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In this paper, we present a novel method for solving a class of quadratically constrained quadratic optimization problems using only additions and multiplications. This approach enables solving constrained optimization problems on private…

Polynomial systems over the binary field have important applications, especially in symmetric and asymmetric cryptanalysis, multivariate-based post-quantum cryptography, coding theory, and computer algebra. In this work, we study the…

Benchmark workloads are extremely important to the database management research community, especially as more machine learning components are integrated into database systems. Here, we propose a Bayesian optimization technique to…

Control and manipulation are two of the most studied types of attacks on elections. In this paper, we study the complexity of control attacks on elections in which there are manipulators. We study both the case where the "chair" who is…

In many high-dimensional problems,polynomial-time algorithms fall short of achieving the statistical limits attainable without computational constraints. A powerful approach to probe the limits of polynomial-time algorithms is to study the…

We show how an algorithm for the problem of inverting a permutation may be used to design one for the problem of unordered search (with a unique solution). Since there is a straightforward reduction in the reverse direction, the problems…

Since the breakthrough superpolynomial multilinear formula lower bounds of Raz (Theory of Computing 2006), proving such lower bounds against multilinear algebraic branching programs (mABPs) has been a longstanding open problem in algebraic…

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…

Two-party one-way quantum communication has been extensively studied in the recent literature. We target the size of minimal information that is necessary for a feasible party to finish a given combinatorial task, such as distinction of…

We study the concurrence of four-qubit quantum states and provide analytical lower bounds of concurrence in terms of the monogamy inequality of concurrence for qubit systems. It is shown that these lower bounds are able to improve the…

The polynomial multiplication problem has attracted considerable attention since the early days of computer algebra, and several algorithms have been designed to achieve the best possible time complexity. More recently, efforts have been…

We introduce a new model for studying quantum data structure problems -- the "quantum cell probe model". We prove a lower bound for the static predecessor problem in the address-only version of this model where we allow quantum parallelism…

We study the dynamics of two lower bounds of concurrence in bipartite quantum systems when one party goes through an arbitrary channel. We show that these lower bounds obey the factorization law similar to that of [Konrad et al., Nat. Phys.…

Many state-of-the-art adversarial training methods for deep learning leverage upper bounds of the adversarial loss to provide security guarantees against adversarial attacks. Yet, these methods rely on convex relaxations to propagate lower…

We prove an exponential separation for the sample complexity between the standard PAC-learning model and a version of the Equivalence-Query-learning model. We then show that this separation has interesting implications for adversarial…

A new quantum algorithm for a search problem and its computational complexity are discussed. It is shown in the search problem containing 2^n objects that our algorithm runs in polynomial time.

The approximate degree of a Boolean function is the minimum degree of real polynomial that approximates it pointwise. For any Boolean function, its approximate degree serves as a lower bound on its quantum query complexity, and generically…

Quantification of quantum entanglement plays a crucial role in the study of quantum information tasks. We present analytical lower bounds for both concurrence and 2-concurrence based on the correlation matrices of bipartite quantum states.…

Aaronson, Bouland, Fitzsimons and Lee introduced the complexity class PDQP (which was original labeled naCQP), an alteration of BQP enhanced with the ability to obtain non-collapsing measurements, samples of quantum states without…

Query complexity is a model of computation in which we have to compute a function $f(x_1, \ldots, x_N)$ of variables $x_i$ which can be accessed via queries. The complexity of an algorithm is measured by the number of queries that it makes.…