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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…
Matrix Product States (MPS) and Operators (MPO) have been proven to be a powerful tool to study quantum many-body systems but are restricted to moderately entangled states as the number of parameters scales exponentially with the…
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…
We present a framework for preparing quantum states from matrix product states (MPS) with open and periodic boundary conditions on quantum devices. The MPS tensors are mapped to unitary gates, which are subsequently decomposed into native…
We present an exact $n$-qubit computational-basis amplitude encoder of real- or complex-valued data vectors of $d=\binom{n}{k}$ components into a subspace of fixed Hamming weight $k$. This represents a polynomial space compression of degree…
We show that the model wave functions used to describe the fractional quantum Hall effect have exact representations as matrix product states (MPS). These MPS can be implemented numerically in the orbital basis of both finite and infinite…
Quantum state tomography (QST) is the process of reconstructing the state of a quantum system (mathematically described as a density matrix) through a series of different measurements, which can be solved by learning a parameterized…
Recently quantum tomography has been proposed as a fundamental tool for prototyping a few qubit quantum device. It allows the complete reconstruction of the state produced from a given input into the device. From this reconstructed density…
Quantum state tomography (QST) is a crucial tool for characterizing quantum states. However, QST becomes impractical for reconstructing multi-qubit density matrices since data sets and computational costs grow exponentially with qubit…
The stable operation of quantum computers will rely on error-correction, in which single quantum bits of information are stored redundantly in the Hilbert space of a larger system. Such encoded qubits are commonly based on arrays of many…
The advent of quantum computers promises exponential speed ups in the execution of various computational tasks. While their capabilities are hindered by quantum decoherence, they can be exactly simulated on classical hardware at the cost of…
Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits are described via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that…
Due to the exponential complexity of the resources required by quantum state tomography (QST), people are interested in approaches towards identifying quantum states which require less effort and time. In this paper, we provide a tailored…
Quantum state tomography, the ability to deduce the density matrix of a quantum system from measured data, is of fundamental importance for the verification of present and future quantum devices. It has been realized in systems with few…
Impressive progress has been made in the past decade in the study of technological applications of varied types of quantum systems. With industry giants like IBM laying down their roadmap for scalable quantum devices with more than…
Quantum state tomography (QST) is a fundamental task in quantum information science that aims to reconstruct unknown quantum states from measurement data. However, the exponential growth of Hilbert-space dimension with system size makes…
Quantum state tomography (QST), the process through which the density matrix of a quantum system is characterized from measurements of specific observables, is a fundamental pillar in the fields of quantum information and computation. In…
Machine learning tasks are an exciting application for quantum computers, as it has been proven that they can learn certain problems more efficiently than classical ones. Applying quantum machine learning algorithms to classical data can…
Slater-type orbitals (STOs) provide the physically correct description of atomic wavefunctions but have been largely replaced by Gaussian-type orbitals in computational chemistry due to the lack of closed-form multi-center integrals. We…
Data representation in quantum state space offers an alternative function space for machine learning tasks. However, benchmarking these algorithms at a practical scale has been limited by ineffective simulation methods. We develop a quantum…