Session J08: NISQ: Quantum Chemistry and Quantum Simulation II

Simulating quantum systems on quantum computers

In this presentation, we discuss a new mapping method—called symmetry configuration mapping (SCM)—that uses the symmetry of the physical system to isolate different parts of the computational space. As well as providing robustness against state leakage, this new approach allows the computation to be separated into a set of smaller independent calculations involving fewer quantum logic gate operations and fewer qubits. For a fluorine molecule, the numbers of quantum logic gate operations and qubits are reduced by factors of 3 and 4, respectively. These reductions have allowed us to solve for the full many-body ground state on the IBM Q “Poughkeepsie” quantum computer. As long as quantum computing resources remain limited, similar target-customized mappings are expected to be employed in quantum computing across all areas of application.   

Studying many-body localization on a universal quantum computer

An interacting disordered system may exhibit localized or thermal behavior depending on the ratio of the disorder to interaction strength. The study of this phenomena has been proposed as an application of near-term quantum computers. However, it is known that most diagnostics of localization such as many-body level statistics and the failure of the eigenstate thermalization hypothesis do not survive coupling to a bath. One robust diagnostic theoretically known to survive introduction of noise are the spectral functions of local operators [1]. Signatures of localization in this diagnostic include a discrete spectrum and a gap at low frequencies. Here, we design an algorithm to compute the spectrum on a universal quantum computer using Trotterized time-evolution. Further, we implement the technique on a three-qubit trapped ion system and find that we can clearly discern the vanishing of the low-frequency response as the disorder increases. Thus, we show that for near-term quantum computers, spectral functions of local operators provide a robust and scalable diagnostic for distinguishing between localized and thermal phases.

[1] Sonika Johri, Rahul Nandkishore and R. N. Bhatt, Phys. Rev. Lett. 114 (11), 117401   

Towards material design applications in a quantum computer

Developing new materials for specific applications is an active field of research for both material science and quantum chemistry communities. The number of atomic compositions of molecular structures scales combinatorically with the size of the molecules, limiting the efficiency of classical algorithms. On the other hand, quantum computers can provide an efficient solution to the sampling of the chemical compound space. In this talk we propose a quantum algorithm with favorable scaling in resource requirements, allowing for the solution of the material design problem in currently available noisy quantum processors. The proposed scheme divides the problem into a classical optimization and a quantum search problem within a hybrid quantum classical algorithm. We demonstrate both in simulations (with and without noise) and in IBMQ quantum hardware the efficiency of our scheme and highlight the results in a few test cases. These preliminary results can serve as a basis for the development of further material design quantum algorithms for near term quantum computers.
  

Simulating quantum field theory in the light-front formulation

We explore the possibility of simulating relativistic field theories in the light-front (LF) formulation and argue that such a framework has numerous advantages as compared to both lattice and second-quantized equal-time approaches. These include a small number of physical degrees of freedom leading to reduced resource requirements, efficient encoding with model-independent asymptotics, and sparse Hamiltonians. Many quantities of physical interest are naturally defined in the LF, resulting in simple measurements.

The LF formulation allows one to trace the connection between relativistic field theories and quantum chemistry, allowing one to use numerous techniques developed in the last decade. It also provides a promising application for NISQ devices, since for certain calculations one may need of an order of hundred qubits. As an example, we provide a detailed algorithm for calculating analogues of QCD parton distribution functions in a simple 1+1-dimensional model. We also discuss the generalization to QCD, and provide estimates.   

Simulating Dynamic Material Properties on Near-Term Quantum Computers

Dynamic simulation of controllable electronic properties of materials offers insight into how to harness such tunability for use in myriad technologies. Recent successes have been achieved in computing static properties of small molecules on currently available quantum computers, however, simulating dynamical properties still remains a challenge. In this work, we demonstrate successful simulation of time-dependent magnetization in a simplified model of an atomically-thin two-dimensional material on IBM’s Q16 Melbourne quantum processor and Rigetti’s Aspen quantum processor. Near overlap between experimental results from the quantum computer and those theoretically derived from simulated noisy qubits indicates there is a good understanding of the largest sources of error currently faced on available quantum computers. This early proof-of-concept gives hope that near-future quantum computers, capable of simulating larger systems, may soon be able to give insights into the dynamic control of tunable electronic properties in material.   

Robust Preparation of Many-body Ground States in Jaynes-Cummings Lattices

Strongly-correlated polaritons in Jaynes-Cummings (JC) lattices can exhibit novel quantum phase transitions at integer fillings. However, it is often challenging to prepare such states with high fidelity, especially near the quantum critical points with a vanishing energy gap. Here we study the robust preparation of the many-body ground states of polaritons in a finite-sized JC lattice by combining the techniques of quantum state engineering and adiabatic evolution. In the deep Mott-insulating or deep superfluid regimes, the many-body ground states can be generated with high fidelity by applying quantum-engineered pulse sequences to the JC lattice. Using these states as the initial state and tuning the system parameters adiabatically, the many-body ground states in the intermediate regime can be reached. Our numerical result shows that the fidelity of the generated states can be significantly improved by employing a nonlinear ramping scheme during the adiabatic evolution. We derive the optimal nonlinear index analytically, which agrees well with the numerical result. This study gives insights into the preparation of many-body states in artificial quantum systems, such as quantum simulators.   

Quantum Algorithm for Simulating a Driven Dissipative 3-site Hubbard Ring

Much research has been done concerning the simulation of closed quantum systems on near term quantum computers. Considerably less focus has been given to the simulation of open quantum systems, despite their importance as realistic models of real world systems. We consider the simulation of a three site Hubbard model driven by an electric field, connected to a Fermionic bath. This is the simplest model capable of stabilizing a non-zero steady state current with the added benefit that the fermionic bath admits an analytic solution in the non-interacting limit. We simulate this model classically using a master equation approach and provide an implementation for simulating it on a quantum computer. Even this simple model shows rich steady state behavior and offers a promising approach for simulating a variety of time dependent, driven, dissipative, open quantum systems.   

Mapping Hamiltonians from material science onto near-term quantum devices

Simulation of quantum Hamiltonians is one of the most promising applications proposed for which quantum hardware may provide significant advances over classical methods. However, significant limitations on near-term hardware size and fidelity pose a significant challenge for implementing known methods for realistic applications in chemistry and material science. Finding realistic systems for which near-term hardware can produce a useful simulation remains an open question. In this work we demonstrate that downfolding Hamiltonians, a process by which real materials are mapped on to model Hamiltonians, can yield a Hamiltonian form and size that is suitable for simulation on near-term quantum hardware. We apply this approach to several example materials and show how to implement it on realistic hardware using generalized swap networks.   

Determining Hamiltonian eigenstates on a quantum computer using quantum imaginary time evolution

The accurate computation of Hamiltonian ground and excited states on quantum computers stands to impact many problems in the physical and computer sciences, from quantum simulation to machine learning. Given the challenges posed in constructing large-scale quantum computers, these tasks should be carried out in a resource-efficient way. We recently introduced [1] the quantum imaginary time evolution and quantum Lanczos algorithms, which are analogues of classical algorithms for finding ground and excited states. Compared with their classical counterparts, they require exponentially less space and time per iteration, and can be implemented without deep circuits and ancillae, or high-dimensional optimizations. We discuss applications to spins and fermions.

[1] M. Motta, C. Sun, A. T. K. Tan, M. J. O'Rourke, E. Ye, A. J. Minnich, F. G. S. L. Brandao and G. K.-L. Chan, arXiv:1901.07653   

Quantum Computation of the Ground and Excited State Energies Using Quantum Imaginary Time Evolution and Quantum Lanczos Methods

Various methods have been developed for quantum computation of the ground and excited states of physical systems, but many of them require either large numbers of ancilla or high dimensional optimization. The quantum imaginary time evolution (QITE) and quantum Lanczos (QLanczos) methods proposed in [1] eschew the aforementioned issues. In this study, we demonstrate the application of these algorithms on a nontrivial quantum computation, using the deuteron binding energy as an example. With the correct choice of initial and final states we showed that the number of time steps in QITE and QLanczos can be reduced significantly, which commensurately simplifies the required quantum circuit and improves compatibility with NISQ devices. We performed these calculations on cloud-accessible IBMQ quantum computers, and with the application of readout error mitigation and Richardson error extrapolation, we obtained ground and approximate excited state energies within 3% of the theory. These results show promise for using the algorithms in future field theory, scattering, and chemistry calculations.
[1] M. Motta, et.al., arXiv:1901.07653v2 [quant-ph] (2019)   

Driven-dissipative quantum mechanics on a lattice: Describing a fermionic reservoir with the master equation

The possibility of simulating dissipative processes with digital circuits and quantum simulators, and using dissipation as a resource for state preparation, have created a renewed interest on the driven-dissipative many body problem.
Here, I address a tight binding model of electrons driven out-of-equilibrium by an electric field, where the system can exchange energy and number of particles with a fermionic reservoir. The problem is solved using the master equation formalism. I use the exact solution for the noninteracting driven-dissipative system to benchmark the accuracy of the results obtained with the master-equation, showing a very good quantitative agreement. Furthermore, to create a better link with the simulation of open quantum systems, I provide with the time dependent Kraus map that pumps the system to the non-equilibrium steady state. Generalizations of such a method to broken symmetry phases (like CDW) and their simulation on quantum computers are discussed too.   

Quantum synchronization on the IBM Q system

We report the first experimental demonstration of quantum synchronization. This is achieved by performing a digital simulation of a spin-1 limit-cycle oscillator on the quantum processors of the IBM Q system. Applying an external signal to the oscillator, we verify typical features of quantum synchronization and demonstrate an interference-based quantum synchronization blockade. Our results show that state-of-the-art noisy intermediate-scale quantum processors are powerful enough to implement realistic open quantum systems. Finally, we discuss limitations of current quantum hardware and define requirements necessary to investigate more complex problems.   

Quantum Digital Cooling

We introduce a new method for digital preparation of ground states of a simulated Hamiltonians, inspired by cooling in nature and adapted to leverage the capabilities of digital quantum hardware. The cold bath is simulated by a single ancillary qubit, which is reset periodically and coupled to the system non-perturbatively. Studying this cooling method on a 1-qubit system toy model allows us to optimize two cooling protocols based on weak-coupling and strong-coupling approaches. Extending these, we develop two scalable protocols for larger systems.
The LogSweep protocol extends the weak-coupling approach by sweeping energies to resonantly match any targeted transition, demonstrating preparation of an approximate ground state for ferromagnetic and critical Ising chain, with error that can be made polinomially small in time.
The BangBang protocol extends the strong-coupling approach, and exploits a heuristics for local Hamiltonians to approximately match transition energies, allowing rapid cooling to an approximation of the ground state, which makes this protocol appealing for near-term simulation applications.   

Resource-Efficient Quantum Algorithm for Protein Folding

Due to the central role of proteins’ 3D structures in chemistry, biology and medicine applications (e.g., in drug discovery), protein folding has been intensively studied for over half a century. Although classical algorithms provide practical solutions for the conformation space sampling of small proteins, they cannot tackle the intrinsic NP-hard complexity of the problem, even reduced to its simplest Hydrophobic-Polar model.
While fault-tolerant quantum computers are still beyond reach for state-of-the-art quantum technologies, there is evidence that quantum algorithms can be successfully used on Noisy Intermediate-Scale Quantum (NISQ) computers to accelerate energy optimization in frustrated systems. In this talk, I will present a folding algorithm that requires resources (number of qubits and gate operations) that scale polynomially with the number of amino acids (AA). In particular, we propose a robust and versatile optimisation scheme to simulate the folding of the 10 AA Angiotensin peptide on 22 qubits and a 7 AA neuropeptide model using 9 qubits on an IBM Q 20-qubit quantum computer.
  

Digital quantum simulation of quantum vibrational dynamics and control

Quantum computers are expected to offer speed-ups for solving certain scientific problems. One example is digital quantum simulation, where sequences of quantum gates can be used to simulate the dynamics of quantum systems in polynomial time. This could have applications in simulations of quantum optimal control, which aim to identify shaped fields to drive a quantum system towards a designated control objective. In this talk, I will explore how digital quantum simulation could be used to make quantum optimal control simulations more tractable. I will introduce a framework that utilizes a quantum computer to simulate the field-induced dynamics of a quantum system in combination with classical optimization to update the field. As a demonstration of this framework, a quantum vibrational control problem will be considered.

Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. SAND2019-11769 PE