Growth reduction of similarity transformed electronic Hamiltonians in qubit space

Accurately solving the electronic structure problem through the variational quantum eigensolver (VQE) is hindered by the available quantum resources of current and near-term devices. One approach to relieving the circuit depth requirements for VQE is to "pre-process" the electronic Hamiltonian by a similarity transformation incorporating some degree of electronic correlation, with the remaining correlation left to be addressed by the circuit ansatz. This often comes at the price of a substantial increase in the number of terms to measure in the unitarily transformed Hamiltonian. In this work, we propose an efficient approach to sampling elements from the unrestricted pool of N-qubit Pauli products which minimize the onset of new terms in the transformed Hamiltonian, while facilitating substantial energy lowering. We find that utilizing an operator selection criteria which takes into account both energy gradients and expected growth can substantially reduce the number of Pauli products in effective Hamiltonians used for a subsequent VQE optimization

Estimating Trotter Approximation Errors to Optimize Hamiltonian Partitioning for Lower Eigenvalue Errors

One of the ways to encode many-body Hamiltonians on a quantum computer to obtain their eigen-energies through Quantum Phase Estimation is by means of the Trotter approximation. There were several ways proposed to assess the quality of this approximation based on estimating the norm of the difference between the exact and approximate evolution operators. Here, we would like to explore how these different error estimates are correlated with each other and whether they can be good predictors for the true Trotter approximation error in finding eigenvalues. For a set of small molecular systems we calculated the exact Trotter approximation errors of the first order Trotter formulas for the ground state electronic energies. Comparison of these errors with previously used upper bounds show almost no correlation over the systems and various Hamiltonian partitionings. On the other hand, building the Trotter approximation error estimation based on perturbation theory up to a second order in the time-step for eigenvalues provides estimates with very good correlations with the Trotter approximation errors. The developed perturbative estimates can be used for practical time-step and Hamiltonian partitioning selection protocols, which are paramount for an accurate assessment of resources needed for the estimation of energy eigenvalues under a target accuracy.Comment: 3 figure

Quantum Kinetic Rates within the Nonequilibrium Steady State

The nonequilibrium steady state (NESS) of a quantum network is central to a host of physical and biological scenarios. Examples include natural processes such as vision and photosynthesis, as well as technical devices such as photocells, both activated by incoherent light (e.g. sunlight) and leading to quantum transport. Here, a completely general approach to defining components of a quantum network in the NESS, and obtaining rates of processes between these components is provided. Quantum effects are explicitly included throughout, both in (a) defining network components via projection operators, and (b) in determining the role of coherences in rate processes. As examples, the methodology is applied to model cases, two versions of the V-level system, and to the spin-boson model, wherein the role of the environment and of internal system properties in determining the rates is examined. In addition, the role of Markovian vs. non-Markovian contributions is quantified, exposing conditions under which NESS rates can be obtained by perturbing the nonequilibrium steady state

Assessment of various Hamiltonian partitionings for the electronic structure problem on a quantum computer using the Trotter approximation

Solving the electronic structure problem via unitary evolution of the electronic Hamiltonian is one of the promising applications of digital quantum computers. One of the practical strategies to implement the unitary evolution is via Trotterization, where a sequence of short-time evolutions of fast-forwardable (i.e. efficiently diagonalizable) Hamiltonian fragments is used. Given multiple choices of possible Hamiltonian decompositions to fast-forwardable fragments, the accuracy of the Hamiltonian evolution depends on the choice of the fragments. We assess efficiency of multiple Hamiltonian partitioning techniques using fermionic and qubit algebras for the Trotterization. Use of symmetries of the electronic Hamiltonian and its fragments significantly reduces the Trotter error. This reduction makes fermionic-based partitioning Trotter errors lower compared to those in qubit-based techniques. However, from the simulation-cost standpoint, fermionic methods tend to introduce quantum circuits with a greater number of T-gates at each Trotter step and thus are more computationally expensive compared to their qubit counterparts.Comment: 13 pages, 4 figure

Assessment of various Hamiltonian partitionings for the electronic structure problem on a quantum computer using the Trotter approximation

Solving the electronic structure problem via unitary evolution of the electronic Hamiltonian is one of the promising applications of digital quantum computers. One of the practical strategies to implement the unitary evolution is via Trotterization, where a sequence of short-time evolutions of fast-forwardable (i.e. efficiently diagonalizable) Hamiltonian fragments is used. Given multiple choices of possible Hamiltonian decompositions to fast-forwardable fragments, the accuracy of the Hamiltonian evolution depends on the choice of the fragments. We assess efficiency of multiple Hamiltonian partitioning techniques using fermionic and qubit algebras for the Trotterization. Use of symmetries of the electronic Hamiltonian and its fragments significantly reduces the Trotter error. This reduction makes fermionic-based partitioning Trotter errors lower compared to those in qubit-based techniques. However, from the simulation-cost standpoint, fermionic methods tend to introduce quantum circuits with a greater number of T-gates at each Trotter step and thus are more computationally expensive compared to their qubit counterparts

Proposal for SPS beam time for the baby MIND and TASD neutrino detector prototypes

The design, construction and testing of neutrino detector prototypes at CERN are ongoing activities. This document reports on the design of solid state baby MIND and TASD detector prototypes and outlines requirements for a test beam at CERN to test these, tentatively planned on the H8 beamline in the North Area, which is equipped with a large aperture magnet. The current proposal is submitted to be considered in light of the recently approved projects related to neutrino activities with the SPS in the North Area in the medium term 2015-2020