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We consider the problem of developing automated techniques for solving recurrence relations to aid the expected-runtime analysis of programs. Several classical textbook algorithms have quite efficient expected-runtime complexity, whereas…
Recent work has explored using the stabilizer formalism to classically simulate quantum circuits containing a few non-Clifford gates. The computational cost of such methods is directly related to the notion of stabilizer rank, which for a…
Here we show how universal quantum computers based on the quantum circuit model can handle mathematical analysis calculations for functions with continuous domains, without any digitalization, and with remarkably few qubits. The basic…
Quantum computing will change the way we tackle certain problems. It promises to dramatically speed-up many chemical, financial, and machine-learning applications. However, to capitalize on those promises, complex design flows composed of…
QAOA is a hybrid quantum-classical algorithm to solve optimization problems in gate-based quantum computers. It is based on a variational quantum circuit that can be interpreted as a discretization of the annealing process that quantum…
Quantum computers promise exponential speedups for problems in cryptography, chemistry, and optimization. Realizing this promise requires fault tolerance: physical qubits are noisy, so logical qubits must be encoded redundantly across many…
Quantum error correction (QEC) codes are traditionally defined and searched for without specifying the manner in which its syndrome extraction circuits are executed using elementary gates and measurements. We show how morphing circuits…
The advent of hybrid computing platforms consisting of quantum processing units integrated with conventional high-performance computing brings new opportunities for algorithm design. By strategically offloading select portions of the…
Simulating quantum circuits using classical computers lets us analyse the inner workings of quantum algorithms. The most complete type of simulation, strong simulation, is believed to be generally inefficient. Nevertheless, several…
Nonlinear programming is explicitly analyzed via a novel perspective/method and from a bottom-up manner. The philosophy is based on the recent findings on convex quadratic equation (CQE), which help clarify a geometric interpretation that…
We identify a broad class of physical processes in an optical quantum circuit that can be efficiently simulated on a classical computer: this class includes unitary transformations, amplification, noise, and measurements. This…
A quantum computer consists of a set of quantum bits upon which operations called gates are applied to perform computations. In order to perform quantum algorithms, physicists would like to design arbitrary gates to apply to quantum bits.…
Quantum computing has the potential to surpass the capabilities of current classical computers when solving complex problems. Combinatorial optimization has emerged as one of the key target areas for quantum computers as problems found in…
Any unitary operation in quantum information processing can be implemented via a sequence of simpler steps - quantum gates. However, actual implementation of a quantum gate is always imperfect and takes a finite time. Therefore, seeking for…
Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum…
The design of efficient quantum circuits is an important issue in quantum computing. It is in general a formidable task to find a highly optimized quantum circuit for a given unitary matrix. We propose a quantum circuit design method that…
Achieving chemical accuracy for strongly correlated molecules is a defining milestone for first-generation, fault-tolerant quantum computers, yet the factorial growth of three, four, and six-index tensor contractions in coupled-cluster…
As quantum technology advances, the efficient design of quantum circuits has become an important area of research. This paper provides an introduction to the MCT quantum circuit design problem for reversible Boolean functions with the…
Qubit reuse offers a promising way to reduce the hardware demands of quantum circuits, but current approaches are largely restricted to reordering measurements and applying qubit resets. In this work, we present an approach to further…
Quantum algorithms manipulate the amplitudes of quantum states to find solutions to computational problems. In this work, we present a framework for applying a general class of non-linear functions to the amplitudes of quantum states, with…