Related papers: Merlinization of complexity classes above BQP
We consider the problem of modifying a quasi-probability kernel in order to improve its properties without changing the set of measures whose conditional probabilities it specifies.
Studying sequential measurements is of the utmost importance to both the foundational aspects of quantum theory and the practical implementations of quantum technologies, with both of these applications being abstractly described by the…
Updating a probability distribution in the light of new evidence is a very basic operation in Bayesian probability theory. It is also known as state revision or simply as conditioning. This paper recalls how locally updating a joint state…
Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…
We provide a computational complexity lens to understand the power of machine learning models, particularly their ability to model complex systems. Machine learning models are often trained on data drawn from sampleable or more complex…
We analyze the estimation of a finite ensemble of quantum bits which have been sent through a depolarizing channel. Instead of using the depolarized qubits directly, we first apply a purification step and show that this improves the…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…
The most general examples of quantum learning advantages involve data labeled by cryptographic or intrinsically quantum functions, where classical learners are limited by the infeasibility of evaluating the labeling functions using…
We study the normal form of multipartite density matrices. It is shown that the correlation matrix (CM) separability criterion can be improved from the normal form we obtained under filtering transformations. Based on CM criterion the…
We propose a method to characterize and quantify multipartite entanglement for pure states. The method hinges upon the study of the probability density function of bipartite entanglement and is tested on an ensemble of qubits in a variety…
The Maximum Likelihood Decoding Problem (MLD) is known to be NP-hard and its complexity is strictly related to the security of some post-quantum cryptosystems, that is, the so-called code-based primitives. Analogously, the Multivariate…
Parameterized complexity theory was developed in the 1990s to enrich the complexity-theoretic analysis of problems that depend on a range of parameters. In this paper we establish a quantum equivalent of classical parameterized complexity…
We consider the computational complexity of Hamiltonians which are sums of commuting terms acting on plaquettes in a square lattice of qubits, and we show that deciding whether the ground state minimizes the energy of each local term…
An extension to computational mechanics complexity measure is proposed in order to tackle quantum states complexity quantification. The method is applicable to any $n-$partite state of qudits through some simple modifications. A Werner…
The m-sophistication of a finite binary string x is introduced as a generalization of some parameter in the proof that complexity of complexity is rare. A probabilistic near sufficient statistic of x is given which length is upper bounded…
Post-Training Quantization (PTQ) converts pre-trained Full-Precision (FP) models into quantized versions without training. While existing methods reduce size and computational costs, they also significantly degrade performance and…
We consider a variation of the multi-party communication complexity scenario where the parties are supplied with an extra resource: particles in an entangled quantum state. We show that, although a prior quantum entanglement cannot be used…
We study structural aspects of randomized parameterized computation. We introduce a new class ${\sf W[P]}$-${\sf PFPT}$ as a natural parameterized analogue of ${\sf PP}$. Our definition uses the machine based characterization of the…
We study two modifications of the Post Correspondence Problem (PCP), namely 1) the bi-infinite version, where it is asked whether there exists a bi-infinite word such that two given morphisms agree on it, and 2) the conjugate version, where…
In this paper we show that there is a link between approximate Bayesian methods and prior robustness. We show that what is typically recognized as an approximation to the likelihood, either due to the simulated data as in the Approximate…