Embedded quantum-error correction and controlled-phase gate for molecular spin qubits

Abstract

A scalable architecture for quantum computing requires logical units supporting quantum-error correction. In this respect, magnetic molecules are particularly promising, since they allow one to define logical qubits with embedded quantum-error correction by exploiting multiple energy levels of a single molecule. The single-object nature of this encoding is expected to facilitate the implementation of error correction procedures and logical operations. In this work, we make progress in this direction by showing how two-qubit gates between error-protected units can be realised, by means of easily implementable sequences of electro-magnetic pulses.

A perspective on scaling up quantum computation with molecular spins

“…30 On the other, effective qudit QEC codes can be implemented exploiting the d = 2S + 1 levels of a spin S system. 49,51,52 The first approach was investigated in Ref. 30, where it was shown that an [ErCeEr] trimer is a promising molecule to encode a logical qubit protected against dephasing by the three-qubit phase-flip code.…”

“…Indeed, the performance of the code can be improved by increasing the number of qudit levels, thus making it possible to correct higher-order dephasing errors. This can be done by considering larger nuclear spins, such as 173 Yb in Yb(trensal) 38 (S = 5/2) or 51 V in VOTPP (S = 7/2), 50 shown in Fig. 3-(d,e).…”

“…Second, large nuclear spins (7/2 in the case of 51 V) paves the way to the use of qudits, embedding quantum error correction. A scheme for implementing two-qubit gates on such error protected nuclear spins has been recently put forward 51 and it could be extended in the near future to a more general class of gates and to quantum simulations.…”

“…Encoding a protected qubit in a single physical object can greatly simplify the practical implementation of both error correction and the quantum logic on the protected subspace. 51,80 In addition, the codes are specifically adapted to the energy level schemes of the molecular spin qudits and to their dominant error sources. Even more, they can be optimized in several ways.…”

Optimal control of molecular spin qudits

“…In addition, there have been proposals for exploiting their multiple states to specific applications. Relevant examples are the digital quantum simulation of spin-boson models [31], where the qudit encodes boson states, and the implementation of quantum error correction codes [30,32,33]. The latter is particularly promising, as embedding in each basic unit, in this case a molecule, a suitably designed protection against its specific decoherence sources might represent a huge competitive advantage.…”