Related papers: On encoded quantum gate generation by iterative Ly…
Quantum computing has the potential to improve our ability to solve certain optimization problems that are computationally difficult for classical computers, by offering new algorithmic approaches that may provide speedups under specific…
One of the challenges in quantum computing is the synthesis of unitary operators into quantum circuits with polylogarithmic gate complexity. Exact synthesis of generic unitaries requires an exponential number of gates in general. We propose…
Transversal gates play an important role in the theory of fault-tolerant quantum computation due to their simplicity and robustness to noise. By definition, transversal operators do not couple physical subsystems within the same code block.…
Recent research in generalizing quantum computation from 2-valued qudits to d-valued qudits has shown practical advantages for scaling up a quantum computer. A further generalization leads to quantum computing with hybrid qudits where two…
We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated…
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…
Scalable quantum computation in realistic devices requires that precise control can be implemented efficiently in the presence of decoherence and operational errors. We propose a general constructive procedure for designing robust unitary…
Quantum state preparation is a crucial process within numerous quantum algorithms, and the need for efficient initialization of quantum registers is ever increasing as demand for useful quantum computing grows. The problem arises as the…
Quantum mechanics offers a fundamentally unpredictable entropy source due to the intrinsic probabilistic nature of quantum measurements, making it attractive for secure random number generation. This paper explores the practicality of…
Quantum computation has attracted much attention, among other things, due to its potentialities to solve classical NP problems in polynomial time. For this reason, there has been a growing interest to build a quantum computer. One of the…
Two level quantum mechanical systems like spin 1/2 particles lend themselves as a natural qubit implementation. However, encoding a single qubit in several spins reduces the resources necessary for qubit control and can protect from…
We perform optimal-control-theory calculations to determine the minimum number of two-qubit CNOT gates needed to perform quantum state preparation and unitary operator synthesis for few-qubit systems. By considering all possible gate…
One of the largest obstacles to building a quantum computer is gate error, where the physical evolution of the state of a qubit or group of qubits during a gate operation does not match the intended unitary transformation. Gate error stems…
Flexible characterization techniques that identify and quantify experimental imperfections under realistic assumptions are crucial for the development of quantum computers. Gate set tomography is a characterization approach that…
We consider the Unitary Permutation problem which consists, given $n$ unitary gates $U_1, \ldots, U_n$ and a permutation $\sigma$ of $\{1,\ldots, n\}$, in applying the unitary gates in the order specified by $\sigma$, i.e. in performing…
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…
This pedagogical review presents the proof of the Solovay-Kitaev theorem in the form of an efficient classical algorithm for compiling an arbitrary single-qubit gate into a sequence of gates from a fixed and finite set. The algorithm can be…
Quantum process tomography (QPT) methods aim at identifying a given quantum process. The present paper focuses on the estimation of a unitary process. This class is of particular interest because quantum mechanics postulates that the…
Quantum computers are a revolutionary class of computational platforms with applications in combinatorial and global optimization, machine learning, and other domains involving computationally hard problems. While these machines typically…
A Lyapunov-based approach for the trajectory generation of an $N$-dimensional Schr{\"o}dinger equation in whole $\RR^N$ is proposed. For the case of a quantum particle in an $N$-dimensional decaying potential the convergence is precisely…