Quantum Rep., Volume 6, Issue 4 (December 2024) – 6 articles

Quantum computing stands at the precipice of technological revolution, promising unprecedented computational capabilities to tackle some of humanity’s most complex problems. The field is highly collaborative and recent developments such as superconducting qubits with increased scaling, reduced error rates, and improved cryogenic infrastructure, trapped-ion qubits with high-fidelity gates and reduced control hardware complexity, and photonic qubits with exploring room-temperature quantum computing are some of the key developments pushing the field closer to demonstrating real-world applications. However, the path to realizing this promise is fraught with significant obstacles across several key platforms, including sensitivity to errors, decoherence, scalability, and the need for new materials and technologies. Through an exploration of various quantum systems, this paper highlights both the potential and the challenges of quantum computing and discusses the essential role of middleware, quantum hardware development, and the strategic investments required to propel the field forward. With a focus on overcoming technical hurdles through innovation and interdisciplinary research, this review underscores the transformative impact quantum computing could have across diverse sectors. Full article

The current developments in the theory of quantum static triplet correlations and their associated structures (real r-space and Fourier k-space) in monatomic fluids are reviewed. The main framework utilized is Feynman’s path integral formalism (PI), and the issues addressed cover quantum diffraction effects and zero-spin bosonic exchange. The structures are associated with the external weak fields that reveal their nature, and due attention is paid to the underlying pair-level structures. Without the pair, level one cannot fully grasp the triplet extensions in the hierarchical ladder of structures, as both the pair and the triplet structures are essential ingredients in the triplet response functions. Three general classes of PI structures do arise: centroid, total continuous linear response, and instantaneous. Use of functional differentiation techniques is widely made, and, as a bonus, this leads to the identification of an exact extension of the “classical isomorphism” when the centroid structures are considered. In this connection, the direct correlation functions, as borrowed from classical statistical mechanics, play a key role (either exact or approximate) in the corresponding quantum applications. Additionally, as an auxiliary framework, the traditional closure schemes for triplets are also discussed, owing to their potential usefulness for rationalizing PI triplet results. To illustrate some basic concepts, new numerical calculations (path integral Monte Carlo PIMC and closures) are reported. They are focused on the purely diffraction regime and deal with supercritical helium-3 and the quantum hard-sphere fluid. Full article

Grover’s search algorithm (GSA) offers quadratic speedup in searching unstructured databases but suffers from exponential circuit depth complexity. Here, we present two quantum circuits called HX and Ry layers for the searching problem. Remarkably, both circuits maintain a fixed circuit depth of two and one, respectively, irrespective of the number of qubits used. When the target element’s position index is known, we prove that either circuit, combined with a single multi-controlled X gate, effectively amplifies the target element’s probability to over 0.99 for any qubit number greater than seven. To search unknown databases, we use the depth-1 Ry layer as the ansatz in the Variational Quantum Search (VQS), whose efficacy is validated through numerical experiments on databases with up to 26 qubits. The VQS with the Ry layer exhibits an exponential advantage, in circuit depth, over the GSA for databases of up to 26 qubits. Full article

As wireless networks advance toward the Sixth Generation (6G), which will support highly heterogeneous scenarios and massive data traffic, conventional computing methods may struggle to meet the immense processing demands in a resource-efficient manner. This paper explores the potential of quantum computing (QC) to address these challenges, specifically by enhancing the efficiency of Maximum-Likelihood detection in Multiple-Input Multiple-Output (MIMO) Non-Orthogonal Multiple Access (NOMA) communication systems, an essential technology anticipated for 6G. The study proposes the use of the Quantum Approximate Optimization Algorithm (QAOA), a variational quantum algorithm known for providing quantum advantages in certain combinatorial optimization problems. While current quantum systems are not yet capable of managing millions of physical qubits or performing high-fidelity, long gate sequences, the results indicate that QAOA is a promising QC approach for radio signal processing tasks. This research provides valuable insights into the potential transformative impact of QC on future wireless networks. This sets the stage for discussions on practical implementation challenges, such as constrained problem sizes and sensitivity to noise, and opens pathways for future research aimed at fully harnessing the potential of QC for 6G and beyond. Full article

A novel solution to the quantum measurement problem is presented by using a new asymmetric equation that is complementary to the Schrödinger equation. Solved for the hydrogen atom, the new equation describes the temporal and spatial evolution of the wavefunction, and the latter is used to calculate the radial probability density for different measurements. The obtained results show that Born’s position measurement postulates naturally emerge from the theory and its first principles. Experimental verification of the theory and its predictions are also proposed. Full article

While the development of quantum computers promises a myriad of advantages over their classical counterparts, care must be taken when designing algorithms that substitute a classical technique with a potentially advantageous quantum method. The probabilistic nature of many quantum algorithms may result in new behavior that could negatively impact the performance of the larger algorithm. The purpose of this work is to preserve the advantages of applying quantum search methods for generalized pattern search algorithms (GPSs) without violating the convergence criteria. It is well known that quantum search methods are able to reduce the expected number of oracle calls needed for finding the solution to a search problem from $O\left(N\right)$ to $O\left(\sqrt{N}\right)$ However, the number of oracle calls needed to determine that no solution exists with certainty is exceedingly high and potentially infinite. In the case of GPS, this is a significant problem since overlooking a solution during an iteration will violate a needed assumption for convergence. Here, we overcome this problem by introducing the quantum improved point search (QIPS), a classical–quantum hybrid variant of the quantum search algorithm QSearch. QIPS retains the $O\left(\sqrt{N}\right)$ oracle query complexity of QSearch when a solution exists. However, it is able to determine when no solution exists, with certainty, using only $O\left(N\right)$ oracle calls. Full article