Related papers: Preentangling Quantum Algorithms -- the Density Ma…
Recently, a framework was established to systematically construct novel universal resource states for measurement-based quantum computation using techniques involving finitely correlated states. With these methods, universal states were…
We provide theory, algorithms, and simulations of non-equilibrium quantum systems using a one-dimensional (1D) completely-positive (CP), matrix-product (MP) density-operator ($\rho$) representation. By generalizing the matrix product…
We address the problem of implementing bottleneck layers from classical pre-trained neural networks on a quantum computer, with the goal of exploring intrinsically quantum ansatz for representing large linear layers within hybrid…
Even in cases where quantum linear solvers provide significant speedup compared to their classical counterparts, their performance depends on some of the same parameters. In particular, the condition number of the matrix which is to be…
Quantum computers may achieve speedups over their classical counterparts for solving linear algebra problems. However, in some cases -- such as for low-rank matrices -- dequantized algorithms demonstrate that there cannot be an exponential…
A major bottleneck in the quest for scalable many-body quantum technologies is the difficulty in benchmarking their preparations, which suffer from an exponential `curse of dimensionality' inherent to their quantum states. We present an…
We introduce two kinds of quantum algorithms to explore microcanonical and canonical properties of many-body systems. The first one is a hybrid quantum algorithm that, given an efficiently preparable state, computes expectation values in a…
The quantum Fourier transform (QFT) plays an important role in many known quantum algorithms such as Shor's algorithm for prime factorisation. In this paper we show that the QFT algorithm can, on a restricted set of input states, be…
As a cornerstone of automated reasoning, equational reasoning finds equivalences between symbolic expressions and fuels advances across scientific disciplines. Yet, its potential remains limited by the exponential growth of equivalent…
The electronic structure problem is one of the main problems in modern theoretical chemistry. While there are many already-established methods both for the problem itself and its applications like semi-classical or quantum dynamics, it…
Quantum algorithms for linear systems produce the solution state $A^{-1}|b\rangle$ by querying two oracles: $O_A$ that block encodes the coefficient matrix and $O_b$ that prepares the initial state. We present a quantum linear system…
Near-term quantum devices generally suffer from shallow circuit depth and hence limited expressivity due to noise and decoherence. To address this, we propose tensor-network-assisted parametrized quantum circuits, which concatenate a…
We introduce canonical weight normalization for convolutional neural networks. Inspired by the canonical tensor decomposition, we express the weight tensors in so-called canonical networks as scaled sums of outer vector products. In…
Variational quantum-classical hybrid algorithms are seen as a promising strategy for solving practical problems on quantum computers in the near term. While this approach reduces the number of qubits and operations required from the quantum…
Quantum machine learning for classical data is currently perceived to have a scalability problem due to (i) a bottleneck at the point of loading data into quantum states, (ii) the lack of clarity around good optimization strategies, and…
We introduce and analyze a novel quantum machine learning model motivated by convolutional neural networks. Our quantum convolutional neural network (QCNN) makes use of only $O(\log(N))$ variational parameters for input sizes of $N$ qubits,…
Utilising dynamic electromagnetic field control over charged particles serves as the basis for a quantum machine learning platform that operates on observables rather than directly on states. Such a platform can be physically realised in…
In this work we investigate methods to improve the efficiency and scalability of quantum algorithms for quantum chemistry applications. We propose a transformation of the electronic structure Hamiltonian in the second quantization framework…
The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in many instances a canonical basis can be chosen,…
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…