Related papers: Creating Boolean Functions for the Five-EPR-Pair, …
A Boolean function is a function that produces a Boolean value output by logical calculation of Boolean inputs. It plays key roles in programing algorithms and design of circuits. Minimization of Boolean function is able to optimize the…
We generalize the construction of quantum error-correcting codes from GF(4)-linear codes by Calderbank et al. to p^m-state systems. Then we show how to determine the error from a syndrome. Finally we discuss a systematic construction of…
We show how a straightforward Bayesian updating procedure allows one to detect and quantify entanglement from any finite set of measurement results. The measurements do not have to be tomographically complete, and may consist of POVMs…
Quantum computing offers significant speedups, but the large number of physical qubits required for quantum error correction introduces engineering challenges for a monolithic architecture. One solution is to distribute the logical quantum…
By using a new way to encode Boolean functions in a reversible gate, an algorithm is developed in quantum computing over Z_2, symbolized QC/2, (as opposed to QC over C) that needs only one function evaluation to solve the Grover Database…
Quantum error correction (QEC) is essential for quantum computers to perform useful algorithms, but large-scale fault-tolerant computation remains out of reach due to demanding requirements on operation fidelity and the number of…
The entanglement of formation gives a necessary and sufficient condition for the existence of a perfect quantum error correction procedure.
Quantum error detection has always been a fundamental challenge in a fault-tolerant quantum computer. Hence, it is of immense importance to detect and deal with arbitrary errors to efficiently perform quantum computation. Several error…
We construct a new class of quantum error-correcting codes for a bosonic mode which are advantageous for applications in quantum memories, communication, and scalable computation. These 'binomial quantum codes' are formed from a finite…
The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general…
We present several families of total boolean functions which have exact quantum query complexity which is a constant multiple (between 1/2 and 2/3) of their classical query complexity, and show that optimal quantum algorithms for these…
The ultimate goal of quantum error correction is to create logical qubits with very low error rates (e.g. 1e-12) and assemble them into large-scale quantum computers capable of performing many (e.g. billions) of logical gates on many (e.g.…
We compare quantum and classical machines designed for learning an N-bit Boolean function in order to address how a quantum system improves the machine learning behavior. The machines of the two types consist of the same number of…
We show that thresholds for fault-tolerant quantum computation are solely determined by the quality of single-system operations if one allows for d-dimensional systems with $8 \leq d \leq 32$. Each system serves to store one logical qubit…
Bell inequality violation is one of the most widely known manifestations of entanglement in quantum mechanics; indicating that experiments on physically separated quantum mechanical systems cannot be given a local realistic description.…
We present a protocol for generating multipartite quantum correlations across a quantum network with a continuous-variable architecture. An arbitrary number of users possess two-mode entangled states, keeping one mode while sending the…
Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing…
We achieve essentially the largest possible separation between quantum and classical query complexities. We do so using a property-testing problem called Forrelation, where one needs to decide whether one Boolean function is highly…
We study the properties of error correcting codes for noise models in the presence of asymmetries and/or correlations by means of the entanglement fidelity and the code entropy. First, we consider a dephasing Markovian memory channel and…
Given a relational specification between Boolean inputs and outputs, the goal of Boolean functional synthesis is to synthesize each output as a function of the inputs such that the specification is met. In this paper, we first show that…