This yields a decay of the system coherences ρ μν( t) = exp(− γ μν t)ρ μν(0) with decay rates (22,23) Starting from the microscopic system-bath Hamiltonian and from the system eigenstates, we derive in the Supporting Information a master equation describing the dynamics of the system in the secular and Born–Markov approximations. The dominant source of decoherence in molecular nanomagnets at low temperature is the hyperfine coupling of the system spins with the surrounding nuclear spins, while phonon-mediated processes are practically negligible. To design optimal molecular systems, we first pinpoint the crucial ingredients related to the spin structure of the eigenstates driving decoherence and then identify the requirements to keep them under control. Finally, we exploit another peculiar feature of the designed molecule, namely, the possibility to induce direct transitions between all the selected energy levels, to actually implement quantum error correction and quantum gates between encoded states.ĭesign of Molecular Nanomagnets with Suppressed Decoherence. OPTIMAL RECOVERY QUANTUM ERROR CORRECTION CODEWe then compare the performance of the QEC code for the same molecular structure with competing versus ferromagnetic exchange interactions (producing a ground spin S multiplet), finding an impressive gain for the former. We numerically compute the resulting effect of dephasing on the lowest energy levels, and we derive code words exploiting superpositions of these levels. We demonstrate this by considering a 7-spin molecule in a bath of nuclear spins, driving decoherence at low temperature. As a consequence, superpositions of all the states belonging to these multiplets are substantially protected from decoherence in a way that does not worsen by adding levels. The optimal units are represented by multispin molecules with antiferromagnetic competing exchange interactions, (30−34) leading to several magnetically similar multiplets at low energy. As a result, the correcting power of the code is largely enhanced, by orders of magnitude compared to the case of a spin S system. This allows us to increase the number of levels in the encoding without being limited by the corresponding loss of coherence. In particular, we theoretically design optimal molecules showing a large number of low-energy states, for which decoherence is strongly suppressed and does not grow with the system size. Here we show that both these challenging tasks can be achieved by fully unleashing the chemical tunability of our molecular hardware, which constitutes its fundamental advantage but was not exploited to date. Instead, to implement complex algorithms, logical units must display errors not increasing significantly with the system size and must support gates between encoded states. Moreover, quantum gates between logical states encoded in spin S qudits are not allowed. However, the dramatic growth of decoherence with S yields only a limited gain in actually performing quantum error correction. (21,22) By increasing S, and hence the number of levels in the encoding, one could in principle increase the correcting capacity of the code. (21,22) The 2 S + 1 states of a spin S ion (for which several examples exist (23−29)) provide the chemically simplest implementation, which already ensures a gain in the lifetime of a quantum memory. (14−20) We have recently shown that these qudits can be exploited to embed QEC within a single object, thus greatly simplifying its actual implementation. In particular, they are typically characterized by many electronic and nuclear spin states (i.e., a qudit structure), which can be coherently manipulated through microwave or radio frequency pulses. Molecular spin systems offer a new alternative perspective, which can overcome major limitations of qubit-based approaches. (13) Even for the most advanced platforms, this makes the actual manipulation of the resulting register practically unfeasible and hence still represents an almost prohibitive goal. Each of these units is usually represented by a large collection of qubits, (11,12) at least 10 3–10 4 to get, for example, a likely success in factoring a 2000-bit number. The only way to get around this hurdle is by replacing two-level qubits with more complex logical units, supporting quantum-error correction (QEC). However, none of the existing technologies (1−10) can suppress errors on each computational qubit to the level required to achieve a real quantum advantage. Quantum computers promise to outclass classical digital devices in the solution of currently intractable problems.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |