Related papers: Hardness of efficiently generating ground states i…
Under suitable assumptions, the quantum phase estimation (QPE) algorithm is able to achieve Heisenberg-limited precision scaling in estimating the ground state energy. However, QPE requires a large number of ancilla qubits and large circuit…
In frustrated antiferromagnets with isotropic exchange interactions, there is typically a manifold of degenerate classical ground states. This degeneracy is broken by the (free) energy of quantum or thermal fluctuations, or the uniform…
We demonstrate a method of creating photonic two-dimensional cluster states that is considerably more efficient than previously proposed approaches. Our method uses only local unitaries and type-I fusion operations. The increased efficiency…
One of the goals in quantum simulation is to adiabatically generate the ground state of a complicated Hamiltonian by starting with the ground state of a simple Hamiltonian and slowly evolving the system to the complicated one. If the…
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…
We consider the task of approximating the ground state energy of two-local quantum Hamiltonians on bounded-degree graphs. Most existing algorithms optimize the energy over the set of product states. Here we describe a family of shallow…
The recent literature on near-term applications for quantum computers contains several examples of the applications of hybrid quantum/classical variational approaches. This methodology can be applied to a variety of optimization problems,…
This paper furthers existing evidence that quantum computers are capable of computations beyond classical computers. Specifically, we strengthen the collapse of the polynomial hierarchy to the second level if: (i) Quantum computers with…
We give new evidence that quantum computers -- moreover, rudimentary quantum computers built entirely out of linear-optical elements -- cannot be efficiently simulated by classical computers. In particular, we define a model of computation…
We propose a training-free quantum generative paradigm, which is fundamentally different from current generative models, which demand substantial computational power, face practical scalability limits, and often function as opaque black…
Time-periodic (Floquet) systems are one of the most interesting nonequilibrium systems. As the computation of energy eigenvalues and eigenstates of time-independent Hamiltonians is a central problem in both classical and quantum…
Quantum pseudorandomness has found applications in many areas of quantum information, ranging from entanglement theory, to models of scrambling phenomena in chaotic quantum systems, and, more recently, in the foundations of quantum…
Ground states of local Hamiltonians are of key interest in many-body physics and also in quantum information processing. Efficient verification of these states are crucial to many applications, but very challenging. Here we propose a…
It is known that three fundamental questions regarding local Hamiltonians -- approximating the ground state energy (the Local Hamiltonian problem), simulating local measurements on the ground space (APX-SIM), and deciding if the low energy…
Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering,…
It is a widely believed, though unproven, conjecture that the capability of postselection increases the language recognition power of both probabilistic and quantum polynomial-time computers. It is also unknown whether polynomial-time…
A (deterministic) polynomial-time algorithm is proposed for approximating the ground state of (general) one-dimensional gapped Hamiltonians. Let $\epsilon,n,\eta$ be the energy gap, the system size, and the desired precision, respectively.…
Estimating ground state energies of many-body Hamiltonians is a central task in many areas of quantum physics. In this work, we give quantum algorithms which, given any $k$-body Hamiltonian $H$, compute an estimate for the ground state…
We present a polynomial-time quantum algorithm making a single query (in superposition) to a classical oracle, such that for every state $|\psi\rangle$ there exists a choice of oracle that makes the algorithm construct an exponentially…
Approximating ground and a fixed number of excited state energies, or equivalently low order Hamiltonian eigenvalues, is an important but computationally hard problem. Typically, the cost of classical deterministic algorithms grows…