Related papers: Quantum-Logic Synthesis of Hermitian Gates
The matrices that can be exactly represented by a circuit over the Toffoli-Hadamard gate set are the orthogonal matrices of the form $M/ \sqrt{2}{}^k$, where $M$ is an integer matrix and $k$ is a nonnegative integer. The exact synthesis…
Most quantum computing architectures to date natively support multi-valued logic, albeit being typically operated in a binary fashion. Multi-valued, or qudit, quantum processors have access to much richer forms of quantum entanglement,…
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…
Implementing polynomial functions of Hermitian matrices on quantum hardware is a foundational task in quantum computing, critical for accurate Hamiltonian simulation, quantum linear system solving, high-fidelity state preparation, machine…
Compiling quantum circuits to account for hardware restrictions is an essential part of the quantum computing stack. Circuit compilation allows us to adapt algorithm descriptions into a sequence of operations supported by real quantum…
Previous schemes of nonadiabatic holonomic quantum computation were focused mainly on realizing a universal set of elementary gates. Multiqubit controlled gates could be built by decomposing them into a series of the universal gates. In…
We describe a family of recursive methods for the synthesis of qubit permutations on quantum computers with limited qubit connectivity. Two objectives are of importance: circuit size and depth. In each case we combine a scalable heuristic…
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…
Dual quaternion matrices have various applications in robotic research and its spectral theory has been extensively studied in recent years. In this paper, we extend Jacobi method to compute all eigenpairs of dual quaternion Hermitian…
Current quantum devices have unutilized high-level quantum resources. More and more attention has been paid to the qudit quantum systems with larger than two dimensions to maximize the potential computing power of quantum computation. Then,…
Unitary operations are the building blocks of quantum programs. Our task is to design effcient or optimal implementations of these unitary operations by employing the intrinsic physical resources of a given n-qubit system. The most common…
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…
The primary objective of quantum circuit synthesis is to efficiently and accurately realize specific quantum algorithms or operations utilizing a predefined set of quantum gates, while also optimizing the circuit size. It holds a pivotal…
We present a synthesis framework to map logic networks into quantum circuits for quantum computing. The synthesis framework is based on LUT networks (lookup-table networks), which play a key role in conventional logic synthesis.…
Quantum circuit synthesis and compilation are critical components in the quantum computing stack, both for contemporary quantum systems, where efficient use of limited resources is essential, as well as for large-scale fault-tolerant…
The creation of composite quantum gates that implement quantum response functions $\hat{U}(\theta)$ dependent on some parameter of interest $\theta$ is often more of an art than a science. Through inspired design, a sequence of $L$…
A new method for compiling quantum algorithms is proposed and tested for a three qubit system. The proposed method is to decompose a a unitary matrix U, into a product of simpler U j via a neural network. These U j can then be decomposed…
Among the many proposals for the realization of a quantum computer, holonomic quantum computation (HQC) is distinguished from the rest in that it is geometrical in nature and thus expected to be robust against decoherence. Here we analyze…
Current quantum programs are mostly synthesized and compiled on the gate-level, where quantum circuits are composed of quantum gates. The gate-level workflow, however, introduces significant redundancy when quantum gates are eventually…
We propose a linear-size synthesis of the multi-controlled Toffoli gate on qudits with at most one borrowed ancilla. This one ancilla can even be saved when the qudit dimension is odd. Our synthesis leads to improvements in various quantum…