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Nature Communications

A modular design of molecular qubits to implement universal quantum gates

Jesús Ferrando–Soria, Eufemio Moreno Pineda, Alessandro Chiesa, Antonio Fernández, Samantha A. Magee, Stefano Carretta, Paolo Maria Santini, Íñigo J. Vitórica‐Yrezábal, Floriana Tuna, Grigore A. Timco, Eric J. L. McInnes, Richard E. P. Winpenny

Published Apr 25, 2016• 253 citations
Publisher

Abstract

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.

DOI
10.1038/ncomms11377

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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.
Molecular nanomagnets are attractive candidate qubits because of their wide inter- and intra-molecular tunability. Uniform magnetic pulses could be exploited to implement one- and two-qubit gates in presence of a properly engineered pattern of interactions, but the synthesis of suitable and potentially scalable supramolecular complexes has proven a very hard task. Indeed, no quantum algorithms have ever been implemented, not even a proof-of-principle two-qubit gate. Here we show that the magnetic couplings in two supramolecular {Cr7Ni}-Ni-{Cr7Ni} assemblies can be chemically engineered to fit the above requisites for conditional gates with no need of local control. Microscopic parameters are determined by a recently developed many-body ab-initio approach and used to simulate quantum gates. We find that these systems are optimal for proof-of-principle two-qubit experiments and can be exploited as building blocks of scalable architectures for quantum simulation.
Quantum information processing (QIP) could revolutionize how we simulate and understand quantum systems. Any QIP scheme requires both individual units (qubits) that have long phase memories and switchable units that can be placed between the qubits. Here, we describe supramolecular systems where {Cr 7 Ni} rings are used as qubits, linked by redox-switchable {Ru 2 M} oxo-centered triangles (M = Zn, Ni, or Co). The supramolecular assemblies have been structurally characterized and involve two {Cr 7 Ni} rings bound to {Ru 2 M} triangles through iso -nicotinate ligands. Detailed physical studies, including electrochemistry and electron paramagnetic resonance spectroscopy, show that when M = Co, the supramolecular assembly has the physical characteristics needed to implement the √iSWAP gate, which is an important entangling two-qubit gate. Detailed simulations show that the fidelity of this gate is potentially very high and depends on the phase memory time of the {Cr 7 Ni} qubits but not the {Ru 2 Co} switch.
Molecular nanomagnets can be considered as serious candidates for the definition of a scalable and reliable quantum computing technology: information is encoded on their spins and they ensure relaxation and decoherence times sufficiently long for the execution of tens of quantum operations. Among these devices, Cr7Ni supramolecular complexes are extremely of interest since they implement a universal set of quantum gates, made of single-qubit gates and the two-qubit Controlled-phase gate. A model for analyzing Cr7Ni molecules and a potential quantum computer architecture are proposed: starting from the energy parameters required for spin manipulations, these systems have been proved to implement elementary quantum algorithms. Within this paper, two, three and four-qubit systems have been analyzed: the simulation of quantum operations and the analysis of dynamical non-idealities have been done in parallel. Our approach enables the definition of an operating point - in terms of magnetic driving fields and latency - in which the execution of elementary quantum algorithms is characterized by negligible errors. The proposed model has been entirely implemented in MATLAB, thus obtaining a software infrastructure for the analysis of Cr7Ni molecules that can be extended to quantum systems with analogous Hamiltonian and behavior.
Simulating the evolution of quantum systems on a classical computer is a yellow very challenging task, which could be easily tackled by digital quantum simulators. These are intrinsically quantum devices whose parameters can be controlled in order to mimic the evolution of a broad class of target Hamiltonians. We describe here a quantum simulator implemented on a linear register of molecular Cr7Ni qubits, linked through Co2+ ions which act as switches of the qubit–qubit interaction. This allows us to implement one- and two-qubit gates on the chain with high-fidelity, by means of uniform magnetic pulses. We demonstrate the effectiveness of the scheme by numerical experiments in which we combine several of these elementary gates to implement the simulation of the transverse field Ising model on a set of three qubits. The very good agreement with the expected evolution suggests that the proposed architecture can be scaled to several qubits.
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The substitution of one metal ion in a Cr-based molecular ring with dominant antiferromagnetic couplings allows the engineering of its level structure and ground-state degeneracy. Here we characterize a Cr7Ni molecular ring by means of low-temperature specific-heat and torque-magnetometry measurements, thus determining the microscopic parameters of the corresponding spin Hamiltonian. The energy spectrum and the suppression of the leakage-inducing S mixing render the Cr7Ni molecule a suitable candidate for the qubit implementation, as further substantiated by our quantum-gate simulations.