相关论文: Counterexamples to Kalai's Conjecture C
I give a brief overview of fault-tolerant quantum computation, with an emphasis on recent work and open questions.
I discuss a variety of issues relating to near-future experiments demonstrating fault-tolerant quantum computation. I describe a family of fault-tolerant quantum circuits that can be performed with 5 qubits arranged on a ring with…
In this short note we present a family of counterexamples to the King's conjecture.
I will give an overview of what I see as some of the most important future directions in the theory of fault-tolerant quantum computation. In particular, I will give a brief summary of the major problems that need to be solved in fault…
Recently, it was realized that use of the properties of quantum mechanics might speed up certain computations dramatically. Interest in quantum computation has since been growing. One of the main difficulties of realizing quantum…
We give a counterexample of Morrison's cone conjecture for a strict Calabi-Yau threefold.
This paper proves the threshold result, which asserts that quantum computation can be made robust against errors and inaccuracies, when the error rate, $\eta$, is smaller than a constant threshold, $\eta_c$. The result holds for a very…
In this short note we report on results on a computational search for a counterexample to the strong coincidence conjecture. In particular, we discuss the method used so that further searches can be conducted.
We introduce a scheme for fault tolerantly dealing with losses (or other "leakage" errors) in cluster state computation that can tolerate up to 50% qubit loss. This is achieved passively using an adaptive strategy of measurement - no…
It has been known that quantum error correction via concatenated codes can be done with exponentially small failure rate if the error rate for physical qubits is below a certain accuracy threshold. Other, unconcatenated codes with their own…
We propose and discuss two conjectures on the nature of information leaks (decoherence) for quantum computers. These conjectures, if (or when) they hold, are damaging for quantum error-correction as required by fault-tolerant quantum…
The Quantum Computer Condition (QCC) provides a rigorous and completely general framework for carrying out analyses of questions pertaining to fault-tolerance in quantum computers. In this paper we apply the QCC to the problem of…
More than ten years ago the author described a parameter $K(\rho )$ for the complexity of $n$-qubit quantum state $\rho$ and raised the conjecture (referred to as "Conjecture C") that when this parameter is superpolynomial in $n$, the state…
In this paper we provide a basic introduction of the core ideas and theories surrounding fault-tolerant quantum computation. These concepts underly the theoretical framework of large-scale quantum computation and communications and are the…
I discuss how to perform fault-tolerant quantum computation with concatenated codes using local gates in small numbers of dimensions. I show that a threshold result still exists in three, two, or one dimensions when next-to-nearest-neighbor…
In this perspective article, we revisit and critically evaluate prevailing viewpoints on the capabilities and limitations of near-term quantum computing and its potential transition toward fully fault-tolerant quantum computing. We examine…
Suppose that we are given a quantum computer programmed ready to perform a computation if it is switched on. Counterfactual computation is a process by which the result of the computation may be learnt without actually running the computer.…
This paper describes a method used to construct infinitely many probable counterexamples of the abc conjecture over the rational integers.
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
We give counterexamples to Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients.