QuICS seminar

Abstract: I will describe a recent quantum algorithm (arXiv:2303.13012) for simulating the classical dynamics of 2^n coupled oscillators (e.g., 2^n masses coupled by springs). The algorithm is based on a mapping between the Schr\"odinger equation and Newton's equations for harmonic potentials such that the amplitudes of the evolved quantum state encode the momenta and displacements of the classical oscillators.

Abstract: Quantum pseudorandom states are efficiently constructable states which nevertheless masquerade as Haar-random states to poly-time observers. First defined by Ji, Liu and Song, such states have found a number of applications ranging from cryptography to the AdS/CFT correspondence. A fundamental question is exactly how much entanglement is required to create such states. Haar-random states, as well as t-designs for t≥2, exhibit near-maximal entanglement.

Abstract: Large machine learning models are revolutionary technologies of artificial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-training and fine-tuning process. Based on quantum Carleman linearization and shadow tomography (QRAM is not necessary), we design the first quantum algorithm for training classical sparse neural networks with end-to-end settings.

Abstract: In recent years Gottesman-Kitaev-Preskill (GKP) codes have witnessed an increasing amount of interest for both their theoretically interesting features and as a possible route towards scalable hardware-efficient error correction.

Abstract: A fundamental distinction between many-body quantum states are those with short- and long-range entanglement (SRE and LRE). The latter, such as cat states, topological order, or critical states cannot be created by finite-depth circuits. Remarkably, examples are known where LRE is obtained by performing single-site measurements on SRE states such as preparing the toric code from measuring a sublattice of a 2D cluster state.

Abstract: Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently this concept has found applications beyond quantum computing---in the classification of topological phases of matter and in the description of chaotic many-body systems. Furthermore, within the context of the AdS/CFT correspondence, it has been postulated that the complexity of a specific time-evolved many-body quantum state is sensitive to the long-time properties of AdS-black hole interiors.

Finding ways to connect quantum systems in a controlled and flexible fashion lies at the core of constructing quantum information processing systems. Superconducting quantum circuits present a particularly promising platform for engineering quantum systems from the ground up: the strong light-matter interactions in these circuits can readily be used to realize interactions between different components. There remain interesting questions, however, about what types of interactions we can realize.

Quantum computations promise the ability to solve problems intractable in the classical setting. Restricting the types of computations considered often allows to establish a provable theoretical quantum advantage, and later demonstrate it experimentally.  I will discuss space-restricted computations, where input is a read-only memory and only one (qu)bit can be computed on. We show that any n-bit symmetric Boolean function can be implemented exactly through the use of quantum signal processing as a space-restricted quantum computation using O(n^2) gates.

A linear optical approach to quantum computing offers highly coherent qubits, high fidelity single qubit gates, and probabilistic entangling operations that can be implemented using well-known quantum optical methods.

Based on the recent breakthrough of Huang (2019), we show that for any total Boolean function f, deg(f) = O(~deg(f)^2): The degree of f is at most quadratic in the approximate degree of f. This is optimal as witnessed by the OR function.  D(f) = O(Q(f)^4): The deterministic query complexity of f is at most quartic in the quantum query complexity of f.  This matches the known separation (up to log factors) due to Ambainis, Balodis, Belovs, Lee, Santha, and Smotrovs (2017).  We apply these results to resolve the quantum analogue of the Aanderaa--Karp--Rosenberg conjecture.