Related papers: Quantum Encoding of Structured Data with Matrix Pr…
Gaussian states hold a fundamental place in quantum mechanics, quantum information, and quantum computing. Many subfields, including quantum simulation of continuous-variable systems, quantum chemistry, and quantum machine learning, rely on…
Numerical simulations are a powerful tool to study quantum systems beyond exactly solvable systems lacking an analytic expression. For one-dimensional entangled quantum systems, tensor network methods, amongst them Matrix Product States…
Both discrete and continuous systems can be used to encode quantum information. Most quantum computation schemes propose encoding qubits in two-level systems, such as a two-level atom or an electron spin. Others exploit the use of an…
Given the excitement for the potential of quantum computing for machine learning methods, a natural subproblem is how to load classical data into a quantum state. Leveraging insights from [GST24] where certain qubits play an outsized role…
The study of tensor network theory is an important field and promises a wide range of experimental and quantum information theoretical applications. Matrix product state is the most well-known example of tensor network states, which…
We reconstruct a matrix product state (MPS) in reduced spaces using density matrix. This scheme applies to a MPS built on a blocked quantum lattice. Each block contains $N$ physical sites that have a local space of rank $R$. The simulation…
Encoding quantum information into superpositions of multiple Fock states of a harmonic oscillator can provide protection against errors, but it comes with the cost of requiring more complex quantum gates that need to address multiple Fock…
Tensor network methods as presented in our open source Matrix Product States software have opened up the possibility to study many-body quantum physics in one and quasi-one-dimensional systems in an easily accessible package similar to…
We implement a hybrid quantum-classical model for image classification that compresses MNIST digit images into a low-dimensional feature space and then maps these features onto a 5-qubit quantum state. First, an autoencoder compresses each…
Quantum image processing is an emerging topic in the field of quantum information and technology. In this paper, we propose a new quantum image representation of RGB images, which is an improvement to all the existing representations in…
Quantum probability provides a novel framework for formulating machine-learning (ML) problems in Hilbert space. We introduce a prototype-based learning scheme where class representatives are encoded as generative matrix product states…
The temporal evolution of a quantum system can be characterized by quantum process tomography, a complex task that consumes a number of physical resources scaling exponentially with the number of subsystems. An alternative approach to the…
High-dimensional quantum states, or qudits, represent a promising resource in the quantum information field. Here we present the experimental generation of four-dimensional quantum states, or ququarts, encoded in the polarization and…
It has been recently shown that a state generated by a one-dimensional noisy quantum computer is well approximated by a matrix product operator with a finite bond dimension independent of the number of qubits. We show that full quantum…
In quantum information theory, it is a fundamental problem to construct multipartite unextendible product bases (UPBs). We show that there exist two families UPBs in Hilbert space…
This work gives a detailed investigation of matrix product state (MPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical…
The generalization of matrix product states (MPS) to continuous systems, as proposed in the breakthrough paper [F. Verstraete, J.I. Cirac, Phys. Rev. Lett. 104, 190405(2010)], provides a powerful variational ansatz for the ground state of…
In this work we propose a simple optical architecture, based on phase-only programmable spatial light modulators, in order to characterize general processes on photonic spatial quantum systems in a $d>2$ Hilbert space. We demonstrate the…
Quantum state tomography is an essential component of modern quantum technology. In application to continuous-variable harmonic-oscilator systems, such as the electromagnetic field, existing tomography methods typically reconstruct the…
Shallow quantum circuits feature not only computational advantages over their classical counterparts but also cutting-edge applications. Storing quantum information generated by shallow circuits is a fundamental question of both theoretical…