Related papers: The Harrow-Hassidim-Lloyd algorithm with qutrits
We introduce two variations of the quantum phase estimation algorithm: quantum shifted phase estimation and quantum punctured phase estimation. The shifted method employs a bit-string left shift to discard the most significant bit and focus…
The transition to the High-Luminosity Large Hadron Collider (HL-LHC) presents a computational challenge where particle reconstruction complexity may outpace classical computing resources. While quantum computing offers potential speedups,…
By using the quantum computing the properties of hypernuclei ${}^5_{\Lambda}$He, ${}^{\ 6}_{{\Lambda\Lambda}}$He and ${}^9_{\Lambda}$Be can be investigated within microscopic cluster model. Our approach combines quantum neural network (QNN)…
Following the celebrated quantum algorithm for solving linear equations (so-called HHL algorithm), Childs, Kothari and Somma [SIAM Journal on Computing, {\bf 46}: 1920, (2017)] provided an approach to solve a linear system of equations with…
Gaussian process (GP) is a powerful modeling method with applications in machine learning for various engineering and non-engineering fields. Despite numerous benefits of modeling using GPs, the computational complexity associated with GPs…
Under the nearing error-corrected era of quantum computing, it is necessary to understand the suitability of certain post-NISQ algorithms for practical problems. One of the most promising, applicable and yet difficult to implement in…
We present a classical enhancement to improve the accuracy of the Hybrid variant (Hybrid HHL) of the quantum algorithm for solving linear systems of equations proposed by Harrow, Hassidim, and Lloyd (HHL). We achieve this by using higher…
High-energy physics is facing increasingly computational challenges in real-time event reconstruction for the near-future high-luminosity era. Using the LHCb vertex detector as a use-case, we explore a new algorithm for particle track…
As quantum devices scale toward practical machine learning applications, the binary qubit paradigm faces expressivity and resource efficiency limitations. Multi-level quantum systems, or qudits, offer a promising alternative by harnessing a…
Recent hardware demonstrations and advances in circuit compilation have made quantum computing with higher-dimensional systems (qudits) on near-term devices an attractive possibility. Some problems have more natural or optimal encodings…
The quantum circuit model is the de-facto way of designing quantum algorithms. Yet any level of abstraction away from the underlying hardware incurs overhead. In the era of near-term, noisy, intermediate-scale quantum (NISQ) hardware with…
We reiterate the contribution made by Harrow, Hassidim, and Llyod to the quantum matrix equation solver with the emphasis on the algorithm description and the error analysis derivation details. Moreover, the behavior of the amplitudes of…
Harrow, Hassidim, and Lloyd showed that for a suitably specified $N \times N$ matrix $A$ and $N$-dimensional vector $\vec{b}$, there is a quantum algorithm that outputs a quantum state proportional to the solution of the linear system of…
The development of a universal fault-tolerant quantum computer that can solve efficiently various difficult computational problems is an outstanding challenge for science and technology. In this work, we propose a technique for an efficient…
In this work we investigate methods to improve the efficiency and scalability of quantum algorithms for quantum chemistry applications. We propose a transformation of the electronic structure Hamiltonian in the second quantization framework…
We construct a quantum algorithm that creates the Laughlin state for an arbitrary number of particles $n$ in the case of filling fraction one. This quantum circuit is efficient since it only uses $n(n-1)/2$ local qudit gates and its depth…
Quantum chemistry provides a target for quantum simulation of considerable scientific interest and industrial importance. The majority of algorithms to date have been based on a second-quantized representation of the electronic structure…
Quantum algorithms with a proven theoretical speedup over classical computation are rare. Among the most prominent is the Harrow-Hassidim-Lloyd (HHL) algorithm for solving sparse linear systems. Here, HHL is applied to encode melodic…
In the recent years, numerous research advancements have extended the limit of classical simulation of quantum algorithms. Although, most of the state-of-the-art classical simulators are only limited to binary quantum systems, which…
Robust quantum computation with d-level quantum systems (qudits) poses two requirements: fast, parallel quantum gates and high fidelity two-qudit gates. We first describe how to implement parallel single qudit operations. It is by now well…