Related papers: Efficient state preparation for multivariate Monte…
We propose a variational approach for preparing entangled quantum states on quantum computers. The methodology involves training a unitary operation to match with a target unitary using the Fubini-Study distance as a cost function. We…
One of the key considerations in the development of Quantum Machine Learning (QML) protocols is the encoding of classical data onto a quantum device. In this chapter we introduce the Matrix Product State representation of quantum systems…
Highly entangled quantum states are an ingredient in numerous applications in quantum computing. However, preparing these highly entangled quantum states on currently available quantum computers at high fidelity is limited by ubiquitous…
Quantum Signal Processing (QSP) and Quantum Singular Value Transformation (QSVT) currently stand as the most efficient techniques for implementing functions of block encoded matrices, a central task that lies at the heart of most prominent…
This tutorial paper introduces quantum approaches to Monte Carlo computation with applications in computational finance. We outline the basics of quantum computing using Grover's algorithm for unstructured search to build intuition. We then…
Quantum state preparation (QSP) for a general $n$-qubit state requires $O(2^n)$ CNOT gates and circuit depth, making exact amplitude encoding (EAE) impractical for near-term quantum hardware. We introduce an ancilla-free hybrid…
Black-box quantum state preparation is an important subroutine in many quantum algorithms. The standard approach requires the quantum computer to do arithmetic, which is a key contributor to the complexity. Here we present a new algorithm…
State preparation is a fundamental routine in quantum computation, for which many algorithms have been proposed. Among them, perhaps the simplest one is the Grover-Rudolph algorithm. In this paper, we analyse the performance of this…
Quantum state tomography (QST) is the gold standard technique for obtaining an estimate for the state of small quantum systems in the laboratory. Its application to systems with more than a few constituents (e.g. particles) soon becomes…
Quantum state preparation involving a uniform superposition over a non-empty subset of $n$-qubit computational basis states is an important and challenging step in many quantum computation algorithms and applications. In this work, we…
We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum computer with fidelity arbitrarily close to 1. Our algorithm is based on Grover's quantum search algorithm. For sequences of states with suitably…
The problems of quantum state preparation and matrix block-encoding are ubiquitous in quantum computing: they are crucial parts of various quantum algorithms for the purpose for initial state preparation as well as loading problem relevant…
Quantum state tomography is a key process in most quantum experiments. In this work, we employ quantum machine learning for state tomography. Given an unknown quantum state, it can be learned by maximizing the fidelity between the output of…
Quantum computers are a highly promising tool for efficiently simulating quantum many-body systems. The preparation of their eigenstates is of particular interest and can be addressed, e.g., by quantum phase estimation algorithms. The…
Preparation of quantum states is of vital importance for performing quantum computations and quantum simulations. In this work, we propose a general framework for preparing ground states of many-body systems by combining the…
We provide in this work a form of Modular Quantum Signal Processing that we call iterated quantum signal processing. This method recursively applies quantum signal processing to the outputs of other quantum signal processing steps, allowing…
Stochastic processes play a fundamental role in physics, mathematics, engineering and finance. One potential application of quantum computation is to better approximate properties of stochastic processes. For example, quantum algorithms for…
Quantum signal processing (QSP), a framework for implementing matrix-valued polynomials, is a fundamental primitive in various quantum algorithms. Despite its versatility, a potentially underappreciated challenge is that all systematic…
We investigate the feasibility of integrating quantum algorithms as subroutines of simulation-based optimisation problems with relevance to and potential applications in mathematical finance. To this end, we conduct a thorough analysis of…
Preparation of quantum state lies at the heart of quantum information processing. The greedy algorithm provides a potential method to effectively prepare quantum states. However, the standard greedy algorithm, in general, cannot take the…