Related papers: Multi-qutrit exact synthesis
If a set $\mathbb{G}$ of quantum gates is countable, then the operators that can be exactly represented by a circuit over $\mathbb{G}$ form a strict subset of the collection of all unitary operators. When $\mathbb{G}$ is universal, one…
Compiling quantum circuits into Clifford+$T$ gates is a central task for fault-tolerant quantum computing using stabilizer codes. In the near term, $T$ gates will dominate the cost of fault tolerant implementations, and any reduction in the…
The quantum circuit synthesis problem bridges quantum algorithm design and quantum hardware implementation in the Noisy Intermediate-Scale Quantum (NISQ) era. In quantum circuit synthesis problems, diagonal unitary synthesis plays a crucial…
Phase gadgets have proved to be an indispensable tool for reasoning about ZX-diagrams, being used in optimisation and simulation of quantum circuits and the theory of measurement-based quantum computation. In this paper we study phase…
We tackle the problem of Clifford isometry compilation, i.e, how to synthesize a Clifford isometry into an executable quantum circuit. We propose a simple framework for synthesis that only exploits the elementary properties of the Clifford…
Qutrit (or ternary) structures arise naturally in many quantum systems, particularly in certain non-abelian anyon systems. We present efficient circuits for ternary reversible and quantum arithmetics. Our main result is the derivation of…
We give three new algorithms for efficient in-place estimation, without using ancilla qubits, of average fidelity of a quantum logic gate acting on a d-dimensional system using much fewer random bits than what was known so far. Previous…
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…
Our goal in this paper is to construct optimal topological generators for compact unitary Lie groups, extending the work of a letter of Sarnak and arXiv:1704.02106 on golden and super-golden gates to higher dimensions. To do so we consider…
While all quantum algorithms can be expressed in terms of single-qubit and two-qubit gates, more expressive gate sets can help reduce the algorithmic depth. This is important in the presence of gate errors, especially those due to…
The use of a few intermediate qutrits for efficient decomposition of 3-qubit unitary gates has been proposed, to obtain an exponential reduction in the depth of the decomposed circuit. An intermediate qutrit implies that a qubit is operated…
We consider the problem of the variational quantum circuit synthesis into a gate set consisting of the CNOT gate and arbitrary single-qubit (1q) gates with the primary target being the minimization of the CNOT count. First we note that…
Existing quantum compilers optimize quantum circuits by applying circuit transformations designed by experts. This approach requires significant manual effort to design and implement circuit transformations for different quantum devices,…
We present an asymptotically improved algorithm for implementing the Quantum Fourier Transform (QFT) in both the exact and approximate settings. Historically, the approximate QFT has been implemented in $\Theta(n \log n)$ gates, and the…
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…
In fault-tolerant quantum computing, errors in unitary gate synthesis is comparable with noise inherent in the gates themselves. While mixed synthesis can suppress such coherent errors quadratically, there is no clear understanding on its…
Current noisy intermediate-scale quantum (NISQ) devices can only execute small circuits with shallow depth, as they are still constrained by the presence of noise: quantum gates have error rates and quantum states are fragile due to…
From a geometric approach, we derive the minimum number of applications needed for an arbitrary Controlled-Unitary gate to construct a universal quantum circuit. A new analytic construction procedure is presented and shown to be either…
The ability to implement the Quantum Fourier Transform (QFT) efficiently on a quantum computer facilitates the advantages offered by a variety of fundamental quantum algorithms, such as those for integer factoring, computing discrete…
With recent advancements in quantum computing technology, optimizing quantum circuits and ensuring reliable quantum state preparation have become increasingly vital. Traditional methods often demand extensive expertise and manual…