Related papers: Computing Local Invariants of Qubit Systems
Quantum computers hold promise to enable efficient simulations of the properties of molecules and materials; however, at present they only permit ab initio calculations of a few atoms, due to a limited number of qubits. In order to harness…
Quantum information quantities, such as mutual information and entropies, are essential for characterizing quantum systems and protocols in quantum information science. In this contribution, we identify types of information measures based…
Although a universal quantum computer is still far from reach, the tremendous advances in controllable quantum devices, in particular with solid-state systems, make it possible to physically implement "quantum simulators". Quantum…
The correspondence between local unitary equivalence of bipartite quantum states and simultaneous orthogonal equivalence is thoroughly investigated and strengthened. It is proved that local unitary equivalence can be studied through…
In terms of the analysis of fixed point subgroup and tensor decomposability of certain matrices, we study the equivalence of of quantum bipartite mixed states under local unitary transformations. For non-degenerate case an operational…
In this article, we propose a Lyapunov stability approach to analyze the convergence of the density operator of a quantum system. In analog to the classical probability measure for Markovian processes, we show that the set of invariant…
We present quantum algorithms for the estimation of n-time correlation functions, the local and non-local density of states, and dynamical linear response functions. These algorithms are all based on block-encodings - a versatile technique…
Loop invariants are properties of a program loop that hold before and after each iteration of the loop. They are often employed to verify programs and ensure that algorithms consistently produce correct results during execution.…
An efficient numerical method is developed using the matrix product formalism for computing the properties at finite energy densities in one-dimensional (1D) many-body localized (MBL) systems. Arguing that any efficient (possibly quantum)…
Certain quantum topological invariants of three manifolds can be written in the form of the Gaussian sum. It is shown that such topological invariants can be approximated efficiently by a quantum computer. The invariants discussed here are…
We investigate the behavior of quantum states under stochastic local quantum operations and classical communication (SLOCC) for fixed numbers of qubits. We explicitly exhibit the homomorphism between complex and real groups for two-qubits,…
We study when a multipartite non--local unitary operation can deterministically or probabilistically simulate another one when local operations of a certain kind -in some cases including also classical communication- are allowed. In the…
The task of testing whether two uncharacterized quantum devices behave in the same way is crucial for benchmarking near-term quantum computers and quantum simulators, but has so far remained open for continuous-variable quantum systems. In…
Determining whether two particle systems are similar is a common problem in particle simulations. When the comparison should be invariant under permutations, orthogonal transformations, and translations of the systems, special techniques…
The classification of stabilizer states under local Clifford (LC) equivalence is of particular importance in quantum error-correction and measurement-based quantum computation. Two stabilizer states are called LC equivalent if there exists…
Measurement correlations in quantum systems can exhibit non-local behavior, a fundamental aspect of quantum mechanics with applications such as device-independent quantum information processing. However, the explicit construction of local…
We introduce a general difference quotient representation for non-local operators associated with a first-order linear operator. We establish new local to non-local estimates and strong localization principles in various spaces of…
It is widely accepted that noisy quantum devices are limited to logarithmic depth circuits unless mid-circuit measurements and error correction are employed. However, this conclusion holds only for unital error channels, such as…
The use of qubits as sensitive magnetometers has been studied theoretically and recent demonstrated experimentally. In this paper we propose a generalisation of this concept, where a scanning two-state quantum system is used to probe the…
We study necessary conditions for the efficient simulation of both bipartite and multipartite Hamiltonians, which are independent of the eigenvalues and based on the algebraic-geometric invariants introduced in [1-2]. Our results indicate…