Session D07: NISQ: Quantum Chemistry and Quantum Simulation I

Demonstration of a large-scale quantum chemistry calculations using the Sycamore quantum processor

Variational simulation of quantum chemistry is a likely first application for noisy intermediate scale quantum (NISQ) computers in the post supremacy age. We simulate a chemistry model that is significantly larger than previous implementations on any quantum computing platform. The model is optimized through a variational outer loop and a new iterative method using an approximate Hessian. Upon application of an error mitigation scheme based on pure-state n-representability conditions our experiments run on Google’s Sycamore quantum processor achieve chemical accuracy. The model provides an efficiently verifiable circuit that has a large degree of entanglement and is a circuit primitive for broader fermionic simulation.   

Energy gap calculation on near-term quantum hardware with robust phase estimation

Can alternative approaches to phase estimation yield better results for chemical simulation on NISQ hardware? Robust phase estimation (RPE) calculates the difference in phases between two eigenstates of a unitary, provided oracular access to that unitary and the relevant eigenstates. In contrast to conventional phase estimation, it does not require a controlled-U and is naturally resistant to state preparation and measurement errors.

We evaluate the suitability of RPE on near-term hardware. In particular, we calculate the energy landscapes of H₂ and H₃ on extant quantum hardware (pre-compiling to emulate hardware with significantly higher fidelities). Resource requirements for larger molecules are considered.   

Quantum simulation of molecular vibronic spectra on a superconducting bosonic processor: Part I

A promising and practical application of quantum machines is the simulation of quantum chemistry. Recent proposals have introduced problems naturally suited for bosonic platforms, such as the simulation of Franck-Condon factors [Huh et. al, Nature Photonics 9 (2015)]. These simulations require a wide range of Gaussian operations and non-Gaussian resources, such as arbitrary state preparation and photon-number measurement. Here, we a present a blueprint for realizing these capabilities in a superconducting architecture consisting of long-lifetime cavity modes coupled to transmon ancillae. Driven four-wave mixing processes implement bilinear interactions such as single-mode squeezing and beamsplitters, which, when combined with resonant displacements, generate a complete set of Gaussian operations. Furthermore, we present a novel single-shot measurement scheme that extracts the binary decomposition of the photon number in each cavity mode.   

Quantum simulation of molecular vibronic spectra on a superconducting bosonic processor: Part II

A promising and practical application of quantum hardware is the simulation of quantum chemistry. As one example, a programmable bosonic machine can be configured to obtain Franck-Condon (FC) factors associated with molecular vibronic spectra [1]. Implementing such an algorithm in the linear optical domain is experimentally challenging due to the imperfect initialization and detection of optical photons. In this talk, we present a superconducting bosonic processor that combines high fidelity non-Gaussian state preparation, a complete set of Gaussian operations, and a novel single-shot photon number resolving measurement scheme. We utilize this processor to extract FC factors for photoelectron processes in H₂O, O₃, NO₂, and SO₂, including those from vibrational excited states. We exemplify the efficiency of this approach by comparing the resources needed to perform our simulation with that of a qubit-based architecture.

[1] Huh et al., Nature Photonics, 9 615-620 (2015)   

Quantum computation of magnon spectra

We demonstrate quantum computation of two-point correlation functions for a Heisenberg spin chain. Using the IBM Q 20 Tokyo machine, we find that for two sites the correlation functions produce the exact results reliably. For four sites, results from the quantum computer are noisy due to read out errors and decoherence. Nevertheless, the correlation functions retain the correct spectral information. This is illustrated in the frequency domain by accurately extracting the magnon energies from peaks in the spectral function.   

Improving chemistry calculations with virtual quantum subspace expansion

Accurate calculations in quantum chemistry require the use of large basis sets which amounts to a large number of molecular spin-orbitals. Each spin-orbital is typically mapped to a separate qubit. Many qubits are therefore necessary to achieve a desired accuracy. However, noisy intermediate-scale quantum computers have only a small number of qubits which limits the reach of quantum computing algorithms in quantum chemistry. A promising approach to overcome this problem is to use a quantum computer to solve only the classically hard part and a classical computer to solve the rest. A recently proposed virtual quantum subspace expansion (VQSE) method achieves this by modeling only the active space, that captures essential quantum effects, on a quantum computer. We report experimental results obtained using the VQSE algorithm to model small molecules. This work explores practical viability of hybrid quantum-classical methods in quantum computing.
  

Accuracy of the effective Hamiltonian in the quantum simulation experiments

Superconducting qubits and cold atom systems can simulate a variety of quantum Hamiltonians by implementing the couplings directly, as opposed to Trotterization of the quantum evolution and gate-based simulation. In this approach, the effective Hamiltonian is often calibrated experimentally to match the desired properties. We develop a rigorous mathematical foundation for the calibration of the building blocks to obtain a target effective Hamiltonian. The building blocks we consider are both superconducting circuits and cold atoms. For both approaches we provide an error estimate: the difference in the norm between the obtained effective Hamiltonian and the target. Our approach extends to time-dependent Hamiltonians via a version of adiabatic theorem.   

Hybrid quantum-classical simulations of correlated materials within Gutzwiller variational approach

We develop a hybrid quantum-classical simulation framework that leverages existing noisy intermediate-scale quantum (NISQ) computing technology to study ground-state properties of correlated electron materials. It combines classical Gutzwiller variational embedding theory with state-of-the-art quantum computing algorithms to solve the effective multi-orbital embedding problem. The theory amounts to finding a self-consistent solution of coupled eigenvalue equations. The effective quasi-particle Hamiltonian is diagonalized efficiently using classical computers, while the ground state of the Gutzwiller embedding Hamiltonian is obtained using variational quantum eigensolvers implemented on quantum computing devices. This is feasible on NISQ devices and takes advantage of relatively shallow quantum circuits for error mitigation. The approach is applied to the periodic Anderson model and Hubbard models. Various variational ansatz and quantum noise forms will be compared on their numerical convergence and calculation accuracy.   

Improvements in quantum algorithms for quantum chemistry and condensed matter

The simulation of many-body systems in condensed matter and chemistry is a challenging task in which quantum computers promise to be of some use. While initial quantum algorithms for such purposes had costly requirements for coherence times or numbers of state preparations needed, a flurry of work in recent years has significantly reduced these costs and found new methods, opening the question whether quantum computers can become of use for this class of problems in the NISQ era. In this talk, I will overview a number of recently developed algorithms and algorithmic improvements, and some experimental implementations thereof, including methods for state preparation, error mitigation, partial state tomography, and derivative estimation on a quantum device.   

Quantum Chemistry as an application-insprired Benchmark on near-term quantum computers

Near term quantum computing applications can inspire benchmarks and can serve as predictors for future machine performance as the hardware improves. We will present results from application-inspired benchmarks, including Quantum Chemistry. The quantum chemistry benchmark for noisy intermediate-scale quantum computers leverages the variational quantum eigensolver, active space reduction, a modified unitary coupled cluster ansatz, and reduced density purification as error mitigation. We demonstrate this benchmark on the 20 qubit IBM Tokyo and 16 qubit Rigetti Aspen processors via the simulation of alkali metal hydrides (NaH, KH, RbH), with accuracy of the ground state energy as the primary benchmark metric. We also show how to reduce the noise in post processing with specific error mitigation techniques. The adaptation of McWeeny purification of noisy density matrices dramatically improves accuracy of quantum computations, which, along with adjustable active space, significantly extends the range of accessible molecular systems. We demonstrate that for specific benchmark settings, the accuracy metric can reach chemical accuracy when computing over the cloud on certain quantum computers.   

Quantum simulation of the dynamics of the Fermi-Hubbard model on Sycamore

Studying strongly correlated systems is among the many applications of a quantum computer. Here, we report such an experiment on the dynamics of the Fermi-Hubbard model using Google’s Sycamore quantum chip. I will discuss the physics that we learned from the experiment as well as the compilation and error mitigation tools that make the experiment possible. I will also walk you through the tutorial that we develop for the Fermi-Hubbard experiment.   

Experimental realization of a nonlinear 3-wave mixing gate for quantum simulation

The ability to simulate an arbitrary Hamiltonian on a quantum device is an important step towards achieving universal quantum computing. We present a simulation of nonlinear 3-wave processes on a single qudit of the LLNL Quantum Design and Integration Testbed (QuDIT) resulting from iterative application of a gate developed to emulate these interactions. We describe our experimental protocol for realizing this simulation on the first three levels of a qudit and present results of average state population as a function of time. This experiment consists of a transmon-style qudit that is capacitively coupled to a superconducting 3D microwave cavity field. The qudit is addressed by a single-input RF signal that has been numerically optimized to perform 3-wave mixing unitary gate operations with fidelity of over 99%. We find that the average population of the qudit states evolve in a manner that matches the theoretically predicted quantum numbers of each wave in the 3-wave mixing process over many gate iterations.   

Matrix product state simulations on a quantum computer

Matrix product states (MPS) afford a compressed representation of many states that are relevant to physical systems. While many classical algorithms have been developed to compute the properties of physical systems using MPS as an ansatz, in many cases of practical interest these algorithms still require exponential resources (for example in the size of the system, or in the evolution time when out of equilibrium). We discuss near-term prospects for using small and non-error-corrected quantum computers to aid in MPS simulations.   

Quantum simulation of nonlinear three-wave interactions with engineered cubic couplings

Quantum three-wave gates are building blocks for simulating lattice gauge theory, nonlinear optics, weak turbulence, and laser plasma interactions. Although the underlying cubic couplings are usually absent in the quantum hardware, we show that effective three-wave vertices can be generated using control pulse engineering. In particular, for a three-wave Hamiltonian whose conserved actions are positive, we show that its Hilbert space can be decomposed into a direct sum of D-dimensional subspaces. Within each subspace, the quantum states are readily mapped onto the memory of quantum computers, and the Hamiltonian matrix becomes tridiagonal. Such a Hamiltonian is realized on the LLNL Quantum Design and Integration Testbed (QuDIT), utilizing three levels of a qudit. The qudit is controlled by digitally synthesized microwave pulses, whose wave forms are optimized numerically. Less accurate but cheaper control pulses may also be generated by interpolation, when parameters of the Hamiltonian vary. The resultant three-wave gates are applied to simulate the temporal three-wave problem, and physically meaningful results are obtained despite noise in the quantum computer.