相关论文: Buildings for Synthesis with Clifford+R

Clifford gates play a role in the optimisation of Clifford+T circuits. Reducing the count and the depth of Clifford gates, as well as the optimal scheduling of T gates, influence the hardware and the time costs of executing quantum…

We study ancilla-free approximation of single-qubit unitaries $U\in {\rm SU}(2)$ by gate sequences over Clifford+$G$, where $G\in\{T,V\}$ or their generalization. Let $p$ denote the characteristic factor of the gate set (e.g., $p=2$ for…

We give a presentation by generators and relations of the group of 3-qubit Clifford+CS operators. The proof roughly consists of two parts: (1) applying the Reidemeister-Schreier theorem recursively to an earlier result of ours; and (2) the…

Stabilizer circuits play an important role in quantum error correction protocols, and will be vital for ensuring fault tolerance in future quantum hardware. While stabilizer circuits are defined on the Clifford generating set, {H, S, CX},…

In this paper, the problem of constructing an efficient quantum circuit for the implementation of an arbitrary quantum computation is addressed. To this end, a basic block based on the cosine-sine decomposition method is suggested which…

We investigate the construction and properties of Clifford algebras by a similar manner as our previous construction of the octonions, namely as a twisting of group algebras of Z_2^n by a cocycle. Our approach is more general than the usual…

The classification of real Clifford algebras in terms of matrix algebras is well--known. Here we consider the real Clifford algebra ${\mathcal Cl}(r,s)$ not as a matrix algebra, but as a Clifford module over itself. We show that ${\mathcal…

Conflict-free replicated data types (CRDTs) are a promising tool for designing scalable, coordination-free distributed systems. However, constructing correct CRDTs is difficult, posing a challenge for even seasoned developers. As a result,…

Quantum error-correcting codes can be used to protect qubits involved in quantum computation. This requires that logical operators acting on protected qubits be translated to physical operators (circuits) acting on physical quantum states.…

We present a complete proof synthesis method for the eight type systems of Barendregt's cube extended with $\eta$-conversion. Because these systems verify the proofs-as-objects paradigm, the proof synthesis method is a one level process…

We give a novel procedure for approximating general single-qubit unitaries from a finite universal gate set by reducing the problem to a novel magnitude approximation problem, achieving an immediate improvement in sequence length by a…

We investigate the problem of synthesizing T-depth optimal quantum circuits over the Clifford+T gate set. First we construct a special subset of T-depth 1 unitaries, such that it is possible to express the T-depth-optimal decomposition of…

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…

Given a semisimple group over a complete non-Archimedean field, it is well known that techniques from non-Archimedean analytic geometry provide an embedding of the corresponding Bruhat-Tits builidng into the analytic space associated to the…

Automated synthesis of reactive systems from specifications has been a topic of research for decades. Recently, a variety of approaches have been proposed to extend synthesis of reactive systems from proposi- tional specifications towards…

The Clifford$+T$ gate set is commonly used to perform universal quantum computation. In such setup the $T$ gate is typically much more expensive to implement in a fault-tolerant way than Clifford gates. To improve the feasibility of…

Synthesis of reversible logic circuits has gained great atten- tion during the last decade. Various synthesis techniques have been pro- posed, some generate optimal solutions (in gate count) and are termed as exact, while others are…

We propose an approach to optimally synthesize quantum circuits from non-permutative quantum gates such as Controlled-Square-Root-of-Not (i.e. Controlled-V). Our approach reduces the synthesis problem to multiple-valued optimization and…

Efficient synthesis of arbitrary quantum states and unitaries from a universal fault-tolerant gate-set e.g. Clifford+T is a key subroutine in quantum computation. As large quantum algorithms feature many qubits that encode coherent quantum…

The relationship between efficient quantum gate synthesis and control theory has been a topic of interest in the quantum control literature. Motivated by this work, we describe in the present article how the dynamic programming technique…