We introduce a unitary coupled-cluster (UCC) ansatz termed k-UpCCGSD that is based on a family of sparse generalized doubles operators, which provides an affordable and systematically improvable ...unitary coupled-cluster wave function 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 excitation operators. We compare its performance in both efficiency of implementation and accuracy with that of the generalized UCC ansatz employing the full generalized single and double excitation operators (UCCGSD), as well as with the standard ansatz employing only single and double excitations (UCCSD). k-UpCCGSD is found to show the best scaling for quantum computing applications, requiring a circuit depth of O ( k N ) , compared with O ( N 3 ) for UCCGSD, and O ( ( N − η ) 2 η ) for UCCSD, where N is the number of spin orbitals and η is the number of electrons. We analyzed the accuracy of these three ansätze by making classical benchmark calculations on the ground state and the first excited state of H4 (STO-3G, 6-31G), H2O (STO-3G), and N2 (STO-3G), making additional comparisons to conventional coupled cluster methods. The results for ground states show that k-UpCCGSD offers a good trade-off between accuracy and cost, achieving chemical accuracy for lower cost of implementation on quantum computers than both UCCGSD and UCCSD. UCCGSD is also found to be more accurate than UCCSD but at a greater cost for implementation. 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 multideterminantal reference state constructed from classical linear response calculations allows these excited state energetics to be improved.
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. This strategy doubles the size of the state preparation circuits but not their depth, while adding a small number of additional two-qubit gates relative to standard variational quantum eigensolver. 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 H4 and the π-system of hexatriene (C6H8).
Machine learning is a promising application of quantum computing, but challenges remain for implementation today because near-term devices have a limited number of physical qubits and high error ...rates. Motivated by the usefulness of tensor networks for machine learning in the classical context, we propose quantum computing approaches to both discriminative and generative learning, with circuits based on tree and matrix product state tensor networks, that could already have benefits with such near-term devices. The result is a unified framework in which classical and quantum computing can benefit from the same theoretical and algorithmic developments, and the same model can be trained classically then transferred to the quantum setting for additional optimization. Tensor network circuits can also provide qubit-efficient schemes in which, depending on the architecture, the number of physical qubits required scales only logarithmically with, or independently of the input or output data sizes. We demonstrate our proposals with numerical experiments, training a discriminative model to perform handwriting recognition using a hybrid quantum-classical optimization procedure that could be carried out on quantum hardware today, and testing the noise resilience of the trained model.
Contemporary quantum computers have relatively high levels of noise, making it difficult to use them to perform useful calculations, even with a large number of qubits. Quantum error correction is ...expected to eventually enable fault-tolerant quantum computation at large scales, but until then, it will be necessary to use alternative strategies to mitigate the impact of errors. We propose a near-term friendly strategy to mitigate errors by entangling and measuringMcopies of a noisy stateρ. This enables us to estimate expectation values with respect to a state with dramatically reduced errorρM/Tr(ρM)without explicitly preparing it, hence the name “virtual distillation.” AsMincreases, this state approaches the closest pure state toρexponentially quickly. We analyze the effectiveness of virtual distillation and find that it is governed in many regimes by the behavior of this pure state (corresponding to the dominant eigenvector of ρ). We numerically demonstrate that virtual distillation is capable of suppressing errors by multiple orders of magnitude and explain how this effect is enhanced as the system size grows. Finally, we show that this technique can improve the convergence of randomized quantum algorithms, even in the absence of device noise.
The power of chemistry to prepare new molecules and materials has driven the quest for new approaches to solve problems having global societal impact, such as in renewable energy, healthcare and ...information science. In the latter case, the intrinsic quantum nature of the electronic, nuclear and spin degrees of freedom in molecules offers intriguing new possibilities to advance the emerging field of quantum information science. In this Perspective, which resulted from discussions by the co-authors at a US Department of Energy workshop held in November 2018, we discuss how chemical systems and reactions can impact quantum computing, communication and sensing. Hierarchical molecular design and synthesis, from small molecules to supramolecular assemblies, combined with new spectroscopic probes of quantum coherence and theoretical modelling of complex systems, offer a broad range of possibilities to realize practical quantum information science applications.
Abstract
We develop a Hamiltonian switching ansatz for bipartite control that is inspired by the quantum approximate optimization algorithm, to mitigate environmental noise on qubits. We demonstrate ...the control for a central spin coupled to bath spins via isotropic Heisenberg interactions, and then make physical applications to the protection of quantum gates performed on superconducting transmon qubits coupling to environmental two-level-systems (TLSs) through dipole-dipole interactions, as well as on such qubits coupled to both TLSs and a Lindblad bath. The control field is classical and acts only on the system qubits. We use reinforcement learning with policy gradient to optimize the Hamiltonian switching control protocols, using a fidelity objective for specific target quantum gates. We use this approach to demonstrate effective suppression of both coherent and dissipative noise, with numerical studies achieving target gate implementations with fidelities over 0.9999 (four nines) in the majority of our test cases and showing improvement beyond this to values of 0.999 999 999 (nine nines) upon a subsequent optimization by GRadient Ascent Pulse Engineering (GRAPE). We analyze how the control depth, total evolution time, number of environmental TLS, and choice of optimization method affect the fidelity achieved by the optimal protocols and reveal some critical behaviors of bipartite control of quantum gates.
Light-harvesting components of photosynthetic organisms are complex, coupled, many-body quantum systems, in which electronic coherence has recently been shown to survive for relatively long ...timescales, despite the decohering effects of their environments. Here, we analyse entanglement in multichromophoric light-harvesting complexes, and establish methods for quantification of entanglement by describing necessary and sufficient conditions for entanglement and by deriving a measure of global entanglement. These methods are then applied to the Fenna-Matthews-Olson protein to extract the initial state and temperature dependencies of entanglement. We show that, although the Fenna-Matthews-Olson protein in natural conditions largely contains bipartite entanglement between dimerized chromophores, a small amount of long-range and multipartite entanglement should exist even at physiological temperatures. This constitutes the first rigorous quantification of entanglement in a biological system. Finally, we discuss the practical use of entanglement in densely packed molecular aggregates such as light-harvesting complexes. PUBLICATION ABSTRACT
Abstract
Variational algorithms are a promising paradigm for utilizing near-term quantum devices for modeling electronic states of molecular systems. However, previous bounds on the measurement time ...required have suggested that the application of these techniques to larger molecules might be infeasible. We present a measurement strategy based on a low-rank factorization of the two-electron integral tensor. Our approach provides a cubic reduction in term groupings over prior state-of-the-art and enables measurement times three orders of magnitude smaller than those suggested by commonly referenced bounds for the largest systems we consider. Although our technique requires execution of a linear-depth circuit prior to measurement, this is compensated for by eliminating challenges associated with sampling nonlocal Jordan–Wigner transformed operators in the presence of measurement error, while enabling a powerful form of error mitigation based on efficient postselection. We numerically characterize these benefits with noisy quantum circuit simulations for ground-state energies of strongly correlated electronic systems.
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