Related papers: Polynomial T-depth Quantum Solvability of Noisy Bi…
In this paper, we propose two new methods for solving Set Constraint Problems, as well as a potential polynomial solution for NP-Complete problems using quantum computation. While current methods of solving Set Constraint Problems focus on…
Quantum computation is a topic of significant recent interest, with practical advances coming from both research and industry. A major challenge in quantum programming is dealing with errors (quantum noise) during execution. Because quantum…
Deep learning has become a promising programming paradigm in software development, owing to its surprising performance in solving many challenging tasks. Deep neural networks (DNNs) are increasingly being deployed in practice, but are…
Quantum computers have long been expected to efficiently solve complex classical differential equations. Most digital, fault-tolerant approaches use Carleman linearization to map nonlinear systems to linear ones and then apply quantum…
In this paper, we study the computational complexity of the quadratic unconstrained binary optimization (QUBO) problem under the functional problem FP^NP categorization. We focus on four sub-classes: (1) When all coefficients are integers…
The Traveling Salesman Problem (TSP) is a classical NP-hard problem that plays a crucial role in combinatorial optimization. In this paper, we are interested in the quantum search framework for the TSP because it has robust theoretical…
In spite of their superior performance, neural probabilistic language models (NPLMs) remain far less widely used than n-gram models due to their notoriously long training times, which are measured in weeks even for moderately-sized…
Quantum computing is deemed to require error correction at scale to mitigate physical noise by reducing it to lower noise levels while operating on encoded logical qubits. Popular quantum error correction schemes include CSS code, of which…
The stabilization of a quantum computer by repeated error correction can be reduced almost entirely to repeated preparation of blocks of qubits in quantum codeword states. These are multi-particle entangled states with a high degree of…
Accurately estimating high-order moments of quantum states is an elementary precondition for many crucial tasks in quantum computing, such as entanglement spectroscopy, entropy estimation, spectrum estimation, and predicting non-linear…
Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing…
Reducing the conditions under which a given set satisfies the stipulations of the subset sum proposition to a set of linear relationships, the question of whether a set satisfies subset sum may be answered in a polynomial number of steps by…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
Despite remarkable achievements in its practical tractability, the notorious class of NP-complete problems has been escaping all attempts to find a worst-case polynomial time-bound solution algorithms for any of them. The vast majority of…
In this work, we consider the problem of blind source separation (BSS) by departing from the usual linear model and focusing on the linear-quadratic (LQ) model. We propose two provably robust and computationally tractable algorithms to…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
Real quantum computers will be subject to complicated, qubit-dependent noise, instead of simple noise such as depolarizing noise with the same strength for all qubits. We can do quantum error correction more effectively if our decoding…
The performance of a neural network for a given task is largely determined by the initial calibration of the network parameters. Yet, it has been shown that the calibration, also referred to as training, is generally NP-complete. This…
Compiling a given quantum algorithm into a target hardware architecture is a challenging optimization problem. The compiler must take into consideration the coupling graph of physical qubits and the gate operation dependencies. The existing…
Realizing computationally complex quantum circuits in the presence of noise and imperfections is a challenging task. While fault-tolerant quantum computing provides a route to reducing noise, it requires a large overhead for generic…