Related papers: Optimising quantum circuits is generally hard
We introduce a fault-tolerant construction to implement a composite quantum operation of four overlapping Toffoli gates. The same construction can produce two independent Toffoli gates. This result lowers resource overheads in designs for…
Parametrised quantum circuits contain phase gates whose phase is determined by a classical algorithm prior to running the circuit on a quantum device. Such circuits are used in variational algorithms like QAOA and VQE. In order for these…
Clifford circuits -- i.e. circuits composed of only CNOT, Hadamard, and $\pi/4$ phase gates -- play a central role in the study of quantum computation. However, their computational power is limited: a well-known result of Gottesman and…
We give a Clifford+T representation of the Toffoli gate of T-depth 1, using four ancillas. More generally, we describe a class of circuits whose T-depth can be reduced to 1 by using sufficiently many ancillas. We show that the cost of…
Optimization of circuits is an essential task for both quantum and classical computers to improve their efficiency. In contrast, classical logic optimization is known to be difficult, and a lot of heuristic approaches have been developed so…
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…
A decision diagram (DD) is a graph-like data structure for homomorphic compression of Boolean and pseudo-Boolean functions. Over the past decades, decision diagrams have been successfully applied to verification, linear algebra, stochastic…
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…
We study how much noise can be tolerated by a universal gate set before it loses its quantum-computational power. Specifically we look at circuits with perfect stabilizer operations in addition to imperfect non-stabilizer gates. We prove…
Optimal implementation of quantum gates is crucial for designing a quantum computer. We consider the matrix representation of an arbitrary multiqubit gate. By ordering the basis vectors using the Gray code, we construct the quantum circuit…
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…
Clique problem has a wide range of applications due to its pattern matching ability. There are various formulation of clique problem like $k$-clique problem, maximum clique problem, etc. The $k$-Clique problem, determines whether an…
The Clifford hierarchy is a nested sequence of sets of quantum gates critical to achieving fault-tolerant quantum computation. Diagonal gates of the Clifford hierarchy and 'nearly diagonal' semi-Clifford gates are particularly important:…
We investigate the amount of noise required to turn a universal quantum gate set into one that can be efficiently modelled classically. This question is useful for providing upper bounds on fault tolerant thresholds, and for understanding…
We perform optimal-control-theory calculations to determine the minimum number of two-qubit CNOT gates needed to perform quantum state preparation and unitary operator synthesis for few-qubit systems. By considering all possible gate…
Fault-tolerant quantum computation (FTQC) is essential to implement quantum algorithms in a noise-resilient way, and thus to enjoy advantages of quantum computers even with presence of noise. In FTQC, a quantum circuit is decomposed into…
Quantum circuits currently constitute a dominant model for quantum computation. Our work addresses the problem of constructing quantum circuits to implement an arbitrary given quantum computation, in the special case of two qubits. We…
Quantum computing has the potential to solve problems that are intractable for classical computers, with possible applications in areas such as drug discovery and high-energy physics. However, the practical implementation of quantum…
Quantum computation offers the potential to solve fundamental yet otherwise intractable problems across a range of active fields of research. Recently, universal quantum-logic gate sets - the building blocks for a quantum computer - have…
The Toffoli gate is a fundamental building block for quantum arithmetic and reversible logic, yet its efficient realization remains a major challenge in both near-term and fault-tolerant quantum architectures. Recent advances in dynamic…