5 research outputs found
Scalable Quantum Computation of Highly Excited Eigenstates with Spectral Transforms
We propose a natural application of Quantum Linear Systems Problem (QLSP)
solvers such as the HHL algorithm to efficiently prepare highly excited
interior eigenstates of physical Hamiltonians in a variational manner. This is
enabled by the efficient computation of inverse expectation values, taking
advantage of the QLSP solvers' exponentially better scaling in problem size
without concealing exponentially costly pre/post-processing steps that usually
accompanies it. We detail implementations of this scheme for both
fault-tolerant and near-term quantum computers, analyse their efficiency and
implementability, and discuss applications and simulation results in many-body
physics and quantum chemistry that demonstrate its superior effectiveness and
scalability over existing approaches.Comment: 16 pages, 6 figure
Stability and Dynamics of Many-Body Localized Systems Coupled to Small Bath
It is known that strong disorder in closed quantum systems leads to many-body
localization (MBL), and that this quantum phase can be destroyed by coupling to
an infinitely large Markovian environment. However, the stability of the MBL
phase is less clear when the system and environment are of finite and
comparable size. Here, we study the stability and eventual localization
properties of a disordered Heisenberg spin chain coupled to a finite
environment, and extensively explore the effects of environment disorder,
geometry, initial state and system-bath coupling strength. By studying the
non-equilibrium dynamics and the eventual steady-state properties of different
initial states, our numerical results indicate that in most cases, the system
retains its localization properties despite the coupling to the finite
environment, albeit to a reduced extent. However, in cases where the system and
environment is strongly coupled in the ladder configuration, the eventual
localization properties are highly dependent on the initial state, and could
lead to either thermalization or localization
Multi-Objective Optimization and Network Routing with Near-Term Quantum Computers
Multi-objective optimization is a ubiquitous problem that arises naturally in
many scientific and industrial areas. Network routing optimization with
multi-objective performance demands falls into this problem class, and finding
good quality solutions at large scales is generally challenging. In this work,
we develop a scheme with which near-term quantum computers can be applied to
solve multi-objective combinatorial optimization problems. We study the
application of this scheme to the network routing problem in detail, by first
mapping it to the multi-objective shortest path problem. Focusing on an
implementation based on the quantum approximate optimization algorithm (QAOA)
-- the go-to approach for tackling optimization problems on near-term quantum
computers -- we examine the Pareto plot that results from the scheme, and
qualitatively analyze its ability to produce Pareto-optimal solutions. We
further provide theoretical and numerical scaling analyses of the resource
requirements and performance of QAOA, and identify key challenges associated
with this approach. Finally, through Amazon Braket we execute small-scale
implementations of our scheme on the IonQ Harmony 11-qubit quantum computer
MANY-BODY LOCALIZED EIGENSTATES AND SCALABLE QUANTUM COMPUTATION OF HAMILTONIAN SPECTRA
Master'sMASTER OF SCIENCE (RSH-FOS
Improving sum uncertainty relations with the quantum Fisher information
International audienceWe show how preparation uncertainty relations that are formulated as sums of variances may be tightened by using the quantum Fisher information to quantify quantum fluctuations. We apply this to derive stronger angular momentum uncertainty relations, which in the case of spin- turn into equalities involving the purity. Using an analogy between pure-state decompositions in the Bloch sphere and the moment of inertia of rigid bodies, we identify optimal decompositions that achieve the convex- and concave-roof decomposition of the variance. Finally, we illustrate how these results may be used to identify the classical and quantum limits on phase estimation precision with an unknown rotation axis