Related papers: Quantum Encoding of Structured Data with Matrix Pr…
The matrix product state (MPS) belongs to the most important mathematical models in, for example, condensed matter physics and quantum information sciences. However, to realize an $N$-qubit MPS with large $N$ and large entanglement on a…
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…
We quantify the representational power of matrix product states (MPS) for entangled qubit systems by giving polynomial expressions in a pure quantum state's amplitudes which hold if and only if the state is a translation invariant matrix…
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…
Image-based data is a popular arena for testing quantum machine learning algorithms. A crucial factor in realizing quantum advantage for these applications is the ability to efficiently represent images as quantum states. Here we present a…
As quantum computing hardware advances, the need for algorithms that facilitate the loading of classical data into the quantum states of these devices has become increasingly important. This study presents a method for producing scalable…
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…
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…
We consider the preparation of matrix product states (MPS) on quantum devices via quantum circuits of local gates. We first prove that faithfully preparing translation-invariant normal MPS of $N$ sites requires a circuit depth…
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…
We obtain an exact matrix-product-state (MPS) representation of a large series of fractional quantum Hall (FQH) states in various geometries of genus 0. The states in question include all paired k=2 Jack polynomials, such as the Moore-Read…
Effective quantum computation relies upon making good use of the exponential information capacity of a quantum machine. A large barrier to designing quantum algorithms for execution on real quantum machines is that, in general, it is…
Matrix product state (MPS) offers a framework for encoding classical data into quantum states, enabling the efficient utilization of quantum resources for data representation and processing. This research paper investigates techniques to…
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…
Preparing arbitrary quantum states requires exponential resources. Matrix Product States (MPS) admit more efficient constructions, particularly when accuracy is traded for circuit complexity. Existing approaches to MPS preparation mostly…
The matrix product state (MPS) is utilized to study the ground state properties and quantum phase transitions (QPTs) of the one-dimensional quantum compass model (QCM). The MPS wavefunctions are argued to be very efficient descriptions of…
Quantum state preparation, also known as encoding or embedding, is a crucial initial step in many quantum algorithms and often constrains theoretical quantum speedup in fields such as quantum machine learning and linear equation solvers.…
Many quantum states arising in algorithms and physical systems occupy only a small, structured subset of the exponentially large Hilbert space, yet standard quantum state tomography fails to exploit this structure. We present an efficient…
Learning the closest matrix product state (MPS) representation of a quantum state enables useful tools for quantum machine learning and analysis of complex quantum systems. In this work, we study the problem of learning MPS in the following…
We introduce an efficient algorithm for the systematic design of shallow-depth quantum circuits capable of preparing many-body quantum states represented as Matrix Product States (MPS). The proposed method leverages Schmidt spectrum…