Showing papers by "Shivaji Lal Sondhi published in 2015"
TL;DR: In this article, local adiabatic manipulations are shown to lead to a nonlocal response, with implications for quantum control in disordered environments, which is relevant to our work.
Abstract: Anderson localization has recently attracted renewed interest in strongly correlated quantum systems. Now, local adiabatic manipulations are shown to lead to a nonlocal response, with implications for quantum control in disordered environments.
98 citations
TL;DR: In this article, the performance of the quantum adiabatic algorithm for the solution of decision problems is investigated and the possible failure mechanisms are divided into two sets: small gaps due to quantum phase transitions and small gaps caused by avoided crossings inside a phase.
Abstract: In this review we consider the performance of the quantum adiabatic algorithm for the solution of decision problems. We divide the possible failure mechanisms into two sets: small gaps due to quantum phase transitions and small gaps due to avoided crossings inside a phase. We argue that the thermodynamic order of the phase transitions is not predictive of the scaling of the gap with the system size. On the contrary, we also argue that, if the phase surrounding the problem Hamiltonian is a Many-Body Localized (MBL) phase, the gaps are going to be typically exponentially small and that this follows naturally from the existence of local integrals of motion in the MBL phase.
60 citations
TL;DR: In this article, the effect of adding quantum dynamics to a classical topological spin liquid, with a particular view of how to best detect its presence in experiment, was considered, and it was shown that quantum effects are most visible in the gauge-charged monopole excitations.
Abstract: We consider the effect of adding quantum dynamics to a classical topological spin liquid, with a particular view of how to best detect its presence in experiment. For the Coulomb phase of spin ice, we find quantum effects to be most visible in the gauge-charged monopole excitations. In the presence of weak dilution with nonmagnetic ions we find a particularly crisp phenomenon, namely, the emergence of hydrogenic excited states in which a magnetic monopole is bound to a vacancy at various distances. Via a mapping to an analytically tractable single particle problem on the Bethe lattice, we obtain an approximate expression for the dynamic neutron scattering structure factor.
19 citations
TL;DR: In this article, the proton correlations present in water ice in its ice rule phase were studied using an effective field theory, an analytic form for the correlation function was derived and then compared against numerics, showing excellent agreement.
Abstract: The authors study the proton correlations present in water ice in its ice rule phase ${I}_{h}$. Using an effective field theory, an analytic form for the correlation function is derived and then compared against numerics, showing excellent agreement. This field theory is argued to be a U(1) gauge theory in its deconfined Coulomb phase.
9 citations
TL;DR: For the simplest 2-SAT/2-QSAT ensemble the exact boundary that separates SAT and UNSAT instances is found by establishing coincident lower and upper bounds on the extent of the UNSat and SAT regions, respectively.
Abstract: Classical satisfiability (SAT) and quantum satisfiability (QSAT) are complete problems for the complexity classes NP and QMA which are believed to be intractable for classical and quantum computers, respectively. Statistical ensembles of instances of these problems have been studied previously in an attempt to elucidate their typical, as opposed to worst case, behavior. In this paper we introduce a new statistical ensemble that interpolates between classical and quantum. For the simplest 2-SAT/2-QSAT ensemble we find the exact boundary that separates SAT and UNSAT instances. We do so by establishing coincident lower and upper bounds, in the limit of large instances, on the extent of the UNSAT and SAT regions, respectively.
2 citations