Molecular nanomagnets: a viable path toward quantum information processing?

Molecular nanomagnets (MNMs), molecules containing interacting spins, have been a playground for quantum mechanics. They are characterized by many accessible low-energy levels that can be exploited to store and process quantum information. This naturally opens the possibility of using them as qudits, thus enlarging the tools of quantum logic with respect to qubit-based architectures. These additional degrees of freedom recently prompted the proposal for encoding qubits with embedded quantum error correction (QEC) in single molecules. QEC is the holy grail of quantum computing and this qudit approach could circumvent the large overhead of physical qubits typical of standard multi-qubit codes. Another important strength of the molecular approach is the extremely high degree of control achieved in preparing complex supramolecular structures where individual qudits are linked preserving their individual properties and coherence. This is particularly relevant for building quantum simulators, controllable systems able to mimic the dynamics of other quantum objects. The use of MNMs for quantum information processing is a rapidly evolving field which still requires to be fully experimentally explored. The key issues to be settled are related to scaling up the number of qudits/qubits and their individual addressing. Several promising possibilities are being intensively explored, ranging from the use of single-molecule transistors or superconducting devices to optical readout techniques. Moreover, new tools from chemistry could be also at hand, like the chiral-induced spin selectivity. In this paper, we will review the present status of this interdisciplinary research field, discuss the open challenges and envisioned solution paths which could finally unleash the very large potential of molecular spins for quantum technologies.

The quantum house of cards

Quantum computers have been proposed to solve a number of important problems such as discovering new drugs, new catalysts for fertilizer production, breaking encryption protocols, optimizing financial portfolios, or implementing new artificial intelligence applications. Yet, to date, a simple task such as multiplying 3 by 5 is beyond existing quantum hardware. This article examines the difficulties that would need to be solved for quantum computers to live up to their promises. I discuss the whole stack of technologies that has been envisioned to build a quantum computer from the top layers (the actual algorithms and associated applications) down to the very bottom ones (the quantum hardware, its control electronics, cryogeny, etc.) while not forgetting the crucial intermediate layer of quantum error correction.

Dual-rail encoding with superconducting cavities

The design of quantum hardware that reduces and mitigates errors is essential for practical quantum error correction (QEC) and useful quantum computation. To this end, we introduce the circuit-Quantum Electrodynamics (QED) dual-rail qubit in which our physical qubit is encoded in the single-photon subspace, [Formula: see text], of two superconducting microwave cavities. The dominant photon loss errors can be detected and converted into erasure errors, which are in general much easier to correct. In contrast to linear optics, a circuit-QED implementation of the dual-rail code offers unique capabilities. Using just one additional transmon ancilla per dual-rail qubit, we describe how to perform a gate-based set of universal operations that includes state preparation, logical readout, and parametrizable single and two-qubit gates. Moreover, first-order hardware errors in the cavities and the transmon can be detected and converted to erasure errors in all operations, leaving background Pauli errors that are orders of magnitude smaller. Hence, the dual-rail cavity qubit exhibits a favorable hierarchy of error rates and is expected to perform well below the relevant QEC thresholds with today's coherence times.

Correcting Coherent Errors by Random Operation on Actual Quantum Hardware

Characterizing and mitigating errors in current noisy intermediate-scale devices is important to improve the performance of the next generation of quantum hardware. To investigate the importance of the different noise mechanisms affecting quantum computation, we performed a full quantum process tomography of single qubits in a real quantum processor in which echo experiments are implemented. In addition to the sources of error already included in the standard models, the obtained results show the dominant role of coherent errors, which we practically corrected by inserting random single-qubit unitaries in the quantum circuit, significantly increasing the circuit length over which quantum computations on actual quantum hardware produce reliable results.

Entanglement of Signal Paths via Noisy Superconducting Quantum Devices

Quantum routers will provide for important functionality in emerging quantum networks, and the deployment of quantum routing in real networks will initially be realized on low-complexity (few-qubit) noisy quantum devices. A true working quantum router will represent a new application for quantum entanglement-the coherent superposition of multiple communication paths traversed by the same quantum signal. Most end-user benefits of this application are yet to be discovered, but a few important use-cases are now known. In this work, we investigate the deployment of quantum routing on low-complexity superconducting quantum devices. In such devices, we verify the quantum nature of the routing process as well as the preservation of the routed quantum signal. We also implement quantum random access memory, a key application of quantum routing, on these same devices. Our experiments then embed a five-qubit quantum error-correcting code within the router, outlining the pathway for error-corrected quantum routing. We detail the importance of the qubit-coupling map for a superconducting quantum device that hopes to act as a quantum router, and experimentally verify that optimizing the number of controlled-X gates decreases hardware errors that impact routing performance. Our results indicate that near-term realization of quantum routing using noisy superconducting quantum devices within real-world quantum networks is possible.

Implementation of Fault-Tolerant Encoding Circuit Based on Stabilizer Implementation and "Flag" Bits in Steane Code

Quantum error correction (QEC) is an effective way to overcome quantum noise and de-coherence, meanwhile the fault tolerance of the encoding circuit, syndrome measurement circuit, and logical gate realization circuit must be ensured so as to achieve reliable quantum computing. Steane code is one of the most famous codes, proposed in 1996, however, the classical encoding circuit based on stabilizer implementation is not fault-tolerant. In this paper, we propose a method to design a fault-tolerant encoding circuit for Calderbank-Shor-Steane (CSS) code based on stabilizer implementation and "flag" bits. We use the Steane code as an example to depict in detail the fault-tolerant encoding circuit design process including the logical operation implementation, the stabilizer implementation, and the "flag" qubits design. The simulation results show that assuming only one quantum gate will be wrong with a certain probability p, the classical encoding circuit will have logic errors proportional to p; our proposed circuit is fault-tolerant as with the help of the "flag" bits, all types of errors in the encoding process can be accurately and uniquely determined, the errors can be fixed. If all the gates will be wrong with a certain probability p, which is the actual situation, the proposed encoding circuit will also be wrong with a certain probability, but its error rate has been reduced greatly from p to p2 compared with the original circuit. This encoding circuit design process can be extended to other CSS codes to improve the correctness of the encoding circuit.

Quantum teleportation of physical qubits into logical code spaces

Quantum error correction is an essential tool for reliably performing tasks for processing quantum information on a large scale. However, integration into quantum circuits to achieve these tasks is problematic when one realizes that nontransverse operations, which are essential for universal quantum computation, lead to the spread of errors. Quantum gate teleportation has been proposed as an elegant solution for this. Here, one replaces these fragile, nontransverse inline gates with the generation of specific, highly entangled offline resource states that can be teleported into the circuit to implement the nontransverse gate. As the first important step, we create a maximally entangled state between a physical and an error-correctable logical qubit and use it as a teleportation resource. We then demonstrate the teleportation of quantum information encoded on the physical qubit into the error-corrected logical qubit with fidelities up to 0.786. Our scheme can be designed to be fully fault tolerant so that it can be used in future large-scale quantum technologies.

Magic state distillation with the ternary Golay code

The ternary Golay code-one of the first and most beautiful classical error-correcting codes discovered-naturally gives rise to an 11-qutrit quantum error correcting code. We apply this code to magic state distillation, a leading approach to fault-tolerant quantum computing. We find that the 11-qutrit Golay code can distil the 'most magic' qutrit state-an eigenstate of the qutrit Fourier transform known as the strange state-with cubic error suppression and a remarkably high threshold. It also distils the 'second-most magic' qutrit state, the Norell state, with quadratic error suppression and an equally high threshold to depolarizing noise.

Combating quasiparticle poisoning with multiple Majorana fermions in a periodically-driven quantum wire

Quasiparticle poisoning has remained one of the main challenges in the implementation of Majorana-based quantum computing. It inevitably occurs when the system hosting Majorana qubits is not completely isolated from its surrounding, thus considerably limiting its computational time. We propose the use of periodic driving to generate multiple Majorana fermions at each end of a single quantum wire, which naturally provides the necessary resources to implement active quantum error corrections with minimal space overhead. In particular, we present a stabilizer code protocol that can specifically detect and correct any single quasiparticle poisoning event. Such a protocol is implementable via existing proximitized semiconducting nanowire proposals, where all of its stabilizer operators can be measured from an appropriate Majorana parity dependent four-terminal conductance.

On the Performance of Interleavers for Quantum Turbo Codes

Quantum turbo codes (QTC) have shown excellent error correction capabilities in the setting of quantum communication, achieving a performance less than 1 dB away from their corresponding hashing bounds. Existing QTCs have been constructed using uniform random interleavers. However, interleaver design plays an important role in the optimization of classical turbo codes. Consequently, inspired by the widely used classical-to-quantum isomorphism, this paper studies the integration of classical interleaving design methods into the paradigm of quantum turbo coding. Simulations results demonstrate that error floors in QTCs can be lowered significantly, while decreasing memory consumption, by proper interleaving design without increasing the overall decoding complexity of the system.

The small stellated dodecahedron code and friends

We explore a distance-3 homological CSS quantum code, namely the small stellated dodecahedron code, for dense storage of quantum information and we compare its performance with the distance-3 surface code. The data and ancilla qubits of the small stellated dodecahedron code can be located on the edges respectively vertices of a small stellated dodecahedron, making this code suitable for three-dimensional connectivity. This code encodes eight logical qubits into 30 physical qubits (plus 22 ancilla qubits for parity check measurements) in contrast with one logical qubit into nine physical qubits (plus eight ancilla qubits) for the surface code. We develop fault-tolerant parity check circuits and a decoder for this code, allowing us to numerically assess the circuit-based pseudo-threshold.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'.

High coherence plane breaking packaging for superconducting qubits

We demonstrate a pogo pin package for a superconducting quantum processor specifically designed with a nontrivial layout topology (e.g., a center qubit that cannot be accessed from the sides of the chip). Two experiments on two nominally identical superconducting quantum processors in pogo packages, which use commercially available parts and require modest machining tolerances, are performed at low temperature (10 mK) in a dilution refrigerator and both found to behave comparably to processors in standard planar packages with wirebonds where control and readout signals come in from the edges. Single- and two-qubit gate errors are also characterized via randomized benchmarking, exhibiting similar error rates as in standard packages, opening the possibility of integrating pogo pin packaging with extensible qubit architectures.