A solid-state quantum processor based on nuclear spins

Quantum computers, systems that process information leveraging quantum mechanical effects, have the potential of outperforming classical systems on some tasks. Instead of storing information as bits, like classical computers, they rely on so-called qubits, units of information that can simultaneously exist in superpositions of 0 and 1.

Researchers at University Paris-Saclay, the Chinese University of Hong Kong and other institutes have developed a new quantum computing platform that utilizes the intrinsic angular momentum (i.e., spin) of nuclei in tungsten-183 (¹⁸³W) atoms as qubits.

Their proposed system, introduced in a paper published in Nature Physics, was found to achieve long coherence times and is compatible with existing superconductor-based quantum information processing platforms.

“For decades, magnetic resonance—NMR and ESR—has been a workhorse of physics, chemistry and biology,” Emmanuel Flurin, senior author of the paper, told Phys.org.

“It was also one of the first platforms used to demonstrate basic quantum computing protocols. However, in its traditional form, it is intrinsically macroscopic: the signals are so weak that one typically needs ensembles of order 10¹⁵ atoms or more just to detect something.”

As part of their study, Flurin and his colleagues set out to improve the sensitivity of magnetic resonance-based quantum computing platforms to observe physical processes down to the single-atom level, all while retaining their quantum coherence. To achieve this, they combined magnetic resonance with superconducting materials, which are known to be highly responsive to electromagnetic signals.

“The main objective of the paper was to show that this combination effectively realizes a quantum version of magnetic resonance,” said Flurin.

“Specifically, we can detect, control and entangle individual nuclear spins in a solid, with coherence times of several seconds, in a chip-scale device that is compatible with microwave quantum technologies.”

A hybrid nuclear-electron spin platform

The quantum information processing system introduced by this team of researchers could be seen as an ultra-sensitive and quantum mechanics-driven version of a magnetic resonance spectrometer, which was built using superconducting circuits. The qubits that the system relies on are nuclear pins of ¹⁸³W atoms within a calcium tungstate CaWO₄ crystal.

“Each of these nuclei sits close to a rare-earth ion, Er³⁺, which carries an unpaired electron spin,” explained Flurin. “The electron spin is much easier to manipulate and detect than the nuclear spin, so it acts as an ancilla or amplifier for the nuclear spin.”

The researchers placed the CaWO₄ crystal on top of a superconducting microwave resonator, a device that stores microwave photons (i.e., particles of light) and that can be used to manipulate quantum states. This resonator was previously patterned direction on a chip. The team subsequently placed the entire device in a so-called dilution refrigerator and cooled it down to a few millikelvin.

“The resonator, combined with a very sensitive microwave detector, makes the setup sensitive enough that the tiny magnetic signal of a single electron spin—and, through it, of a single nuclear spin—becomes measurable,” said Flurin.

“A crucial aspect is that our method only relies on the magnetic resonance properties of the spins. We do not require any additional optical transition (as in NV centers) or particular electrical properties (as in semiconductor donors). This means that, in principle, all the species and techniques developed over decades in NMR and ESR can be directly imported into this platform.”

The team’s newly introduced quantum computing platform has several advantages over previously introduced magnetic resonance-driven systems. Most notably, the researchers were able to improve their system’s magnetic resonance sensitivity by many orders of magnitude, down to the level of single nuclear spins.

“We attained very long coherence times, of the order of seconds, because the qubits are nuclear spins,” said Flurin. “We also developed a general and adaptable method that does not rely on special optical or electrical tricks. Notably, our all-microwave, chip-based architecture is naturally compatible with existing superconducting quantum processors.”

Initial assessment of the team’s system

To assess the potential of their proposed platform, the researchers realized a prototype system and characterized the coherence of two individual nuclear spins in their system.

Ultimately, they demonstrated high-fidelity and single-shot readout, while also implementing microwave-driven single- and two-qubit gates between the two nuclear spins.

“First, we show that one can effectively do NMR/ESR at the single-spin level in a solid-state device,” said Flurin. “We demonstrate individual nuclear spin qubits with coherence times of several seconds, which brings the extraordinary stability of NMR into a fully microscopic, single-qubit regime.”

In their paper, Flurin and his colleagues also introduced a new readout technique that is highly sensitive and non-invasive (i.e., that does not disrupt the system). Coupling the spin of electrons in Er³⁺ atoms to a superconducting resonator and employing a quantum-limited microwave detector, they were able to perform single-shot, quantum non-demolition measurements of each nuclear spin.

“Because this readout is purely magnetic, it is in principle applicable to a broad range of spin species, without relying on optical fluorescence or transport measurements,” explained Flurin.

“We also showed that this platform satisfies the usual requirements for quantum computing. Using only microwave signals, we implement single- and two-qubit gates between nuclear spins and create a long-lived Bell state whose coherence exceeds one second.”

The results of this recent study further highlight the potential of quantum information processing platforms that rely on nuclear spins. The researchers were able to use the nuclear spins of atoms in a solid as fully-fledged qubits, which was not achieved in earlier NMR-related quantum computing experiments relying on large ensembles and pseudo-pure states.

Future applications and research directions

This recent study could soon open new possibilities for the development of quantum technologies, including both quantum computing systems and sensing devices.

“On the one hand, future studies could explore a sensing and spectroscopy route, where this device becomes a kind of quantum magnetic resonance microscope, capable in principle of probing individual molecules and resolving their structure with very high spectral resolution,” said Flurin.

“As we look at individual spins instead of large ensembles, we are not limited by the ‘blurring’ that occurs when many slightly different environments are averaged together. On the other hand, we are pursuing the quantum computing route.”

The researchers showed that long-lived nuclear spins can be highly stable qubits in chip-based quantum computing architectures. As part of their ongoing studies, they are working on an architecture consisting of several small nuclei clusters that can store quantum data. Each of these clusters is coupled to a single electron spin ancilla.

“This ancilla both provides single-shot readout of its local nuclear cluster and acts as a link between neighboring clusters by exchanging microwave photons,” said Flurin. “What we have demonstrated here is the elementary operation of one such cluster: coherent control, second long entanglement and high-fidelity readout of a small set of nuclear spins.”

In their next studies, Flurin and his colleagues plan to take further steps toward the development of quantum sensing and computing systems that build on their recently introduced platform. In the context of sensing, their hope is to successfully use their system to probe individual molecules and more complex systems.

“At the single-spin level, one can in principle access much sharper spectral features than in conventional NMR, where ensemble averaging and inhomogeneous broadening tend to wash out fine details,” explained Flurin. “This could enable a form of single-molecule magnetic resonance spectroscopy with quantum-limited resolution.”

The second goal of the team’s future studies will be to develop increasingly advanced quantum computing systems that leverage their design. To do this, they will try to continuously increase the number of controllable spins in their system and boost gate fidelities.

“With coherence times in the second range and gate times in the millisecond range, there is a lot of room to optimize device design and control protocols, and to start implementing small quantum algorithms or simple error-correcting codes using nuclear spin registers,” said Flurin.

Importantly, the platform introduced by the researchers is driven solely by magnetic resonance and does not rely on specific optical or electrical properties of materials.

Flurin and his colleagues eventually plan to also explore the potential of other types of spins and materials for the realization of their system. In addition, they will try to utilize nuclear spin qubits as long-lived memories or registers in larger superconducting-circuit architectures.

“An important conceptual point for us is that there is a strong synergy between quantum computing and quantum sensing in this platform,” added Flurin.

“A sophisticated magnetic resonance experiment can be viewed as a quantum circuit: each pulse sequence corresponds to a sequence of quantum gates, and the measured spectrum is the output of a quantum algorithm that encodes structural information about the molecule. Our approach makes this connection explicit at the single-spin level.

“This means that advances in quantum computing—for instance in optimal control or error mitigation—can directly benefit next-generation molecular spectroscopy, and, conversely, that the very rich toolbox of NMR and ESR can inspire new ways of processing quantum information.”