Related papers: Parameter-optimal unitary synthesis with flag deco…
A general scheme is presented to decompose a $d$-by-$d$ unitary matrix as the product of two-level unitary matrices with additional structure and prescribed determinants. In particular, the decomposition can be done by using two-level…
Despite rapid progress in the field, it is still challenging to discover new ways to take advantage of quantum computation: all quantum algorithms need to be designed by hand, and quantum mechanics is notoriously counterintuitive. In this…
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…
In this paper we consider circuit synthesis for n-wire linear reversible circuits using the C-NOT gate library. These circuits are an important class of reversible circuits with applications to quantum computation. Previous algorithms,…
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…
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…
Given an arbitrary $2^w \times 2^w$ unitary matrix $U$, a powerful matrix decomposition can be applied, leading to four different syntheses of a $w$-qubit quantum circuit performing the unitary transformation. The demonstration is based on…
Quantum optimal control plays a crucial role in the development of quantum technologies, particularly in the design and implementation of fast and accurate gates for quantum computing. Here, we present a method to synthesize gates using the…
As quantum processors grow in scale and reliability, the need for efficient quantum gate decomposition of circuits to a set of specific available gates, becomes ever more critical. The decomposition of a particular algorithm into a sequence…
Universal multiport interferometers (UMIs) have emerged as a key tool for performing arbitrary linear transformations on optical modes, enabling precise control over the state of light in essential applications of classical and quantum…
Recursive Cartan decompositions (CDs) provide a way to exactly factorize quantum circuits into smaller components, making them a central tool for unitary synthesis. Here we present a detailed overview of recursive CDs, elucidating their…
When the gate set has continuous parameters, synthesizing a unitary operator as a quantum circuit is always possible using exact methods, but finding minimal circuits efficiently remains a challenging problem. The landscape is very…
An algorithm is proposed to convert arbitrary unitary matrix to a sequence of $X$ gates and fully controlled $R_y, R_z$ and $R_1$ gates. This algorithm is used to generate Q# implementation for arbitrary unitary matrix. Some optimizations…
The design and optimization of quantum circuits is central to quantum computation. This paper presents new algorithms for compiling arbitrary 2^n x 2^n unitary matrices into efficient circuits of (n-1)-controlled single-qubit and…
In this paper we provide an explicit parameterization of arbitrary unitary transformation acting on n qubits, in terms of one and two qubit quantum gates. The construction is based on successive Cartan decompositions of the semi-simple Lie…
Flag manifolds encode nested sequences of subspaces and serve as powerful structures for various computer vision and machine learning applications. Despite their utility in tasks such as dimensionality reduction, motion averaging, and…
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…
We construct fast, structure-preserving iterations for computing the sign decomposition of a unitary matrix $A$ with no eigenvalues equal to $\pm i$. This decomposition factorizes $A$ as the product of an involutory matrix $S =…
We provide a simple framework for the synthesis of quantum circuits based on a numerical optimization algorithm. This algorithm is used in the context of the trapped-ions technology. We derive theoretical lower bounds for the number of…
We present quantum circuits with a brick wall structure using the optimal number of parameters and two-qubit gates to parametrize $SU(2^n)$, and provide evidence that these circuits are universal for $n\leq 5$. For this, we successfully…