Related papers: BQP and the Polynomial Hierarchy
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…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by being based on two…
The degree of a polynomial representing (or approximating) a function f is a lower bound for the number of quantum queries needed to compute f. This observation has been a source of many lower bounds on quantum algorithms. It has been an…
NP complete problem is one of the most challenging issues. The question of whether all problems in NP are also in P is generally considered one of the most important open questions in mathematics and theoretical computer science as it has…
We show, under natural assumptions for qubit systems, that measurement-based quantum computations (MBQCs) which compute a non-linear Boolean function with high probability are contextual. The class of contextual MBQCs includes an example…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by having it follow from…
A fundamental question in computer science is: Is it harder to solve $n$ instances independently than to solve them simultaneously? This question, known as the direct sum question or direct sum theorem, has been paid much attention in…
Quantum algorithms are a very promising field. However, creating and manipulating these kind of algorithms is a very complex task, specially for software engineers used to work at higher abstraction levels. The work presented here is part…
It is usually assumed that a quantum computation is performed by applying gates in a specific order. One can relax this assumption by allowing a control quantum system to switch the order in which the gates are applied. This provides a more…
This paper initiates the study of quantum computing within the constraints of using a polylogarithmic ($O(\log^k n), k\geq 1$) number of qubits and a polylogarithmic number of computation steps. The current research in the literature has…
A recent line of work has shown the unconditional advantage of constant-depth quantum computation, or $\mathsf{QNC^0}$, over $\mathsf{NC^0}$, $\mathsf{AC^0}$, and related models of classical computation. Problems exhibiting this advantage…
We consider non-local properties of quanternionic quantum mechanics, in which the complex numbers are replaced by the quaternions as the underlying algebra. Specifically, we show that it is possible to construct a non-local box. This allows…
In the near future, there will likely be special-purpose quantum computers with 40-50 high-quality qubits. This paper lays general theoretical foundations for how to use such devices to demonstrate "quantum supremacy": that is, a clear…
Can the computational complexity theory of computer science and mathematics say something new about unresolved problems in quantum physics? Particularly, can the P versus NP question in the computational complexity theory be a factor in the…
Recent work shows that quantum signal processing (QSP) and its multi-qubit lifted version, quantum singular value transformation (QSVT), unify and improve the presentation of most quantum algorithms. QSP/QSVT characterize the ability, by…
Conjunctive query (CQ) evaluation is NP-complete, but becomes tractable for fragments of bounded hypertreewidth. Approximating a hard CQ by a query from such a fragment can thus allow for an efficient approximate evaluation. While…
In this paper, we propose two new methods for solving Set Constraint Problems, as well as a potential polynomial solution for NP-Complete problems using quantum computation. While current methods of solving Set Constraint Problems focus on…
We propose a definition of QNC, the quantum analog of the efficient parallel class NC. We exhibit several useful gadgets and prove that various classes of circuits can be parallelized to logarithmic depth, including circuits for encoding…
Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g. in computation, communication and control. Fully random transformations require exponential time for either classical or quantum…
The recent proliferation of NISQ devices has made it imperative to understand their computational power. In this work, we define and study the complexity class $\textsf{NISQ} $, which is intended to encapsulate problems that can be…