Related papers: On exact counting and quasi-quantum complexity
We study safety verification for multithreaded programs with recursive parallelism (i.e. unbounded thread creation and recursion) as well as unbounded integer variables. Since the threads in each program configuration are structured in a…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
The topical quantum computation paradigm is a transposition of the Turing machine into the quantum framework. Implementations based on this paradigm have limitations as to the number of: qubits, computation steps, efficient quantum…
We investigate the classical communication over quantum channels when assisted by no-signaling (NS) and positive-partial-transpose-preserving (PPT) codes, for which both the optimal success probability of a given transmission rate and the…
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 higher than classical efficiency exhibited by some quantum algorithms is here ascribed to their non-mechanistic character, which becomes evident by joining the notions of entanglement and quantum measurement. Measurement analogically…
Catalytic computing concerns space bounded computation which starts with memory full of data that have to be restored by the end of the computation. Lossy catalytic computing, defined by Gupta et al. (2024) and fully characterized by…
A key issue of current quantum advantage experiments is that their verification requires a full classical simulation of the ideal computation. This limits the regime in which the experiments can be verified to precisely the regime in which…
We introduce a quantum-like classical computational model, called affine computation, as a generalization of probabilistic computation. After giving the basics of affine computation, we define affine finite automata (AfA) and compare it…
Estimation of unknown qubit elementary gates and alignment of reference frames are formally the same problem. Using quantum states made out of $N$ qubits, we show that the theoretical precision limit for both problems, which behaves as…
We explore in the framework of Quantum Computation the notion of computability, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm that exploits the quantum adiabatic processes is considered…
In this paper, we prove that the numerical-semigroup-gap counting problem is #NP-complete as a main theorem. A numerical semigroup is an additive semigroup over the set of all nonnegative integers. A gap of a numerical semigroup is defined…
Motivated by results on generic-case complexity in group theory, we apply the ideas of effective Baire category and effective measure theory to study complexity classes of functions which are "fractionally computable" by a partial…
The emergence of variational quantum applications has led to the development of automatic differentiation techniques in quantum computing. Recently, Zhu et al. (PLDI 2020) have formulated differentiable quantum programming with bounded…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
In the final paper of the Graph Minors series N. Robertson and P. Seymour proved that graphs are well-quasi-ordered under the immersion ordering. A direct implication of this theorem is that each class of graphs that is closed under taking…
We consider the class of counting problems,i.e. functions in $\#$P, which are self reducible, and have easy decision version, i.e. for every input it is easy to decide if the value of the function $f(x)$ is zero. For example,…
We present authorized quantum computation, where only a user with a non-cloneable quantum authorization key can perform a unitary operation created by an authenticated programmer. The security of our authorized quantum computation is based…
Classical probabilistic models of (noisy) quantum systems are not only relevant for understanding the non-classical features of quantum mechanics, but they are also useful for determining the possible advantage of using quantum resources…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…