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arXiv:cond-mat/0702620 · Physical Review B

Long-range coupling and scalable architecture for superconducting flux qubits

Austin G. Fowler, William F. Thompson, Zhizhong Yan, Ashley M. Stephens, B. L. T. Plourde, Frank K. Wilhelm

Published Nov 12, 2007• 46 citations
arXivHTMLPDF

Abstract

Constructing a fault-tolerant quantum computer is a daunting task. Given any design, it is possible to determine the maximum error rate of each type of component that can be tolerated while still permitting arbitrarily large-scale quantum computation. It is an underappreciated fact that including an appropriately designed mechanism enabling long-range qubit coupling or transport substantially increases the maximum tolerable error rates of all components. With this thought in mind, we take the superconducting flux qubit coupling mechanism described by Plourde et al. [Phys. Rev. B 70, 140501(R) (2004)] and extend it to allow approximately $500\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$ coupling of square flux qubits, $50\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ a side, at a distance of up to several millimeters. This mechanism is then used as the basis of two scalable architectures for flux qubits taking into account cross-talk and fault-tolerant considerations such as permitting a universal set of logical gates, parallelism, measurement and initialization, and data mobility.

DOI
10.1103/physrevb.76.174507

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Constructing a fault-tolerant quantum computer is a daunting task. Given any design, it is possible to determine the maximum error rate of each type of component that can be tolerated while still permitting arbitrarily large-scale quantum computation. It is an under-appreciated fact that including an appropriately designed mechanism enabling long-range qubit coupling or transport substantially increases the maximum tolerable error rates of all components. With this thought in mind, we take the superconducting flux qubit coupling mechanism described in Plourde et al. (Phys. Rev. B, 70, 140501(R) (2004)) and extend it to allow approximately 500~MHz coupling of square flux qubits, 50 µm a side, at a distance of up to several mm. This mechanism is then used as the basis of two scalable architectures for flux qubits taking into account crosstalk and fault-tolerant considerations such as permitting a universal set of logical gates, parallelism, measurement and initialization, and data mobility.PACS No.: 03.67.Lx
The technological development of hardware heading toward universal fault-tolerant quantum computation requires a large-scale processing unit with high performance. While fluxonium qubits are promising with high coherence and large anharmonicity, their scalability has not been systematically explored. In this work, we propose a superconducting quantum information processor based on compact high-coherence fluxoniums with suppressed crosstalk, reduced design complexity, improved operational efficiency, high-fidelity gates, and resistance to parameter fluctuations. In this architecture, the qubits are readout dispersively using individual resonators connected to a common bus and manipulated via combined on-chip RF and DC control lines, both of which can be designed to have low crosstalk. A multi-path coupling approach enables exchange interactions between the high-coherence computational states and at the same time suppresses the spurious static ZZ rate, leading to fast and high-fidelity entangling gates. We numerically investigate the cross resonance controlled-NOT and the differential AC-Stark controlled-Z operations, revealing low gate error for qubit-qubit detuning bandwidth of up to 1 GHz. Our study on frequency crowding indicates high fabrication yield for quantum processors consisting of over thousands of qubits. In addition, we estimate low resource overhead to suppress logical error rate using the XZZX surface code. These results promise a scalable quantum architecture with high performance for the pursuit of universal quantum computation.
Efficient quantum error correction and fault-tolerant quantum computing require scalable, high-fidelity long-range connectivity. In neutral-atom quantum computers, this is commonly achieved through atom transport, but shuttling introduces latency and motional heating that worsen with system size. Here, we introduce a neutral-atom architecture based on static atomic buses, in which auxiliary mediator atoms enable long-range entangling operations without qubit transport. The architecture naturally supports long-range stabilizer measurements in high-rate LDPC codes and transversal logical gates between neighboring surface-code patches, enabling a modular framework for efficient logical memories, Clifford computation, and magic-state distillation. To realize these capabilities, we co-design optimal-control protocols for bus-mediated controlled-Z gates that incorporate both microscopic neutral-atom dynamics and architectural constraints. We obtain smooth bus-mediated gates with fidelities approaching 99.9% and durations of a few hundred nanoseconds by combining time-optimal control with interaction-flatness and robustness constraints. Large-scale simulations of quantum error correction and logical entangling operations between neighboring surface-code patches predict more than an order-of-magnitude improvement in logical error rates compared with atom-shuttling architectures under realistic noise. The architecture achieves logical gate times of approximately 100 us and quantum-error-correction cycle times of about 1 ms for code distances d<12. These results establish static atomic buses as a practical alternative to atom shuttling for scalable fault-tolerant neutral-atom quantum computing.
The path toward practical superconducting quantum processors requires the integration of a large number of high-performance qubits. Modular architectures could offer a way to address the scaling limitations of monolithic designs by partitioning a large quantum processor into physically separated modules, or chiplets, linked through long-range interconnects. In this context, although fluxonium qubits have emerged as a compelling platform for quantum computing due to their long coherence times and high-fidelity gates, existing coupling schemes remain restricted to qubits in close proximity on a single chip. This limitation inherently precludes the long-range interconnects essential for modular integration. In this work, we propose a long-range tunable coupler designed to interconnect fluxonium qubits separated by more than one centimeter, thereby supporting the realization of modular fluxonium quantum processors. Under realistic assumptions, the proposed coupler has the potential to achieve inter-module two-qubit gate performance, specifically sub-100-ns gates with intrinsic errors below 10−410^{-4}10−4, comparable to that of intra-module (intra-chiplet) gates, while enabling modular integration with low quantum crosstalk, a key requirement for scalable systems. We further discuss the integration of this coupler into modular fluxonium lattices and explore its feasibility for achieving the higher connectivity and longer coupling range required for complex quantum error correction codes. This work could contribute to the development of large-scale fluxonium quantum processors by bridging their demonstrated potential with modular scalability.
Recently, fault tolerant quantum computation such as surface coding and topological quantum computation has been paid attention to due to high threshold against computational errors compared with that of conventional gate-model quantum computation.These schemes use a two or three-dimensional cluster state as universal resources for quantum computation.We can generate a cluster state by performing controlled-phase gates on an initial state prepared in |+⟩ state, where the control-phase gates are realized by nearest neighbor Ising type interactions.There are many proposal to realize Ising type interaction such as ultracold atoms in an optical lattice, superconducting charge qubits, superconducting spin qubits, resonator wave guides, nitrogen-vacancy centers, and quantum dots.Among many candidates, we especially discuss superconducting flux qubits.Superconducting flux qubits have a strong anharmonicity, so that we can perform high-speed single-qubit rotation with excellent fidelity.Usually, implementation of high-fidelity two-qubit gates is the hardest part for the realization of quantum computation.Two qubit gates require in-situ turn on/off the interaction between qubits by the external control apparatus.Since imperfection of the interaction control tends to induce spatially correlated errors between qubits, sophisticated technology is required to suppress such error rate below the threshold of fault tolerant quantum computation.Up to now, the generation of a large cluster state using solid-state qubit has not been demonstrated in a scalable manner yet.One of the main obstacles is the requirement for independent control of two-qubit gates that are necessary for the scalable quantum information processing.For a superconducting flux qubit, existing method uses applied magnetic field to control the interaction.It is known that the application of magnetic field to local area is difficult.Thus, it is hard to implement local control of the interaction without cross-talk problem where unwanted errors occurs between qubits.Firstly, we propose a novel way to control a number of two-qubit gates independently without using the on/off switching of locally applied magnetic field.Specifically, we assume the superconducting flux qubits that are inductively coupled with each other via always-on Ising interaction.Unlike the previous method to change the interaction strength with unitary operations, we fully make use of non-unitary properties of projective measurements so that we can effectively turn on/off the interaction via quantum feedforward.Also, we show how to generate a two or three-dimensional cluster state that are universal resource for fault tolerant quantum computation with constant stepsize operations.The on/off switching of locally applied magnetic field is not necessary to First of all, I would like to thank my adviser Professor Hiroshi Imai for his valuable comments and continuous support during the last five years.
Maintaining or even improving gate performance with growing numbers of parallel controlled qubits is a vital requirement for fault-tolerant quantum computing.For superconducting quantum processors, though isolated one-or two-qubit gates have been demonstrated with high fidelity, implementing these gates in parallel commonly shows worse performance.Generally, this degradation is attributed to various crosstalks between qubits, such as quantum crosstalk due to residual inter-qubit coupling.An understanding of the exact nature of these crosstalks is critical to figuring out respective mitigation schemes and improved qubit architecture designs with low crosstalk.Here we give a theoretical analysis of quantum crosstalk impact on simultaneous gate operations in a qubit architecture, where fixed-frequency transmon qubits are coupled via a tunable bus, and sub-100-ns controlled-Z (CZ) gates can be realized by applying a baseband flux pulse on the bus.Our analysis shows that for microwave-driven single-qubit gates, the dressing from the qubit-qubit coupling can cause non-negligible cross-driving errors when qubits operate near frequency collision regions.During CZ gate operations, although unwanted nearest-neighbor interactions are nominally turned off, sub-MHz parasitic next-nearest-neighbor interactions involving spectator qubits can still exist, causing considerable leakage or control error when one operates qubit systems around these parasitic resonance points.To ensure high-fidelity simultaneous operations, a request could be raised to figure out a better way to balance the gate error from target qubit systems themselves and the error from nonparticipating spectator qubits.Overall, our analysis suggests that towards useful quantum processors, the qubit architecture should be examined carefully in the context of high-fidelity simultaneous gate operations in a scalable qubit lattice.