Related papers: Lower Bounds for Learning Hamiltonians from Time E…
We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of 10-dimensional qudits that makes it possible to realize universal quantum computing without any external control during the computational process.…
The problem of simulating sparse Hamiltonians on quantum computers is well studied. The evolution of a sparse N x N Hamiltonian H for time t can be simulated using O(||Ht||poly(log N)) operations, which is essentially optimal due to a…
All elementary Hamiltonians in nature are expected to be invariant under rotation. Despite this restriction, we usually assume that any arbitrary measurement or unitary time evolution can be implemented on a physical system, an assumption…
We introduce a simple framework for estimating lower bounds on the runtime of a broad class of adiabatic quantum algorithms. The central formula consists of calculating the variance of the final Hamiltonian with respect to the initial…
In this article we develop quantum algorithms for learning and testing juntas, i.e. Boolean functions which depend only on an unknown set of k out of n input variables. Our aim is to develop efficient algorithms: - whose sample complexity…
Learning quantum Hamiltonians with high precision is important for quantum physics and quantum information science. We propose a multi-stage neural network framework that significantly enhances Hamiltonian learning precision through…
Identifying unknown Hamiltonians from their quantum dynamics is a pivotal challenge in quantum technologies. In this paper, we introduce Hamiltonian recognition, a framework that bridges quantum hypothesis testing and quantum metrology,…
Estimating parameters of quantum systems is usually done by performing a sequence of predetermined experiments and post-processing the resulting data. It is known that online design, where the choice of the next experiment is based on the…
The classical and quantum dynamics of simple time-reparametrization- invariant models containing two degrees of freedom are studied in detail. Elimination of one ``clock'' variable through the Hamiltonian constraint leads to a description…
Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems on a quantum computer. The existing algorithms generally approximate the time evolution operators, which may need a deep…
The adiabatic theorem has been recently used to design quantum algorithms of a new kind, where the quantum computer evolves slowly enough so that it remains near its instantaneous ground state which tends to the solution [Farhi et al.,…
We study constrained Hamiltonian systems by utilizing general forms of time discretization. We show that for explicit discretizations, the requirement of preserving the canonical Poisson bracket under discrete evolution imposes strong…
We provide a general method for efficiently simulating time-dependent Hamiltonian dynamics on a circuit-model based quantum computer. Our approach is based on approximating the truncated Dyson series of the evolution operator, extending the…
We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound…
We present a quantum algorithm for simulating the time evolution generated by any bounded, time-dependent operator $-A$ with non-positive logarithmic norm, thereby serving as a natural generalization of the Hamiltonian simulation problem.…
Learned index structures aim to accelerate queries by training machine learning models to approximate the rank function associated with a database attribute. While effective in practice, their theoretical limitations are not fully…
Classical hardness-of-sampling results are largely established for random quantum circuits, whereas analog simulators natively realize time evolutions under geometrically local Hamiltonians. Does a typical such Hamiltonian already yield…
Simulating the long-time evolution of Hamiltonian systems is limited by the small timesteps required for stable numerical integration. To overcome this constraint, we introduce a framework to learn Hamiltonian Flow Maps by predicting the…
Evolution time of a qubit under a Hamiltonian operation is one of the key issues in quantum control, quantum information processing and quantum computing. It has a lower bound in Hermitian system, which is limited by the coupling between…
For any pair of quantum states, an initial state |I> and a final quantum state |F>, in a Hilbert space, there are many Hamiltonians H under which |I> evolves into |F>. Let us impose the constraint that the difference between the largest and…