Related papers: Closing gaps of a quantum advantage with short-tim…
Structure-preserving algorithms and algorithms with uniform error bound have constituted two interesting classes of numerical methods. In this paper, we blend these two kinds of methods for solving nonlinear Hamiltonian systems with highly…
Dynamic simulation of materials is a promising application for near-term quantum computers. Current algorithms for Hamiltonian simulation, however, produce circuits that grow in depth with increasing simulation time, limiting feasible…
This thesis aims to establish notions of symmetry for quantum states and channels as well as describe algorithms to test for these properties on quantum computers. Ideally, the work will serve as a self-contained overview of the subject. We…
Simulation of quantum dynamics is a grand challenge of computational physics. In this work we investigate methods for reducing the demands of such simulation by identifying reduced-order models for dynamics generated by parameterized…
Building on recent advances in quantum algorithms which measure and reuse qubits and in efficient classical simulation leveraging projective measurements, we extend these frameworks to real-time dynamics of quantum many-body systems…
Motivated by various applications, unbounded Hamiltonian simulation has recently garnered great attention. Quantum Magnus algorithms, designed to achieve commutator scaling for time-dependent Hamiltonian simulation, have been found to be…
Inference problems with conjectured statistical-computational gaps are ubiquitous throughout modern statistics, computer science and statistical physics. While there has been success evidencing these gaps from the failure of restricted…
We define a general formulation of quantum PCPs, which captures adaptivity and multiple unentangled provers, and give a detailed construction of the quantum reduction to a local Hamiltonian with a constant promise gap. The reduction turns…
Discrete translational symmetry plays a fundamental role in condensed matter physics and lattice gauge theories, enabling the analysis of systems that would otherwise be intractable. Despite this, many open problems remain. Quantum…
We provide new constructions of unitary $t$-designs for general $t$ on one qudit and $N$ qubits, and propose a design Hamiltonian, a random Hamiltonian of which dynamics always forms a unitary design after a threshold time, as a basic…
Hamiltonian quantum simulation of bosons on digital quantum computers requires truncating the Hilbert space to finite dimensions. The method of truncation and the choice of basis states can significantly impact the complexity of the quantum…
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 work has characterised rigorously what it means for one quantum system to simulate another, and demonstrated the existence of universal Hamiltonians -- simple spin lattice Hamiltonians that can replicate the entire physics of any…
Demonstration of quantum advantage for classical machine learning tasks remains a central goal for quantum technologies and artificial intelligence. Two major bottlenecks to this goal are the high dimensionality of practical datasets and…
Hamiltonian quantum gates controlled by classical electromagnetic fields form the basis of any realistic model of quantum computers. In this letter, we derive a lower bound on the field energy required to implement such gates and relate…
Simulating quantum many-body systems is crucial for advancing physics but poses substantial challenges for classical computers. Quantum simulations overcome these limitations, with analog simulators offering unique advantages over digital…
We present a novel method to simulate the Lindblad equation, drawing on the relationship between Lindblad dynamics, stochastic differential equations, and Hamiltonian simulations. We derive a sequence of unitary dynamics in an enlarged…
Electronic structure simulation is an anticipated application for quantum computers. Due to high-dimensional quantum entanglement in strongly correlated systems, the quantum resources required to perform such simulations are far beyond the…
We study the properties of output distributions of noisy, random circuits. We obtain upper and lower bounds on the expected distance of the output distribution from the "useless" uniform distribution. These bounds are tight with respect to…
We examine the stability versus different types of perturbations of recently proposed shortcuts-to-adiabaticity to speed up the population inversion of a two-level quantum system. We find optimally robust processes using invariant based…