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Quantum signal processing (QSP) provides a systematic framework for implementing a polynomial transformation of a linear operator, and unifies nearly all known quantum algorithms. In parallel, recent works have developed randomized…
We show enough evidence that a structured version of Adiabatic Quantum Computation (AQC) is efficient for most satisfiability problems. More precisely, when the success probability is fixed beforehand, the computational resources grow…
We consider the effects of decoherence on Landau-Zener crossings encountered in a large-scale adiabatic-quantum-computing setup. We analyze the dependence of the success probability, i.e. the probability for the system to end up in its new…
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.…
We develop a quantum algorithm to solve combinatorial optimization problems through quantum simulation of a classical annealing process. Our algorithm combines techniques from quantum walks, quantum phase estimation, and quantum Zeno…
The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm for finding the minimum eigenvalue of a Hamiltonian that involves the optimization of a parameterized quantum circuit. Since the resulting optimization…
We design a variational quantum algorithm to solve multi-dimensional Poisson equations with mixed boundary conditions that are typically required in various fields of computational science. Employing an objective function that is formulated…
Iterative phase estimation has long been used in quantum computing to estimate Hamiltonian eigenvalues. This is done by applying many repetitions of the same fundamental simulation circuit to an initial state, and using statistical…
We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size $n$. We use as an example the…
Besides the intrinsic noise resilience property, nonadiabatic geometric phases are of the fast evolution nature, and thus can naturally be used in constructing quantum gates with excellent performance, i.e., the so-called nonadiabatic…
The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far either suffer from lack of accuracy and/or are limited to very small sizes of the…
The temporal behavior of quantum mechanical systems is reviewed. We study the so-called quantum Zeno effect, that arises from the quadratic short-time behavior, and the analytic properties of the ``survival" amplitude. It is shown that the…
The field of quantum computing has experienced a rapid expansion in recent years, with ongoing exploration of new technologies, a decrease in error rates, and a growth in the number of qubits available in quantum processors. However,…
As quantum machine learning continues to develop at a rapid pace, the importance of ensuring the robustness and efficiency of quantum algorithms cannot be overstated. Our research presents an analysis of quantum randomized smoothing, how…
The accelerated progress in manufacturing noisy intermediate-scale quantum (NISQ) computing hardware has opened the possibility of exploring its application in transforming approaches to solving computationally challenging problems. The…
The success of adiabatic quantum computation (AQC) depends crucially on the ability to maintain the quantum computer in the ground state of the evolution Hamiltonian. The computation process has to be sufficiently slow as restricted by the…
We propose a general, fully gate-based quantum algorithm for counterdiabatic driving. The algorithm does not depend on heuristics as in previous variational methods, and exploits regularisation of the adiabatic gauge potential to suppress…
Estimating the eigenvalues of a unitary transformation U by standard phase estimation requires the implementation of controlled-U-gates which are not available if U is only given as a black box. We show that a simple trick allows to measure…
The Quantum Approximate Optimization Algorithm (QAOA) exhibits significant potential for tackling combinatorial optimization problems. Despite its promise for near-term quantum devices, a major challenge in applying QAOA lies in the cost of…
We present an efficient method for estimating the eigenvalues of a Hamiltonian $H$ from the expectation values of the evolution operator for various times. For a given quantum state $\rho$, our method outputs a list of eigenvalue estimates…