Related papers: Efficient Universal Quantum Compilation: An Invers…
A quantum circuit is generalized to a nonunitary one whose constituents are nonunitary gates operated by quantum measurement. It is shown that a specific type of one-qubit nonunitary gates, the controlled-NOT gate, as well as all one-qubit…
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 study a method of producing approximately diagonal 1-qubit gates. For each positive integer, the method provides a sequence of gates that are defined iteratively from a fixed diagonal gate and an arbitrary gate. These sequences are…
It was shown by M.A. Nielsen and I.L. Chuang 1997, that it is impossible to build strictly universal programmable quantum gate array, that could perform any unitary operation precisely and it was suggested to use probabilistic gate arrays…
Random quantum circuits are commonly viewed as hard to simulate classically. In some regimes this has been formally conjectured, and there had been no evidence against the more general possibility that for circuits with uniformly random…
Motivated by understanding the power of quantum computation with restricted number of qubits, we give two complete characterizations of unitary quantum space bounded computation. First we show that approximating an element of the inverse of…
Quantum computing with qudits, quantum systems with $d > 2$ levels, offers a powerful extension beyond qubits, expanding the computational possibilities of quantum systems, allowing the simplification of the implementation of several…
Fault-tolerant quantum computation is a technique that is necessary to build a scalable quantum computer from noisy physical building blocks. Key for the implementation of fault-tolerant computations is the ability to perform a universal…
Quantum computing can enable a variety of breakthroughs in research and industry in the future. Although some quantum algorithms already exist that show a theoretical speedup compared to the best known classical algorithms, the…
Consider a compact connected Lie group $G$ and the corresponding Lie algebra $\cal L$. Let $\{X_1,...,X_m\}$ be a set of generators for the Lie algebra $\cal L$. We prove that $G$ is uniformly finitely generated by $\{X_1,...,X_m\}$. This…
Constructing appropriate unitary matrix operators for new quantum algorithms and finding the minimum cost gate sequences for the implementation of these unitary operators is of fundamental importance in the field of quantum information and…
The Clifford$+T$ gate set is commonly used to perform universal quantum computation. In such setup the $T$ gate is typically much more expensive to implement in a fault-tolerant way than Clifford gates. To improve the feasibility of…
Quantum algorithms may be described by sequences of unitary transformations called quantum gates and measurements applied to the quantum register of n quantum bits, qubits. A collection of quantum gates is called universal if it can be used…
The quantum Fourier transform (QFT) is a fundamental primitive in quantum computation and quantum information. In this work, we generalize the QFT for finite groups to a QFT for finite-dimensional semisimple algebras, and give efficient…
Quantum compilation is the process of converting a target unitary operation into a trainable unitary represented by a quantum circuit. It has a wide range of applications, including gate optimization, quantum-assisted compiling, quantum…
In leading fault-tolerant quantum computing schemes, accurate transformation are obtained by a two-stage process. In a first stage, a discrete, universal set of fault-tolerant operations is obtained by error-correcting noisy transformations…
The most general structure (in matrix form) of a single-qubit gate is presented. Subsequently, used that to obtain a set of conditions for testing (a) whether a given 2-qubit gate is genuinely a 2-qubit gate, i.e., not decomposable into two…
We devise greedy heuristics tailored for synthesizing quantum circuits that implement a specified set of Pauli rotations. Our heuristics are designed to minimize either the count of entangling gates or the depth of entangling gates, and…
We show that if an efficient classical representation of the dynamics exists, optimal control problems on many-body quantum systems can be solved efficiently with finite precision. We show that the size of the space of parameters necessary…
The virtual Z gate has been established as an important tool for performing quantum gates on various platforms, including but not limited to superconducting systems. Many such platforms offer a limited set of calibrated gates and compile…