We explore the connection between the area law for entanglement and geometry by representing the entanglement entropies corresponding to all $2^N$ bipartitions of an $N$-party pure quantum system by means of a (generalized) adjacency matrix. In the cases where the representation is exact, the elements of that matrix coincide with the mutual information between pairs of sites. In others, it provides a very good approximation, and in all the cases it yields a natural entanglement contour which is similar to previous proposals. Moreover, for one-dimensional conformal invariant systems, the generalized adjacency matrix is given by the two-point correlator of an entanglement current operator. We conjecture how this entanglement current may give rise to a metric entirely built from entanglement.

We present a spectral realization of the Riemann zeros based on the propagation of a massless Dirac fermion in a region of Rindler spacetime and under the action of delta function potentials localized on the square free integers. The corresponding Hamiltonian admits a self-adjoint extension that is tuned to the phase of the zeta function, on the critical line, in order to obtain the Riemann zeros as bound states. The model suggests a proof of the Riemann hypothesis in the limit where the potentials vanish. Finally, we propose an interferometer that may yield an experimental observation of the Riemann zeros.

We investigate lattice effects on wave functions that are lattice analogs of bosonic and fermionic Laughlin wave functions with number of particles per flux $\nu =1/q$ in the Landau levels. These wave functions are defined analytically on lattices with $\mu$ particles per lattice site, where $\mu$ may be different than $\nu$. We give numerical evidence that these states have the same topological properties as the corresponding continuum Laughlin states for different values of $q$ and for different fillings $\mu$. These states define, in particular, particle-hole symmetric lattice fractional quantum Hall states when the lattice is half filled. On the square lattice it is observed that for $q\le 4$ this particle-hole symmetric state displays the topological properties of the continuum Laughlin state at filling fraction $\nu =1/q$, while for larger $q$ there is a transition towards long-range ordered antiferromagnets. This effect does not persist if the lattice is deformed from a square to a triangular lattice, or on the kagome lattice, in which case the topological properties of the state are recovered. We then show that changing the number of particles while keeping the expression of these wave functions identical gives rise to edge states that have the same correlations in the bulk as the reference lattice Laughlin states but a different density at the edge. We derive an exact parent Hamiltonian for which all these edge states are ground states with different number of particles. In addition this Hamiltonian admits the reference lattice Laughlin state as its unique ground state of filling factor $1/q$. Parent Hamiltonians are also derived for the lattice Laughlin states at other fillings of the lattice, when $\mu \le 1/q$ or $\mu \ge 1-1/q$ and when $q=4$ also at half filling.

Error mitigation is likely to be key in obtaining near term quantum advantage. In this work we present one of the first implementations of several Clifford data regression (CDR) based methods which are used to mitigate the effect of noise in real quantum data. We explore the dynamics of the 1D Ising model with transverse and longitudinal magnetic fields, highlighting signatures of confinement. We find in general CDR based techniques are advantageous in comparison with zero-noise extrapolation and obtain quantitative agreement with exact results for systems of nine qubits with circuit depths of up to 176, involving hundreds of CNOT gates. This is the largest systems investigated so far in a study of this type. We also investigate the two-point correlation function and find the effect of noise on this more complicated observable can be mitigated using Clifford quantum circuit data highlighting the utility of these methods.

We present a variational treatment of the ground state of the two-leg $t-J$ ladder, which combines the dimer and the hard-core boson models into one effective model. This model allows us to study the local structure of the hole pairs as a function of doping. A second-order recursion relation is used to generate the variational wave function, which substantially simplifies the computations. We obtain good agreement with numerical density matrix renormalization group results for the ground state energy in the strong-coupling regime. We find that the local structure of the pairs depends upon whether the ladder is slightly or strongly dopped.

Using the Boltzmann weights of classical statistical-mechanics vertex models we define a new class of tensor product Ansätze for two-dimensional quantum-lattice systems, characterized by a strong anisotropy, which gives rise to stripelike structures. In the case of the six-vertex model we compute exactly, in the thermodynamic limit, the norm of the Ansatz, and other observables. Employing this Ansatz we study the phase diagram of a Hamiltonian given by the sum of XXZ Hamiltonians along the legs coupled by an Ising term. Finally, we suggest a connection between the six- and eight-vertex anisotropic tensor-product Ansätze, and their associated Hamiltonians, with the smectic-stripe phases recently discussed in the literature.