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Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…
We present a variational algorithm for fault tolerant quantum computing to solve a system of linear equations which directly maximises the parameters of the target fidelity. This so-called measurement test algorithm can be applied to any…
Grover's unstructured search algorithm is one of the best examples to date for the superiority of quantum algorithms over classical ones. Its applicability, however, has been questioned by many due to its oracular nature. We propose a…
Scalable quantum technologies will present challenges for characterizing and tuning quantum devices. This is a time-consuming activity, and as the size of quantum systems increases, this task will become intractable without the aid of…
The hybrid quantum-classical learning scheme provides a prominent way to achieve quantum advantages on near-term quantum devices. A concrete example towards this goal is the quantum neural network (QNN), which has been developed to…
In quantum computing, knowing the symmetries a given system or state obeys or disobeys is often useful. For example, Hamiltonian symmetries may limit allowed state transitions or simplify learning parameters in machine learning…
A broad class of hybrid quantum-classical algorithms known as "variational algorithms" have been proposed in the context of quantum simulation, machine learning, and combinatorial optimization as a means of potentially achieving a quantum…
The Grover quantum search algorithm is generalized to deal with an arbitrary mixed initial state. The probability to measure a marked state as a function of time is calculated, and found to depend strongly on the specific initial state. The…
Finding the optimal solution to a complex optimization problem is of great importance in practically all fields of science, technology, technical design and econometrics. We demonstrate that a modified Grover's quantum algorithm can be…
Symmetries in a Hamiltonian play an important role in quantum physics because they correspond directly with conserved quantities of the related system. In this paper, we propose quantum algorithms capable of testing whether a Hamiltonian…
Motivated by the need to uncover some underlying mathematical structure of optimal quantum computation, we carry out a systematic analysis of a wide variety of quantum algorithms from the majorization theory point of view. We conclude that…
Grover's quantum search algorithm provides a quadratic speedup over the classical one. The computational complexity is based on the number of queries to the oracle. However, depth is a more modern metric for noisy intermediate-scale quantum…
It is known that any quantum algorithm for Graph Isomorphism that works within the framework of the hidden subgroup problem (HSP) must perform highly entangled measurements across Omega(n log n) coset states. One of the only known models…
We assess the potential of quantum computing to accelerate computation of central tasks in genomics, focusing on often-neglected theoretical limitations. We discuss state-of-the-art challenges of quantum search, optimization, and machine…
The dual tasks of quantum Hamiltonian learning and quantum Gibbs sampling are relevant to many important problems in physics and chemistry. In the low temperature regime, algorithms for these tasks often suffer from intractabilities, for…
Quantum algorithm, as compared to classical algorithm, plays a notable role in solving linear systems of equations with an exponential speedup. Here, we demonstrate a method for solving a particular system of equations by using the concept…
Recent studies have been spurred on by the promise of advanced quantum computing technology, which has led to the development of quantum computer simulations on classical hardware. Grover's quantum search algorithm is one of the well-known…
Gaussian building blocks are essential for photonic quantum information processing, and universality can be practically achieved by equipping Gaussian circuits with adaptive measurement and feedforward. The number of adaptive steps then…
Evolution of entanglement with the proceeding of quantum algorithms affects the outcome of the algorithm. Particularly, the performance of Grover's search algorithm gets worsened if the initial state of the algorithm is an entangled one.…
For any symmetric key cryptosystem with $n$-bit secret key, the key can be recovered in $O(2^{n/2})$ exploiting Grover search algorithm, resulting in the effective key length to be half. In this direction, subsequent work has been done on…