Related papers: Measurement-Driven Adaptive Low-Overhead Implement…
Reversible computation has been proposed as a future paradigm for energy efficient computation, but so far few implementations have been realised in practice. Quantum circuits, running on quantum computers, are one construct known to be…
Prior work of Beverland et al. has shown that any exact Clifford+$T$ implementation of the $n$-qubit Toffoli gate must use at least $n$ $T$ gates. Here we show how to get away with exponentially fewer $T$ gates, at the cost of incurring a…
In this paper we show that it is possible to adapt a qudit scheme for creating a controlled-Toffoli created by Ralph et al. [Phys. Rev. A 75 011213] to be applicable to qubits. While this scheme requires more gates than standard schemes for…
Quantum algorithms are a promising framework for unfolding the causal configurations of multiloop Feynman diagrams, which is equivalent to querying the \textit{directed acyclic graph} (DAG) configurations of undirected graphs in graph…
Controlled quantum gates play a crucial role in enabling quantum universal operations by facilitating interactions between qubits. Direct implementation of three-qubit gates simplifies the design of quantum circuits, thereby being conducive…
Quantum computation is conventionally performed using quantum operations acting on two-level quantum bits, or qubits. Qubits in modern quantum computers suffer from inevitable detrimental interactions with the environment that cause errors…
Verifying the correct functioning of quantum gates is a crucial step towards reliable quantum information processing, but it becomes an overwhelming challenge as the system size grows due to the dimensionality curse. Recent theoretical…
Lloyd et al. were first to demonstrate the promise of quantum algorithms for computing Betti numbers, a way to characterize topological features of data sets. Here, we propose, analyze, and optimize an improved quantum algorithm for…
We present a general method to construct fault-tolerant quantum logic gates with a simple primitive, which is an analog of quantum teleportation. The technique extends previous results based on traditional quantum teleportation (Gottesman…
Three-qubit quantum gates are key ingredients for quantum error correction and quantum information processing. We generate quantum-control procedures to design three types of three-qubit gates, namely Toffoli, Controlled-Not-Not and Fredkin…
Since an n-qubit circuit consisting of CNOT gates can have up to $\Omega(n^2/\log{n})$ CNOT gates, it is natural to expect that $\Omega(n^2/\log{n})$ Toffoli gates are needed to apply a controlled version of such a circuit. We show that the…
In this thesis, we study concepts in quantum computing using graphical languages, specifically using the ZX-calculus. The core of the research revolves around (graphical) stabilizer decompositions. The first major focus is on the…
Implementing quantum operations in the form of natural Hamiltonian dynamics is desirable, since they almost require no external control or feedback. In this work, we propose a NISQ-friendly quantum-classical hybrid approach to designing a…
Topological quantum computing promises intrinsic fault tolerance by encoding quantum information in non-Abelian anyons, where quantum gates are implemented via braiding. While braiding operations are robust against local perturbations, a…
Fault tolerance is widely regarded as indispensable for achieving scalable and reliable quantum computing. However, the spacetime overhead required for fault-tolerant quantum computating remains prohibitively large. A critical challenge…
We study the realization of a Toffoli gate with superconducting qubits in a circuit-QED setup using quantum-control methods. Starting with optimized piecewise-constant control fields acting on all qubits and typical strengths of XY-type…
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…
The progress in building quantum computers to execute quantum algorithms has recently been remarkable. Grover's search algorithm in a binary quantum system provides considerable speed-up over classical paradigm. Further, Grover's algorithm…
Algorithms for quantum information processing are usually decomposed into sequences of quantum gate operations, most often realized with single- and two- qubit gates[1]. While such operations constitute a universal set for quantum…
Quantum Error Correction (QEC) codes form the foundation of Fault-Tolerant Quantum Computing (FTQC) and predominantly use the Clifford+T gate set. Recently, Clifford operations have become the key performance bottleneck in implementing QEC.…