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arXiv:2202.03284 · Journal of Chemical Theory and Computation

Toward Quantum Computing with Molecular Electronics

Phillip W. K. Jensen, Lasse Bjørn Kristensen, Cyrille Lavigne, Alán Aspuru‐Guzik

Published May 10, 2022• 14 citations
arXivHTMLPDF

Abstract

In this study, we explore the use of molecules and molecular electronics for quantum computing. We construct one-qubit gates using one-electron scattering in molecules and two-qubit controlled-phase gates using electron-electron scattering along metallic leads. Furthermore, we propose a class of circuit implementations, and show initial applications of the framework by illustrating one-qubit gates using the molecular electronic structure of molecular hydrogen as a baseline model.

DOI
10.1021/acs.jctc.2c00162

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In this study, we explore the use of molecules and molecular electronics for quantum computing. We construct one-qubit gates using one-electron scattering in molecules and two-qubit controlled-phase gates using electron-electron scattering along metallic leads. Furthermore, we propose a class of circuit implementations, and show initial applications of the framework by illustrating one-qubit gates using the molecular electronic structure of molecular hydrogen as a baseline model.
Determining properties of molecules and materials is one of the premier applications of quantum computing. A major question in the thesis is: how might we use long- and near-term quantum computers to solve problems of chemical interest? First, we give an overview of the standard model in electronic structure theory. Electronic structure methods have been improved significantly in the last decades; however, it is still a non-trivial task to fit experimental results for complex molecular systems. Second, we introduce quantum computation and quantum algorithms as an alternative device to solve the electronic structure problem. In the remaining part of the thesis, we describe the research projects. The thesis covers two (rather different) research directions: software and hardware projects. For the software part, we contribute with two new algorithms: Phase-Estimation Interval Target Energy Readout (PHILTER) and Recursive Variational Series Estimation (RVSE), where both are designed to be run on a quantum digital computer and extract materials and molecular properties. The PHILTER algorithm is a modification of the Quantum Phase Estimation and is designed to compute excited state energies within a target energy-interval for cases where good approximations for the states in the target energy-interval are either unknown or hard to prepare. For the RVSE algorithm, we pose the question: how might we use imperfect near-term quantum computers to solve problems of practical value? In this work, we introduce a method to compute expectation values of general functions of a Hamiltonian with respect to an input state using low depth quantum circuits suitable for noisy intermediate-scale quantum computers. For the hardware part, we propose a new chemical quantum computer by using molecular electronics as a basis for quantum computing. In this work, we pose the question: can scattering of electrons in molecules produce quantum gates? We construct one-qubit gates using one-electron scattering in molecules, and two-qubit controlled-phase gates using electron-electron scattering along metallic leads. We show initial applications of the framework by illustrating one-qubit gates using the molecular electronic structure of molecular hydrogen as a baseline model.
In this educational paper, we will discuss calculations on the hydrogen molecule on both classical and quantum computers. In the former case, we will discuss the calculation of molecular integrals that can then be used to calculate potential energy curves at the Hartree-Fock level and to correct them by obtaining the exact results for all states in the minimal basis. Some aspects of spin-symmetry will also be discussed. In the case of quantum computing, we will start out from the second-quantized Hamiltonian and qubit mappings. We then provide circuits for quantum phase estimation using two different algorithms: Trotterization and qubitization. Finally, the significance of quantum error correction will be briefly discussed.
Molecules are serious candidates for building hardware for quantum computers. They can encode quantum information onto electron or nuclear spins and some of them show important features as the scalability of the number of qubits and a universal set of quantum gates. In this paper we present our advances in the development of a classical simulation infrastructure for molecular Quantum Computing: starting from the definition of simplified models taking into account the main physical features of each analyzed molecule, quantum gates are defined over these models, thus permitting to take into account the real behavior of each technology during the simulation. An interface with a hardware-agnostic description language has been also developed. The knowledge of the behavior of real systems permits to optimize the design of quantum circuits at both physical and compilation levels. Elementary quantum algorithms have been simulated on three different molecular technologies by changing the physical parameters of polarization and manipulation and quantum circuit design strategies. Results confirm the dependency of the fidelity of the results on both levels, thus proving that the choice of optimal operating points and circuit optimization techniques as virtual-Z gates are fundamental for ensuring the execution of quantum circuits with negligible errors.
We review the progress made in integrating magnetic molecules containing transition metal ions into nanoelectronic solid-state devices and using them as molecular spin qubits. Molecular spin qubits offer numerous advantages over other material platforms, such as being inherently quantum systems with discrete energy levels, having a rich variety of possible chemical designs, and being synthesizable in large quantities with atomic precision. However, the integration of magnetic molecules into practical and scalable molecular spin qubit devices (MSQDs) that offer initialization, coherent control, and readout of quantum spin states remains one of the major bottlenecks on the way toward applications of these systems in quantum computing technologies. We discuss the evolution of the field of MSQDs and review the first successful implementation of essential qubit operations in a single-molecule transistor based on a TbPc 2 molecule. Further development has been achieved through the merging of molecular electronics with the circuit quantum electrodynamics (cQED) approach where molecular spin states can be manipulated by the microwave frequency photons confined in a superconducting waveguide resonator. We discuss examples of such hybrid devices operating via coupling of a superconducting resonator to large spin ensembles, such as bulk samples and thin films. We also review a possible architecture for single-molecule cQED devices and the potential advantages that it offers. Then, we highlight the possibility and benefits of the optical initialization and readout of molecular spin states. This approach has been realized by using an optical pumping technique for the initialization and changes in photoluminescence for the readout of large molecular spin ensembles coupled to a superconducting resonator. The field of MSQDs is highly interdisciplinary, bringing together progress in synthetic chemistry, molecular electronics, cQED, and optical measurements. While it is still in its infancy, there are promising theoretical designs and encouraging proof-of-concept experiments, and we discuss several proposed device architectures that are eagerly awaiting experimental realization. Advances in hybrid MSQDs will open horizons for quantum technologies.
The physical implementation of quantum information processing relies on individual modules-qubits-and operations that modify such modules either individually or in groups-quantum gates. Two examples of gates that entangle pairs of qubits are the controlled NOT-gate (CNOT) gate, which flips the state of one qubit depending on the state of another, and the gate that brings a two-qubit product state into a superposition involving partially swapping the qubit states. Here we show that through supramolecular chemistry a single simple module, molecular {Cr7Ni} rings, which act as the qubits, can be assembled into structures suitable for either the CNOT or gate by choice of linker, and we characterize these structures by electron spin resonance spectroscopy. We introduce two schemes for implementing such gates with these supramolecular assemblies and perform detailed simulations, based on the measured parameters including decoherence, to demonstrate how the gates would operate.
Abstract Quantum Hamiltonian Computing is a recent approach that uses quantum systems, in particular a single molecule, to perform computational tasks. Within this approach, we present explicit methods to construct logic gates using two different designs, where the logical outputs are encoded either at fixed energy and spatial positioning of the quantum states, or at different energies. We use these results to construct quantum Boolean adders involving a minimal number of quantum states with the two designs. We also establish a matrix algebra giving an analogy between classical Boolean logic gates and quantum ones, and assess the possibilities of both designs for more complex gates.