Related papers: Merlinization of complexity classes above BQP
We prove two sets of results concerning computational complexity classes. The first concerns a variation of the random oracle hypothesis posed by Bennett and Gill after they showed that relative to a randomly chosen oracle, P not equal NP…
Tokenization is the first -- and often least scrutinized -- step of most NLP pipelines. Standard algorithms for learning tokenizers rely on frequency-based objectives, which favor languages dominant in the training data and consequently…
We consider the problem of correctly classifying a given quantum two-level system (qubit) which is known to be in one of two equally probable quantum states. We assume that this task should be performed by a quantum machine which does not…
This paper presents an efficient parallel approximation scheme for a new class of min-max problems. The algorithm is derived from the matrix multiplicative weights update method and can be used to find near-optimal strategies for…
This paper introduces quantum ``multiple-Merlin''-Arthur proof systems in which Arthur receives multiple quantum proofs that are unentangled with each other. Although classical multi-proof systems are obviously equivalent to classical…
Post-training quantization reduces the computational cost of large language models but fundamentally alters their social biases in ways that aggregate metrics fail to capture. We present the first large-scale study of 50 quantized models…
Quantum descriptions of polarization show the rich degrees of freedom underlying classical light. While changes in polarization of light are well-described classically, a full quantum description of polarimetry, which characterizes…
This paper studies complexity theoretic aspects of quantum refereed games, which are abstract games between two competing players that send quantum states to a referee, who performs an efficiently implementable joint measurement on the two…
Improving generalization is one of the main challenges for training deep neural networks on classification tasks. In particular, a number of techniques have been proposed, aiming to boost the performance on unseen data: from standard data…
This article surveys quantum computational complexity, with a focus on three fundamental notions: polynomial-time quantum computations, the efficient verification of quantum proofs, and quantum interactive proof systems. Properties of…
In this paper, we extend the techniques used in our previous work to show that there exists a probabilistic Turing machine running within time $O(n^k)$ for all $k\in\mathbb{N}_1$ accepting a language $L_d$ that is different from any…
The exact semiclassical quantization condition represents a cumbersome series expansion, so that only the main term of it is usually taken into account. We propose a way to find next terms without new additional calculations. Results are…
The problem of determining whether a given quantum state is entangled lies at the heart of quantum information processing, which is known to be an NP-hard problem in general. Despite the proposed many methods such as the positive partial…
In this note we generalize Nielsen's marjoization criterion for the convertibility of bipartite pure states [Phys. Rev. Lett \textbf{83}, 436(1999)] to a special class of multipartite pure states which have generalized Schmidt…
We study the sample complexity of semi-supervised learning (SSL) and introduce new assumptions based on the mismatch between a mixture model learned from unlabeled data and the true mixture model induced by the (unknown) class conditional…
In automated complexity analysis, noninterference-based type systems statically guarantee, via soundness, the property that well-typed programs compute functions of a given complexity class, e.g., the class FP of functions computable in…
Learning properties of quantum states and channels is known to benefit from resources such as entangled operations, auxiliary qubits, and adaptivity, whereas the resource structure of measurement learning, namely, learning properties of…
Motivated by description logics, we investigate what happens to the complexity of modal satisfiability problems if we only allow formulas built from literals, $\wedge$, $\Diamond$, and $\Box$. Previously, the only known result was that the…
We introduce a new family of separability criteria that are based on the existence of extensions of a bipartite quantum state $\rho$ to a larger number of parties satisfying certain symmetry properties. It can be easily shown that all…
In the Possible Winner problem in computational social choice theory, we are given a set of partial preferences and the question is whether a distinguished candidate could be made winner by extending the partial preferences to linear…