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This chapter provides an introduction to the surface code, discussing details about how physical qubits are connected and operated to create logical qubits, how errors are handled, and what performance metrics are needed to generate logical qubits with performance that exceeds their underlying physical qubit performance.
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... These optimized pulses are robust to thermal fluctuations but are relatively more sensitive to the excitation field variations. Our results provide a promising protocol for an improved high-fidelity and fast gate operation under practical experimental parameters, which explores a parameter regime beyond the adiabatic operation and paves the way toward deeper quantum circuits and foreseeable fault-tolerant quantum computing [11,12,[43][44][45][46][47][48][49]. ...
High-fidelity control-$Z$ ($C_Z$) gates are essential and mandatory to build a large-scale quantum computer. In neutral atoms, the strong dipole-dipole interactions between their Rydberg states make them one of the pioneering platforms to implement $C_Z$ gates. Here we numerically investigate the time-optimal pulses to generate a high-fidelity Rydberg $C_{Z}$ gate in a three-level ladder-type atomic system. By tuning the temporal shapes of Gaussian or segmented pulses, the populations on the intermediate excited states are shown to be suppressed within the symmetric gate operation protocol, which leads to a $C_{Z}$ gate with a high Bell fidelity up to $99.92\%$. These optimized pulses are robust to thermal fluctuations and the excitation field variations. Our results promise a high-fidelity and fast gate operation under amenable and controllable experimental parameters, which goes beyond the adiabatic operation regime under a finite Blockade strength.
... These optimized pulses are robust to thermal fluctuations but are relatively more sensitive to the excitation field variations. Our results provide a promising protocol for an improved high-fidelity and fast gate operation under practical experimental parameters, which explores a parameter regime beyond the adiabatic operation and paves the way toward deeper quantum circuits and foreseeable fault-tolerant quantum computing [11,12,[37][38][39][40][41][42][43]. ...
High-fidelity control-$Z$ ($C_Z$) gates are essential and mandatory to build a large-scale quantum computer. In neutral atoms, the strong dipole-dipole interactions between their Rydberg states make them one of the pioneering platforms to implement $C_Z$ gates. Here we numerically investigate the time-optimal pulses to generate a high-fidelity Rydberg $C_{Z}$ gate in a three-level ladder-type atomic system. By tuning the temporal shapes of Gaussian or segmented pulses, the populations on the intermediate excited states are shown to be suppressed within the symmetric gate operation protocol, which leads to a $C_{Z}$ gate with a high Bell fidelity up to $0.9998$. These optimized pulses are robust to thermal fluctuations and the excitation field variations. Our results promise a high-fidelity and fast gate operation under amenable and controllable experimental parameters, which goes beyond the adiabatic operation regime under a finite Blockade strength.
... able to start with QEC; reducing error rates even further can only be advantageous. As an illustration, the very popular Surface Code [106] needs a large number of physical qubits to obtain a single error tolerant logical qubit at current error rates (on the order of 1000 to 10000 9 [107]). Using a hardware efficient approach, involving storing information in the states of a harmonic oscillator, bosonic codes can have exponentially lower bit flip rates than standard transmons [30], potentially allowing us to reduce the hardware overhead dramatically to only a few tens of qubits [108]. ...
Superconducting qubits are at the heart of many experiments exploring elementary quantum mechanics and are one of the principal candidates for use in a future quantum computer. In both cases, a high level of control over both the quantum system and its environment is necessary. The first chapters of this thesis describe several techniques used to engineer the effect of the environment in circuit QED with a focus on the promising Fluxonium qubit. We give a detailed treatment of the theoretical basis for protected qubits and analyse device design and dilution refrigerator wiring from the perspective of environment noise reduction. As an application of these methods, we reproduce state of the art conditions for Fluxonium experiments in order to study the effect of the environment on the qubit. We show how photons in the cavity used to measure the quantum bit and a high temperature of the dilution refrigerator in which the device is placed can have detrimental effects on the stability of the quantum state. Critically, this shows that there remain several problems still to solve regarding the dispersive readout of Fluxoniums before using them as the basis for a quantum computer.Theoretically, the decoherence of a qubit can be broken down into many coherent exchanges with the qubit environment about which the observer has no information. In the last part of the thesis, we show the results of an experiment providing insight into the thermodynamics of quantum measurement and operations by observing the coherent energy exchange between a propagating field and a qubit under measurement. We provide an interpretation of the preparation of a qubit state by a coherent light pulse as a weak measurement of the pulse by the qubit.
Nowadays, predominant asymmetric cryptographic schemes are considered to be secure because discrete logarithms are believed to be hard to be computed. The algorithm of Shor can effectively compute discrete logarithms, i.e. it can brake such asymmetric schemes. But the algorithm of Shor is a quantum algorithm and at the time this algorithm has been invented, quantum computers that may successfully execute this algorithm seemed to be far out in the future. The latter has changed: quantum computers that are powerful enough are likely to be available in a couple of years. In this article, we first describe the relation between discrete logarithms and two well-known asymmetric security schemes, RSA and Elliptic Curve Cryptography. Next, we present the foundations of lattice-based cryptography which is the bases of schemes that are considered to be safe against attacks by quantum algorithms (as well as by classical algorithms). Then we describe two such quantum-safe algorithms (Kyber and Dilithium) in more detail. Finally, we give a very brief and selective overview of a few actions currently taken by governments and industry as well as standardization in this area. The article especially strives towards being self-contained: the required mathematical foundations to understand post-quantum cryptography are provided and examples are given.
A bstract
Lattice gauge theories (LGT) play a central role in modern physics, providing insights into high-energy physics, condensed matter physics, and quantum computation. Due to the nontrivial structure of the Hilbert space of LGT systems, entanglement in such systems is tricky to define. However, when one limits themselves to superselection-resolved entanglement, that is, entanglement corresponding to specific gauge symmetry sectors (commonly denoted as superselection sectors), this problem disappears, and the entanglement becomes well-defined. The study of superselection-resolved entanglement is interesting in LGT for an additional reason: when the gauge symmetry is strictly obeyed, superselection-resolved entanglement becomes the only distillable contribution to the entanglement. In our work, we study the behavior of superselection-resolved entanglement in LGT systems. We employ a tensor network construction for gauge-invariant systems as defined by Zohar and Burrello [1] and find that, in a vast range of cases, the leading term in superselection-resolved entanglement depends on the number of corners in the partition — corner-law entanglement. To our knowledge, this is the first case of such a corner-law being observed in any lattice system.
Fabrication errors on qubits can render data and syndrome qubits faulty, impacting quantum-processor reliability. Our proposed method focuses on the recovery of faulty syndrome qubits, preserving the functionality of neighboring qubits and minimizing the loss of data qubits. Through experimental simulation, we demonstrate that our approach significantly improves percolation rates and reduces logical error rates while enhancing the robustness of the surface code against fabrication errors. Moreover, our approach raises the critical point for syndrome-fabrication errors by 29.4% on average and 33.33% when the percolation rate reaches 100%. Furthermore, it reduces logical error rates by 18.42% on average and achieves a 50% reduction in low computational Pauli error rates.
Quantum computers have made extraordinary progress over the past decade, and significant milestones have been achieved along the path of pursuing universal fault-tolerant quantum computers. Quantum advantage, the tipping point heralding the quantum era, has been accomplished along with several waves of breakthroughs. Quantum hardware has become more integrated and architectural compared to its toddler days. The controlling precision of various physical systems is pushed beyond the fault-tolerant threshold. Meanwhile, quantum computation research has established a new norm by embracing industrialization and commercialization. The joint power of governments, private investors, and tech companies has significantly shaped a new vibrant environment that accelerates the development of this field, now at the beginning of the noisy intermediate-scale quantum era. Here, we first discuss the progress achieved in the field of quantum computation by reviewing the most important algorithms and advances in the most promising technical routes, and then summarizing the next-stage challenges. Furthermore, we illustrate our confidence that solid foundations have been built for the fault-tolerant quantum computer and our optimism that the emergence of quantum killer applications essential for human society shall happen in the future.
