Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation

We introduce a unitary coupled-cluster (UCC) ansatz termed $k$-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. $k$-UpCCGSD employs $k$ 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). $k$-UpCCGSD is found to show the best scaling for quantum computing applications, requiring a circuit depth of $\mathcal O(kN)$, compared with $\mathcal O(N^3)$ for UCCGSD and $\mathcal O((N-\eta)^2 \eta)$ for UCCSD where $N$ is the number of spin orbitals and $\eta$ 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$_4$ (STO-3G, 6-31G), H$_2$O (STO-3G), and N$_2$ (STO-3G), making additional comparisons to conventional coupled cluster methods. The results for ground states show that $k$-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

Matchgate Shadows for Fermionic Quantum Simulation

"Classical shadows" are estimators of an unknown quantum state, constructed from suitably distributed random measurements on copies of that state [Nature Physics 16, 1050-1057]. Here, we analyze classical shadows obtained using random matchgate circuits, which correspond to fermionic Gaussian unitaries. We prove that the first three moments of the Haar distribution over the continuous group of matchgate circuits are equal to those of the discrete uniform distribution over only the matchgate circuits that are also Clifford unitaries; thus, the latter forms a "matchgate 3-design." This implies that the classical shadows resulting from the two ensembles are functionally equivalent. We show how one can use these matchgate shadows to efficiently estimate inner products between an arbitrary quantum state and fermionic Gaussian states, as well as the expectation values of local fermionic operators and various other quantities, thus surpassing the capabilities of prior work. As a concrete application, this enables us to apply wavefunction constraints that control the fermion sign problem in the quantum-classical auxiliary-field quantum Monte Carlo algorithm (QC-AFQMC) [Nature 603, 416-420], without the exponential post-processing cost incurred by the original approach.Comment: 53 pages, 1 figur

A principled approach to the measurement of situation awareness in commercial aviation

The issue of how to support situation awareness among crews of modern commercial aircraft is becoming especially important with the introduction of automation in the form of sophisticated flight management computers and expert systems designed to assist the crew. In this paper, cognitive theories are discussed that have relevance for the definition and measurement of situation awareness. These theories suggest that comprehension of the flow of events is an active process that is limited by the modularity of attention and memory constraints, but can be enhanced by expert knowledge and strategies. Three implications of this perspective for assessing and improving situation awareness are considered: (1) Scenario variations are proposed that tax awareness by placing demands on attention; (2) Experimental tasks and probes are described for assessing the cognitive processes that underlie situation awareness; and (3) The use of computer-based human performance models to augment the measures of situation awareness derived from performance data is explored. Finally, two potential example applications of the proposed assessment techniques are described, one concerning spatial awareness using wide field of view displays and the other emphasizing fault management in aircraft systems

A Non-Orthogonal Variational Quantum Eigensolver

Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the ground state of a system by solving a generalized eigenvalue problem in a subspace spanned by a collection of parametrized quantum states. This allows for the systematic improvement of a logical wavefunction ansatz without a significant increase in circuit complexity. To minimize the circuit complexity of this approach, we propose a strategy for efficiently measuring the Hamiltonian and overlap matrix elements between states parametrized by circuits that commute with the total particle number operator. We also propose a classical Monte Carlo scheme to estimate the uncertainty in the ground state energy caused by a finite number of measurements of the matrix elements. We explain how this Monte Carlo procedure can be extended to adaptively schedule the required measurements, reducing the number of circuit executions necessary for a given accuracy. We apply these ideas to two model strongly correlated systems, a square configuration of H$_4$ and the $\pi$-system of Hexatriene (C$_6$H$_8$)

Can solid body destruction explain abundance discrepancies in planetary nebulae?

In planetary nebulae, abundances of oxygen and other heavy elements derived from optical recombination lines are systematically higher than those derived from collisionally excited lines. We investigate the hypothesis that the destruction of solid bodies may produce pockets of cool, high-metallicity gas that could explain these abundance discrepancies. Under the assumption of maximally efficient radiative ablation, we derive two fundamental constraints that the solid bodies must satisfy in order that their evaporation during the planetary nebula phase should generate a high enough gas phase metallicity. A local constraint implies that the bodies must be larger than tens of meters, while a global constraint implies that the total mass of the solid body reservoir must exceed a few hundredths of a solar mass. This mass greatly exceeds the mass of any population of comets or large debris particles expected to be found orbiting evolved low- to intermediate-mass stars. We therefore conclude that contemporaneous solid body destruction cannot explain the observed abundance discrepancies in planetary nebulae. However, similar arguments applied to the sublimation of solid bodies during the preceding asymptotic giant branch (AGB) phase do not lead to such a clear-cut conclusion. In this case, the required reservoir of volatile solids is only one ten-thousandth of a solar mass, which is comparable to the most massive debris disks observed around solar-type stars, implying that this mechanism may contribute to abundance discrepancies in at least some planetary nebulae, so long as mixing of the high metallicity gas is inefficient.Comment: 8 pages, no figures, ApJ in pres

On quantum backpropagation, information reuse, and cheating measurement collapse

The success of modern deep learning hinges on the ability to train neural networks at scale. Through clever reuse of intermediate information, backpropagation facilitates training through gradient computation at a total cost roughly proportional to running the function, rather than incurring an additional factor proportional to the number of parameters - which can now be in the trillions. Naively, one expects that quantum measurement collapse entirely rules out the reuse of quantum information as in backpropagation. But recent developments in shadow tomography, which assumes access to multiple copies of a quantum state, have challenged that notion. Here, we investigate whether parameterized quantum models can train as efficiently as classical neural networks. We show that achieving backpropagation scaling is impossible without access to multiple copies of a state. With this added ability, we introduce an algorithm with foundations in shadow tomography that matches backpropagation scaling in quantum resources while reducing classical auxiliary computational costs to open problems in shadow tomography. These results highlight the nuance of reusing quantum information for practical purposes and clarify the unique difficulties in training large quantum models, which could alter the course of quantum machine learning.Comment: 29 pages, 2 figure