Related papers: Complexity limitations on quantum computation
Consider the model of computation where we start with two halves of a $2n$-qubit maximally entangled state. We get to apply a universal quantum computation on one half, measure both halves at the end, and perform classical postprocessing.…
The complexity class NP is quintessential and ubiquitous in theoretical computer science. Two different approaches have been made to define "Quantum NP," the quantum analogue of NP: NQP by Adleman, DeMarrais, and Huang, and QMA by Knill,…
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…
The complexity of the quantum state of a multiparticle system and the maximum possible accuracy of its quantum description are connected by a relation similar to the coordinate-momentum uncertainty relation. The coefficient in this relation…
In a recent preprint by Deutsch et al. [1995] the authors suggest the possibility of polynomial approximability of arbitrary unitary operations on $n$ qubits by 2-qubit unitary operations. We address that comment by proving strong lower…
The Polynomial-Time Hierarchy ($\mathsf{PH}$) is a staple of classical complexity theory, with applications spanning randomized computation to circuit lower bounds to ''quantum advantage'' analyses for near-term quantum computers.…
By considering quantum computation as a communication process, we relate its efficiency to a communication capacity. This formalism allows us to rederive lower bounds on the complexity of search algorithms. It also enables us to link the…
This paper proves the polynomial equivalence of a broad class of definitions of quantum computational complexity. We study right-invariant metrics on the unitary group -- often called `complexity geometries' following the definition of…
In this tutorial, we will survey known results on the complexity of conjunctive query evaluation in different settings, ranging from Boolean queries over counting to more complex models like enumeration and direct access. A particular focus…
With a combination of the quantum repeater and the cluster state approaches, we show that efficient quantum computation can be constructed even if all the entangling quantum gates only succeed with an arbitrarily small probability $p$. The…
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…
The quantum version of communication complexity allows the two communicating parties to exchange qubits and/or to make use of prior entanglement (shared EPR-pairs). Some lower bound techniques are available for qubit communication…
Models of computation operating over the real numbers and computing a larger class of functions compared to the class of general recursive functions invariably introduce a non-finite element of infinite information encoded in an arbitrary…
By analyzing the key properties of black holes from the point of view of quantum information, we derive a model-independent picture of black hole quantum computing. It has been noticed that this picture exhibits striking similarities with…
Loop quantum cosmology applies techniques derived for a background independent quantization of general relativity to cosmological situations and draws conclusions for the very early universe. Direct implications for the singularity problem…
General relativity is unable to determine the topology of the Universe. We propose to apply quantum approach. Quantization of dynamics of a test particle is sensitive to the spacetime topology. Presented results for a particle in de Sitter…
We investigate unitary and state $t$-designs from a computational complexity perspective. First, we address the problems of computing frame potentials that characterize (approximate) $t$-designs. We present a quantum algorithm for computing…
In this paper we give an overview of the quantum computational complexity class QMA and a description of known QMA-complete problems to date. Such problems are believed to be difficult to solve, even with a quantum computer, but have the…
I study the class of problems efficiently solvable by a quantum computer, given the ability to "postselect" on the outcomes of measurements. I prove that this class coincides with a classical complexity class called PP, or Probabilistic…
We study the precise computational complexity of deciding satisfiability of first-order quantified formulas over the theory of fixed-size bit-vectors with binary-encoded bit-widths and constants. This problem is known to be in EXPSPACE and…