Related papers: Eigenlevel statistics of the quantum adiabatic alg…
Accurately solving the Schr\"odinger equation remains a central challenge in computational physics, chemistry, and materials science. Here, we propose an alternative eigenvalue problem based on a system's autocorrelation function, avoiding…
Preparing the ground state of a local Hamiltonian is a crucial problem in understanding quantum many-body systems, with applications in a variety of physics fields and connections to combinatorial optimization. While various quantum…
The eigenfunctions of quantized chaotic systems cannot be described by explicit formulas, even approximate ones. This survey summarizes (selected) analytical approaches used to describe these eigenstates, in the semiclassical limit. The…
We present a quantum eigenstate filtering algorithm based on quantum signal processing (QSP) and minimax polynomials. The algorithm allows us to efficiently prepare a target eigenstate of a given Hamiltonian, if we have access to an initial…
In this note we use ideas of Farhi, Goldstone, Gosset, Gutmann, Nagaj and Shor who link a lower bound on the run time of their quantum adiabatic search algorithm to an upper bound on the energy gap above the ground-state of the generators…
We review our work on the interplay between non-resonant gates and solid state environment in various solid state quantum computer architectures and the resulting gate errors. Particular, we show that adiabatic condition can be satisfied in…
Matching problems on 3D shapes and images are challenging as they are frequently formulated as combinatorial quadratic assignment problems (QAPs) with permutation matrix constraints, which are NP-hard. In this work, we address such problems…
Estimating the eigenstate properties of quantum systems is a long-standing, challenging problem for both classical and quantum computing. Existing universal quantum algorithms typically rely on ideal and efficient query models (e.g. time…
We analyze the efficiency of protocols for adiabatic quantum state transfer assisted by an engineered reservoir. The target dynamics is a quantum trajectory in the Hilbert space and is a fixed point of a time-dependent master equation in…
Adiabatic state preparation provides an analytical solution for generating the ground state of a target Hamiltonian, starting from an easily prepared ground state of the initial Hamiltonian. While effective for time-dependent Hamiltonians…
We show that any short-range Hamiltonian with a gap between the ground and excited states can be written as a sum of local operators, such that the ground state is an approximate eigenvector of each operator separately. We then show that…
A geometric phase is found for a general quantum state that undergoes adiabatic evolution. For the case of eigenstates, it reduces to the original Berry's phase. Such a phase is applicable in both linear and nonlinear quantum systems.…
A new and intuitive perturbative approach to time-dependent quantum mechanics problems is presented, which is useful in situations where the evolution of the Hamiltonian is slow. The state of a system which starts in an instantaneous…
For multi-level time-dependent quantum systems one can construct superadiabatic representations in which the coupling between separated levels is exponentially small in the adiabatic limit. Based on results from [BeTe1] for special…
Computing excited-state properties of molecules and solids is considered one of the most important near-term applications of quantum computers. While many of the current excited-state quantum algorithms differ in circuit architecture,…
Advances in quantum algorithms suggest a tentative scaling advantage on certain combinatorial optimization problems. Recent work, however, has also reinforced the idea that barren plateaus render variational algorithms ineffective on large…
Adiabatic quantum computing~(AQC) is based on the adiabatic principle, where a quantum system remains in an instantaneous eigenstate of the driving Hamiltonian. The final state of the Hamiltonian encodes solution to the problem of interest.…
A computation in adiabatic quantum computing is implemented by traversing a path of nondegenerate eigenstates of a continuous family of Hamiltonians. We introduce a method that traverses a discretized form of the path: At each step we apply…
An accurate theory describing adiabatic following of the dark, nonabsorbing state in the three-level system is developed. An analytical solution for the wave function of the particle experiencing Raman excitation is found as an expansion in…
We present an adiabatic quantum algorithm for the abstract problem of searching marked vertices in a graph, or spatial search. Given a random walk (or Markov chain) $P$ on a graph with a set of unknown marked vertices, one can define a…