Progress Towards Using Quantum Computers for Solving Quantum Chemistry and Machine Learning

IonQ used its trapped-ion computer and a scalable
co-design framework for solving chemistry problems. They applied it to compute the ground-state energy of the water molecule. The robust operation of the trapped ion quantum computer yields energy estimates with errors approaching the chemical accuracy, which is the target threshold necessary for predicting the rates of chemical reaction dynamics.

Quantum chemistry is a promising application where quantum computing might overcome the limitations of known classical algorithms, hampered by an exponential scaling of computational resource requirements. One of the most challenging tasks in quantum chemistry is to determine molecular energies to within chemical accuracy.

At the end of 2018, IonQ announced that they had loaded 79 operating qubits into their trapped ion system and had loaded 160 ions for storage in another test. This new research shows that they are making progress applying their system to useful quantum chemistry problems. They are leveraging the trapped-ions system longer stability to process many steps. The new optimization methods developed for this first major quantum chemistry problem can also be used to solve significant optimization and machine learning problems.

Above – : Apparatus and performance. a, Schematic representation of the trapped-ion QC. The qubit register is implemented in a linear chain of 171Yb+ ions residing inside an ultra-high vacuum chamber (not shown), and high-NA imaging optics enable individual addressing and readout of the ion qubits. The Raman beams (shown in red and purple) are generated from a pulsed laser at 355 nm and drive a two-photon transition between |0i and |1i. Full control of the amplitude, frequency, and phase of the individual addressing beams enables implementations of arbitrary single– and two–qubit operators. b, SPAM characterization on a three-ion chain. From top to bottom, we show the SPAM error of each three-qubit state, the per-qubit SPAM error for |0i and |1i, and a bar plot of the full SPAM matrix where the color is log-scaled for visibility. We see no indication of measurement crosstalk between qubits.

Early quantum computational techniques to simulate many-body Fermi systems or calculate molecular energies have dramatically improved over the past decade, but the resource requirements for useful chemical simulations still remain out of reach. Hybrid approaches might relax these requirements, where a short quantum computation serves as a subroutine to calculate classically difficult quantities. The variational quantum eigensolver (VQE) method is one example, which estimates the ground state of a system by positing an ansatz state defined by a set of variational parameters and minimizing its energy.

IonQ has used a generic VQE approach that scales to much larger molecular systems and use it to compute the ground-state energy of the water molecule (H2O). They used co-design principles to fully optimize the quantum circuits for a trapped-ion QC, and experimentally compute the first three correction terms beyond the mean-field (Hatree-Fock) approximation.

They performed a 50 step calculation with 1 error in 250 per gate.

IonQ has implemented a number of circuit optimization techniques that take advantage of the unique features available in the IonQ trapped-ion QC, but are generic in the sense that they are applicable to any target molecule to be simulated. The strategies described here are executed by a full-stack, modularized software toolchain, which automatically produces optimized circuits for generating the ansatz state of a molecular system.

Given the circuit requirements outlined below and the gate fidelity achieved, IonQ believes that executing a full simulation towards the FCI energy is within reach using current trapped-ion quantum computer technology.

This framework yields near-optimal quantum circuits that can be run on existing NISQ ( noisy
intermediate-scale quantum) hardware.

Without any error mitigation, the experimental results for the first three correction terms are in excellent agreement with the theory at the level of chemical accuracy, both in the predicted values and their precision.

While these results are specific to a particular quantum chemistry problem and the trapped-ion QC hardware, the computational methodology we develop is completely general to simulating quantum systems. We anticipate that similar advances can be applied to other optimization problems that work on variational methods, such as the quantum approximate optimization algorithm and various quantum machine learning applications. Increased attention to co-design principles like those demonstrated here will be necessary to push the boundary of possibility in near-term quantum computation.

SOURCES- IonQ, Arxiv

Written By Brian Wang. Nextbigfuture.com