Related papers: Matrix Product States for Quantum Stochastic Model…
Sampling problems have emerged as a central avenue for demonstrating quantum advantage on noisy intermediate-scale quantum devices. However, physical noise can fundamentally alter their computational complexity, often making them…
We introduce the concept of concatenated tensor networks to efficiently describe quantum states. We show that the corresponding concatenated tensor network states can efficiently describe time evolution and possess arbitrary block-wise…
Adaptive quantum circuits, which combine local unitary gates, midcircuit measurements, and feedforward operations, have recently emerged as a promising avenue for efficient state preparation, particularly on near-term quantum devices…
A systematic and compact treatment of arbitrary $su(2)$ invariant spin-$s$ quantum chains with nearest-neighbour interactions is presented. The ground-state is derived in terms of matrix product states (MPS). The fundamental MPS…
We present a matrix product state (MPS) method for including decoherence processes in calculations involving waveguide quantum electrodynamics (waveguide QED) using density matrices. The approach is based on collision quantum optics, where…
State Space Models (SSMs), particularly recent selective variants like Mamba, have emerged as a leading architecture for sequence modeling, challenging the dominance of Transformers. However, the success of these state-of-the-art models…
In this note, we describe a method for reconstructing matrix product states from a small number of efficiently-implementable measurements. Our method is exponentially faster than standard tomography, and it can also be used to certify that…
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…
We show that general string-net condensed states have a natural representation in terms of tensor product states (TPS) . These TPS's are built from local tensors. They can describe both states with short-range entanglement (such as the…
We derive an exact formula for a matrix product state (MPS) representation (or a PEPS in higher number of dimensions) of the ground state of translationally invariant bosonic lattice systems in terms of a single one-dimensional Euclidean…
We show that infinite Matrix Product States (MPS) constructed from conformal field theories can describe ground states of one-dimensional critical systems with open boundary conditions. To illustrate this, we consider a simple infinite MPS…
Model predictive control (MPC) has proven useful in enabling safe and optimal motion planning for autonomous vehicles. In this paper, we investigate how to achieve MPC-based motion planning when a neural state-space model represents the…
Identifying and extracting the past information relevant to the future behaviour of stochastic processes is a central task in the quantitative sciences. Quantum models offer a promising approach to this, allowing for accurate simulation of…
This work presents a comparative study of new and existing optimization and diagonalization methods for solving time-independent partial differential equations (PDEs) using matrix product states (MPS) in the quantized tensor-train formalism…
Matrix product states are useful representations for a large variety of naturally occurring quantum states. Studying their typical properties is important for understanding universal behavior, including quantum chaos and thermalization, as…
We extend the formalism of Matrix Product States (MPS) to describe one-dimensional gapped systems of fermions with both unitary and anti-unitary symmetries. Additionally, systems with orientation-reversing spatial symmetries are considered.…
Condensed Matter Physics (CMP) seeks to understand the microscopic interactions of matter at the quantum and atomistic levels, and describes how these interactions result in both mesoscopic and macroscopic properties. CMP overlaps with many…
One of the key considerations in the development of Quantum Machine Learning (QML) protocols is the encoding of classical data onto a quantum device. In this chapter we introduce the Matrix Product State representation of quantum systems…
This paper introduces a stochastic hybrid system (SHS) framework in state space model to capture sensor, communication, and system contingencies in modern power systems (MPS). Within this new framework, the paper concentrates on the…
Quantum technologies offer a promising route to the efficient sampling and analysis of stochastic processes, with potential applications across the sciences. Such quantum advantages rely on the preparation of a quantum sample state of the…