Quantum-chaotic cryptography

Computational complexity of nonequilibrium steady states of quantum spin chains

“…We want to stress that the mapping of quantum circuits to the auxiliary space relies upon the MPO structure of the NESS (6), which is a correspondence between Pauli matrices of physical spins and matrices A (k) s on the auxiliary space. The NESS (6) has many matrix elements in the auxiliary space, like the right-hand-side of (8) for a single spin chain or of (11) for many spin chains, each one is a coefficient of a suitable operator basis expansion.…”

“…where the product of matrices A (k) s is replaced by the product of the corresponding Pauli matrices in (6), and j is the position where the encoder starts in the k-th chain. Since a general polynomial is a linear combination of monomials, the general single qubit gate…”

“…Examples are the Heisenberg XXZ model or the XY Hamiltonian, solved by Bethe Ansatz and fermionization respectively, that describe magnetic phenomena [3] and spin chain materials [4]. Moreover, quantum information and complexity offer elaborated characterisations of properties of quantum correlated systems [5][6][7][8][9][10]. In particular, computational complexity theory [11][12][13] studies the complexity of certain mathematical problems as compared to known hard ones.…”

“…PEPS were also studied from the perspective of computational complexity, proving that both creating them and computing their local expectation values are very hard problems (PP and #P respectively) [34], at least as hard as more famous NP-complete problems [35]. Furthermore, decision prob-lems for ground states of many Hamiltonians are QMAcomplete [5][6][7][8][9], the quantum analogue of NP-complete.…”

Scalable effective-temperature reduction for quantum annealers via nested quantum annealing correction

“…Quantum annealing (QA) [1][2][3][4][5] is a predecessor of the quantum adiabatic algorithm (QAA) [6,7] and adiabatic quantum optimization (AQO) [8,9], originally conceived as an algorithm that exploits simulated quantum (rather than thermal) fluctuations and tunneling to providing a quantum-inspired version of simulated annealing (SA) [10] for the solution of combinatorial optimization problems. Nowadays it is considered a special case of adiabatic quantum computation (AQC) [11], a paradigm that is universal for quantum computation [12][13][14][15][16][17][18][19]. For reviews see [20,21].…”