相关论文: Canonical forms for single-qutrit Clifford+T opera…

We study single-qutrit gates composed of Clifford and $T$ gates, using the qutrit version of the $T$ gate proposed by Howard and Vala. We propose a normal form for single-qutrit gates analogous to the Matsumoto-Amano normal form for qubits.…

We propose a normal form for single-qudit gates composed of Clifford and $T$-gates for qudits of odd prime dimension $p\geq 5$. We prove that any single-qudit Clifford+$T$ operator can be re-expressed in this normal form in polynomial time.…

Matsumoto and Amano (2008) showed that every single-qubit Clifford+T operator can be uniquely written of a particular form, which we call the Matsumoto-Amano normal form. In this mostly expository paper, we give a detailed and streamlined…

Given an arbitrary single-qubit operation, an important task is to efficiently decompose this operation into an (exact or approximate) sequence of fault-tolerant quantum operations. We derive a depth-optimal canonical form for single-qubit…

We present an algorithm, along with its implementation that finds T-optimal approximations of single-qubit Z-rotations using quantum circuits consisting of Clifford and T gates. Our algorithm is capable of handling errors in approximation…

We prove that a unitary matrix has an exact representation over the Clifford+T gate set with local ancillas if and only if its entries are in the ring Z[1/sqrt(2),i]. Moreover, we show that one ancilla always suffices. These facts were…

Kliuchnikov, Maslov, and Mosca proved in 2012 that a $2\times 2$ unitary matrix $V$ can be exactly represented by a single-qubit Clifford+$T$ circuit if and only if the entries of $V$ belong to the ring $\mathbb{Z}[1/\sqrt{2},i]$. Later…

IBM has made several quantum computers available to researchers around the world via cloud services. Two architectures with five qubits, one with 16, and one with 20 qubits are available to run experiments. The IBM architectures implement…

We present an algorithm that decomposes any $n$-qubit Clifford operator into a circuit consisting of three subcircuits containing only CNOT or CPHASE gates with layers of one-qubit gates before and after each of these subcircuits. As with…

We develop an angular momentum representation and implementation of the Clifford+T set of unitaries for qutrits. We show that local gates from this set can be realized by the sole use of suitable rotations and one-axis-twisting operations,…

We present new optimal and heuristic algorithms for exact synthesis of multi-qubit unitaries and isometries. For example, our algorithms find Clifford and T circuits for unitaries with entries in $\mathbb{Z}[i,1/\sqrt{2}]$. The optimal…

We consider quantum circuits composed of Clifford and T gates. In this context the T gate has a special status since it confers universal computation when added to the (classically simulable) Clifford gates. However it can be very expensive…

We study two-qubit circuits over the Clifford+CS gate set, which consists of the Clifford gates together with the controlled-phase gate CS=diag(1,1,1,i). The Clifford+CS gate set is universal for quantum computation and its elements can be…

We describe a new method for the decomposition of an arbitrary $n$ qubit operator with entries in $\mathbb{Z}[i,\frac{1}{\sqrt{2}}]$, i.e., of the form $(a+b\sqrt{2}+i(c+d\sqrt{2}))/{\sqrt{2}^{k}}$, into Clifford+$T$ operators where $n\le…

Exact synthesis provides unconditional optimality and canonical structure, but is often limited to small, carefully scoped regimes. We present an exact synthesis framework for two-qubit circuits over the Clifford+$T$ gate set that optimizes…

For a number of useful quantum circuits, qudit constructions have been found which reduce resource requirements compared to the best known or best possible qubit construction. However, many of the necessary qutrit gates in these…

Efficiently implementing Clifford circuits is crucial for quantum error correction and quantum algorithms. Linear reversible circuits, equivalent to circuits composed of CNOT gates, have important applications in classical computing. In…

The Clifford group plays a central role in quantum randomized benchmarking, quantum tomography, and error correction protocols. Here we study the structural properties of this group. We show that any Clifford operator can be uniquely…

In this work, we introduce a new circuit optimization technique to reduce the number of T gates in Clifford+T circuits by treating T gates conjugated by Clifford gates as $\frac{\pi}{4}$-rotations around Pauli operators. The tested…

Executing quantum algorithms on a quantum computer requires compilation to representations that conform to all restrictions imposed by the device. Due to devices' limited coherence times and gate fidelities, the compilation process has to…