Related papers: Fine-grained quantum advantage beyond double-logar…
A proof of quantumness is a protocol through which a classical machine can test whether a purportedly quantum device, with comparable time and memory resources, is performing a computation that is impossible for classical computers.…
Quantum finite automata (QFA) are basic computational devices that make binary decisions using quantum operations. They are known to be exponentially memory efficient compared to their classical counterparts. Here, we demonstrate an…
It is a widely believed, though unproven, conjecture that the capability of postselection increases the language recognition power of both probabilistic and quantum polynomial-time computers. It is also unknown whether polynomial-time…
We present a quantum algorithm which identifies with certainty a hidden subgroup of an arbitrary finite group G in only a polynomial (in log |G|) number of calls to the oracle. This is exponentially better than the best classical algorithm.…
We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…
We establish the first general connection between the design of quantum algorithms and circuit lower bounds. Specifically, let $\mathfrak{C}$ be a class of polynomial-size concepts, and suppose that $\mathfrak{C}$ can be PAC-learned with…
Quantum resources outperform classical ones for certain communication and computational tasks. Remarkably, in some cases, the quantum advantage cannot be improved using hypothetical postquantum resources. A class of tasks with this property…
The main purpose of this paper is to show that we can exploit the difference ($l_1$-norm and $l_2$-norm) in the probability calculation between quantum and probabilistic computations to claim the difference in their space efficiencies. It…
Quantum computing, a prominent non-Von Neumann paradigm beyond Moore's law, can offer superpolynomial speedups for certain problems. Yet its advantages in efficiency for tasks like machine learning remain under investigation, and quantum…
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…
The computation of \(\operatorname{tr}(AB)\) is essential in quantum science and artificial intelligence, yet classical methods for \( d \)-dimensional matrices \( A \) and \( B \) require \( O(d^2) \) complexity, which becomes infeasible…
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 give new bounds on the circuit complexity of the quantum Fourier transform (QFT). We give an upper bound of O(log n + log log (1/epsilon)) on the circuit depth for computing an approximation of the QFT with respect to the modulus 2^n…
Quantum theory promises computational speed-ups over classical approaches. The celebrated Gottesman-Knill Theorem implies that the full power of quantum computation resides in the specific resource of "magic" states -- the secret sauce to…
It has been known for almost three decades that many $\mathrm{NP}$-hard optimization problems can be solved in polynomial time when restricted to structures of constant treewidth. In this work we provide the first extension of such results…
Several classes of quantum circuits have been shown to provide a quantum computational advantage under certain assumptions. The study of ever more restricted classes of quantum circuits capable of quantum advantage is motivated by possible…
Polylogarithmic time delineates a relevant notion of feasibility on several classical computational models such as Boolean circuits or parallel random access machines. As far as the quantum paradigm is concerned, this notion yields the…
We give a quantum algorithm for evaluating a class of boolean formulas (such as NAND trees and 3-majority trees) on a restricted set of inputs. Due to the structure of the allowed inputs, our algorithm can evaluate a depth $n$ tree using…
Existing schemes for demonstrating quantum computational advantage are subject to various practical restrictions, including the hardness of verification and challenges in experimental implementation. Meanwhile, analog quantum simulators…
We study quantum algorithms for testing bipartiteness and expansion of bounded-degree graphs. We give quantum algorithms that solve these problems in time O(N^(1/3)), beating the Omega(sqrt(N)) classical lower bound. For testing expansion,…