Related papers: Matrix Product States for Quantum Stochastic Model…
We present a tensorization algorithm for constructing tensor train/matrix product state (MPS) representations of functions, drawing on sketching and cross interpolation ideas. The method only requires black-box access to the target function…
We present and test a protocol to learn the matrix-product operator (MPO) representation of an experimentally prepared quantum state. The protocol takes as an input classical shadows corresponding to local randomized measurements, and…
Quantum neural networks (QNNs), as currently formulated, are near-term quantum machine learning architectures that leverage parameterized quantum circuits with the aim of improving upon the performance of their classical counterparts. In…
Most scientific publications follow the familiar recipe of (i) obtain data, (ii) fit a model, and (iii) comment on the scientific relevance of the effects of particular covariates in that model. This approach, however, ignores the fact that…
I introduce a modification of continuous matrix product states (CMPS) that makes them adapted to relativistic quantum field theories (QFT). These relativistic CMPS can be used to solve genuine 1+1 dimensional QFT without UV cutoff and…
Matrix product purifications (MPPs) are a very efficient tool for the simulation of strongly correlated quantum many-body systems at finite temperatures. When a system features symmetries, these can be used to reduce computation costs…
The method of choice to study one-dimensional strongly interacting many body quantum systems is based on matrix product states and operators. Such method allows to explore the most relevant, and numerically manageable, portion of an…
We investigate ensembles of Matrix Product States (MPSs) generated by quantum circuit evolution followed by projection onto MPSs with a fixed bond dimension $\chi$. Specifically, we consider ensembles produced by: (i) random sequential…
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…
Based on the MPS formalism, we introduce an ansatz for capturing excited states in finite systems with open boundary conditions, providing a very efficient method for computing, e.g., the spectral gap of quantum spin chains. This method can…
A brief pedagogical overview of recent advances in tensor network state methods are presented that have the potential to broaden their scope of application radically for strongly correlated molecular systems. These include global fermionic…
Correlator product states (CPS) are a class of tensor network wavefunctions applicable to strongly correlated problems in arbitrary dimensions. Here, we present a method for optimizing and evaluating the energy of the CPS wavefunction that…
We develop a numerical method based on matrix product states for simulating quantum many-body systems at finite temperatures without importance sampling and evaluate its performance in spin 1/2 systems. Our method is an extension of the…
Quantum state tomography (QST) remains the gold standard for benchmarking and verification of near-term quantum devices. While QST for a generic quantum many-body state requires an exponentially large amount of resources, most physical…
Modeling probability distributions via the wave function of a quantum state is central to quantum-inspired generative modeling and quantum state tomography (QST). We investigate a common failure mode in training randomly initialized matrix…
Capturing the correlation emerging between constituents of many-body systems accurately is one of the key challenges for the appropriate description of various systems whose properties are underpinned by quantum mechanical fundamentals.…
A way of constructing continuous matrix product states (cMPS) for coupled fields is presented here. The cMPS is a variational \emph{ansatz} for the ground state of quantum field theories in one dimension. Our proposed scheme is based in the…
Matrix Product States (MPS) and Projected Entangled Pair States (PEPS) are powerful analytical and numerical tools to assess quantum many-body systems in one and higher dimensions, respectively. While MPS are comprehensively understood, in…
Exact diagonalization is a powerful tool to study fractional quantum Hall (FQH) systems. However, its capability is limited by the exponentially increasing computational cost. In order to overcome this difficulty,…
The simulation of quantum systems is a task for which quantum computers are believed to give an exponential speedup as compared to classical ones. While ground states of one-dimensional systems can be efficiently approximated using Matrix…