QuICS seminar

We derive general results relating revivals in the dynamics of quantum many-body systems to the entanglement properties of energy eigenstates. For a lattice system of N sites initialized in a low-entangled and short-range correlated state, our results show that a perfect revival of the state after a time at most poly(N) implies the existence of "quantum many-body scars", whose number grows at least as the square root of N up to poly-logarithmic factors.

The past decade has seen a dramatic increase in the degree, quality, and sophistication of control over quantum-mechanical interactions available between artificial degrees of freedom in a variety of experimental platforms. The geometrical structure of these interactions, however, remains largely constrained by the underlying rectilinear geometry of three-dimensional Euclidean space.

Can a quantum computer help us analyze a large classical data set? Data stored classically cannot be queried in superposition, which rules out direct Grover searches, and it can often be classically accessed with some level of parallelism, which would negate the advantage of Grover even if it were possible.

Exactly solvable models are essential in physics. For many-body spin-1/2 systems, an important class of such models consists of those that can be mapped to free fermions hopping on a graph. We provide a complete characterization of models which can be solved this way. Specifically, we reduce the problem of recognizing such spin models to the graph-theoretic problem of recognizing line graphs, which has been solved optimally. A corollary of our result is a complete set of constant-sized commutation structures that constitute the obstructions to a free-fermion solution.

Given a nonlocal game, we'd like to be able to find the optimal quantum winning probability, and the set of optimal strategies. However, the recent MIP*=RE result implies that we cannot determine the quantum winning probability to within constant error.

Interference is an essential part of quantum mechanics.  However, an important class of Hamiltonians considered are those with "no sign problem", where all off-diagonal matrix elements of the Hamiltonian are non-negative.  This means that the ground state wave function can be chosen to have all amplitudes real and positive.  In a sense, no destructive interference is possible for these Hamiltonians so that they are "almost classical", and there are several simulation algorithms which work well in practice on classical computers today.  In this talk, I'll discuss what happens when one consid

Machine learning (ML) provides the potential to solve challenging quantum many-body problems in physics and chemistry. Yet, this prospect has not been fully justified. In this work, we establish rigorous results to understand the power of classical ML and the potential for quantum advantage in an important example application: predicting outcomes of quantum mechanical processes. We prove that for achieving a small average prediction error, one can always design a classical ML model whose sample complexity is comparable to the best quantum ML model (up to a small polynomial factor).

Recent technological developments have focused the interest of the quantum computing community on investigating how near-term devices could outperform classical computers for practical applications. A central question that remains open is whether their noise can be overcome or it fundamentally restricts any potential quantum advantage. We present a transparent way of comparing classical algorithms to quantum ones running on near-term quantum devices for a large family of problems that include optimization problems and approximations to the ground state energy of Hamiltonians.

The accurate computation of ground and excited states of many-fermion quantum systems is one of the most important challenges in the physical and computational sciences whose solution stands to benefit significantly from the advent of quantum computing devices. Existing methodologies using phase estimation or variational algorithms have potential drawbacks such as deep circuits requiring substantial error correction or non-trivial high-dimensional classical optimization.

Quantum metrology, which studies parameter estimation in quantum systems, has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on the estimation precision, called the Heisenberg limit, which is achievable in noiseless quantum systems, but is in general not for noisy systems. This talk is a summary of some recent works by the speaker and collaborators on quantum metrology enhanced by quantum error correction.