Related papers: Applying Grover's algorithm to AES: quantum resour…
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…
Quantum computers have the potential to break classical cryptographic systems by efficiently solving problems such as the elliptic curve discrete logarithm problem using Shor's algorithm. While resource estimates for factoring-based…
Quantum state preparation is a crucial process within numerous quantum algorithms, and the need for efficient initialization of quantum registers is ever increasing as demand for useful quantum computing grows. The problem arises as the…
We present a quantum algorithmic routine that extends the realm of Grover-based heuristics for tackling combinatorial optimization problems with arbitrary efficiently computable objective and constraint functions. Building on previously…
The state of the art of quantum circuits using the ripple-carry strategy for the addition and comparison of two n-bit numbers is presented, as well as optimizations in the Clifford+T gate set, both in terms of CNOT-depth and T-depth, or…
It has been established that quantum algorithms can solve several key cryptographic problems more efficiently than classical computers. As progress continues in the field of quantum computing it is important to understand the risks they…
This thesis deals with the problematics of the scalability of fault-tolerant quantum computing. This question is studied under the angle of estimating the resources needed to set up such computers. What we call a resource is, in principle,…
Fully homomorphic encryption is an encryption method with the property that any computation on the plaintext can be performed by a party having access to the ciphertext only. Here, we formally define and give schemes for quantum homomorphic…
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…
We show how to realize a general quantum circuit involving gates between arbitrary pairs of qubits by means of geometrically local quantum operations and efficient classical computation. We prove that circuit-level local stochastic noise…
Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…
This study presents a roadmap towards utilizing a single arbitrary gate for universal quantum computing. Since two decades ago, it has been widely accepted that almost any single arbitrary gate with qubit number $>2$ is universal. Utilizing…
Code-switching offers a route to universal, fault-tolerant quantum computation by circumventing the limitation implied by the Eastin-Knill theorem against a universal transversal gate set within a single quantum code. Here, we present a…
We study the resources required to achieve universal quantum computing via the gate sets that provide the fundamental instructions from which quantum algorithms are built. While single-gate universal sets are known, they rely on precisely…
We give quantum circuits that simulate an arbitrary two-qubit unitary operator up to global phase. For several quantum gate libraries we prove that gate counts are optimal in worst and average cases. Our lower and upper bounds compare…
Classical simulation of noisy quantum circuits is essential for understanding quantum computing experiments. It enables scalable error characterization, analysis of how noise impacts quantum algorithms, and optimized implementations of…
State of the art qubit systems are reaching the gate fidelities required for scalable quantum computation architectures. Further improvements in the fidelity of quantum gates demands characterization and benchmarking protocols that are…
In general, a quantum circuit is constructed with elementary gates, such as one-qubit gates and CNOT gates. It is possible, however, to speed up the execution time of a given circuit by merging those elementary gates together into larger…
The Quantum Skip Gate (QSG) is a unitary circuit primitive that coherently superposes the execution and omission of an expensive quantum subroutine based on the outcome of a cheaper preceding subroutine, without mid-circuit measurement or…
Building a network that is resilient to a component failure is vital. Our access to electricity and telecommunications or the internet of things all hinge on an uninterrupted service provided by a robust network. Calculating the network…