Related papers: Classical circuits can simulate quantum aspects
It is shown that a good estimate of the fidelity of an experimentally realized quantum process can be obtained by measuring the outputs for only two complementary sets of input states. The number of measurements required to test a quantum…
Tensor networks are a popular and computationally efficient approach to simulate general quantum systems on classical computers and, in a broader sense, a framework for dealing with high-dimensional numerical problems. This paper presents a…
We introduce a new approach to analyzing the interaction between classical and quantum systems that is based on a limiting procedure applied to multi-particle Schr\"{o}dinger equations. The limit equations obtained by this procedure, which…
The celebrated quantum no-cloning theorem states that an arbitrary quantum state cannot be cloned perfectly. This raises questions about cloning of classical states, which have also attracted attention. Here, we present a physical approach…
Generic open quantum systems are notoriously difficult to simulate unless one looks at specific regimes. In contrast, classical dissipative systems can often be effectively described by stochastic processes, which are generally less…
Quantum computers process information with the laws of quantum mechanics. Current quantum hardware is noisy, can only store information for a short time, and is limited to a few quantum bits, i.e., qubits, typically arranged in a planar…
In recent years, new algorithms and cryptographic protocols based on the laws of quantum physics have been designed to outperform classical communication and computation. We show that the quantum world also opens up new perspectives in the…
A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce thermodynamic and structural properties. The motivation is to allow application of classical strong coupling theories and molecular…
The power of quantum computers is still somewhat speculative. While they are certainly faster than classical ones at some tasks, the class of problems they can efficiently solve has not been mapped definitively onto known classical…
Quantum computers have the potential to simulate chemical systems beyond the capability of classical computers. Recent developments in hybrid quantum-classical approaches enable the determinations of the ground or low energy states of…
We compare the performance of randomized classical and quantum neural networks (NNs) as well as classical and quantum-classical hybrid convolutional neural networks (CNNs) for the task of supervised binary image classification. We keep the…
This paper introduces quantum circuit $C^*$-algebra net, which provides a connection between $C^*$-algebra nets proposed in classical machine learning and quantum circuits. Using $C^*$-algebra, a generalization of the space of complex…
We present a classical simulation method for fermionic quantum systems which, without loss of generality, can be represented by parity-preserving circuits made of two-qubit gates in a brick-wall structure. We map such circuits to a…
Algorithms are described for efficiently simulating quantum mechanical systems on quantum computers. A class of algorithms for simulating the Schrodinger equation for interacting many-body systems are presented in some detail. These…
We consider the task of verifying the correctness of quantum computation for a restricted class of circuits which contain at most two basis changes. This contains circuits giving rise to the second level of the Fourier Hierarchy, the lowest…
We present a classical protocol, using the matrix product state representation, to simulate cluster-state quantum computation at a cost polynomial in the number of qubits in the cluster and exponential in d -- the width of the cluster. We…
Classical electromagnetic fields and quantum mechanics -- both obey the principle of superposition alike. This opens up many avenues for simulation of a large variety of phenomena and algorithms, which have hitherto been considered quantum…
It is shown that the transmission line technology can be suitably used for simulating quantum mechanics. Using manageable and at the same time non-expensive technology, several quantum mechanical problems can be simulated for significant…
In breakthrough work, Bravyi, Gosset, and K\"{o}nig (BGK) [Science, 2018] unconditionally proved that constant depth quantum circuits are more powerful than their classical counterparts. Their result is equivalent to saying that a…
We present elementary mappings between classical lattice models and quantum circuits. These mappings provide a general framework to obtain efficiently simulable quantum gate sets from exactly solvable classical models. For example, we…