Related papers: Quantum Decoding Algorithms: Quantum Speedups in O…
Many combinatorial optimization problems admit a maximin fairness variant, where the aim is to find a distribution over possible solutions which maximizes an expected worst-case outcome. However, the support for an optimal distribution may…
Considerable effort has been made recently in the development of heuristic quantum algorithms for solving combinatorial optimization problems. Meanwhile, these problems have been studied extensively in classical computing for decades. In…
Quantum computing is an emerging paradigm with the potential to offer significant computational advantage over conventional classical computing by exploiting quantum-mechanical principles such as entanglement and superposition. It is…
We give a quantum speedup for solving the canonical semidefinite programming relaxation for binary quadratic optimization. This class of relaxations for combinatorial optimization has so far eluded quantum speedups. Our methods combine…
The Quantum Approximate Optimization Algorithm (QAOA) is a promising candidate algorithm for demonstrating quantum advantage in optimization using near-term quantum computers. However, QAOA has high requirements on gate fidelity due to the…
Quantum linear system algorithms (QLSAs) have the potential to speed up algorithms that rely on solving linear systems. Interior Point Methods (IPMs) yield a fundamental family of polynomial-time algorithms for solving optimization…
Here, we study the capacity of a quantum channel, assuming linear optical encoding, as a function of available photons and optical modes. First, we observe that substantial improvement is made possible by not restricting ourselves to a…
In recent years, parameterized quantum circuits have become a major tool to design quantum algorithms for optimization problems. The challenge in fully taking advantage of a given family of parameterized circuits lies in finding a good set…
Quantum error correction is a critical component for scaling up quantum computing. Given a quantum code, an optimal decoder maps the measured code violations to the most likely error that occurred, but its cost scales exponentially with the…
Optimization problems are critical across various domains, yet existing quantum algorithms, despite their great potential, struggle with scalability and accuracy due to excessive reliance on entanglement. To address these limitations, we…
Dense coding with non-maximally entangled states has been investigated in many different scenarios. We revisit this problem for protocols adopting the standard encoding scheme. In this case, the set of possible classical messages cannot be…
A model of quantum noisy channel with input encoding by a classical random vector is described. An equation of optimality is derived to determine a complete set of wave functions describing quantum decodings based on quasi-measurements…
Solving differential equations is one of the most promising applications of quantum computing. Recently we proposed an efficient quantum algorithm for solving one-dimensional Poisson equation avoiding the need to perform quantum arithmetic…
Quantum algorithms can be used to perform unsupervised machine learning tasks like data clustering by mapping the distance between data points to a graph optimization problem (i.e. MAXCUT) and finding optimal solution through energy…
Quantum Annealing (QA) relies on mixing two Hamiltonian terms, a simple driver and a complex problem Hamiltonian, in a linear combination. The time-dependent schedule for this mixing is often taken to be linear in time: improving on this…
In the rapidly advancing domain of quantum optimization, the confluence of quantum algorithms such as Quantum Annealing (QA) and the Quantum Approximate Optimization Algorithm (QAOA) with robust optimization methodologies presents a…
Quantum error correction is an essential technique for constructing a scalable quantum computer. In order to implement quantum error correction with near-term quantum devices, a fast and near-optimal decoding method is demanded. A decoder…
Despite the promise that fault-tolerant quantum computers can efficiently solve classically intractable problems, it remains a major challenge to find quantum algorithms that may reach computational advantage in the present era of noisy,…
Assessment of practical quantum information processing (QIP) remains partial without understanding limits imposed by noise. Unfortunately, mere description of noise grows exponentially with system size, becoming cumbersome even for modest…
Current quantum computing devices have different strengths and weaknesses depending on their architectures. This means that flexible approaches to circuit design are necessary. We address this task by introducing a novel space-efficient…