Related papers: Implementing the Grover Algorithm in Homomorphic E…
We study a reduced quantum circuit computation paradigm in which the only allowable gates either permute the computational basis states or else apply a "global Hadamard operation", i.e. apply a Hadamard operation to every qubit…
Universal quantum computation can be realised using both continuous-time and discrete-time quantum walks. We present a version based on single particle discrete-time quantum walk to realize multi-qubit computation tasks. The scalability of…
Transversality is a simple and effective method for implementing quantum computation fault-tolerantly. However, no quantum error-correcting code (QECC) can transversally implement a quantum universal gate set (Eastin and Knill, Phys. Rev.…
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…
Using the tensor product representation in the density matrix renormalization group, we show that a quantum circuit of Grover's algorithm, which has one-qubit unitary gates, generalized Toffoli gates, and projective measurements, can be…
We present a systematic construction of quantum circuits implementing Grover's database search algorithm for arbitrary number of targets. We introduce a new operator which flips the sign of the targets and evaluate its circuit complexity.…
It is well known that Grover's algorithm asymptotically transforms an equal superposition state into an eigenstate (of a given basis). Here, we demonstrate a verification algorithm based on weak measurement which can achieve the same…
A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…
Realizing a conceptual quantum algorithm on an actual physical device necessitates the algorithm's quantum circuit description to undergo certain transformations in order to adhere to all constraints imposed by the hardware. In this regard,…
Encryption schemes often derive their power from the properties of the underlying algebra on the symbols used. Inspired by group theoretic tools, we use the centralizer of a subgroup of operations to present a private-key quantum…
Quantum algorithms are still challenging to solve linear systems of equations on real devices. This challenge arises from the need for deep circuits and numerous ancilla qubits. We introduce the quantum conjugate gradient (QCG) method using…
This study introduces a superconducting quantum chip architecture designed to simultaneously preserve entanglement and readout fidelity, addressing one of the key trade-offs in the development of scalable quantum hardware. In conventional…
The Grover search algorithm is a pivotal advancement in quantum computing, promising a remarkable speedup over classical algorithms in searching unstructured large databases. Here, we report results for the implementation and…
In 2009, Gentry proposed the first Fully Homomorphic Encryption (FHE) scheme, an extremely powerful cryptographic primitive that enables to perform computations, i.e., to evaluate circuits, on encrypted data without decrypting them first.…
We analyze three different quantum search algorithms, the traditional Grover's algorithm, its continuous-time analogue by Hamiltonian evolution, and finally the quantum search by local adiabatic evolution. We show that they are closely…
Protecting the dynamics of coupled quantum systems from decoherence by the environment is a key challenge for solid-state quantum information processing. An idle qubit can be efficiently insulated from the outside world via dynamical…
Grover's quantum algorithm can find a marked item from an unstructured database faster than any classical algorithm, and hence it has been used for several applications such as cryptanalysis and optimization. When there exist multiple…
In this work, we develop a novel mathematical framework for universal digital quantum computation using algebraic probability theory. We rigorously define quantum circuits as finite sequences of elementary quantum gates and establish their…
We present recursive multiport schemes for implementing quantum Fourier transforms and the inversion step in Grover's algorithm on an integrated linear optics device. In particular, each scheme shows how to execute a quantum operation on…
Distributed quantum computation has garnered immense attention in the noisy intermediate-scale quantum (NISQ) era, where each computational node necessitates fewer qubits and quantum gates. In this paper, we focus on a generalized search…