Related papers: N-representability is QMA-complete
We study the characterization of multipartite entanglement for the random states of an $n$-qbit system. Unable to solve the problem exactly we generalize it, changing complex numbers into real vectors with $N_c$ components (the original…
In this article I expound an understanding of the quantum mechanics of so-called "indistinguishable" systems in which permutation invariance is taken as a symmetry of a special kind, namely the result of representational redundancy. This…
P representation techniques, which have been very successful in quantum optics and in other fields, are also useful for general bosonic quantum dynamical many-body calculations such as Bose-Einstein condensation. We introduce a…
Quantum Monte Carlo simulations, while being efficient for bosons, suffer from the "negative sign problem'' when applied to fermions - causing an exponential increase of the computing time with the number of particles. A polynomial time…
Quantum computing is gaining increased attention as a potential way to speed up simulations of physical systems, and it is also of interest to apply it to simulations of classical plasmas. However, quantum information science is…
We propose a new formalism of quantum subsystems which allows to unify the existing and new methods of reduced description of quantum systems. The main mathematical ingredients are completely positive maps and correlation functions. In this…
Quantum computing is being extensively used in quantum chemistry, especially in simulating simple molecules and evaluating properties like the ground state energy, dipole moment, etc. The transformation of a molecular Hamiltonian from the…
It is proposed to map the quantum information qubit not to individual spin 1/2 states, but to the collective spin states being eigenfunctions of the Hamiltonian including spin-spin interactions, which may be not small. Such an approach…
Standard quantum inference converts quantum data into classical outputs. We study an alternative inference setting in which the desired output is quantum, preserving coherence. Such settings include quantum purity amplification (QPA),…
We present a quantum algorithm for the simulation of molecular systems that is asymptotically more efficient than all previous algorithms in the literature in terms of the main problem parameters. As in previous work [Babbush et al., New…
What could happen if we pinned a single qubit of a system and fixed it in a particular state? First, we show that this can greatly increase the complexity of static questions -- ground state properties of local Hamiltonian problems with…
Conservation of symmetries plays a crucial role in both classical and quantum simulations of many-body systems, enabling the tracking of states with specific symmetry properties and leading to substantial reductions in the number of…
In recent years, many computational tasks have been proposed as candidates for showing a quantum computational advantage, that is an advantage in the time needed to perform the task using a quantum instead of a classical machine.…
Modern cryptography is largely based on complexity assumptions, for example, the ubiquitous RSA is based on the supposed complexity of the prime factorization problem. Thus, it is of fundamental importance to understand how a quantum…
Fermions are fundamental particles which obey seemingly bizarre quantum-mechanical principles, yet constitute all the ordinary matter that we inhabit. As such, their study is heavily motivated from both fundamental and practical incentives.…
For each oriented surface $\Sigma$ of genus $g$ we study a limit of quantum representations of the mapping class group arising in TQFT derived from the Kauffman bracket. We determine that these representations converge in the Fell topology…
We establish dimerization in $O(n)$-invariant quantum spin chains with big enough $n$, in a large part of the phase diagram where this result is expected. This includes identifying two distinct ground states which are translations of one…
We elucidate the profound connection between physics and computation by proposing and examining the model of the non-Hermitian quantum computer (NQC). In addition to conventional quantum gates such as the Hadamard, phase, and CNOT gates,…
We present an overview of the method of Neural Quantum States applied to the many-body problem of atomic nuclei. Through the lens of group representation theory, we focus on the problem of constructing neural-network ans\"atze that respect…
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…