Related papers: Complexity limitations on quantum computation
This paper considers the realizability of quantum gates from the perspective of information complexity. Since the gate is a physical device that must be controlled classically, it is subject to random error. We define the complexity of gate…
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 examine the computational complexity of testing and finding small plans in probabilistic planning domains with both flat and propositional representations. The complexity of plan evaluation and existence varies with the plan type sought;…
We initiate a study of the complexity of quantum field theories (QFTs) by proposing a measure of information contained in a QFT and its observables. We show that from minimal assertions, one is naturally led to measure complexity by two…
In this paper we study the complexity of quantum query algorithms computing the value of Boolean function and its relation to the degree of algebraic polynomial representing this function. We pay special attention to Boolean functions with…
The apparent impossibility of extending non-relativistic quantum mechanics to a relativistic quantum theory is shown to be due to the insufficient structural richness of the field of complex numbers over which quantum mechanics is built. A…
We consider the issue of computability at the most fundamental level of physical reality: the Planck scale. To this aim, we consider the theoretical model of a quantum computer on a non commutative space background, which is a computational…
In this paper we give a framework for describing how abstract systems can be used to compute if no randomness or error is involved. Using this we describe a class of classical "physical" computation systems whose computational capabilities…
Notions of circuit complexity and cost play a key role in quantum computing and simulation where they capture the (weighted) minimal number of gates that is required to implement a unitary. Similar notions also become increasingly prominent…
Quantum information science explores the frontier of highly complex quantum states, the "entanglement frontier." This study is motivated by the observation (widely believed but unproven) that classical systems cannot simulate highly…
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…
We study approximation of embeddings between finite dimensional L_p spaces in the quantum model of computation. For the quantum query complexity of this problem matching (up to logarithmic factors) upper and lower bounds are obtained. The…
What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only…
An effective formalism for quantum constrained systems is presented which allows manageable derivations of solutions and observables, including a treatment of physical reality conditions without requiring full knowledge of the physical…
The quantum world is fascinating. It presents a description of nature that defies our most rooted concepts about what reality is. For example, quantum objects possess \lq\lq spooky\rq\rq\ properties that allow them to be in multiple places…
Quantum computational supremacy arguments, which describe a way for a quantum computer to perform a task that cannot also be done by a classical computer, typically require some sort of computational assumption related to the limitations of…
In this note, we provide a unifying framework to investigate the computational complexity of classical spin models and give the full classification on spin models in terms of system dimensions, randomness, external magnetic fields and types…
The polynomial hierarchy plays a central role in classical complexity theory. Here, we define a quantum generalization of the polynomial hierarchy, and initiate its study. We show that not only are there natural complete problems for the…
Is the universe computable? If so, it may be much cheaper in terms of information requirements to compute all computable universes instead of just ours. I apply basic concepts of Kolmogorov complexity theory to the set of possible…
We study the computational difficulty of computing the ground state degeneracy and the density of states for local Hamiltonians. We show that the difficulty of both problems is exactly captured by a class which we call #BQP, which is the…