Related papers: Approximation algorithms for quantum many-body pro…
To analyze quantum many-body Hamiltonians, recently, machine learning techniques have been shown to be quite useful and powerful. However, the applicability of such machine learning solvers is still limited. Here, we propose schemes that…
We derive an explicit Hamiltonian for copying the basis up and down states of a quantum two-state system - a qubit - onto n "copy" qubits initially all prepared in the down state. In terms of spin components, for spin-1/2 particle spin…
In this paper, we show that there is a large class of fermionic systems for which it is possible to find, for any dimension, a finite closed set of eigenoperators and eigenvalues of the Hamiltonian. Then, the hierarchy of the equations of…
We present an exact spin-elimination technique that reduces the dimensionality of both quadratic and k-local Ising Hamiltonians while preserving their original ground-state configurations. By systematically replacing each removed spin with…
We introduce a quantum algorithm to efficiently prepare states with a small energy variance at the target energy. We achieve it by filtering a product state at the given energy with a Lorentzian filter of width $\delta$. Given a local…
Learning the structure of the entanglement Hamiltonian (EH) is central to characterizing quantum many-body states in analog quantum simulation. We describe a protocol where spatial deformations of the many-body Hamiltonian, physically…
The utility of solving the Fermi-Hubbard model has been estimated in the billions of dollars. Digital quantum computers can in principle address this task, but have so far been limited to quasi one-dimensional models. This is because of…
Understanding and approximating extremal energy states of local Hamiltonians is a central problem in quantum physics and complexity theory. Recent work has focused on developing approximation algorithms for local Hamiltonians, and in…
Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation.…
Performing large-scale, accurate quantum simulations of many-fermion systems is a central challenge in quantum science, with applications in chemistry, materials, and high-energy physics. Despite significant progress, realizing generic…
Prethermalization refers to the transient phenomenon where a system thermalizes according to a Hamiltonian that is not the generator of its evolution. We provide here a rigorous framework for quantum spin systems where prethermalization is…
A quantum state for being an eigenstate of some local Hamiltonian should be constraint by zero energy variance and consequently, the constraint is rather strong that a single eigenstate may uniquely determine the Hamiltonian. For…
Large-scale quantum devices provide insights beyond the reach of classical simulations. However, for a reliable and verifiable quantum simulation, the building blocks of the quantum device require exquisite benchmarking. This benchmarking…
The Markov decision process is the mathematical formalization underlying the modern field of reinforcement learning when transition and reward functions are unknown. We derive a pseudo-Boolean cost function that is equivalent to a K-spin…
Understanding the mechanisms responsible for the equilibration of isolated quantum many-body systems is a long-standing open problem. In this work we obtain a statistical relationship between the equilibration properties of Hamiltonians and…
We propose a method for obtaining effective classical Hamiltonians \cal H for many-body quantum spin systems with large spins. This method uses the coherent-state representation of the partition function Z and the cumulant expansion in…
Keeping in view the ordering ambiguity that arises due to the presence of position-dependent effective mass in the kinetic energy term of the Hamiltonian, a general scheme for obtaining algebraic solutions of quantum mechanical systems with…
Local Hamiltonians with topological quantum order exhibit highly entangled ground states that cannot be prepared by shallow quantum circuits. Here, we show that this property may extend to all low-energy states in the presence of an on-site…
By allowing measurements of observables other than the state of the qubits in a quantum computer, one can find eigenvectors very quickly. If a unitary operation U is implemented as a time-independent Hamiltonian, for instance, one can…
Quantum Hamiltonian identification is important for characterizing the dynamics of quantum systems, calibrating quantum devices and achieving precise quantum control. In this paper, an effective two-step optimization (TSO) quantum…