Entanglement generation using molecular spin-qubits

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With the rapidly growing interest in quantum technologies, different physical systems are being tested in parallel as potential platforms for quantum information processing (QIP). Although most current commercial efforts are being put in quantum computing based on superconducting circuits and quantum communications based on photons, quantum two-level systems based on spin states, known as “spin qubits”, have also proven to be a promising platform, since they offer the possibility of solid state devices. In recent years, spin qubits embodied by molecular nanomagnets (in short molecular spin qubits) have gained attention by both Physicists and Chemists, because their spin Hamiltonian can be tuned both physically and chemically with a high degree of sophistication and at a relatively low cost.

A key step towards practical QIP using molecular spin qubits is to generate a maximally entangled state between at least two spin qubits. Indeed, quantum entanglement is a fundamental resource of quantum information processing. Like every manipulation of quantum states, generating entanglement requires solving a trade-off between two contradictory requirements: (a) isolating the qubits from the environment to preserve a long quantum coherence time and (b) coupling the qubits to our external stimuli to allow a short operational gating time. For obtaining reliable entanglement, the coherence time must vastly exceed the gating time. More generally speaking another desidered feature is to have simple and distinguishable physical ways to implement each distinct logical operation, whether this is a single-qubit gate or a two-qubit gate. For us, in practice, this meant distinguishable single-qubit transitions and a switchable operating qubit space to activate two-qubit rotations.

In our paper Electrical two-qubit gates within a pair of clock-qubit magnetic molecules DOI [10.1038/s41534-022-00647-8], we proposed a scheme of two-qubit entanglement gate in a molecular spin-qubit candidate [Ho(W5O18)2]9- (in short HoW10). While this work is theoretical, we have demonstrated the proposed scheme both quantitatively and qualitatively. This is, to we aimed not only to circumvent the above listed contradiction between the requirements for entanglement generation but also to provide detailed experimental guidelines for its practical implementation.

HoW10 is a polyoxometalate molecular anion whose spin-qubit dynamics are protected against magnetic noise at optimal operating points known as atomic clock transitions (CTs). However, for the same reason, they are insensitive to magnetic signals at those points. Moreover, the crystal unit cell contains two inversion-symmetry related HoW10 anions, which, when not at a CT, are coupled through weak dipolar interaction (Fig. a). In a recent collaborative work from our group on HoW10, experimental and theoretical study showed that one can achieve coherent control over the spin using an electric field pulse of modest strength to manipulate the CT frequency: Quantum coherent spin–electric control in a molecular nanomagnet at clock transitions DOI[10.1038/s41567-021-01355-4]. This is realized in practice due to a strong spin–electric coupling (SEC), which arises from intrinsic symmetry breaking, a soft and electrically polarizable environment of the spin carriers, and a spin spectrum that is highly sensitive to distortions. The inversion-symmetry in the crystal allows us to selectively address the spins of otherwise identical HoW10 molecules based simply upon the fact that they are pointing in opposite directions, and thus are distorted in different ways by an electric field. 

Two-qubit entanglement generation. (a) A weakly dipolar coupled HoW10--HoW10, (b) two-qubit Hilbert space in absence and presence of an E-field.ion

In pursuit of generating an entangled spins state using HoW10 with overcoming the necessary requirements, listed above, we took advantage simultaneously of the clock-transition phenomenon and of the E-field control of spins. 

As a preparatory step of our scheme, we determined decoherence times of single qubit for different magnetic fields (B-field) at different temperatures. This is to find optimal operational conditions, so that we don't lose the physical characteristic of qubit. Indeed, we found that moderate cooling (down to 2 or 3K) is expected to provide a long enough coherent time (above 25 microseconds, with a pulse sequence encoding a very general quantum logical operation taking about 7 microseconds). Then we moved on to fulfill the key requirements i.e., distinguishable transitions and a switchable operating qubit space. The former can be achieved by the electric field, and the latter by switching it off, in presence of dipolar interaction, i.e. operating at a magnetic field that is not exactly at the CTs (Fig. b). We gave the details (temperature, magnitude of electric and magnetic fields, pulse sequences for a few example quantum circuits) for the physical implementation of our proposal using Electron Paramagnetic Resonance (EPR). 

We hope that the work presented in our paper will serve to further stimulate the research in the field of molecular spin-qubits. In any case, it brings us a step closer to making a realistic molecular spin qubit based quantum processor. But it also opens new questions, such as scalability for considering more than two qubits and how to perform error correction to finally achieve fault-tolerant quantum computing. 

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