Related papers: Testing matrix product states
Solving quantum many-body systems is one of the most significant regimes where quantum computing applies. Currently, as a hardware-friendly computational paradigms, variational algorithms are often used for finding the ground energy of…
Common wisdom says that the entanglement of fermionic systems can be low in the second quantization formalism but is extremely large in the first quantization. Hence Matrix Product State (MPS) methods based on moderate entanglement have…
Tree tensor network states (TTNS) generalize the notion of having low Schmidt-rank to multipartite quantum states, through a parameter known as the bond dimension. This leads to succinct representations of quantum many-body systems with a…
The reconstruction of quantum states from experimental measurements, often achieved using quantum state tomography (QST), is crucial for the verification and benchmarking of quantum devices. However, performing QST for a generic…
Encoding classical data in a quantum state is a key prerequisite of many quantum algorithms. Recently matrix product state (MPS) methods emerged as the most promising approach for constructing shallow quantum circuits approximating input…
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…
Nonstabilizerness, also known as magic, quantifies the number of non-Clifford operations needed in order to prepare a quantum state. As typical measures either involve minimization procedures or a computational cost exponential in the…
We study the set of random matrix product states (RMPS) introduced in arXiv:0908.3877 as a tool to explore foundational aspects of quantum statistical mechanics. In the present work, we provide an accurate numerical and analytical…
This work is devoted to the study Translation-Invariant (TI) Matrix Product State (MPS) representations of quantum states with periodic boundary conditions (PBC). We pursue two directions: we introduce new methods for constructing TI MPS…
We give a test that can distinguish efficiently between product states of n quantum systems and states which are far from product. If applied to a state psi whose maximum overlap with a product state is 1-epsilon, the test passes with…
The term Tensor Network States (TNS) refers to a number of families of states that represent different ans\"atze for the efficient description of the state of a quantum many-body system. Matrix Product States (MPS) are one particular case…
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…
We present a method to apply the well-known matrix product state (MPS) formalism to partially separable states in solid state systems. The computational effort of our method is equal to the effort of the standard density matrix…
In quantum physics, multiparticle systems are described by quantum states acting on tensor products of Hilbert spaces. This product structure leads to the distinction between product states and entangled states; moreover, one can quantify…
Suppose we have an unknown multipartite quantum state, how can we experimentally find out whether it is genuine multipartite entangled or not? Recall that even for a bipartite quantum state whose density matrix is known, it is already…
Quantum machine learning (QML) is a rapidly expanding field that merges the principles of quantum computing with the techniques of machine learning. One of the powerful mathematical frameworks in this domain is tensor networks. These…
We investigate the use of matrix product states (MPS) to approximate ground states of critical quantum spin chains with periodic boundary conditions (PBC). We identify two regimes in the (N,D) parameter plane, where N is the size of the…
Efficient encoding of classical information plays a fundamental role in numerous practical quantum algorithms. However, the preparation of an arbitrary amplitude-encoded state has been proven to be time-consuming, and its deployment on…
As in the density matrix renormalization group (DMRG) method, approximating many-body wave function of electrons using a matrix product state (MPS) is a promising way to solve electronic structure problems. The expressibility of an MPS is…
In the era of noisy, intermediate-scale quantum (NISQ) devices, the efficient preparation of many-body resource states is a task of paramount importance. In this paper we focus on the deterministic preparation of matrix-product states (MPS)…