arXiv subjects

Ciaran McGoldrick

Publications and source records attributed to Ciaran McGoldrick.

5 recordsLinked to original sources

arXiv2026

Exact and Optimal Recursive Quantum Search via Hilbert-Space Decomposition

Current approaches to quantum search fail to deeply exploit extant structure in the underlying Hilbert space. Decomposing the search by this structure empowers new strategies and formulations for quantum search and algorithm design. We present a new decomposition technique acting directly on this structure by recursively decomposing the Hilbert space and constructing the search operator from reflections over the resulting partition. When initial and target states factorise over this partition, dynamics reduce to a single rotation in a two-dimensional plane at each level, with angle given by a scalar recurrence. This recurrence avoids error accumulation from separately bounding success probabilities at each level, yielding an exact state description enabling treatment of the recursion as a whole. We obtain the target state deterministically and derive oracle and non-oracle costs independently of the search setting. For unstructured search, our approach attains the simultaneously optimal $Θ(\sqrt{N})$ oracle and non-oracle gate counts. For spatial search on $d$-dimension grids, it recovers the $O(\sqrt{N})$ time for $d\geq3$ and the $O\bigl(\sqrt{N}(\log N)^{3/2}\bigr)$ bound of Aaronson and Ambainis for $d=2$. The exact description of the recursion extends over our decomposition to new subdivision structures and provides a new approach for applying and analysing recursion in quantum algorithm design.

quant-ph↗

arXiv2026

Quantum Search without Global Diffusion

Quantum search is among the most important algorithms in quantum computing. At its core is quantum amplitude amplification, a technique that achieves a quadratic speedup over classical search by combining two global reflections: the oracle, which marks the target, and the diffusion operator, which reflects about the initial state. We show that this speedup can be preserved when the oracle is the only global operator, with all other operations acting locally on non-overlapping partitions of the search register. We present a recursive construction that, when the initial and target states both decompose as tensor products over these chosen partitions, admits an exact closed-form solution for the algorithm's dynamics. This is enabled by an intriguing degeneracy in the principal angles between successive reflections, which collapse to just two distinct values governed by a single recursively defined angle. Applied to unstructured search, a problem that naturally satisfies the tensor decomposition, the approach retains the $O(\sqrt{N})$ oracle complexity of Grover search when each partition contains at least $\log_2(\log_2 N)$ qubits. On an 18-qubit search problem, partitioning into two stages reduces the non-oracle circuit depth by as much as 51%-96% relative to Grover, requiring up to 9% additional oracle calls. For larger problem sizes this oracle overhead rapidly diminishes, and valuable depth reductions persist when the oracle circuit is substantially deeper than the diffusion operator. More broadly, these results show that a global diffusion operator is not necessary to achieve the quadratic speedup in quantum search, offering a new perspective on this foundational algorithm. Moreover, the scalar reduction at the heart of our analysis inspires and motivates new directions and innovations in quantum algorithm design and evaluation.

quant-ph↗

arXiv2025

Deterministic Quantum Search via Recursive Oracle Expansion

We introduce a novel deterministic quantum search algorithm that provides a practical alternative to conventional probabilistic search approaches. Our scheme eliminates the inherent uncertainty of quantum search without relying on arbitrary phase rotations, a key limitation of other deterministic methods. The algorithm achieves certainty by recursively expanding the base oracle so that it marks all states prefixed by the same two bits as the target, encompassing exactly one-quarter of the search space. This enables a step-by-step reduction of the superposition until the target state can be measured with certainty. The algorithm achieves deterministic success with a query complexity of $O(N^{\log_2(3)/2}) \approx O(N^{0.7925})$, falling between Grover's $O(\sqrt{N})$ scaling and the classical $O(N)$. Our approach relies exclusively on two-qubit nearest-neighbour diffusion operators, avoiding global diffusion entirely. We show that, despite the increased query complexity, this design reduces the total number of two-qubit gates required for diffusion by more than an order of magnitude for search spaces up to at least 18 qubits, with even greater advantages on hardware with limited qubit connectivity. The scheme's inherent determinism, reliance on simple nearest-neighbour, low-depth operations, and scalable recursive structure make it well-suited for hardware implementation. Additionally, we show that the algorithm naturally supports partial database search, enabling deterministic identification of selected target bits without requiring a full search, further broadening its applicability.

quant-ph↗

arXiv2018

XYZ Privacy

Future autonomous vehicles will generate, collect, aggregate and consume significant volumes of data as key gateway devices in emerging Internet of Things scenarios. While vehicles are widely accepted as one of the most challenging mobility contexts in which to achieve effective data communications, less attention has been paid to the privacy of data emerging from these vehicles. The quality and usability of such privatized data will lie at the heart of future safe and efficient transportation solutions. In this paper, we present the XYZ Privacy mechanism. XYZ Privacy is to our knowledge the first such mechanism that enables data creators to submit multiple contradictory responses to a query, whilst preserving utility measured as the absolute error from the actual original data. The functionalities are achieved in both a scalable and secure fashion. For instance, individual location data can be obfuscated while preserving utility, thereby enabling the scheme to transparently integrate with existing systems (e.g. Waze). A new cryptographic primitive Function Secret Sharing is used to achieve non-attributable writes and we show an order of magnitude improvement from the default implementation.

cs.CR↗

arXiv2016

Mobile Privacy-Preserving Crowdsourced Data Collection in the Smart City

Smart cities rely on dynamic and real-time data to enable smart urban applications such as intelligent transport and epidemics detection. However, the streaming of big data from IoT devices, especially from mobile platforms like pedestrians and cars, raises significant privacy concerns. Future autonomous vehicles will generate, collect and consume significant volumes of data to be utilized in delivering safe and efficient transportation solutions. The sensed data will, inherently, contain personally identifiable and attributable information - both external (other vehicles, environmental) and internal (driver, passengers, devices). The autonomous vehicles are connected to the infrastructure cloud (e.g., Amazon), the edge cloud, and also the mobile cloud (vehicle to vehicle). Clearly these different entities must co-operate and interoperate in a timely fashion when routing and transferring the highly dynamic data. In order to maximise the availability and utility of the sensed data, stakeholders must have confidence that the data they transmit, receive, aggregate and reason on is appropriately secured and protected throughout. There are many different metaphors for providing end-to-end security for data exchanges, but they commonly require a management and control sidechannel. This work proposes a scalable smart city privacy-preserving architecture named Authorized Analytics that enables each node (e.g. vehicle) to divulge (contextually) local privatised data. Authorized Analytics is shown to scale gracefully to IoT scope deployments.

cs.CR↗