Scientific Series

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.

MIP* denotes the class of problems that admit interactive proofs with quantum entangled provers. It has been an outstanding question to characterize the complexity of this class. Most notably, there was no known computable upper bound on MIP*.

We show that MIP* is equal to the class RE, the set of recursively enumerable languages. In particular, this shows that MIP* contains uncomputable problems. Through a series of known connections, this also yields a negative answer to Connes’ Embedding Problem from the theory of operator algebras. In this talk, I will explain the connection between Connes' Embedding Problem, quantum information theory, and complexity theory. I will then give an overview of our approach, which involves reducing the Halting Problem to the problem of approximating the entangled value of nonlocal games.

Joint work with Zhengfeng Ji, Anand Natarajan, Thomas Vidick, and John Wright.

Schur-Weyl duality is a ubiquitous tool in quantum information. At its heart is the statement that the space of operators that commute with the tensor powers of all unitaries is spanned by the permutations of the tensor factors. In this work, we describe a similar duality theory for tensor powers of Clifford unitaries. The Clifford group is a central object in many subfields of quantum information, most prominently in the theory of fault-tolerance. The duality theory has a simple and clean description in terms of finite geometries. We demonstrate its effectiveness in several applications: (1) We resolve an open problem in quantum property testing by showing that "stabilizerness" is efficiently testable: There is a protocol that, given access to six copies of an unknown state, can determine whether it is a stabilizer state, or whether it is far away from the set of stabilizer states. We give a related membership test for the Clifford group. (2) We find that tensor powers of stabilizer states have an increased symmetry group. We provide corresponding de Finetti theorems, showing that the reductions of arbitrary states with this symmetry are well-approximated by mixtures of stabilizer tensor powers (in some cases, exponentially well). (3) We show that the distance of a pure state to the set of stabilizers can be lower-bounded in terms of the sum-negativity of its Wigner function. This gives a new quantitative meaning to the sum-negativity (and the related mana) -- a measure relevant to fault-tolerant quantum computation. The result constitutes a robust generalization of the discrete Hudson theorem. (4) We show that complex projective designs of arbitrary order can be obtained from a finite number (independent of the number of qudits) of Clifford orbits. To prove this result, we give explicit formulas for arbitrary moments of random stabilizer states. (5) Lastly, we comment on the structure of the irreducible representations of the Clifford group.

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.

We compute the partition function of 2D Jackiw-Teitelboim (JT) gravity at finite cutoff in two ways: (i) via an exact evaluation of the Wheeler-DeWitt wave-functional in radial quantization and (ii) through a direct computation of the Euclidean path integral. Both methods deal with Dirichlet boundary conditions for the metric and the dilaton. In the first approach, the radial wavefunctionals are found by reducing the constraint equations to two first order functional derivative equations that can be solved exactly, including factor ordering. In the second approach we perform the path integral exactly when summing over surfaces with disk topology, to all orders in perturbation theory in the cutoff. Both results precisely match the recently derived partition function in the Schwarzian theory deformed by an operator analogous to the TT¯ deformation in 2D CFTs. This equality can be seen as concrete evidence for the proposed holographic interpretation of the TT¯ deformation as the movement of the AdS boundary to a finite radial distance in the bulk.

Quantum-reduced loop gravity is a model of loop quantum gravity, whose characteristic feature is the considerable simplicity of its kinematical structure in comparison with that of full loop quantum gravity. The model therefore provides an accessible testing ground for probing the physical implications of loop quantum gravity. In my talk I will give a brief introduction to quantum-reduced loop gravity, and examine the relation between the quantum-reduced model and full loop quantum gravity. In particular, I will focus on clarifying how the operators of the quantum reduced model are related to those of the full theory. I will show that despite their simplicity, the operators of the quantum-reduced model are simply the operators of the full theory acting on states in the Hilbert space of the quantum-reduced model. In order to pass from the full theory operators to the "reduced" operators, one only has to keep in mind that the states of the quantum-reduced model are labeled with large spins, and discard terms which are of lower than leading order in j.

A standard approach to quantifying resources is to determine which operations on the resources are freely available and to deduce the ordering relation among the resources that these operations induce. If the resource of interest is the nonclassicality of the correlations embodied in a quantum state, that is, entanglement, then it is typically presumed that the appropriate choice of free operations is local operations and classical communication (LOCC). We here argue that, in spite of the near-universal endorsement of the LOCC paradigm by the quantum information community, this is the wrong choice for one of the most prominent applications of entanglement theory, namely, the study of Bell scenarios. The nonclassicality of correlations in such scenarios, we argue, should be quantified instead by local operations and shared randomness (LOSR). We support this thesis by showing that various perverse features of the interplay between entanglement and nonlocality are merely an artifact of the use of LOCC-entanglement and that the interplay between LOSR-entanglement and nonlocality is natural and intuitive. Specifically, we show that the LOSR paradigm (i) provides a resolution of the "anomaly of nonlocality", wherein partially entangled states exhibit more nonlocality than maximally entangled states, (ii) entails a notion of genuine multipartite entanglement that is distinct from the conventional one and which is free of several of its pathological features, and (iii) makes possible a resource-theoretic account of the self-testing of entangled states which simplifies and generalizes prior results. Along the way, we derive some fundamental results concerning the necessary and sufficient conditions for convertibility between pure entangled states under LOSR and highlight some of their consequences, such as the impossibility of catalysis for bipartite pure states. 

We comment on the recently introduced Gauss-Bonnet gravity in four dimensions. We argue that it does not make sense to consider this theory to be defined by a set of D->4 solutions of the higher-dimensional Gauss-Bonnet gravity. We show that a well-defined D->4 limit of Gauss-Bonnet Gravity is obtained generalizing a method employed by Mann and Ross to obtain a limit of the Einstein gravity in D=2 dimensions. This is a scalar-tensor theory of the Horndeski type obtained by dimensional reduction methods. By considering simple spacetimes beyond spherical symmetry (Taub-NUT spaces) we show that the naive limit of the higher-dimensional theory to four dimensions is not well defined and contrast the resultant metrics with the actual solutions of the new theory. Theory and solutions in lower dimensions will also be briefly discussed.

Light dark photons are subject to various plasma effects, such as Debye screening and resonant oscillations, which can lead to a more complex cosmological evolution than is experienced by conventional cold dark matter candidates. Maintaining a consistent history of dark photon dark matter requires ensuring that the super-thermal abundance present in the early Universe (i) does not deviate significantly after the formation of the CMB, and (ii) does not excessively leak into the Standard Model plasma after BBN. In this talk, I will clarify the roles of resonant and non-resonant absorption and address some implications of plasma inhomogeneities on resonant transitions.

The information paradox can be realized in two-dimensional models of gravity. In this setting, we show that the large discrepancy between the von Neumann entropy as calculated by Hawking and the requirement of unitarity is fixed by including new saddles in the gravitational path integral. These saddles arise in the replica method as wormholes connecting different copies of the black hole. We will discuss their appearance both in asymptotically AdS and asymptotically flat theories of gravity.

In this talk I will discuss ongoing efforts at UChicago to explore matter made of light. I will begin with a broad introduction to the challenges associated with making matter from photons, focusing specifically on (1) how to trap photons and imbue them with synthetic mass and charge; (2) how to induce photons to collide with one another; and (3) how to drive photons to order, by cooling or otherwise. I will then provide as examples two state-of-the-art photonic quantum matter platforms: microwave photons coupled to superconducting resonators and transmon qubits, and optical photons trapped in multimode optical cavities and made to interact through Rydberg-dressing. In each case I will describe a synthetic material created in that platform: a Mott insulator of microwave photons, stabilized by coupling to an engineered, non-Markovian reservoir, and a Laughlin molecule of optical photons prepared by scattering photons through the optical cavity. Indeed, building materials photon-by-photon will provide us with a unique opportunity to learn what all of the above words mean, and why they are important for quantum-materials science. Finally, I will conclude with my view of the broad prospects of photonic matter in particular, and of synthetic matter more generally.