Related papers: Bootstrapping Shape Invariance: Numerical Bootstra…
The range of motion of a particle with certain energy $E$ confined in a potential is determined from the energy conservation law in classical mechanics. The counterpart of this question in quantum mechanics can be regarded as what the…
Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the…
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…
With the help of recent developments in quantum algorithms for semidefinite programming, we discuss the possibility for quantum speedup for the numerical conformal bootstrap in conformal field theory. We show that quantum algorithms may…
We analyze the bootstrap approach (a dual optimization method to the variational approach) to one-dimensional spin chains, leveraging semidefinite programming to extract numerical results. We study how correlation functions in the ground…
We demonstrate that combining the positivity of density matrices with steady-state conditions yields a systematic bootstrap method for studying open quantum many-body systems governed by Lindblad master equations on infinite lattices, which…
We extend molecular bootstrap embedding to make it appropriate for implementation on a quantum computer. This enables solution of the electronic structure problem of a large molecule as an optimization problem for a composite Lagrangian…
Recently, the ``Bootstrap" technique was applied in Quantum Mechanics to solve the eigenspectra of Hermitian Hamiltonians and extended to non-Hermitian PT-symmetric systems. However, its application has been limited to real spectra. In this…
We consider the properties of the bootstrap as a tool for inference concerning the eigenvalues of a sample covariance matrix computed from an $n\times p$ data matrix $X$. We focus on the modern framework where $p/n$ is not close to 0 but…
Although eigenspectra of one dimensional shape invariant potentials with unbroken supersymmetry are easily obtained, this procedure is not applicable when the parameters in these potentials correspond to broken supersymmetry, since there is…
The scattering equations are a set of algebraic equations connecting the kinematic space of massless particles and the moduli space of Riemann spheres with marked points. We present an efficient method for solving the scattering equations…
Important properties of a quantum system are not directly measurable, but they can be disclosed by how fast the system changes under controlled perturbations. In particular, asymmetry and entanglement can be verified by reconstructing the…
Bootstrapping can produce confidence levels for hypotheses about quadratic regression models - such as whether the U-shape is inverted, and the location of optima. The method has several advantages over conventional methods: it provides…
Understanding and controlling engineered quantum systems is key to developing practical quantum technology. However, given the current technological limitations, such as fabrication imperfections and environmental noise, this is not always…
The bootstrap method has proven useful for a wide range of matrix models. Here, we show that the computed momenta can be used to reconstruct the underlying eigenvalue probability distribution, which in turn allows us to compute the free…
Bootstrap is an idea that imposing consistency conditions on a physical system may lead to rigorous and nontrivial statements about its physical observables. In this work, we discuss the bootstrap problem for the invariant measure of the…
We consider matrix quantum mechanics with multiple bosonic matrices, including those obtained from dimensional reduction of Yang-Mills theories. Using the matrix bootstrap, we study simple observables like $\langle \mathop{tr} X^2 \rangle$…
Encrypted dynamic controllers that operate for an unlimited time have been a challenging subject of research. The fundamental difficulty is the accumulation of errors and scaling factors in the internal state during operation.…
We present a novel geometric approach for determining the unique structure of a Hamiltonian and establishing an instability criterion for quantum quadratic systems. Our geometric criterion provides insights into the underlying geometric…
Reliable forward uncertainty quantification in engineering requires methods that account for aleatory and epistemic uncertainties. In many applications, epistemic effects arising from uncertain parameters and model form dominate prediction…