Related papers: Optimal polynomial based quantum eigenstate filter…
We consider the problem of minimum-error quantum state discrimination for single-qubit mixed states. We present a method which uses the Helstrom conditions constructively and analytically; this algebraic approach is complementary to…
Numerous quantum algorithms operate under the assumption that classical data has already been converted into quantum states, a process termed Quantum State Preparation (QSP). However, achieving precise QSP requires a circuit depth that…
Quantum state filtering is a variant of the unambiguous state discrimination problem: the states are grouped in sets and we want to determine to which particular set a given input state belongs.The simplest case, when the N given states are…
Quantum machine learning seeks a computational advantage in data processing by evaluating functions of quantum states, such as their similarity, that can be classically intractable to compute. For quantum advantage to be possible, however,…
Quantum annealing and D-Wave quantum annealer attracted considerable attention for their ability to solve combinatorial optimization problems. In order to solve other type of optimization problems, it is necessary to apply certain kinds of…
A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems. For this task, there is a well-studied quantum algorithm that performs quantum phase estimation on an initial trial state that…
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…
Linear system solvers are widely used in scientific computing, with the primary goal of solving linear system problems. Classical iterative algorithms typically rely on the conjugate gradient method. The rise of quantum computing has…
Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing…
We propose a general-purpose quantum algorithm for preparing ground states of quantum Hamiltonians from a given trial state. The algorithm is based on techniques recently developed in the context of solving the quantum linear systems…
Quantum state preparation (QSP) is a key component in many quantum algorithms. In particular, the problem of sparse QSP (SQSP) $\unicode{x2013}$ the task of preparing the states with only a small number of non-zero amplitudes…
Quantum signal processing (QSP) is a powerful toolbox for the design of quantum algorithms and can lead to asymptotically optimal computational costs. Its realization on noisy quantum computers without fault tolerance, however, is…
There exist numerous problems in nature inherently described by finite $D$-dimensional states. Formulating these problems for execution on qubit-based quantum hardware requires mapping the qudit Hilbert space to that of multiqubit which may…
Background: Solving nuclear many-body problems with an ab initio approach is widely recognized as a computationally challenging problem. Quantum computers offer a promising path to address this challenge. There are urgent needs to develop…
We propose an iterative algorithm for incomplete quantum process tomography, with the help of quantum state estimation, based on the combined principles of maximum-likelihood and maximum-entropy. The algorithm yields a unique estimator for…
The Quantum Approximate Optimisation Algorithm is a $p$ layer, time-variable split operator method executed on a quantum processor and driven to convergence by classical outer loop optimisation. The classical co-processor varies individual…
We present a quantum algorithm for estimating the matrix determinant based on quantum spectral sampling. The algorithm estimates the logarithm of the determinant of an $n \times n$ positive sparse matrix to an accuracy $\epsilon$ in time…
We propose a novel quantum algorithm for solving linear optimization problems by quantum-mechanical simulation of the central path. While interior point methods follow the central path with an iterative algorithm that works with successive…
We propose applying the adiabatic algorithm to prepare high-energy eigenstates of integrable models on a quantum computer. We first review the standard adiabatic algorithm to prepare ground states in each magnetization sector of the…
Finding the solution to linear systems is at the heart of many applications in science and technology. Over the years a number of algorithms have been proposed to solve this problem on a digital quantum device, yet most of these are too…