Related papers: A Note on Oracle Separations for BQP
It is a long-standing open question in quantum complexity theory whether the definition of $\textit{non-deterministic}$ quantum computation requires quantum witnesses $(\textsf{QMA})$ or if classical witnesses suffice $(\textsf{QCMA})$. We…
The Quantum Oracle Classification (QOC) problem is to classify a function, given only quantum black box access, into one of several classes without necessarily determining the entire function. Generally, QOC captures a very wide range of…
We already know that several problems like the inequivalence of P and EXP as well as the undecidability of the acceptance problem and halting problem relativize. However, relativization is a limited tool which cannot separate other…
We explore the computational implications of a superposition of spacetimes, a phenomenon hypothesized in quantum gravity theories. This was initiated by Shmueli (2024) where the author introduced the complexity class $\mathbf{BQP^{OI}}$…
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…
The complexity class $\exists\mathbb R$, standing for the complexity of deciding the existential first order theory of the reals as real closed field in the Turing model, has raised considerable interest in recent years. It is well known…
We construct a family of functions suitable for establishing lower bounds on the oracle complexity of first-order minimization of smooth strongly-convex functions. Based on this construction, we derive new lower bounds on the complexity of…
Much mathematical writing exists that is, explicitly or implicitly, based on set theory, often Zermelo-Fraenkel set theory (ZF) or one of its variants. In ZF, the domain of discourse contains only sets, and hence every mathematical object…
We say that a function is rare-case hard against a given class of algorithms (the adversary) if all algorithms in the class can compute the function only on an $o(1)$-fraction of instances of size $n$ for large enough $n$. Starting from any…
We consider the minimization problem of a sum of a number of functions having Lipshitz $p$-th order derivatives with different Lipschitz constants. In this case, to accelerate optimization, we propose a general framework allowing to obtain…
We investigate the dividing line between classical and quantum computational power in estimating properties of matrix functions. More precisely, we study the computational complexity of two primitive problems: given a function $f$ and a…
AWPP is a complexity class introduced by Fenner, Fortnow, Kurtz, and Li, which is defined using GapP functions. Although it is an important class as the best upperbound of BQP, its definition seems to be somehow artificial, and therefore it…
We construct a classical oracle relative to which $\mathsf{P} = \mathsf{NP}$ yet single-copy secure pseudorandom quantum states exist. In the language of Impagliazzo's five worlds, this is a construction of pseudorandom states in…
We construct a classical oracle proving that, in a relativized setting, the set of languages decidable by an efficient quantum verifier with a quantum witness (QMA) is strictly bigger than those decidable with access only to a classical…
Descriptive Complexity has been very successful in characterizing complexity classes of decision problems in terms of the properties definable in some logics. However, descriptive complexity for counting complexity classes, such as FP and…
We give new evidence that quantum circuits are substantially more powerful than classical circuits. We show, relative to a random oracle, that polynomial-size quantum circuits can sample distributions that subexponential-size classical…
In 1986, Saks and Wigderson conjectured that the largest separation between deterministic and zero-error randomized query complexity for a total boolean function is given by the function $f$ on $n=2^k$ bits defined by a complete binary tree…
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…
We close three open problems in the separation complexity of valid inequalities for the knapsack polytope. Specifically, we establish that the separation problems for extended cover inequalities, (1,k)-configuration inequalities, and weight…
We show that any quantum algorithm to decide whether a function f:[n]->[n] is a permutation or far from a permutation must make Omega(n^{1/3}/w) queries to f, even if the algorithm is given a w-qubit quantum witness in support of f being a…