Seminar

Differential equations are ubiquitous throughout mathematics, natural and social science, and engineering. There has been extensive previous work on efficient quantum algorithms for linear differential equations. However, analogous progress for nonlinear differential equations has been severely limited due to the linearity of quantum mechanics. We give the first quantum algorithm for dissipative nonlinear differential equations that is efficient provided the dissipation is sufficiently strong relative to the nonlinearity and the inhomogeneity.

Analog quantum algorithms are formulated in terms of Hamiltonians rather than unitary gates and include quantum adiabatic computing, quantum annealing, and the quantum approximate optimization algorithm (QAOA).  These algorithms are promising candidates for near-term quantum applications, but they often require fine tuning via the annealing schedule or variational parameters.  In this work we connect all these algorithms to the optimal analog procedure.  Notably, we explore how the optimal procedure approaches a smooth adiabatic procedure but with a superposed oscillato

Recently, works such as the landmark MIP*=RE paper by Ji et. al. have established deep connections between computability theory and the power of nonlocal games with entangled provers. Many of these works start by establishing compression procedures for nonlocal games, which exponentially reduce the verifier's computational task during a game. These compression procedures are then used to construct reductions from uncomputable languages to nonlocal games, by a technique known as iterated compression.

Commuting projector models (CPMs) have provided microscopic theories for a host of gauge theories and are the venue for Kitaev’s toric code. An immediate question that arises is whether there exist CPMs for the Hall effect, the discovery of which ignited a revolution in modern condensed matter physics. In fact, a no-go theorem has recently appeared suggesting that no CPM can host a nonzero Hall conductance. In this talk, we present a CPM for just that: U(1) states with nonzero Hall conductance.

Please note that this is a special industry speaker seminar.

We finally made it to what seemed like sci-fi wishful thinking. Quantum computers are real and available on the cloud, and their power is growing at a greater-than-Moore’s-Law pace. What does this mean for those entering the job market soon? What will we be using these qubit-loaded behemoths for? Join us for some informal Q&A about this post-quantum era we find ourselves within.

For non-interacting fermions at zero temperature, it is well established that charge transport is quantized whenever the chemical potential lies in a gap of the single-body Hamiltonian. Proving the same result with interactions was an open problem for nearly 30 years until it was solved a few years ago by Hastings and Michalakis.  The solution uses new tools originally developed in the context of the classification of exotic phases of matter, and was used before in the proof of the many-dimensional Lieb-Schultz-Mattis theorem.

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.

We present an optimal protocol for encoding an unknown qubit state into a multiqubit Greenberger-Horne-Zeilinger-like state and, consequently, transferring quantum information in large systems exhibiting power-law (1/r^α) interactions. For all power-law exponents α between d and 2d+1, where d is the dimension of the system, the protocol yields a polynomial speedup for α>2d and a superpolynomial speedup for α≤2d, compared to the state of the art.

We propose a scheme to create electronic Floquet vortex states by irradiating the circularly-polarized laser light carrying non-zero orbital angular momentum on the two-dimensional semiconductor. We study the properties of the Floquet vortex states analytically and numerically using methods analogous to the techniques used for the analysis of superconducting vortex states, while we exhibit that the Floquet vortex created in the current system has the wider tunability.

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.