相关论文: Complexity limitations on quantum computation

A central problem in quantum computing is to identify computational tasks which can be solved substantially faster on a quantum computer than on any classical computer. By studying the hardest such tasks, known as BQP-complete problems, we…

Query complexity measures the amount of information an algorithm needs about a problem to compute a solution. On a quantum computer there are different realizations of a query and we will show that these are not always equivalent. Our…

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…

Quantum systems may contain underlying correlations which are inaccessible to computationally bounded observers. We capture this distinction through a framework that analyses bipartite states only using efficiently implementable quantum…

We study the computational complexity of certain integrable quantum theories in 1+1 dimensions. We formalize a model of quantum computation based on these theories. In this model, distinguishable particles start out with known momenta and…

We establish a connection between continuous-variable quantum computing and high-dimensional integration by showing that the outcome probabilities of continuous-variable instantaneous quantum polynomial (CV-IQP) circuits are given by…

Quantum computing involving physical systems with continuous degrees of freedom, such as the quantum states of light, has recently attracted significant interest. However, a well-defined quantum complexity theory for these bosonic…

This is a philosophical paper. It claims that there is a gap to be filled in the relationship between complexity theory (CT) and quantum theory (QT). This gap concerns two very distinct understandings of time. The paper provides the ground…

There's something really strange about quantum mechanics. It's not just that cats can be dead and alive at the same time, and that entanglement seems to violate the principle of locality; quantum mechanics seems to be what Aaronson calls…

The number of qubits used by a quantum algorithm will be a crucial computational resource for the foreseeable future. We show how to obtain the classical query complexity for continuous problems. We then establish a simple formula for a…

Whether the class QMA (Quantum Merlin Arthur) is equal to QMA1, or QMA with one-sided error, has been an open problem for years. This note helps to explain why the problem is difficult, by using ideas from real analysis to give a "quantum…

We show that universal quantum computation can be achieved in the standard pure-state circuit model while, at any time, the entanglement entropy of all bipartitions is small---even tending to zero with growing system size. The result is…

Although a quantum state requires exponentially many classical bits to describe, the laws of quantum mechanics impose severe restrictions on how that state can be accessed. This paper shows in three settings that quantum messages have only…

We examine the computational complexity of testing and finding small plans in probabilistic planning domains with succinct representations. We find that many problems of interest are complete for a variety of complexity classes: NP, co-NP,…

An intense effort is being made today to build a quantum computer. Instead of presenting what has been achieved, I invoke here analogies from the history of science in an attempt to glimpse what the future might hold. Quantum computing is…

More than a speculative technology, quantum computing seems to challenge our most basic intuitions about how the physical world should behave. In this thesis I show that, while some intuitions from classical computer science must be…

We will find a lower bound on the recognition complexity of the theories that are nontrivial relative to some equivalence relation (this relation may be equality), namely, each of these theories is consistent with the formula, whose sense…

Most continuous mathematical formulations arising in science and engineering can only be solved numerically and therefore approximately. We shall always assume that we're dealing with a numerical approximation to the solution. There are two…

Complexity theory as practiced by physicists and computational complexity theory as practiced by computer scientists both characterize how difficult it is to solve complex problems. Here it is shown that the parameters of a specific model…

Algorithms with unitary oracles can be nested, which makes them extremely versatile. An example is the phase estimation algorithm used in many candidate algorithms for quantum speed-up. The search for new quantum algorithms benefits from…