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For the solution of time-dependent nonlinear differential equations, we present variational quantum algorithms (VQAs) that encode both space and time in qubit registers. The spacetime encoding enables us to obtain the entire time evolution…
The Green-function technique, termed the irreducible Green functions (IGF) method, that is a certain reformulation of the equation-of motion method for double-time temperature dependent Green functions is presented. This method was…
Digital quantum simulation is a promising application for quantum computers. Their free programmability provides the potential to simulate the unitary evolution of any many-body Hamiltonian with bounded spectrum by discretizing the time…
Quantum machine learning models that leverage quantum circuits as quantum feature maps (QFMs) are recognized for their enhanced expressive power in learning tasks. Such models have demonstrated rigorous end-to-end quantum speedups for…
We propose using variational quantum algorithms (VQAs) to simulate established quantum algorithms under realistic noise conditions, aiming to surpass the fidelity of theoretical circuits in noisy environments. Focusing on the Quantum…
Correlations of an environment are crucial for the dynamics of non-Markovian quantum systems, which may not be known in advance. In this paper, we propose a gradient algorithm for identifying the correlations in terms of time-varying…
Noise on quantum devices is much more complex than it is commonly given credit. Far from usual models of decoherence, nearly all quantum devices are plagued both by a continuum of environments and temporal instabilities. These induce noisy…
Fast, gradient-based structural optimization has long been limited to a highly restricted subset of problems -- namely, density-based compliance minimization -- for which gradients can be analytically derived. For other objective functions,…
Effective quantum computation relies upon making good use of the exponential information capacity of a quantum machine. A large barrier to designing quantum algorithms for execution on real quantum machines is that, in general, it is…
Modern supercomputers are increasingly relying on Graphic Processing Units (GPUs) and other accelerators to achieve exa-scale performance at reasonable energy usage. The challenge of exploiting these accelerators is the incompatibility…
Parameterized quantum circuits as machine learning models are typically well described by their representation as a partial Fourier series of the input features, with frequencies uniquely determined by the feature map's generator…
Following a proposal by Aronov and Ioselevich, we express the Green functions (GF) of a noninteracting disordered Fermi system as a functional integral on a real time/frequency lattice. The normalizing denominator of this functional…
Coded computation techniques provide robustness against straggling servers in distributed computing, with the following limitations: First, they increase decoding complexity. Second, they ignore computations carried out by straggling…
Quantum circuits consisting of Clifford and matchgates are two classes of circuits that are known to be efficiently simulatable on a classical computer. We introduce a unified framework that shows in a transparent way the special structure…
What makes a class of quantum circuits efficiently classically simulable on average? I present a framework that applies harmonic analysis of groups to circuits with a structure encoded by group parameters. Expanding the circuits in a…
Quantum machine learning deals with leveraging quantum theory with classic machine learning algorithms. Current research efforts study the advantages of using quantum mechanics or quantum information theory to accelerate learning time or…
Randomized algorithms are crucial subroutines in quantum computing, but the requirement to execute many types of circuits on a real quantum device has been challenging to their extensive implementation. In this study, we propose an…
Response functions of quantum systems, such as electron Green's functions, magnetic, or charge susceptibilities, describe the response of a system to an external perturbation. They are the central objects of interest in field theories and…
Many computer vision applications need to recover structure from imperfect measurements of the real world. The task is often solved by robustly fitting a geometric model onto noisy and outlier-contaminated data. However, recent theoretical…
Several quantities important in condensed matter physics, quantum information, and quantum chemistry, as well as quantities required in meta-optimization of machine learning algorithms, can be expressed as gradients of implicitly defined…