Related papers: Low-rank tensor decompositions of quantum circuits
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…
Tensor product state (TPS) based methods are powerful tools to efficiently simulate quantum many-body systems in and out of equilibrium. In particular, the one-dimensional matrix-product (MPS) formalism is by now an established tool in…
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…
The study of quantum circuit simulation using classical computers is a key research topic that helps define the boundary of verifiable quantum advantage, solve quantum many-body problems, and inform development of quantum hardware and…
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…
In this study, we introduce a novel family of tensor networks, termed constrained matrix product states (MPS), designed to incorporate exactly arbitrary discrete linear constraints, including inequalities, into sparse block structures.…
The process tensor framework to open quantum systems provides the most general description of multi-time correlations in non-Markovian quantum dynamics. A compressed representation of a process tensor in terms of matrix product operators…
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…
The amplitude encoding of an arbitrary $n$-qubit state vector requires $\Omega(2^n)$ gate operations, owing to the exponential dimension of the Hilbert space. We can, however, form dimensionality-reduced representations of quantum states…
We investigate quantum algorithms derived from tensor networks to simulate the static and dynamic properties of quantum many-body systems. Using a sequentially prepared quantum circuit representation of a matrix product state (MPS) that we…
In recent years, efficient quantum circuit simulations incorporating ideal noise assumptions have relied on tensor network simulators, particularly leveraging the matrix product density operator (MPDO) framework. However, experiments on…
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…
As the number of qubits in a sensor increases, the complexity of designing and controlling the quantum circuits grows exponentially. Manually optimizing these circuits becomes infeasible. Optimizing entanglement distribution in large-scale…
We find an efficient approach to approximately convert matrix product states (MPSs) into restricted Boltzmann machine wave functions consisting of a multinomial hidden unit through a canonical polyadic (CP) decomposition of the MPSs. This…
Representations of quantum computations are almost always based on a tensor product $\otimes$-structure. This coincides with what we are able to execute in our experiments, as well as what we observe in Nature, but it makes certain familiar…
Understanding the quantum evolution of light in nonlinear media is central to the development of next-generation quantum technologies. Yet modeling these processes remains computationally demanding, as the required resources grow rapidly…
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…
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…
Gauging a global symmetry of a system amounts to introducing new degrees of freedom whose transformation rule makes the overall system observe a local symmetry. In quantum systems there can be obstructions to gauging a global symmetry. When…
Ultra-short pulses propagating in nonlinear nanophotonic waveguides can simultaneously leverage both temporal and spatial field confinement, promising a route towards single-photon nonlinearities in an all-photonic platform. In this…