Seminar

The difficulty of efficiently simulating quantum many-body systems was one of the first motivations for developing quantum computers and may also be one of the first applications to find practical computational advantage on real quantum hardware. With the relatively recent advent of publicly available quantum technologies, we have now entered the era of noisy intermediate-scale quantum (NISQ) computing.

Circuit QED enables the combined use of qubits and oscillator modes. Despite a variety of available gate sets, many hybrid qubit-boson (i.e., oscillator) operations are realizable only through optimal control theory (OCT) which is oftentimes intractable and uninterpretable. We introduce an analytic approach with rigorously proven error bounds for realizing specific classes of operations via two matrix product formulas commonly used in Hamiltonian simulation, the Lie–Trotter and Baker–Campbell–Hausdorff product formulas.

In an isolated quantum many-body system undergoing unitary evolution, the entropy of a subsystem (smaller than half the system size) thermalizes if at long times, it is to leading order equal to the thermodynamic entropy of the subsystem at the same energy. We prove entropy thermalization for a nearly integrable Sachdev-Ye-Kitaev model initialized in a pure product state. The model is obtained by adding random all-to-all 4-body interactions as a perturbation to a random free-fermion model.

Understanding the Hubbard model is crucial for investigating various quantum many-body states and its fermionic and bosonic versions have been largely realized separately. Recently, transition metal dichalcogenides heterobilayers have emerged as a promising platform for simulating the rich physics of the Hubbard model. In this work, we explore the interplay between fermionic and bosonic populations, using a WS2/WSe2 heterobilayer device that hosts this hybrid particle density.

Can the current generation quantum computers solve science problems that conventional computers cannot? The jury is still out on this, but key to achieving this goal is the ability to perform robust quantum computation on near-term hardware.

Hamiltonian simulation is one of the most promising applications of quantum computing. Recent experimental results suggest that continuous-time analog quantum simulation would be advantageous over gate-based digital quantum simulation in the Noisy Intermediate-Size Quantum (NISQ) machine era. However, programming such analog quantum simulators is much more challenging due to the lack of a unified interface between hardware and software, and the only few known examples are all hardware-specific.

Over the past 6 years, a series of works have shown unconditional separations between the computational power of constant depth quantum and classical circuits. This talk will begin with a review of these circuit classes and separations. Then we'll discuss some tips and tricks -- essentially circuit identities -- which are useful when constructing constant depth quantum circuits with superclassical computational power.

Quantum query complexity is a fundamental model in quantum computation, which captures known quantum algorithms such as Grover's search algorithm, and also enables rigorous comparison between classical and quantum models of computation. The polynomial method has become one of the main paradigms for proving lower bounds on quantum query complexity.

A spontaneous symmetry-breaking order is conventionally described by a tensor-product wave-function of some few-body clusters. We discuss a type of symmetry-breaking orders, dubbed entanglement-enabled symmetry-breaking orders, which cannot be realized by any tensor-product state. Given a symmetry breaking pattern, we propose a criterion to diagnose if the symmetry-breaking order is entanglement-enabled, by examining the compatibility between the symmetries and the tensor-product description.

Strong light-matter coupling in optical cavities can alter the dynamics of molecular and material systems resulting in polaritonic excitation spectra and modified reaction pathways. For strongly coupled photon modes close in energy to nuclear vibrations the Cavity Born Oppenheimer Approximation (CBOA) in the context of quantum-electrodynamical density functional theory (QEDFT) has been demonstrated to be an appropriate description of the coupled light-matter system.