Related papers: Derandomised tensor product gap amplification for …
We present an efficient sampling method for computing a partition function and accelerating configuration sampling. The method performs a random walk in the $\lambda$ space, with $\lambda$ being any thermodynamic variable that characterizes…
We analyze the quantum walk in higher spatial dimensions and compare classical and quantum spreading as a function of time. Tensor products of Hadamard transformations and the discrete Fourier transform arise as natural extensions of the…
The field of quantum Hamiltonian complexity lies at the intersection of quantum many-body physics and computational complexity theory, with deep implications to both fields. The main object of study is the LocalHamiltonian problem, which is…
Recent advancements in image mixing and generative data augmentation have shown promise in enhancing image classification. However, these techniques face the challenge of balancing semantic fidelity with diversity. Specifically, image…
Recent advances in analog and digital quantum-simulation platforms have enabled exploration of the spectrum of entanglement Hamiltonians via variational algorithms. In this work we analyze the convergence properties of the variationally…
The efficient implementation of matrix arithmetic operations underpins the speedups of many quantum algorithms. We develop a suite of methods to perform matrix arithmetics -- with the result encoded in the off-diagonal blocks of a…
There are well developed theoretical tools to analyse how quantum dynamics can solve computational problems by varying Hamiltonian parameters slowly, near the adiabatic limit. On the other hand, there are relatively few tools to understand…
We search for efficient disentanglers on random Clifford circuits of two-qubit gates arranged in a brick-wall pattern, using the proximal policy optimization (PPO) algorithm \cite{schulman2017proximalpolicyoptimizationalgorithms}.…
We present a low-space overhead simulation algorithm based on the truncated Dyson series for time-dependent quantum dynamics. This algorithm is applied to simulating time-independent Hamiltonians by transitioning to the interaction picture,…
Tensor PCA is a stylized statistical inference problem introduced by Montanari and Richard to study the computational difficulty of estimating an unknown parameter from higher-order moment tensors. Unlike its matrix counterpart, Tensor PCA…
In the study of alternative or extended theories of gravity, Dirac's Hamiltonian constraint algorithm is invaluable for enumerating the propagating modes and gauge symmetries. For gravity, this canonical approach is frequently applied as a…
Estimating the eigenvalue or energy gap of a Hamiltonian H is vital for studying quantum many-body systems. Particularly, many of the problems in quantum chemistry, condensed matter physics, and nuclear physics investigate the energy gap…
We study a certain polytope arising from embedding the Hamiltonian cycle problem in a discounted Markov decision process. The Hamiltonian cycle problem can be reduced to finding particular extreme points of a certain polytope associated…
The relative power of quantum algorithms, using an adaptive access to quantum devices, versus classical post-processing methods that rely only on an initial quantum data set, remains the subject of active debate. Here, we present evidence…
The randomized power method has gained significant interest due to its simplicity and efficient handling of large-scale spectral analysis and recommendation tasks. However, its application to large datasets containing personal information…
The scaling slope of the anti-symmetric mass gap M of compact U(1)_{2+1} lattice gauge theory is obtained analytically in the Hamiltonian formalism using the plaquette expansion. Based on the first four moments of the Hamiltonian with…
We consider whether or not Hamiltonians which are sums of commuting projectors have "trivial" ground states which can be constructed by a local quantum circuit of bounded depth and range acting on a product state. While the toric code only…
A conventional resonant detector is often subject to a trade-off between bandwidth and peak sensitivity that can be traced back to quantum Cramer-Rao Bound. Anomalous dispersion has been shown to improve it by signal amplification and is…
The conventional toy-model constructions of phase diagrams often use various versions of the standard Hermitian Bose-Hubbard Hamiltonians $H$. These studies were recently extended to cover several non-Hermitian PT-symmetric versions of the…
We revisit the finite Abelian hidden subgroup problem (AHSP) from a mathematical perspective and make the following contributions. First, by employing amplitude amplification, we present an exact quantum algorithm for the finite AHSP, our…