Related papers: Decomposing Quantum Generalized Toffoli with an Ar…

We introduce conditionally clean ancilla qubits, a new quantum resource, recently explored by [NZS24], that bridges the gap between traditional clean and dirty ancillae. Like dirty ancillae, they begin and end in an unknown state and can be…

Multi-controlled Toffoli gates are fundamental building blocks in quantum computation, with applications in quantum arithmetic, simulation, and search algorithms. In fault-tolerant architectures, their realization is constrained by the high…

The problem of finding efficient decompositions of multi-qubit gates is of importance for quantum computing, especially, in application to existing noisy intermediate-scale quantum devices, whose resources are substantially limited. Here we…

The decomposition for controlled-$ZX$ gate in [Phys. Rev. A, 87, 062318 (2013)] has a shallow circuit depth $8n-20$ with no ancilla. Here we modify this decomposition to decompose $n$-qubit Toffoli gate with only $2n-3$ additional…

An efficient implementation of the Toffoli gate is of conceptual importance for running various quantum algorithms, including Grover's search and Shor's integer factorization. However, direct implementation of the Toffoli gate either…

Physical implementation of scalable quantum architectures faces an immense challenge in form of fragile quantum states. To overcome it, quantum architectures with fault tolerance is desirable. This is achieved currently by using surface…

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…

The synthesis of quantum operators involves decomposing general quantum gates into the gate set supported by a given quantum device. Multi-controlled gates are essential components in this process. In this work, we present an improved…

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…

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…

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…

We present quantum networks for a n-qubit controlled gate C^{n-1}(U) which use a higher dimensional (qudit) ancilla as a catalyser. In its simplest form the network has only n two-particle gates (qubit-qudit) -- this is the minimum number…

We show a significant reduction of the number of quantum operations and the improvement of the circuit depth for the realization of the Toffoli gate by using qudits. This is done by establishing a general relation between the dimensionality…

Many quantum algorithms make use of ancilla, additional qubits used to store temporary information during computation, to reduce the total execution time. Quantum computers will be resource-constrained for years to come so reducing ancilla…

Quantum computation is traditionally expressed in terms of quantum bits, or qubits. In this work, we instead consider three-level qu$trits$. Past work with qutrits has demonstrated only constant factor improvements, owing to the $\log_2(3)$…

The progress in building quantum computers to execute quantum algorithms has recently been remarkable. Grover's search algorithm in a binary quantum system provides considerable speed-up over classical paradigm. Further, Grover's algorithm…

In this paper we show that it is possible to adapt a qudit scheme for creating a controlled-Toffoli created by Ralph et al. [Phys. Rev. A 75 011213] to be applicable to qubits. While this scheme requires more gates than standard schemes for…

We present reversible classical circuits for performing various arithmetic operations aided by dirty ancillae (i.e. extra qubits in an unknown state that must be restored before the circuit ends). We improve the number of clean qubits…

The Toffoli gate is a fundamental building block for quantum arithmetic and reversible logic, yet its efficient realization remains a major challenge in both near-term and fault-tolerant quantum architectures. Recent advances in dynamic…

Reversible single-target gates are a generalization of Toffoli gates which are a helpful formal representation for the description of synthesis algorithms but are too general for an actual implementation based on some technology. There is…