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Efficient encoding of classical data into quantum state -- currently referred to as quantum encoding -- holds crucial significance in quantum computation. For finite-size databases and qubit registers, a common strategy of the quantum…
This paper presents the implementation of a quantum sequence alignment (QSA) algorithm on biological data in environments simulating noisy intermediate-scale quantum (NISQ) computers. The approach to quantum bioinformatics adapts the…
The study of classical algorithms is supported by an immense understructure, founded in logic, type, and category theory, that allows an algorithmist to reason about the sequential manipulation of data irrespective of a computation's…
Quantum error correction is necessary to perform large-scale quantum computation, but requires extremely large overheads in both space and time. High-rate quantum low-density-parity-check (qLDPC) codes promise a route to reduce qubit…
In this paper, we present a novel formulation of traditional sampling-based motion planners as database-oracle structures that can be solved via quantum search algorithms. We consider two complementary scenarios: for simpler sparse…
Quantum linear-system algorithms (QLSAs) have rigorous worst-case complexity guarantees, but their runtimes are often chosen from spectral information assumed in advance. What is largely lacking is an a posteriori progress flag: most QLSA…
Quantum Signal Processing (QSP), together with the quantum singular value transformation, is one of the central quantum algorithms due to its efficiency and generality in many fields including quantum simulation, quantum machine learning,…
As physical realizations of quantum computers move closer towards practical applications, the need for tools to analyze and verify quantum algorithms grows. Among the algorithms and data structures used to tackle such problems, decision…
Both discrete and continuous systems can be used to encode quantum information. Most quantum computation schemes propose encoding qubits in two-level systems, such as a two-level atom or an electron spin. Others exploit the use of an…
In contexts where relevant problems can easily attain configuration spaces of enormous sizes, solving Linear Differential Equations (LDEs) can become a hard achievement for classical computers; on the other hand, the rise of quantum…
Despite rapid advances in quantum hardware, noise remains a central obstacle to deploying quantum algorithms on near-term devices. In particular, random coherent errors that accumulate during circuit execution constitute a dominant and…
Quantum search algorithms offer a remarkable advantage of quadratic reduction in query complexity using quantum superposition principle. However, how an actual architecture may access and handle the database in a quantum superposed state…
Numerous quantum algorithms operate under the assumption that classical data has already been converted into quantum states, a process termed Quantum State Preparation (QSP). However, achieving precise QSP requires a circuit depth that…
Given the limitations of current hardware, the theoretical gains promised by quantum computing remain unrealized across practical applications. But the gap between theory and hardware is closing, assisted by developments in quantum…
Quantum computations are typically compiled into a circuit of basic quantum gates. Just like for classical circuits, a quantum compiler should optimize the quantum circuit, e.g. by minimizing the number of required gates. Optimizing quantum…
Semidefinite programming (SDP) is a fundamental convex optimization problem with wide-ranging applications. However, solving large-scale instances remains computationally challenging due to the high cost of solving linear systems and…
Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the…
We present a systematic pathway for solving differential equations within the quantum linear systems framework by combining block encoding with Quantum Singular Value Transformation (QSVT). The approach is demonstrated on a complex…
We provide a detailed estimate for the logical resource requirements of the quantum linear system algorithm (QLSA) [Phys. Rev. Lett. 103, 150502 (2009)] including the recently described elaborations [Phys. Rev. Lett. 110, 250504 (2013)].…
Quantum data loading plays a central role in quantum algorithms and quantum information processing. Many quantum algorithms hinge on the ability to prepare arbitrary superposition states as a subroutine, with claims of exponential speedups…