takes exponential resources to produce Haar-random unitaries drawn from the full n-qubit group, one often resorts to t-designs. Unitary t-designs mimic the Haar-measure up to t-th moments. It is known that Clifford operations can implement at most 3-designs. In this work, we quantify the non-Clifford resources required to break this barrier. We find that it suffices to inject O(t^4 log^2(t) log(1/ε)) many non-Clifford gates into a polynomial-depth random Clifford circuit to obtain an ε-approximate t-design. Strikingly, the number of non-Clifford gates required is independent of the system size – asymptotically, the density of non-Clifford gates is allowed to tend to zero. We also derive novel bounds on the convergence time of random Clifford circuits to the t-th moment of the uniform distribution on the Clifford group. Our proofs exploit a recently developed variant of Schur-Weyl duality for the Clifford group, as well as bounds on restricted spectral gaps of averaging operators. Joint work with J. Haferkamp, F. Montealegre-Mora, M. Heinrich, J. Eisert, and D. Gross.

Given the large push by academia and industry (e.g., IBM and Google), quantum computers with hundred(s) of qubits are at the brink of existence with the promise of outperforming any classical computer. Demonstration of computational advantages of noisy near-term quantum computers over classical computers is an imperative near-term goal. The foremost candidate task for showing this is Random Circuit Sampling (RCS), which is the task of sampling from the output distribution of a random circuit. This is exactly the task that recently Google experimentally performed on 53-qubits.

Stockmeyer's theorem implies that efficient sampling allows for estimation of probability amplitudes. Therefore, hardness of probability estimation implies hardness of sampling. We prove that estimating probabilities to within small errors is #P-hard on average (i.e. for random circuits), and put the results in the context of previous works.

Some ingredients that are developed to make this proof possible are construction of the Cayley path as a rational function valued unitary path that interpolate between two arbitrary unitaries, an extension of Berlekamp-Welch algorithm that efficiently and exactly interpolates rational functions, and construction of probability distributions over unitaries that are arbitrarily close to the Haar measure.

Basic statistical properties of quantum many-body systems in thermal equilibrium can be obtained from their partition function. In this talk, I will present a quasi-polynomial time classical algorithm that estimates the partition function of quantum many-body systems at temperatures above the thermal phase transition point. It is known that in the worst case, the same problem is NP-hard below this temperature. This shows that the transition in the phase of a quantum system is also accompanied by a transition in the computational hardness of estimating its statistical properties. The key to this result is a characterization of the phase transition and the critical behavior of the system in terms of the complex zeros of the partition function. I will also discuss the relation between these complex zeros and another signature of the thermal phase transition, namely, the exponential decay of correlations. I will show that in a system of n particles above the phase transition point, where the complex zeros are far from the real axis, the correlation between two observables whose distance is at least log(n) decays exponentially. This is based on joint work with Aram Harrow and Saeed Mehraban.

Cooling atomic gases to ultracold temperatures revolutionized the field of atomic physics, connecting with and impacting many other areas in physics. Advances in producing ultracold molecules suggest similarly dramatic discoveries are on the horizon. First, I will review the physics of ultracold molecules, including our work bringing a new class of molecules to nanokelvin temperatures. Chemistry at these temperatures has a very different character than at room temperature. One striking effect is our recent result using spin states of reactants to control chemical reaction pathways. I will also describe how the strong electric dipole moments of ultracold molecules present an exciting new tool for quantum information and quantum computing.

There has been tremendous progress in the many layers needed to realize large-scale quantum computing, from the hardware layers to the high level software. There has also been vastly increased exploration into the potentially useful applications of quantum computers, which will drive the desire to build quantum computers and make them available to users. I will describe some of my research in quantum algorithmics and quantum compiling.

The knowledge and tools developed for these positive applications give us insight into the cost of implementing quantum cryptanalysis of today's cryptographic algorithms, which is a key factor in estimating when quantum computers will be cryptographically relevant (the "collapse time"). In addition to my own estimates, I will summarize the estimates of 22 other thought leaders in quantum computing.

What quantum cryptanalysis means to an organization or a sector depends not only on the collapse time, but also on the time to migrate to quantum-safe algorithms as well as the shelf-life of information assets being protected. In recent years, we have gained increasing insight into the challenges of a wide-scale migration of existing systems. We must also be proactive as we deploy new systems. Open-source platforms, like OpenQuantumSafe and OpenQKDNetwork, are valuable resources in helping meet many of these challenges.

While awareness of the challenges and the path forward has increased immensely, there is still a long road ahead as we work together with additional stakeholders not only to prepare our digital economy to be resilient to quantum attacks, but also to make us more resilient to other threats that emerge.

As of late March 2020, Covid-19 has already secured its status among the most expansive pandemics of the last century. Covid-19 is caused by a coronavirus--SARS-CoV-2--that causes a severe respiratory disease in a fraction of those infected, and is typified by several important features: ability to infect cells of various kinds, contagiousness prior to the onset of symptoms, and a widely varying experience with disease across patient demographics.

In this seminar, I discuss the many lessons that the scientific community has learned from Covid-19, including insight from molecular evolution, cell biology, and epidemiology. I discuss the role of mathematical and computational modeling efforts in understanding the trajectory of the epidemic, and highlight modern findings and potential research questions at the interface of virology and materials science. I will also introduce areas of inquiry that might be of interest to the physics community.