465 research outputs found
Optimality of feedback control for qubit purification under inefficient measurement
A quantum system may be purified, i.e., projected into a pure state, faster if one applies feedback operations during the measurement process. However, the existing results suggest that such an enhancement is only possible when the measurement efficiency exceeds 0.5, which is difficult to achieve experimentally. We address the task of finding the global optimal feedback control for purifying a single qubit in the presence of measurement inefficiency. We use the Bloch vector length, a more physical and practical quantity than purity, to assess the quality of the state, and employ a backward-iteration algorithm to find the globally optimal strategy. Our results show that a speedup is available for quantum efficiencies well below 0.5, which opens the possibility of experimental implementation in existing systems
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
Cluster decomposition of full configuration interaction wave functions: a tool for chemical interpretation of systems with strong correlation
Approximate full configuration interaction (FCI) calculations have recently
become tractable for systems of unforeseen size thanks to stochastic and
adaptive approximations to the exponentially scaling FCI problem. The result of
an FCI calculation is a weighted set of electronic configurations, which can
also be expressed in terms of excitations from a reference configuration. The
excitation amplitudes contain information on the complexity of the electronic
wave function, but this information is contaminated by contributions from
disconnected excitations, i.e. those excitations that are just products of
independent lower-level excitations. The unwanted contributions can be removed
via a cluster decomposition procedure, making it possible to examine the
importance of connected excitations in complicated multireference molecules
which are outside the reach of conventional algorithms. We present an
implementation of the cluster decomposition analysis and apply it to both true
FCI wave functions, as well as wave functions generated from the adaptive
sampling CI (ASCI) algorithm. The cluster decomposition is useful for
interpreting calculations in chemical studies, as a diagnostic for the
convergence of various excitation manifolds, as well as as a guidepost for
polynomially scaling electronic structure models. Applications are presented
for (i) the double dissociation of water, (ii) the carbon dimer, (iii) the
{\pi} space of polyacenes, as well as (iv) the chromium dimer. While the
cluster amplitudes exhibit rapid decay with increasing rank for the first three
systems, even connected octuple excitations still appear important in Cr,
suggesting that spin-restricted single-reference coupled-cluster approaches may
not be tractable for some problems in transition metal chemistry.Comment: 15 pages, 5 figure
What is the optimal way to prepare a Bell state using measurement and feedback?
Recent work has shown that the use of quantum feedback can significantly enhance both the speed and success rate of measurement-based remote entanglement generation, but it is generally unknown what feedback protocols are optimal for these tasks. Here we consider two common measurements that are capable of projecting into pairwise entangled states, namely half- and full-parity measurements of two qubits, and determine in each case a globally optimal protocol for generation of entanglement. For the half-parity measurement, we rederive a previously described protocol using more general methods and prove that it is globally optimal for several figures of merit, including maximal concurrence or fidelity and minimal time to reach a specified concurrence or fidelity. For the full-parity measurement, we derive a protocol for rapid entanglement generation related to that of (Hill, Ralph, Phys. Rev. A 77, 014305), and then map the dynamics of the concurrence of the state to the Bloch vector length of an effective qubit. This mapping allows us to prove several optimality results for feedback protocols with full-parity measurements. We further show that our full-parity protocol transfers entanglement optimally from one qubit to the other amongst all measurement-based schemes. The methods developed here will be useful for deriving feedback protocols and determining their optimality properties in many other quantum systems subject to measurement and unitary operations
A deterministic alternative to the full configuration interaction quantum Monte Carlo method
Development of exponentially scaling methods has seen great progress in
tackling larger systems than previously thought possible. One such technique,
full configuration interaction quantum Monte Carlo, is a useful algorithm that
allows exact diagonalization through stochastically sampling determinants. The
method derives its utility from the information in the matrix elements of the
Hamiltonian, along with a stochastic projected wave function, to find the
important parts of Hilbert space. However, the stochastic representation of the
wave function is not required to search Hilbert space efficiently, and here we
describe a highly efficient deterministic method to achieve chemical accuracy
for a wide range of systems, including the difficult Cr dimer. In
addition our method also allows efficient calculation of excited state
energies, for which we illustrate with benchmark results for the excited states
of C.Comment: 4 pages, 2 figure
Realistic and verifiable coherent control of excitonic states in a light harvesting complex
We explore the feasibility of coherent control of excitonic dynamics in light
harvesting complexes, analyzing the limits imposed by the open nature of these
quantum systems. We establish feasible targets for phase and phase/amplitude
control of the electronically excited state populations in the
Fenna-Mathews-Olson (FMO) complex and analyze the robustness of this control
with respect to orientational and energetic disorder, as well as decoherence
arising from coupling to the protein environment. We further present two
possible routes to verification of the control target, with simulations for the
FMO complex showing that steering of the excited state is experimentally
verifiable either by extending excitonic coherence or by producing novel states
in a pump-probe setup. Our results provide a first step toward coherent control
of these complex biological quantum systems in an ultrafast spectroscopy setup.Comment: 12 pages, 8 figure
Modern Approaches to Exact Diagonalization and Selected Configuration Interaction with the Adaptive Sampling CI Method.
Recent advances in selected configuration interaction methods have made them competitive with the most accurate techniques available and, hence, creating an increasingly powerful tool for solving quantum Hamiltonians. In this work, we build on recent advances from the adaptive sampling configuration interaction (ASCI) algorithm. We show that a useful paradigm for generating efficient selected CI/exact diagonalization algorithms is driven by fast sorting algorithms, much in the same way iterative diagonalization is based on the paradigm of matrix vector multiplication. We present several new algorithms for all parts of performing a selected CI, which includes new ASCI search, dynamic bit masking, fast orbital rotations, fast diagonal matrix elements, and residue arrays. The ASCI search algorithm can be used in several different modes, which includes an integral driven search and a coefficient driven search. The algorithms presented here are fast and scalable, and we find that because they are built on fast sorting algorithms they are more efficient than all other approaches we considered. After introducing these techniques, we present ASCI results applied to a large range of systems and basis sets to demonstrate the types of simulations that can be practically treated at the full-CI level with modern methods and hardware, presenting double- and triple-ζ benchmark data for the G1 data set. The largest of these calculations is Si2H6 which is a simulation of 34 electrons in 152 orbitals. We also present some preliminary results for fast deterministic perturbation theory simulations that use hash functions to maintain high efficiency for treating large basis sets
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