Related papers: A hybrid quantum-classical algorithm for Bayes-opt…
Quantum mechanics fundamentally forbids deterministic discrimination of quantum states and processes. However, the ability to optimally distinguish various classes of quantum data is an important primitive in quantum information science. In…
The problem of optimally discriminating between two completely unknown qubit states is generalized by allowing an error margin. It is visualized as a device---the programmable discriminator---with one data and two program ports, each fed…
We propose a semidefinite programming (SDP) algorithm for community detection in the stochastic block model, a popular model for networks with latent community structure. We prove that our algorithm achieves exact recovery of the latent…
Semidefinite programs (SDP) are one of the most versatile frameworks in numerical optimization, serving as generalizations of many conic programs and as relaxations of NP-hard combinatorial problems. Their main drawback is their…
Quantum state separation is a probabilistic map that transforms a given set of pure states into another set of more distinguishable ones. Here we investigate such a map acting onto uniparametric families of symmetric linearly dependent or…
In this work, a scalable algorithm for the approximate quantum state preparation problem is proposed, facing a challenge of fundamental importance in many topic areas of quantum computing. The algorithm uses a variational quantum circuit…
Quantum computing has demonstrated the potential to solve computationally intensive problems more efficiently than classical methods. Many software engineering tasks, such as test case selection, static analysis, code clone detection, and…
Evaluating the entanglement spectrum is essential for characterizing exotic quantum phases such as quantum criticality and topological order. However, for large quantum many-body systems, this task is hindered by the exponential measurement…
We describe a class of programmable devices that can discriminate between two quantum states. We consider two cases. In the first, both states are unknown. One copy of each of the unknown states is provided as input, or program, for the two…
Semidefinite programming (SDP) is a central topic in mathematical optimization with extensive studies on its efficient solvers. In this paper, we present a proof-of-principle sublinear-time algorithm for solving SDPs with low-rank…
Determining whether a quantum state is separable or entangled is a problem of fundamental importance in quantum information science. It has recently been shown that this problem is NP-hard. There is a highly inefficient `basic algorithm'…
As the title indicates, this chapter presents a brief, self-contained introduction to five fundamental problems in Quantum Information Science (QIS) that are especially well-suited to be formulated as Semi-definite Programs (SDP). We have…
We study and extend the semidefinite programming (SDP) hierarchies introduced in [Phys. Rev. Lett. 115, 020501] for the characterization of the statistical correlations arising from finite dimensional quantum systems. First, we introduce…
It is well-known that by adding integrality constraints to the semidefinite programming (SDP) relaxation of the max-cut problem, the resulting integer semidefinite program is an exact formulation of the problem. In this paper we show…
We study a broad class of quantum process discrimination problems that can handle many optimization strategies such as the Bayes, Neyman-Pearson, and unambiguous strategies, where each process can consist of multiple time steps and can have…
Variational hybrid quantum-classical algorithms are promising candidates for near-term implementation on quantum computers. In these algorithms, a quantum computer evaluates the cost of a gate sequence (with speedup over classical cost…
Constraint programming (CP) is a paradigm used to model and solve constraint satisfaction and combinatorial optimization problems. In CP, problems are modeled with constraints that describe acceptable solutions and solved with backtracking…
Encoding in a high-dimensional Hilbert space improves noise resilience in quantum information processing. This approach, however, may result in cross-mode coupling and detection complexities, thereby reducing quantum cryptography…
We present two quantum interior point methods for semidefinite optimization problems, building on recent advances in quantum linear system algorithms. The first scheme, more similar to a classical solution algorithm, computes an inexact…
We show that any boolean function can be evaluated optimally by a quantum query algorithm that alternates a certain fixed, input-independent reflection with a second reflection that coherently queries the input string. Originally introduced…