Related papers: Minimum Toffoli depth for the multi-controlled Tof…
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…
Unitary operations are expressed in the quantum circuit model as a finite sequence of elementary gates, such as controlled-not gates and single qubit gates. We prove that the simplified Toffoli gate by Margolus, which coincides with the…
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…
Since an n-qubit circuit consisting of CNOT gates can have up to $\Omega(n^2/\log{n})$ CNOT gates, it is natural to expect that $\Omega(n^2/\log{n})$ Toffoli gates are needed to apply a controlled version of such a circuit. We show that the…
The circuit model of a quantum computer consists of sequences of gate operations between quantum bits (qubits), drawn from a universal family of discrete operations. The ability to execute parallel entangling quantum gates offers clear…
Any unitary operation in quantum information processing can be implemented via a sequence of simpler steps - quantum gates. However, actual implementation of a quantum gate is always imperfect and takes a finite time. Therefore, seeking for…
We introduce three compact graph states that can be used to perform a measurement-based Toffoli gate. Given a weighted graph of six, seven or eight qubits, we show that success probabilities of 1/4, 1/2 and 1 respectively can be achieved.…
Executing quantum algorithms over distributed quantum systems requires quantum circuits to be divided into sub-circuits which communicate via entanglement-based teleportation. Naively mapping circuits to qubits over multiple quantum…
The use of a few intermediate qutrits for efficient decomposition of 3-qubit unitary gates has been proposed, to obtain an exponential reduction in the depth of the decomposed circuit. An intermediate qutrit implies that a qubit is operated…
Universal quantum entangling gates are a crucial building block in the large-scale quantum computation and quantum communication, and it is an important task to find simple ways to implement them. Here an effective quantum circuit for the…
MQuantum algorithms of matrix operations are of great significance in many fields in science and technology. In this paper, by leveraging multi-qubit Toffoli gates and basic single-qubit operations, the quantum algorithms of matrix…
Distributed Quantum Computing (DQC) provides a means for scaling available quantum computation by interconnecting multiple quantum processor units (QPUs). A key challenge in this domain is efficiently allocating logical qubits from quantum…
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…
The construction of quantum computers is based on the synthesis of low-cost quantum circuits. The quantum circuit of any Boolean function expressed in a Positive Polarity Reed-Muller $PPRM$ expansion can be synthesized using…
We provide evidence that commonly held intuitions when designing quantum circuits can be misleading. In particular we show that: a) reducing the T-count can increase the total depth; b) it may be beneficial to trade CNOTs for measurements…
We propose a many-qubit network with cavity QED by encoding qubits in decoherence-free subspace, based on which we can implement many-logic-qubit conditional gates by means of cavity assisted interaction with single-photon pulses. Our…
Recent experimental advances have made it possible to implement logical multi-qubit transversal gates on surface codes in a multitude of platforms. A transversal controlled-NOT (tCNOT) gate on two surface codes introduces correlated errors…
Quantum teleportation~\cite{Bennett1993} is of both fundamental interest and great practical importance in quantum information science. To date, quantum teleportation has been implemented in various physical systems~\cite{Pirandola2015},…
Controlled operations are fundamental building blocks of quantum algorithms. Decomposing $n$-control-NOT gates ($C^n(X)$) into arbitrary single-qubit and CNOT gates, is a crucial but non-trivial task. This study introduces $C^n(X)$ circuits…
Building a quantum computer is a daunting challenge since it requires good control but also good isolation from the environment to minimize decoherence. It is therefore important to realize quantum gates efficiently, using as few operations…