Related papers: Local Hamiltonians in Quantum Computation
One of the difficulties in adiabatic quantum computation is the limit on the computation time. Here we propose two schemes to speed-up the adiabatic evolution. To apply this controlled adiabatic evolution to adiabatic quantum computation,…
We investigate the irreconcilability issue that raises in translating the search algorithm from the Continuous-Time Quantum Walk (CTQW) framework to the Adiabatic Quantum Computing (AQC) framework. For the AQC formulation to evolve along…
We present an extension of Adiabatic Quantum Computing (AQC) algorithm for the unstructured search to the case when the number of marked items is unknown. The algorithm maintains the optimal Grover speedup and includes a small counting…
While the impact of locality restrictions on quantum dynamics and algorithmic complexity has been well studied in the general case of time-dependent Hamiltonians, the capabilities of time-independent protocols are less well understood.…
Take a cellular automaton, consider that each configuration is a basis vector in some vector space, and linearize the global evolution function. If lucky, the r esult could actually make sense physically, as a valid quantum evolution; but…
Finding a local Hamiltonian $\hat{\mathcal{H}}$ having a given many-body wavefunction $|\psi\rangle$ as its ground state, i.e. a parent Hamiltonian, is a challenge of fundamental importance in quantum technologies. Here we introduce a…
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.,…
The motivation for studying non-Hermitian systems and the role of $\mathcal{PT}$-symmetry is discussed. We investigate the use of a quantum algorithm to find the eigenvalues and eigenvectors of non-Hermitian Hamiltonians, with applications…
Hamiltonian learning protocols are essential tools to benchmark quantum computers and simulators. Yet rigorous methods for time-dependent Hamiltonians and Lindbladians remain scarce despite their wide use. We close this gap by learning the…
The efficient implementation of matrix arithmetic operations underpins the speedups of many quantum algorithms. We develop a suite of methods to perform matrix arithmetics -- with the result encoded in the off-diagonal blocks of a…
We study necessary conditions for the efficient simulation of both bipartite and multipartite Hamiltonians, which are independent of the eigenvalues and based on the algebraic-geometric invariants introduced in [1-2]. Our results indicate…
While quantum simulation is one of the most promising applications of modern quantum devices, accessible simulation times are fundamentally limited by finite coherence times due to omnipresent noise. Based on the ideas of relational…
Models of quantum computation are important because they change the physical requirements for achieving universal quantum computation (QC). For example, one-way QC requires the preparation of an entangled "cluster" state followed by…
Under suitable assumptions, the algorithms in [Lin, Tong, Quantum 2020] can estimate the ground state energy and prepare the ground state of a quantum Hamiltonian with near-optimal query complexities. However, this is based on a block…
Compared with time independent Hamiltonians, the dynamics of generic quantum Hamiltonians $H(t)$ are complicated by the presence of time ordering in the evolution operator. In the context of digital quantum simulation, this difficulty…
We show how to apply the quantum adiabatic algorithm directly to the quantum computation of molecular properties. We describe a procedure to map electronic structure Hamiltonians to 2-local qubit Hamiltonians with a small set of physically…
The simulation of quantum systems is a task for which quantum computers are believed to give an exponential speedup as compared to classical ones. While ground states of one-dimensional systems can be efficiently approximated using Matrix…
Adiabatic passage employs a slowly varying time-dependent Hamiltonian to control the evolution of a quantum system along the Hamiltonian eigenstates. For processes of finite duration, the exact time evolving state may deviate from the…
We investigate the power of quantum systems for the simulation of Hamiltonian time evolutions on a cubic lattice under the constraint of translational invariance. Given a set of translationally invariant local Hamiltonians and short range…
Suppression of diabatic transitions in quantum adiabatic evolution stands as a significant challenge for ground state preparations. Counterdiabatic driving has been proposed to compensate for diabatic losses and achieve shortcut to…