Related papers: Quantum circuits of T-depth one
While Clifford operations are relatively easy to implement in fault-tolerant quantum computers,continuous rotation gates remain a significant bottleneck in typical quantum algorithms. In this work, we ask the question: "What is the most…
Quantum magic is a necessary resource for quantum computers to be not efficiently simulable by classical computers. Previous results have linked the amount of quantum magic, characterized by the number of $T$ gates or stabilizer rank, to…
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…
A number of quantum algorithms have been performed on small quantum computers; these include Shor's prime factorization algorithm, error correction, Grover's search algorithm and a number of analog and digital quantum simulations. Because…
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 two Clifford+$T$ synthesis algorithms that are optimal with respect to $T$-count. The first algorithm, called deterministic synthesis, approximates any single-qubit unitary by a single-qubit Clifford+$T$ circuit with the minimum…
We present numerical results which show how two-bit logic gates can be used in the design of a quantum computer. We show that the Toffoli gate, which is a universal gate for all classical reversible computation, can be implemented using a…
Quantum circuits are time dependent diagrams describing the process of quantum computation. Usually, a quantum algorithm must be mapped into a quantum circuit. Optimal synthesis of quantum circuits is intractable and heuristic methods must…
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…
Multi-controlled gates are fundamental components in the design of quantum algorithms, where efficient decompositions of these operators can enhance algorithm performance. The best asymptotic decomposition of an n-controlled X gate with one…
Reducing the number of non-Clifford quantum gates present in a circuit is an important task for efficiently implementing quantum computations, especially in the fault-tolerant regime. We present a new method for reducing the number of…
Quantum circuit complexity quantifies the minimal number of gates needed to realize a unitary transformation and plays a central role in quantum computation. In this work, we investigate the complexity of quantum circuits through coherence…
Ouyang et al. proposed an $(n,n)$ threshold quantum secret sharing scheme, where the number of participants is limited to $n=4k+1,k\in Z^+$, and the security evaluation of the scheme was carried out accordingly. In this paper, we propose an…
A cost-effective n-bit Toffoli gate is proposed to be realized (or transpiled) based on the layouts (linear, T-like, and I-like) and the number of n physical qubits for IBM quantum computers. This proposed gate is termed the "layout-aware…
We show that the quantum parity gate on $n > 3$ qubits cannot be cleanly simulated by a quantum circuit with two layers of arbitrary C-SIGN gates of any arity and arbitrary 1-qubit unitary gates, regardless of the number of allowed ancilla…
Uniformly controlled one-qubit gates are quantum gates which can be represented as direct sums of two-dimensional unitary operators acting on a single qubit. We present a quantum gate array which implements any n-qubit gate of this type…
Let $n\geq 8$ be divisible by 4. The Clifford-cyclotomic gate set $\mathcal{G}_n$ is the universal gate set obtained by extending the Clifford gates with the $z$-rotation $T_n = \mathrm{diag}(1,\zeta_n)$, where $\zeta_n$ is a primitive…
Quantum circuits for basic mathematical functions such as the square root are required to implement scientific computing algorithms on quantum computers. Quantum circuits that are based on Clifford+T gates can easily be made fault tolerant…
We present an algorithm for computing depth-optimal decompositions of logical operations, leveraging a meet-in-the-middle technique to provide a significant speed-up over simple brute force algorithms. As an illustration of our method we…
In circuit-based quantum computing, the available gate set typically consists of single-qubit gates acting on each individual qubit and at least one entangling gate between pairs of qubits. In certain physical architectures, however, some…