Related papers: Buildings for Synthesis with Clifford+R
We present an exact synthesis algorithm for qutrit unitaries in $\mathcal{U}_{3^n}(\mathbb{Z}[1/3,e^{2\pi i/3}])$ over the Clifford$+T$ gate set with at most one ancilla. This extends the already known result of qutrit metaplectic gates…
We developed a general framework for synthesizing target gates by using a finite set of basic gates, which is a crucial step in quantum compilation. When approximating a gate in SU($n$), a naive brute-force search requires a computational…
We generalize an efficient exact synthesis algorithm for single-qubit unitaries over the Clifford+T gate set which was presented by Kliuchnikov, Maslov and Mosca. Their algorithm takes as input an exactly synthesizable single-qubit…
We describe a new method for approximating an arbitrary $n$ qubit unitary with precision $\varepsilon$ using a Clifford and T circuit with $O(4^{n}n(\log(1/\varepsilon)+n))$ gates. The method is based on rounding off a unitary to a unitary…
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…
Exact synthesis is a tool used in algorithms for approximating an arbitrary qubit unitary with a sequence of quantum gates from some finite set. These approximation algorithms find asymptotically optimal approximations in probabilistic…
The Clifford+T gate set is a topological generating set for PU(2), which has been well-studied from the perspective of quantum computation on a single qubit. The discovery that it generates a full S-arithmetic subgroup of PU(2) has led to a…
A popular universal gate set for quantum computing with qubits is Clifford+T, as this can be readily implemented on many fault-tolerant architectures. For qutrits, there is an equivalent T gate, that, like its qubit analogue, makes…
The problem of decomposing an arbitrary Clifford element into a sequence of Clifford gates is known as Clifford synthesis. Drawing inspiration from similarities between this and the famous Rubik's Cube problem, we develop a machine learning…
Since quantum computing is currently in the NISQ-Era, compilation strategies to reduce the number of gates executed on specific hardware are required. In this work, we utilize the concept of synthesis of a data structure called Clifford…
We present two deterministic algorithms to approximate single-qutrit gates. These algorithms utilize the Clifford + $\mathbf{R}$ group to find the best approximation of diagonal rotations. The first algorithm exhaustively searches over the…
In this paper, we show the equivalence of the set of unitaries computable by the circuits over the Clifford and T library and the set of unitaries over the ring $\mathbb{Z}[\frac{1}{\sqrt{2}},i]$, in the single-qubit case. We report an…
Resource-efficient and high-precision approximate synthesis of quantum circuits expressed in the Clifford+T gate set is vital for Fault-Tolerant quantum computing. Efficient optimal methods are known for single-qubit RZ unitaries, otherwise…
This paper presents a deep reinforcement learning approach for synthesizing unitaries into quantum circuits. Unitary synthesis aims to identify a quantum circuit that represents a given unitary while minimizing circuit depth, total gate…
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…
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…
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…
We tackle the problem of Clifford isometry compilation, i.e, how to synthesize a Clifford isometry into an executable quantum circuit. We propose a simple framework for synthesis that only exploits the elementary properties of the Clifford…
We present pygridsynth, an open-source Python library for ancilla-free approximate Clifford+$T$ synthesis that runs in $O(\log(1/\epsilon))$ for precision $\epsilon$. For $n=1, 2$ qubits, the library builds upon established efficient and…
Circuit synthesis is the task of decomposing a given logical functionality into a sequence of elementary gates. It is (depth-)optimal if it is impossible to achieve the desired functionality with even shorter circuits. Optimal synthesis is…