Related papers: Parallelizing quantum circuit synthesis
Using error correcting codes and fault tolerant techniques, it is possible, at least in theory, to produce logical qubits with significantly lower error rates than the underlying physical qubits. Suppose, however, that the gates that act on…
Faults are stochastic by nature while most man-made systems, and especially computers, work deterministically. This necessitates the linking of probability theory with mathematical logics, automata, and switching circuit theory. This paper…
Currently available quantum computing hardware platforms have limited 2-qubit connectivity among their addressable qubits. In order to run a generic quantum algorithm on such a platform, one has to transform the initial logical quantum…
We conduct a systematic study of quantum circuits composed of multiple-control $Z$-rotation (MCZR) gates as primitives, since they are widely-used components in quantum algorithms and also have attracted much experimental interest in recent…
Quantum walk serves as a versatile tool for universal quantum computing and algorithmic research. However, the implementation of discrete-time quantum walks (DTQWs) with superconducting circuits is still constrained by some limitations such…
We study two-qubit circuits over the Clifford+CS gate set, which consists of the Clifford gates together with the controlled-phase gate CS=diag(1,1,1,i). The Clifford+CS gate set is universal for quantum computation and its elements can be…
There are various gate sets that can be used to describe a quantum computation. A particularly popular gate set in the literature on quantum computing consists of arbitrary single-qubit gates and 2-qubit CNOT gates. A CNOT gate is however…
Quantum computers are expected to contribute more efficient and accurate ways of modeling economic processes. Quantum hardware is currently available at a relatively small scale, but effective algorithms are limited by the number of logic…
Unitary decomposition is a widely used method to map quantum algorithms to an arbitrary set of quantum gates. Efficient implementation of this decomposition allows for translation of bigger unitary gates into elementary quantum operations,…
Quantum walks are a promising framework for developing quantum algorithms and quantum simulations. They represent an important test case for the application of quantum computers. Here we present different forms of discrete-time quantum…
The purpose of unitary synthesis is to find a gate sequence that optimally approximates a target unitary transformation. A new synthesis approach, called probabilistic synthesis, has been introduced, and its superiority has been…
Quantum error correction is essential for achieving practical quantum computing but has a significant computational overhead. Among fault-tolerant (FT) gate operations, non-Clifford gates, such as $T$, are particularly expensive due to…
We propose two Clifford+$T$ synthesis algorithms that are optimal with respect to $T$-count. The first algorithm, called deterministic synthesis, approximates any single-qubit unitary by a single-qubit Clifford+$T$ circuit with the minimum…
We study how parallelism can speed up quantum simulation. A parallel quantum algorithm is proposed for simulating the dynamics of a large class of Hamiltonians with good sparse structures, called uniform-structured Hamiltonians, including…
Quantum Random Walks, which have drawn much attention over the past few decades for their distinctly non-classical behavior, is a promising subfield within Quantum Computing. Theoretical framework and applications for these walks have seen…
Circuit synthesis is the task of decomposing a given logical functionality into a sequence of elementary gates. It is (depth-)optimal if it is impossible to achieve the desired functionality with even shorter circuits. Optimal synthesis is…
Quantum computing is expected to become a foundational technology for solving problems that exceed the capabilities of classical systems. As quantum algorithms and hardware technologies continue to advance, the need for scalable…
Increasing quantum circuit fidelity requires an efficient instruction set to avoid errors from decoherence. The choice of a two-qubit (2Q) hardware basis gate depends on a quantum modulator's native Hamiltonian interactions and applied…
Quantum walks, both discrete and continuous, serve as fundamental tools in quantum information processing with diverse applications. This work introduces a hybrid quantum walk model that integrates the coin mechanism of discrete walks with…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…