Related papers: On the Computational Complexity of Curing the Sign…
A quantum system will stay near its instantaneous ground state if the Hamiltonian that governs its evolution varies slowly enough. This quantum adiabatic behavior is the basis of a new class of algorithms for quantum computing. We test one…
Nonstoquastic Hamiltonians are hard to simulate due to the sign problem in quantum Monte Carlo simulation. It is however unclear whether nonstoquasticity can lead to advantage in quantum annealing. Here we show that YY-interaction between…
The non-trivial phase structure of the eigenstates of many-body quantum systems severely limits the applicability of quantum Monte Carlo, variational, and machine learning methods. Here, we study real-valued signful ground-state wave…
Quantum Monte Carlo methods are powerful tools for studying quantum many-body systems but face difficulties in accessing excited states and in treating sign problems. We present a continuous-time path-integral Monte Carlo method for…
We initiate the study of parameterized complexity of $\textsf{QMA}$ problems in terms of the number of non-Clifford gates in the problem description. We show that for the problem of parameterized quantum circuit satisfiability, there exists…
Quantum Mechanical ground states of many-body systems can be important resources for various investigations: for quantum sensing, as the initial state for nonequilibrium quantum dynamics following quenches, and the simulation of quantum…
We present a computational framework to identify Hamiltonians of interacting quantum many-body systems that host non-ergodic excited states. We combine quantum Monte Carlo simulations with the recently proposed eigenstate-to-Hamiltonian…
The NP-complete problem of the travelling salesman (TSP) is considered in the framework of quantum adiabatic computation (QAC). We first derive a remarkable lower bound for the computation time for adiabatic algorithms in general as a…
We consider QM with non-Hermitian quasi-diagonalizable Hamiltonians, i.e. the Hamiltonians having a number of Jordan cells in particular biorthogonal bases. The "self-orthogonality" phenomenon is clarified in terms of a correct spectral…
We present a new approach for numerical solutions of ab initio quantum chemistry systems. The main idea of the approach, which we call canonical diagonalization, is to diagonalize directly the second quantized Hamiltonian by a sequence of…
Current universal quantum computers have a limited number of noisy qubits. Because of this, it is difficult to use them to solve large-scale complex optimization problems. In this paper we tackle this issue by proposing a quantum…
We introduce a Quantum Monte Carlo (QMC) method which efficiently simulates in a sign-problem-free way a broad class of frustrated $S=1/2$ models with competing antiferromagnetic interactions. Our scheme uses the basis of total spin…
This paper deals with the sign problem in full configuration-interaction quantum Monte Carlo. After putting this article on the arxiv, it was pointed out to us that our argument applies to a number of model Hamiltonians we considered…
It is well known that the ground state energy of many-particle Hamiltonians involving only 2-body interactions can be obtained using constrained optimizations over density matrices which arise from reducing an N-particle state. While…
Protecting quantum information from the detrimental effects of decoherence and lack of precise quantum control is a central challenge that must be overcome if a large robust quantum computer is to be constructed. The traditional approach to…
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…
We introduce a family of Hamiltonian systems for measurement-based quantum computation with continuous variables. The Hamiltonians (i) are quadratic, and therefore two body, (ii) are of short range, (iii) are frustration-free, and (iv)…
An adiabatic quantum algorithm is essentially given by three elements: An initial Hamiltonian with known ground state, a problem Hamiltonian whose ground state corresponds to the solution of the given problem and an evolution schedule such…
We consider the computational complexity of Hamiltonians which are sums of commuting terms acting on plaquettes in a square lattice of qubits, and we show that deciding whether the ground state minimizes the energy of each local term…
A central problem in quantum computing is to identify computational tasks which can be solved substantially faster on a quantum computer than on any classical computer. By studying the hardest such tasks, known as BQP-complete problems, we…