1,527 research outputs found
Macroscopicity of quantum superpositions on a one-parameter unitary path in Hilbert space
We analyze quantum states formed as superpositions of an initial pure product
state and its image under local unitary evolution, using two measurement-based
measures of superposition size: one based on the optimal quantum binary
distinguishability of the branches of the superposition and another based on
the ratio of the maximal quantum Fisher information of the superposition to
that of its branches, i.e., the relative metrological usefulness of the
superposition. A general formula for the effective sizes of these states
according to the branch distinguishability measure is obtained and applied to
superposition states of quantum harmonic oscillators composed of Gaussian
branches. Considering optimal distinguishability of pure states on a
time-evolution path leads naturally to a notion of distinguishability time that
generalizes the well known orthogonalization times of Mandelstam and Tamm and
Margolus and Levitin. We further show that the distinguishability time provides
a compact operational expression for the superposition size measure based on
the relative quantum Fisher information. By restricting the maximization
procedure in the definition of this measure to an appropriate algebra of
observables, we show that the superposition size of, e.g., N00N states and
hierarchical cat states, can scale linearly with the number of elementary
particles comprising the superposition state, implying precision scaling
inversely with the total number of photons when these states are employed as
probes in quantum parameter estimation of a 1-local Hamiltonian in this
algebra
Distinguishability times and asymmetry monotone-based quantum speed limits in the Bloch ball
For both unitary and open qubit dynamics, we compare asymmetry monotone-based
bounds on the minimal time required for an initial qubit state to evolve to a
final qubit state from which it is probabilistically distinguishable with fixed
minimal error probability (i.e., the minimal error distinguishability time).
For the case of unitary dynamics generated by a time-independent Hamiltonian,
we derive a necessary and sufficient condition on two asymmetry monotones that
guarantees that an arbitrary state of a two-level quantum system or a separable
state of two-level quantum systems will unitarily evolve to another state
from which it can be distinguished with a fixed minimal error probability
. This condition is used to order the set of qubit states
based on their distinguishability time, and to derive an optimal release time
for driven two-level systems such as those that occur, e.g., in the
Landau-Zener problem. For the case of non-unitary dynamics, we compare three
lower bounds to the distinguishability time, including a new type of lower
bound which is formulated in terms of the asymmetry of the uniformly
time-twirled initial system-plus-environment state with respect to the
generator of the Stinespring isometry corresponding to the dynamics,
specifically, in terms of ,
where .Comment: 13 pages, 4 figure
A probability current analysis of energy transport in open quantum systems
We introduce a probability current analysis of excitation energy transfer
between states of an open quantum system. Expressing the energy transfer
through currents of excitation probability between the states in a site
representation enables us to gain key insights into the energy transfer
dynamics. It allows to, i) identify the pathways of energy transport in large
networks of sites and to quantify their relative weights, ii) quantify the
respective contributions of unitary dynamics, dephasing, and
relaxation/dissipation processes to the energy transfer, and iii) quantify the
contribution of coherence to the energy transfer. Our analysis is general and
can be applied to a broad range of open quantum system descriptions (with
coupling to non-Markovian environments) in a straightforward manner
Continuous Measurement of a Non-Markovian Open Quantum System
Continuous quantum measurement is the backbone of various methods in quantum
control, quantum metrology, and quantum information. Here, we present a
generalized formulation of dispersive measurement of a complex quantum systems.
We describe the complex system as an open quantum system that is strongly
coupled to a non-Markovian environment, enabling the treatment of a broad
variety of natural or engineered complex systems. The system is monitored via a
probe resonator coupled to a broadband (Markovian) reservoir. Based on this
model, we derive a formalism of Stochastic Hierarchy Equations of Motion (SHEM)
describing the decoherence dynamics of the system conditioned on the
measurement record. Furthermore, we demonstrate a spectroscopy method based on
weak quantum measurement to reveal the non-Markovian nature of the environment,
which we term weak spectroscopy.Comment: Published version, the section on continuous state tomography will be
published in a separate manuscrip
Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
We introduce a unitary coupled-cluster (UCC) ansatz termed -UpCCGSD that
is based on a family of sparse generalized doubles (D) operators which provides
an affordable and systematically improvable unitary coupled-cluster
wavefunction suitable for implementation on a near-term quantum computer.
-UpCCGSD employs products of the exponential of pair coupled-cluster
double excitation operators (pCCD), together with generalized single (S)
excitation operators. We compare its performance in both efficiency of
implementation and accuracy with that of the generalized UCC ansatz employing
the full generalized SD excitation operators (UCCGSD), as well as with the
standard ansatz employing only SD excitations (UCCSD). -UpCCGSD is found to
show the best scaling for quantum computing applications, requiring a circuit
depth of , compared with for UCCGSD and
for UCCSD where is the number of spin
orbitals and is the number of electrons. We analyzed the accuracy of
these three ans\"atze by making classical benchmark calculations on the ground
state and the first excited state of H (STO-3G, 6-31G), HO (STO-3G),
and N (STO-3G), making additional comparisons to conventional coupled
cluster methods. The results for ground states show that -UpCCGSD offers a
good tradeoff between accuracy and cost, achieving chemical accuracy for lower
cost of implementation on quantum computers than both UCCGSD and UCCSD. Excited
states are calculated with an orthogonally constrained variational quantum
eigensolver approach. This is seen to generally yield less accurate energies
than for the corresponding ground states. We demonstrate that using a
specialized multi-determinantal reference state constructed from classical
linear response calculations allows these excited state energetics to be
improved
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