相关论文: Tight adversary bounds for composite functions

Finite-sum optimization has wide applications in machine learning, covering important problems such as support vector machines, regression, etc. In this paper, we initiate the study of solving finite-sum optimization problems by quantum…

Many efficient data structures use randomness, allowing them to improve upon deterministic ones. Usually, their efficiency and correctness are analyzed using probabilistic tools under the assumption that the inputs and queries are…

The quantum approximate optimization algorithm (QAOA) is a hybrid quantum-classical variational algorithm that offers the potential to handle combinatorial optimization problems. Introducing constraints in such combinatorial optimization…

State conversion generalizes query complexity to the problem of converting between two input-dependent quantum states by making queries to the input. We characterize the complexity of this problem by introducing a natural…

Quantum state learning is a fundamental problem in physics and computer science. As near-term quantum devices are error-prone, it is important to design error-resistant algorithms. Apart from device errors, other unexpected factors could…

In this paper, we introduce a new quantum query lower bound framework. It is inspired by Zhandry's compressed oracle technique, but it also subsumes the polynomial method as a special case. Compared to Zhandry's technique, our approach has…

The polynomial method and the Ambainis's lower bound (or \emph{Alb}, for short) method are two main quantum lower bound techniques. While recently Ambainis showed that the polynomial method is not tight, the present paper aims at studying…

We study the problem of constrained efficient global optimization, where both the objective and constraints are expensive black-box functions that can be learned with Gaussian processes. We propose CONFIG (CONstrained efFIcient Global…

There are two main attack models considered in the adversarial robustness literature: black-box and white-box. We consider these threat models as two ends of a fine-grained spectrum, indexed by the number of queries the adversary can ask.…

While variational quantum algorithms (VQAs) have demonstrated considerable success in unconstrained optimization, their application to constrained combinatorial problems face a trade-off. Penalty-based methods, despite their circuit…

Quantum-inspired classical algorithms provide us with a new way to understand the computational power of quantum computers for practically-relevant problems, especially in machine learning. In the past several years, numerous efficient…

We prove a general lower bound of quantum decision tree complexity in terms of some entropy notion. We regard the computation as a communication process in which the oracle and the computer exchange several rounds of messages, each round…

The problem of finding a local minimum of a black-box function is central for understanding local search as well as quantum adiabatic algorithms. For functions on the Boolean hypercube {0,1}^n, we show a lower bound of Omega(2^{n/4}/n) on…

We provide bounds on the efficiency of secure one-sided output two-party computation of arbitrary finite functions from trusted distributed randomness in the statistical case. From these results we derive bounds on the efficiency of…

Quantum capacities are fundamental quantities that are notoriously hard to compute and can exhibit surprising properties such as superadditivity. Thus, a vast amount of literature is devoted to finding tight and computable bounds on these…

We study Online Convex Optimization (OCO) with adversarial constraints, where an online algorithm must make sequential decisions to minimize both convex loss functions and cumulative constraint violations. We focus on a setting where the…

We describe new lower bounds for randomized communication complexity and query complexity which we call the partition bounds. They are expressed as the optimum value of linear programs. For communication complexity we show that the…

We present several quantum algorithms for performing nearest-neighbor learning. At the core of our algorithms are fast and coherent quantum methods for computing distance metrics such as the inner product and Euclidean distance. We prove…

The method is introduced for fast data processing by reducing the probability amplitudes of undesirable elements. The algorithm has a mathematical description and circuit implementation on a quantum processor. The idea is to make a quick…

Quantum optimization solvers typically rely on one-variable-to-one-qubit mapping. However, the low qubit count on current quantum computers is a major obstacle in competing against classical methods. Here, we develop a qubit-efficient…