Related papers: Classical verification of quantum circuits contain…
We investigate the power of quantum computers when they are required to return an answer that is guaranteed to be correct after a time that is upper-bounded by a polynomial in the worst case. We show that a natural generalization of Simon's…
Quantum computers provide an opportunity to efficiently sample from probability distributions that include non-trivial interference effects between amplitudes. Using a simple process wherein all possible state histories can be specified by…
With the race to build large-scale quantum computers and efforts to exploit quantum algorithms for efficient problem solving in science and engineering disciplines, the requirement to have efficient and scalable verification methods are of…
Quantum computing promises exponential speed-ups for important simulation and optimization problems. It also poses new CAD problems that are similar to, but more challenging, than the related problems in classical (non-quantum) CAD, such as…
The Polynomial-Time Hierarchy ($\mathsf{PH}$) is a staple of classical complexity theory, with applications spanning randomized computation to circuit lower bounds to ''quantum advantage'' analyses for near-term quantum computers.…
We study the classical simulatability of commuting quantum circuits with n input qubits and O(log n) output qubits, where a quantum circuit is classically simulatable if its output probability distribution can be sampled up to an…
Quasiprobability representation is an important tool for analyzing a quantum system, such as a quantum state or a quantum circuit. In this work, we propose classical algorithms specialized for approximating outcome probabilities of a linear…
The classical limit of quantum mechanics is discussed for closed quantum systems in terms of observational aspects. Initially, the failure of the limit h->0 is explicitly demonstrated in a model of two quantum mechanically interacting…
Variational quantum circuits (VQCs) are a central component of many quantum machine learning algorithms, offering a hybrid quantum-classical framework that, under certain aspects, can be considered similar to classical deep neural networks.…
Quantum computing opens exciting opportunities for kernel-based machine learning methods, which have broad applications in data analysis. Recent works show that quantum computers can efficiently construct a model of a classifier by…
This paper furthers existing evidence that quantum computers are capable of computations beyond classical computers. Specifically, we strengthen the collapse of the polynomial hierarchy to the second level if: (i) Quantum computers with…
Motivated by the recent experimental demonstrations of quantum supremacy, proving the hardness of the output of random quantum circuits is an imperative near term goal. We prove under the complexity theoretical assumption of the…
The quantum permutation algorithm provides computational speed-up over classical algorithms in determining the parity of a given cyclic permutation. For its $n$-qubit implementations, the number of required quantum gates scales…
While quantum speed-up in solving certain decision problems by a fault-tolerant universal quantum computer has been promised, a timely research interest includes how far one can reduce the resource requirement to demonstrate a provable…
In the absence of any efficient classical schemes for verifying a universal quantum computer, the importance of limiting the required quantum resources for this task has been highlighted recently. Currently, most of efficient quantum…
It is one of the most fundamental objectives in quantum information science to understand the boundary between the computational power of classical and quantum computers. One possible avenue to explore this boundary is to identify classes…
In the quantum computation verification problem, a quantum server wants to convince a client that the output of evaluating a quantum circuit $C$ is some result that it claims. This problem is considered very important both theoretically and…
Equivalence checking of hybrid quantum circuits is of primary importance, given that quantum circuit transformations are omnipresent along the quantum compiler chain. While some approaches exist for automating this task, most focus on the…
Rapid development of quantum computing technology has led to a wide variety of sophisticated quantum devices. Benchmarking these systems becomes crucial for understanding their capabilities and paving the way for future advancements. The…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…