Related papers: On the CNOT-complexity of CNOT-PHASE circuits
This paper presents novel methods for optimizing multi-controlled quantum gates, which naturally arise in high-level quantum programming. Our primary approach involves rewriting $U(2)$ gates as $SU(2)$ gates, utilizing one auxiliary qubit…
There are various gate sets that can be used to describe a quantum computation. A particularly popular gate set in the literature on quantum computing consists of arbitrary single-qubit gates and 2-qubit CNOT gates. A CNOT gate is however…
A Hadamard-free Clifford transformation is a circuit composed of quantum Phase (P), CZ, and CNOT gates. It is known that such a circuit can be written as a three-stage computation, -P-CZ-CNOT-, where each stage consists only of gates of the…
We investigate quantum circuits built from arbitrary single-qubit operations combined with programmable all-to-all multiqubit entangling gates that are native to, among other systems, trapped-ion quantum computing platforms. We report a…
With the successful demonstration of transversal CNOTs in many recent experiments, it is the right moment to examine its implications on one of the most critical parts of fault-tolerant computation -- magic state preparation. Using an…
From a geometric approach, we derive the minimum number of applications needed for an arbitrary Controlled-Unitary gate to construct a universal quantum circuit. A new analytic construction procedure is presented and shown to be either…
CNOT circuits are a common building block of general quantum circuits. The problem of synthesizing and optimizing such circuits has received a lot of attention in the quantum computing literature. This problem is especially challenging for…
CNOT gates are fundamental to quantum computing, as they facilitate entanglement, a crucial resource for quantum algorithms. Certain classes of quantum circuits are constructed exclusively from CNOT gates. Given their widespread use, it is…
We present a framework for the synthesis of phase polynomials that addresses both cases of full connectivity and partial connectivity for NISQ architectures. In most cases, our algorithms generate circuits with lower CNOT count and CNOT…
In quantum computation every unitary operation can be decomposed into quantum circuits-a series of single-qubit rotations and a single type entangling two-qubit gates, such as controlled-NOT (CNOT) gates. Two measures are important when…
We study the problem of finding the best approximate circuit that is the closest (in some pertinent metric) to a target circuit, and which satisfies a number of hardware constraints, like gate alphabet and connectivity. We look at the…
The work proposes an extension of the quantum circuit formalism where qubits (wires) are circular instead of linear. The left-to-right interpretation of a quantum circuit is replaced by a circular representation which allows to select the…
While mapping a quantum circuit to the physical layer one has to consider the numerous constraints imposed by the underlying hardware architecture. Connectivity of the physical qubits is one such constraint that restricts two-qubit…
Quantum circuit synthesis is the task of decomposing a given quantum operator into a sequence of elementary quantum gates. Since the finite target gate set cannot exactly implement any given operator, approximation is often necessary. Model…
Minimizing the use of CNOT gates in quantum state preparation is a crucial step in quantum compilation, as they introduce coupling constraints and more noise than single-qubit gates. Reducing the number of CNOT gates can lead to more…
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…
The conventional circuit paradigm, utilizing a limited number of gates to construct arbitrary quantum circuits, is hindered by significant noise overhead. For instance, the standard gate paradigm employs two CNOT gates for the partial…
In this note we present explicit canonical forms for all the elements in the two-qubit CNOT-Dihedral group, with minimal numbers of controlled-S (CS) and controlled-X (CX) gates, using the generating set of quantum gates [X, T, CX, CS]. We…
Controlled-NOT (CNOT) gates are commonly included in the standard gate set of quantum processors and provide an important way to entangle qubits. For fixed-frequency qubits using the cross-resonance entangling technique, using the…
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…