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Decoherence of quantum hardware is currently limiting its practical applications. At the same time, classical algorithms for simulating quantum circuits have progressed substantially. Here, we demonstrate a hybrid framework that integrates…
Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation.…
In the last years, we have been witnessing a tremendous push to demonstrate that quantum computers can solve classically intractable problems. This effort, initially focused on the hardware, progressively included the simplification of the…
A recent breakthrough by Tang (STOC 2019) showed how to "dequantize" the quantum algorithm for recommendation systems by Kerenidis and Prakash (ITCS 2017). The resulting algorithm, classical but "quantum-inspired", efficiently computes a…
We present quantum algorithms to efficiently perform discriminant analysis for dimensionality reduction and classification over an exponentially large input data set. Compared with the best-known classical algorithms, the quantum algorithms…
Topological invariants of a dataset, such as the number of holes that survive from one length scale to another (persistent Betti numbers) can be used to analyze and classify data in machine learning applications. We present an improved…
Though quantum algorithm acts as an important role in quantum computation science, not only for providing a great vision for solving classically unsolvable problems, but also due to the fact that it gives a potential way of understanding…
Quantum computing enables the efficient resolution of complex problems, often outperforming classical methods across various applications. In 2009, Harrow, Hassidim and Lloyd proposed an algorithm for solving linear systems of equations,…
Quantum-inspired classical algorithms has received much attention due to its exponential speedup compared to existing algorithms, under certain data storage assumptions. The improvements are noticeable in fundamental linear algebra tasks.…
We present a quantum algorithm to solve systems of linear equations of the form $A\mathbf{x}=\mathbf{b}$, where $A$ is a tridiagonal Toeplitz matrix and $\mathbf{b}$ results from discretizing an analytic function, with a circuit complexity…
A previously developed quantum search algorithm for solving 1-SAT problems in a single step is generalized to apply to a range of highly constrained k-SAT problems. We identify a bound on the number of clauses in satisfiability problems for…
We present two quantum algorithms based on evolution randomization, a simple variant of adiabatic quantum computing, to prepare a quantum state $\vert x \rangle$ that is proportional to the solution of the system of linear equations $A…
Quantum annealing (QA) has the potential to significantly improve solution quality and reduce time complexity in solving combinatorial optimization problems compared to classical optimization methods. However, due to the limited number of…
Simulating the time evolution of a physical system at quantum mechanical levels of detail -- known as Hamiltonian Simulation (HS) -- is an important and interesting problem across physics and chemistry. For this task, algorithms that run on…
We demonstrate the feasibility of quantum computing for large-scale, realistic chemical systems through the development of a new interface using a quantum circuit simulator and CP2K, a highly efficient first-principles calculation software.…
Making new methods for quantum problems often relies on using basic operations in linear algebra. Often these routines are hidden behind well-known libraries that have been optimized over decades. Attempting to improve on those basic…
We apply the framework of block-encodings, introduced by Low and Chuang (under the name standard-form), to the study of quantum machine learning algorithms and derive general results that are applicable to a variety of input models,…
We present a quantum algorithm for the simulation of molecular systems that is asymptotically more efficient than all previous algorithms in the literature in terms of the main problem parameters. As in previous work [Babbush et al., New…
We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our…
Achieving a provable exponential quantum speedup for an important machine learning task has been a central research goal since the seminal HHL quantum algorithm for solving linear systems and the subsequent quantum recommender systems…