Related papers: Different Bootstrap Matrices in Many QM Systems
Accurate uncertainty estimates can significantly improve the performance of iterative design of experiments, as in Sequential and Reinforcement learning. For many such problems in engineering and the physical sciences, the design task…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic…
The existing doubling algorithms have been proven efficient for several important nonlinear matrix equations arising from real-world engineering applications. In a nutshell, the algorithms iteratively compute a basis matrix, in one of the…
Quantum machine learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure…
Machine learning has emerged as a promising approach to study the properties of many-body systems. Recently proposed as a tool to classify phases of matter, the approach relies on classical simulation methods$-$such as Monte Carlo$-$which…
We study the numerical bounds obtained using a conformal-bootstrap method - advocated in ref. [1] but never implemented so far - where different points in the plane of conformal cross ratios $z$ and $\bar z$ are sampled. In contrast to the…
A bootstrap approach to the effective action in quantum field theory is discussed which entails the invariance under quantum fluctuations of the effective action describing physical reality (via the S-matrix).
Eigenspaces of covariance matrices play an important role in statistical machine learning, arising in variety of modern algorithms. Quantitatively, it is convenient to describe the eigenspaces in terms of spectral projectors. This work…
We present a polynomial-time quantum algorithm for obtaining the energy spectrum of a physical system, i.e. the differences between the eigenvalues of the system's Hamiltonian, provided that the spectrum of interest contains at most a…
We show that bootstrap methods based on the positivity of probability measures provide a systematic framework for studying both synchronous and asynchronous nonequilibrium stochastic processes on infinite lattices. First, we formulate…
Using duality in optimization theory we formulate a dual approach to the S-matrix bootstrap that provides rigorous bounds to 2D QFT observables as a consequence of unitarity, crossing symmetry and analyticity of the scattering matrix. We…
Quantum states of a few-particle system capacitively coupled to a metal gate can be discriminated by measuring the quantum capacitance, which can be identified with the second derivative of the system energy with respect to the gate…
Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same…
The quantum mechanical tunneling through multiple quantum barriers is a long-standing and well-known problem. Three methods proposed earlier to calculate the tunneling probabilities and energy splitting: (1). Instanton Method (2) WKb…
We introduce two kinds of quantum algorithms to explore microcanonical and canonical properties of many-body systems. The first one is a hybrid quantum algorithm that, given an efficiently preparable state, computes expectation values in a…
We consider three different approaches to analyze the quantum mechanical problems in multi-well potentials: i) the standard matrix diagonalization technique in the basis sets of harmonic oscillator eigenfunctions or plain waves; ii) the…
Quantum Monte Carlo (QMC) methods are one of the most important tools for studying interacting quantum many-body systems. The vast majority of QMC calculations in interacting fermion systems require a constraint to control the sign problem.…
The last several decades have seen significant advances in the theoretical modeling of materials within the fields of solid-state physics and materials science, but many methods commonly applied to this problem struggle to capture strong…
We use the numerical conformal bootstrap to study boundary quantum electrodynamics, the theory of a four dimensional photon in a half space coupled to charged conformal matter on the boundary. This system is believed to be a boundary…