Related papers: The simplified Toffoli gate implementation by Marg…
We propose a direct (non-recursive) algorithm for applying a rotation $R_{\theta^\ast}$, $\epsilon$-close to a desired rotation $R_\theta$, to a single qubit using the Clifford+Toffoli gate set. Our algorithm does not rely on repeatedly…
Two different algorithms are presented for generating a quantum circuit realization of a matrix representing a permutation on $2^n$ letters. All circuits involve $n$ qubits and only use multi--controlled Toffoli gates. The first algorithm…
Optimal implementation of quantum gates is crucial for designing a quantum computer. The necessary condition for optimal construction of a two-qubit unitary operation is obtained. It can be proved that the B gate is the unique gate that can…
Controlled and multi-controlled quantum gates, whose action on a target qubit depends on the state of multiple control qubits, represent a fundamental logical building block for complex quantum algorithms. We propose a scheme for realizing…
We analyze the nonlinear optical response of a six-level atomic system under a configuration of electromagnetically induced transparency. The giant fifth-order nonlinearity generated in such a system with a relatively large cross-phase…
Optimal construction of quantum operations is a fundamental problem in the realization of quantum computation. We here introduce a newly discovered quantum gate, B, that can implement any arbitrary two-qubit quantum operation with minimal…
Quantum algorithms are a promising framework for unfolding the causal configurations of multiloop Feynman diagrams, which is equivalent to querying the \textit{directed acyclic graph} (DAG) configurations of undirected graphs in graph…
The reversible implementation of classical functions accounts for the bulk of most known quantum algorithms. As a result, a number of reversible circuit constructions over the Clifford+$T$ gate set have been developed in recent years which…
In an ordinary quantum algorithm the gates are applied in a fixed order on the systems. The introduction of indefinite causal structures allows to relax this constraint and control the order of the gates with an additional quantum state. It…
We propose a one-step scheme to implement a multiqubit controlled phase gate of one qubit simultaneously controlling multiple qubits with three-level atoms at distant nodes in coupled cavity arrays. The selective qubit-qubit couplings are…
Recently, reversible circuit synthesis has been intensively studied. One of the problems that has not been solved for a long time was exact minimization of gate count (GC) in 4-bit circuits. Finally, last year a tool of practical usage for…
We consider the problem of carrying an initial Bloch vector to a final Bloch vector in a specified amount of time under the action of three control fields (a vector control field). We show that this control problem is solvable and therefore…
Qubits, which are quantum counterparts of classical bits, are used as basic information units for quantum information processing, whereas underlying physical information carriers, e.g. (artificial) atoms or ions, admit encoding of more…
Non-Gaussian quantum gates are essential components for optical quantum information processing. However, the efficient implementation of practically important multi-mode higher-order non-Gaussian gates has not been comprehensively studied.…
It has been known that quantum error correction via concatenated codes can be done with exponentially small failure rate if the error rate for physical qubits is below a certain accuracy threshold. Other, unconcatenated codes with their own…
Compilation and optimization of quantum circuits are critical components in the execution of algorithms on quantum computers. These components must successfully balance two competing priorities: minimizing the number of expensive resources,…
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,…
Quantum computers promise to solve certain problems exponentially faster than possible classically but are challenging to build because of their increased susceptibility to errors. Remarkably, however, it is possible to detect and correct…
We propose a new no-go theorem by proving the impossibility of constructing a deterministic quantum circuit that iterates a unitary oracle by calling it only once. Different schemes are provided to bypass this result and to approximately…
Qubitization is a modern approach to estimate Hamiltonian eigenvalues without simulating its time evolution. While in this way approximation errors are avoided, its resource and gate requirements are more extensive: qubitization requires…