Related papers: Quantum advantage from random geometrically-two-lo…
Demonstrating a quantum computational speedup is a crucial milestone for near-term quantum technology. Recently, quantum simulation architectures have been proposed that have the potential to show such a quantum advantage, based on commonly…
The problem of sampling outputs of quantum circuits has been proposed as a candidate for demonstrating a quantum computational advantage (sometimes referred to as quantum "supremacy"). In this work, we investigate whether quantum advantage…
The efficient simulation of quantum dynamics and ground states is a central challenge in physics and a key frontier for quantum advantage. While short-time evolution in one-dimensional systems can often be simulated classically, extending…
Sampling from Gibbs states -- states corresponding to system in thermal equilibrium -- has recently been shown to be a task for which quantum computers are expected to achieve super-polynomial speed-up compared to classical computers,…
Recent experiments demonstrated quantum computational advantage in random circuit sampling and Gaussian boson sampling. However, it is unclear whether these experiments can lead to practical applications even after considerable research…
One of the key challenges in quantum machine learning is finding relevant machine learning tasks with a provable quantum advantage. A natural candidate for this is learning unknown Hamiltonian dynamics. Here, we tackle the supervised…
Implementing the time evolution under a desired target Hamiltonian is critical for various applications in quantum science. Due to the exponential increase in the number of parameters with system size and experimental imperfections, this…
A framework for statistical-mechanical analysis of quantum Hamiltonians is introduced. The approach is based upon a gradient flow equation in the space of Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve toward…
Randomness generation through quantum-chaotic evolution underpins foundational questions in statistical mechanics and applications across quantum information science, including benchmarking, tomography, metrology, and demonstrations of…
We study the problem of learning the Hamiltonian of a quantum many-body system given samples from its Gibbs (thermal) state. The classical analog of this problem, known as learning graphical models or Boltzmann machines, is a well-studied…
Quantum computers solve intractable problems which classically require an exponentially long time to compute. With the development of large-scale experiments that claim quantum advantage, a vital issue has now emerged. What are the errors,…
As quantum machine learning continues to develop at a rapid pace, the importance of ensuring the robustness and efficiency of quantum algorithms cannot be overstated. Our research presents an analysis of quantum randomized smoothing, how…
A quantum system coupled to a bath at some fixed, finite temperature converges to its Gibbs state. This thermalization process defines a natural, physically-motivated model of quantum computation. However, whether quantum computational…
This work concerns a study of the quantum mechanical extension of the work of Horwitz et al. [1] on the stability of classical Hamiltonian systems by geometrical methods. Simulations are carried out for several important examples, these…
Glassiness -- a phenomenon in physics characterized by a rough free-energy landscape -- implies hardness for stable classical algorithms. For example, it can obstruct constant-time Langevin dynamics and message-passing in random $k$-SAT and…
Photonics is a promising platform for demonstrating a quantum computational advantage (QCA) by outperforming the most powerful classical supercomputers on a well-defined computational task. Despite this promise, existing proposals and…
Recent breakthroughs in generative machine learning, powered by massive computational resources, have demonstrated unprecedented human-like capabilities. While beyond-classical quantum experiments can generate samples from classically…
The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation…
Projective measurements of a single two-level quantum mechanical system (a qubit) evolving under a time-independent Hamiltonian produce a probability distribution that is periodic in the evolution time. The period of this distribution is an…
We study the regimes in which Hamiltonian simulation benefits from randomization. We introduce a sparse-QSVT construction based on composite stochastic decompositions, where dominant terms are treated deterministically and smaller…