Related papers: stateQIP = statePSPACE
Complexity theory typically focuses on the difficulty of solving computational problems using classical inputs and outputs, even with a quantum computer. In the quantum world, it is natural to apply a different notion of complexity, namely…
Whereas quantum complexity theory has traditionally been concerned with problems arising from classical complexity theory (such as computing boolean functions), it also makes sense to study the complexity of inherently quantum operations…
State transformation problems such as compressing quantum information or breaking quantum commitments are fundamental quantum tasks. However, their computational difficulty cannot easily be characterized using traditional complexity theory,…
The complexity class $PSPACE$ includes all computational problems that can be solved by a classical computer with polynomial memory. All $PSPACE$ problems are known to be solvable by a quantum computer too with polynomial memory and are,…
In our thesis, we try to shed more light onto the complexity of quantum complexity classes by refining the related part of the hierarchy. First, we review the basic concepts of quantum computing in general. Then, inspired by BQP, we define…
We begin by establishing structural results for several fundamental quantum complexity classes: p/mBQP, p/mQ(C)MA, $\text{p/mQSZK}_{\text{hv}}$, p/mQIP, p/mBQP/qpoly, p/mBQP/poly, and p/mPSPACE. This includes identifying complete problems,…
Testing the symmetries of quantum states and channels provides a way to assess their usefulness for different physical, computational, and communication tasks. Here, we establish several complexity-theoretic results that classify the…
We prove that the complexity class QIP, which consists of all problems having quantum interactive proof systems, is contained in PSPACE. This containment is proved by applying a parallelized form of the matrix multiplicative weights update…
The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous…
Quantum information and computation provide a fascinating twist on the notion of proofs in computational complexity theory. For instance, one may consider a quantum computational analogue of the complexity class \class{NP}, known as QMA, in…
This article surveys quantum computational complexity, with a focus on three fundamental notions: polynomial-time quantum computations, the efficient verification of quantum proofs, and quantum interactive proof systems. Properties of…
The complexity of a quantum state may be closely related to the usefulness of the state for quantum computation. We discuss this link using the tree size of a multiqubit state, a complexity measure that has two noticeable (and, so far,…
Perturbation theory is an important technique for reducing computational cost and providing physical insights in simulating quantum systems with classical computers. Here, we provide a quantum algorithm to obtain perturbative energies on…
Uhlmann's theorem is a central result in quantum information theory, which associates the closeness of two quantum states with that of their purifications. The theorem also well characterizes a fundamental task: how close a pure quantum…
The term "machine learning" especially refers to algorithms that derive mappings, i.e. intput/output transforms, by using numerical data that provide information about considered transforms. These transforms appear in many problems, related…
One of the key steps in quantum algorithms is to prepare an initial quantum superposition state with different kinds of features. These so-called state preparation algorithms are essential to the behavior of quantum algorithms, and…
We present a polynomial-time quantum algorithm making a single query (in superposition) to a classical oracle, such that for every state $|\psi\rangle$ there exists a choice of oracle that makes the algorithm construct an exponentially…
This paper considers the following problem. Two mixed-state quantum circuits Q and R are given, and the goal is to determine which of two possibilities holds: (i) Q and R act nearly identically on all possible quantum state inputs, or (ii)…
Complexity theory can be viewed as the study of the relationship between computation and applications, understood the former as complexity classes and the latter as problems. Completeness results are clearly central to that view. Many…
We give a polynomial time algorithm that, given copies of an unknown quantum state $\vert\psi\rangle=U\vert 0^n\rangle$ that is prepared by an unknown constant depth circuit $U$ on a finite-dimensional lattice, learns a constant depth…