The effect of defects and disorder on the electronic properties of ZnIr2O4.

We analyze by means of ab initio calculations the role of imperfections on the electronic structure of ZnIr2O4, ranging from point defects in the spinel phase to the fully amorphous phase. We find that interstitial defects and anion vacancies in the spinel have large formation energies, in agreement with the trends observed in other spinels. In contrast, cation vacancies and antisites have lower formation energies. Among them, the zinc antisite and the zinc vacancy are the defects with the lowest formation energy. They are found to act as acceptors, and may be responsible for the spontaneous hole doping in the material. They may also induce optical transitions that would reduce the transparency of the material. Amorphization of ZnIr2O4 leads a large decrease of the band gap and appearance of localized states at the edges of the band gap region, which may act as charge traps and prevent amorphous ZnIr2O4 from being a good hole conductor.Financial support for this work is provided by the European Commission through contract No.NMP3-LA-2010-246334 (ORAMA). We acknowledge computational support from the UK national high performance computing service ARCHER, for which access was obtained via the UKCP consortium and funded by EPSRC grant EP/K014560/1.This is the final version of the article. It was originally published by AIP in The Journal of Chemical Physics here: http://scitation.aip.org/content/aip/journal/jcp/141/8/10.1063/1.4893556

Impact of amorphization on the electronic properties of Zn-Ir-O systems.

We analyze the geometry and electronic structure of a series of amorphous Zn-Ir-O systems using classical molecular dynamics followed by density functional theory taking into account two different charge states of Ir (+3 and  +4). The structures obtained consist of a matrix of interconnected metal-oxygen polyhedra, with Zn adopting preferentially a coordination of 4 and Ir a mixture of coordinations between 4 and 6 that depend on the charge state of Ir and its concentration. The amorphous phases display reduced band gaps compared to crystalline ZnIr2O4 and exhibit localized states near the band edges, which harm their transparency and hole mobility. Increasing amounts of Ir in the Ir(4+) phases decrease the band gap further while not altering it significantly in the Ir(3+) phases. The results are consistent with recent transmittance and resistivity measurements.This is the final version of the article. It first appeared from IOP Science via https://doi.org/10.1088/0953-8984/28/34/34550

Simulating non-unitary dynamics using quantum signal processing with unitary block encoding

We adapt a recent advance in resource-frugal quantum signal processing - the Quantum Eigenvalue Transform with Unitary matrices (QET-U) - to explore non-unitary imaginary time evolution on early fault-tolerant quantum computers using exactly emulated quantum circuits. We test strategies for optimising the circuit depth and the probability of successfully preparing the desired imaginary-time evolved states. For the task of ground state preparation, we confirm that the probability of successful post-selection is quadratic in the initial reference state overlap $\gamma$ as $O(\gamma^2)$. When applied instead to thermal state preparation, we show QET-U can directly estimate partition functions at exponential cost. Finally, we combine QET-U with Trotter product formula to perform non-normal Hamiltonian simulation in the propagation of Lindbladian open quantum system dynamics. We find that QET-U for non-unitary dynamics is flexible, intuitive and straightforward to use, and suggest ways for delivering quantum advantage in simulation tasks.Comment: 14 pages, 10 figures, minor corrections and updated citation

Demonstrating Bayesian Quantum Phase Estimation with Quantum Error Detection

Quantum phase estimation (QPE) serves as a building block of many different quantum algorithms and finds important applications in computational chemistry problems. Despite the rapid development of quantum hardware, experimental demonstration of QPE for chemistry problems remains challenging due to its large circuit depth and the lack of quantum resources to protect the hardware from noise with fully fault-tolerant protocols. In the present work, we take a step towards fault-tolerant quantum computing by demonstrating a QPE algorithm on a Quantinuum trapped-ion computer. We employ a Bayesian approach to QPE and introduce a routine for optimal parameter selection, which we combine with a $[[ n+2,n,2 ]]$ quantum error detection code carefully tailored to the hardware capabilities. As a simple quantum chemistry example, we take a hydrogen molecule represented by a two-qubit Hamiltonian and estimate its ground state energy using our QPE protocol. In the experiment, we use the quantum circuits containing as many as 920 physical two-qubit gates to estimate the ground state energy within $6\times 10^{-3}$ hartree of the exact value.Comment: 16 pages, 9 figure

Non-unitary Trotter circuits for imaginary time evolution

We propose an imaginary time equivalent of the well-established Pauli gadget primitive for Trotter-decomposed real time evolution, using mid-circuit measurements on a single ancilla qubit. Imaginary time evolution (ITE) is widely used for obtaining the ground state of a system on classical hardware, computing thermal averages, and as a component of quantum algorithms that perform non-unitary evolution. Near-term implementations on quantum hardware rely on heuristics, compromising their accuracy. As a result, there is growing interest in the development of more natively quantum algorithms. Since it is not possible to implement a non-unitary gate deterministically, we resort to the implementation of probabilistic imaginary time evolution (PITE) algorithms, which rely on a unitary quantum circuit to simulate a block encoding of the ITE operator - that is, they rely on successful ancillary measurements to evolve the system non-unitarily. Compared with previous PITE proposals, the suggested block encoding in this paper results in shorter circuits and is simpler to implement, requiring only a slight modification of the Pauli gadget primitive. This scheme was tested on the transverse Ising model and the fermionic Hubbard model and is demonstrated to converge to the ground state of the system.Comment: Added more explanation of the Pauli gadget primitive and motivation for using Trotter decomposition

Evaluating the noise resilience of variational quantum algorithms

We simulate the effects of different types of noise in state preparation circuits of variational quantum algorithms. We first use a variational quantum eigensolver to find the ground state of a Hamiltonian in presence of noise, and adopt two quality measures in addition to the energy, namely fidelity and concurrence. We then extend the task to the one of constructing, with a layered quantum circuit ansatz, a set of general random target states. We determine the optimal circuit depth for different types and levels of noise, and observe that the variational algorithms mitigate the effects of noise by adapting the optimised parameters. We find that the inclusion of redundant parameterised gates makes the quantum circuits more resilient to noise. For such overparameterised circuits different sets of parameters can result in the same final state in the noiseless case, which we denote as parameter degeneracy. Numerically, we show that this degeneracy can be lifted in the presence of noise, with some states being significantly more resilient to noise than others. We also show that the average deviation from the target state is linear in the noise level, as long as this is small compared to a circuit-dependent threshold. In this region the deviation is well described by a stochastic model. Above the threshold, the optimisation can converge to states with largely different physical properties from the true target state, so that for practical applications it is critical to ensure that noise levels are below this threshold.Comment: 22 pages, 13 figure

Variational Phase Estimation with Variational Fast Forwarding

Subspace diagonalisation methods have appeared recently as promising means to access the ground state and some excited states of molecular Hamiltonians by classically diagonalising small matrices, whose elements can be efficiently obtained by a quantum computer. The recently proposed Variational Quantum Phase Estimation (VQPE) algorithm uses a basis of real time-evolved states, for which the energy eigenvalues can be obtained directly from the unitary matrix $U=e^{-iH{\Delta}t}$, which can be computed with cost linear in the number of states used. In this paper, we report a circuit-based implementation of VQPE for arbitrary molecular systems and assess its performance and costs for the $H_2$, $H_3^+$ and $H_6$ molecules. We also propose using Variational Fast Forwarding (VFF) to decrease to quantum depth of time-evolution circuits for use in VQPE. We show that the approximation provides a good basis for Hamiltonian diagonalisation even when its fidelity to the true time evolved states is low. In the high fidelity case, we show that the approximate unitary U can be diagonalised instead, preserving the linear cost of exact VQPE