Related papers: Assessing fault-tolerant quantum advantage for $k$…
Quantum computing, a prominent non-Von Neumann paradigm beyond Moore's law, can offer superpolynomial speedups for certain problems. Yet its advantages in efficiency for tasks like machine learning remain under investigation, and quantum…
We recast Grover's generalised search algorithm in a geometric language even when the states are not approximately orthogonal. We provide a possible search algorithm based on an arbitrary unitary transformation which can speed up the steps…
Grover's search algorithm can be applied to a wide range of problems; even problems not generally regarded as searching problems, can be reformulated to take advantage of quantum parallelism and entanglement, and lead to algorithms which…
The study of quantum computation has been motivated by the hope of finding efficient quantum algorithms for solving classically hard problems. In this context, quantum algorithms by local adiabatic evolution have been shown to solve an…
Rapid development in quantum computing leads to the appearance of several quantum applications. Quantum Fourier Transformation (QFT) sits at the heart of many of these applications. Existing work leverages SAT solver or heuristics to…
While there is strong evidence for advantages of quantum over classical computation, the repertoire of computational primitives with proven or conjectured quantum advantage remains limited. A big challenge of quantum algorithmic design is a…
In symmetric cryptanalysis, the model of superposition queries has led to surprising results, with many constructions being broken in polynomial time thanks to Simon's period-finding algorithm. But the practical implications of these…
An error avoiding quantum code is presented which is capable of stabilizing Grover's quantum search algorithm against a particular class of coherent errors. This error avoiding code consists of states only which are factorizable in the…
We study some extensions of Grover's quantum searching algorithm. First, we generalize the Grover iteration in the light of a concept called amplitude amplification. Then, we show that the quadratic speedup obtained by the quantum searching…
Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or compilation. This means that the number…
We investigate the issue of speed-up and the necessity of entanglement in Grover's quantum search algorithm. We find that in a pure state implementation of Grover's algorithm entanglement is present even though the initial and target states…
A central roadblock to analyzing quantum algorithms on quantum states is the lack of a comparable input model for classical algorithms. Inspired by recent work of the author [E. Tang, STOC'19], we introduce such a model, where we assume we…
Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian…
Boolean satisfiability (SAT) problem is of fundamental importance in computer science and many application domains. For Grover's algorithm, solving the SAT problem requires $\mathcal{O}(\sqrt{2^n})$ queries--where n denotes the number of…
A robust definition of quantum runtime is essential for assessing the performance of quantum algorithms and claims of quantum advantage. While for most classical hardware the total runtime is well approximated by computation plus a weakly…
Quantum algorithm design plays a crucial role in exploiting the computational advantage of quantum devices. Here we develop a deep-reinforcement-learning based approach for quantum adiabatic algorithm design. Our approach is generically…
Grover's search algorithm (GSA) is known to experience a loss of its quadratic speedup when exposed to quantum noise. In this study, we partially agree with this result and present our findings. First, we examine different typical…
Low-energy estimation and state preparation for general $k$-local Hamiltonians are fundamental challenges in quantum complexity theory. For constant relative accuracy, Buhrman et al. (PRL 2025) recently broke the natural Grover bound…
Grover's search algorithm is the optimal quantum algorithm that can search an unstructured database quadratically faster than any known classical algorithm. The role of entanglement and correlations in the search algorithm have been studied…
We give a quantum speedup for solving the canonical semidefinite programming relaxation for binary quadratic optimization. This class of relaxations for combinatorial optimization has so far eluded quantum speedups. Our methods combine…