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Classification is at the core of data-driven prediction and decision-making, representing a fundamental task in supervised machine learning. Recently, several quantum machine learning algorithms that use quantum kernels as a measure of…
Quantum amplitude amplification algorithm is an important and basic technique in quantum computing. In this paper, our goal is to study distributed quantum amplitude amplification algorithms, and the main contributions are: (1) A…
Ubiquitous in quantum computing is the step to encode data into a quantum state. This process is called quantum state preparation, and its complexity for non-structured data is exponential on the number of qubits. Several works address this…
There is increasing interest in quantum algorithms that are based on the imaginary-time evolution (ITE), a successful classical numerical approach to obtain ground states. However, most of the proposals so far require heavy post-processing…
Studying the computational complexity and designing fast algorithms for determining winners under voting rules are classical and fundamental questions in computational social choice. In this paper, we accelerate voting by leveraging quantum…
In quantum algorithms discovered so far for simulating scattering processes in quantum field theories, state preparation is the slowest step. We present a new algorithm for preparing particle states to use in simulation of Fermionic Quantum…
The initial state creation is a starting point of many quantum algorithms and usually is considered as a separate subroutine not included into the algorithm itself. There are many algorithms aimed on creation of special class of states. Our…
Phase estimation is a quantum algorithm for measuring the eigenvalues of a Hamiltonian. We propose and rigorously analyse a randomized phase estimation algorithm with two distinctive features. First, our algorithm has complexity independent…
The propagation of errors severely compromises the reliability of quantum computations. The quantum adiabatic algorithm is a physically motivated method to prepare ground states of classical and quantum Hamiltonians. Here, we analyze the…
A computation in adiabatic quantum computing is implemented by traversing a path of nondegenerate eigenstates of a continuous family of Hamiltonians. We introduce a method that traverses a discretized form of the path: At each step we apply…
Accurate state preparation is a critical bottleneck in many quantum algorithms, particularly those for ground state energy estimation. Even in fault-tolerant quantum computing, preparing a quantum state with sufficient overlap to the…
Quantum Phase Estimation (QPE), the quantum algorithm for estimating eigenvalues of a given Hermitian matrix and preparing its eigenvectors, is considered the most promising approach to finding the ground states and their energies of…
Variational quantum algorithms (VQAs) are prominent candidates for near-term quantum advantage but lack rigorous guarantees of convergence and generalization. By contrast, quantum phase estimation (QPE) provides provable performance under…
The unavoidable finite time intervals between the sequential operations needed for performing practical quantum computing can degrade the performance of quantum computers. During these delays, unwanted relative dynamical phases are produced…
When preparing a pure state with a quantum circuit, there is an unavoidable approximation error due to the compilation error in fault-tolerant implementation. A recently proposed approach called probabilistic state synthesis, where the…
Quantum phase estimation algorithm (PEA) is one of the most important algorithms in early studies of quantum computation. It is also a key for many other quantum algorithms, such as the quantum counting algorithm and the Shor's integer…
In this brief paper, we go through the theoretical steps of the spectral clustering on quantum computers by employing the phase estimation and the amplitude amplification algorithms. We discuss circuit designs for each step and show how to…
A fast implementation of the quantum imaginary time evolution (QITE) algorithm called Fast QITE is proposed. The algorithmic cost of QITE typically scales exponentially with the number of particles it nontrivially acts on in each Trotter…
The task of learning a quantum circuit to prepare a given mixed state is a fundamental quantum subroutine. We present a variational quantum algorithm (VQA) to learn mixed states which is suitable for near-term hardware. Our algorithm…
While Quantum phase estimation (QPE) is at the core of many quantum algorithms known to date, its physical implementation (algorithms based on quantum Fourier transform (QFT)) is highly constrained by the requirement of high-precision…