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Register a new userRents rule and extensibility in quantum computing
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Quantum computing is on the verge of a transition from fundamental research to practical applications. Yet, to make the step to large-scale quantum computation, an extensible qubit system has to be developed. In classical semiconductor technology, this was made possible by the invention of the integrated circuit, which allowed to interconnect large numbers of components without having to solder to each and every one of them. Similarly, we expect that the scaling of interconnections and control lines with the number of qubits will be a central bottleneck in creating large-scale quantum technology. Here, we define the quantum Rents exponent $p$ to quantify the progress in overcoming this challenge at different levels throughout the quantum computing stack. We further discuss the concept of quantum extensibility as an indicator of a platforms potential to reach the large quantum volume needed for universal quantum computing and review extensibility limits faced by different qubit implementations on the way towards truly large-scale qubit systems.
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Understanding the interaction between light and matter is very relevant for fundamental studies of quantum electrodynamics and for the development of quantum technologies. The quantum Rabi model captures the physics of a single atom interacting with a single photon at all regimes of coupling strength. We report the spectroscopic observation of a resonant transition that breaks a selection rule in the quantum Rabi model, implemented using an $LC$ resonator and an artificial atom, a superconducting qubit. The eigenstates of the system consist of a superposition of bare qubit-resonator states with a relative sign. When the qubit-resonator coupling strength is negligible compared to their own frequencies, the matrix element between excited eigenstates of different sign is very small in presence of a resonator drive, establishing a sign-preserving selection rule. Here, our qubit-resonator system operates in the ultrastrong coupling regime, where the coupling strength is 10% of the resonator frequency, allowing sign-changing transitions to be activated and, therefore, detected. This work shows that sign-changing transitions are an unambiguous, distinctive signature of systems operating in the ultrastrong coupling regime of the quantum Rabi model. These results pave the way to further studies of sign-preserving selection rules in multiqubit and multiphoton models.
$mathbb{Z}_d$ Parafermions are exotic non-Abelian quasiparticles generalizing Majorana fermions, which correspond to the case $d=2$. In contrast to Majorana fermions, braiding of parafermions with $d>2$ allows to perform an entangling gate. This has spurred interest in parafermions and a variety of condensed matter systems have been proposed as potential hosts for them. In this work, we study the computational power of braiding parafermions more systematically. We make no assumptions on the underlying physical model but derive all our results from the algebraical relations that define parafermions. We find a familiy of $2d$ representations of the braid group that are compatible with these relations. The braiding operators derived this way reproduce those derived previously from physical grounds as special cases. We show that if a $d$-level qudit is encoded in the fusion space of four parafermions, braiding of these four parafermions allows to generate the entire single-qudit Clifford group (up to phases), for any $d$. If $d$ is odd, then we show that in fact the entire many-qudit Clifford group can be generated.
We propose a method for the implementation of one-way quantum computing in superconducting circuits. Measurement-based quantum computing is a universal quantum computation paradigm in which an initial cluster-state provides the quantum resource, while the iteration of sequential measurements and local rotations encodes the quantum algorithm. Up to now, technical constraints have limited a scalable approach to this quantum computing alternative. The initial cluster state can be generated with available controlled-phase gates, while the quantum algorithm makes use of high-fidelity readout and coherent feedforward. With current technology, we estimate that quantum algorithms with above 20 qubits may be implemented in the path towards quantum supremacy. Moreover, we propose an alternative initial state with properties of maximal persistence and maximal connectedness, reducing the required resources of one-way quantum computing protocols.
Fault-tolerant schemes can use error correction to make a quantum computation arbitrarily ac- curate, provided that errors per physical component are smaller than a certain threshold and in- dependent of the computer size. However in current experiments, physical resource limitations like energy, volume or available bandwidth induce error rates that typically grow as the computer grows. Taking into account these constraints, we show that the amount of error correction can be opti- mized, leading to a maximum attainable computational accuracy. We find this maximum for generic situations where noise is scale-dependent. By inverting the logic, we provide experimenters with a tool to finding the minimum resources required to run an algorithm with a given computational accuracy. When combined with a full-stack quantum computing model, this provides the basis for energetic estimates of future large-scale quantum computers.
Quantum simulators are attractive as a means to study many-body quantum systems that are not amenable to classical numerical treatment. A versatile framework for quantum simulation is offered by superconducting circuits. In this perspective, we discuss how superconducting circuits allow the engineering of a wide variety of interactions, which in turn allows the simulation of a wide variety of model Hamiltonians. In particular we focus on strong photon-photon interactions mediated by nonlinear elements. This includes on-site, nearest-neighbour and four-body interactions in lattice models, allowing the implementation of extended Bose-Hubbard models and the toric code. We discuss not only the present state in analogue quantum simulation, but also future perspectives of superconducting quantum simulation that open up when concatenating quantum gates in emerging quantum computing platforms.
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