This is an updated version of supplementary information to accompany "Quantum supremacy using a programmable superconducting processor", an article published in the October 24, 2019 issue of Nature. The main article is freely available at this https URL. Summary of changes since arXiv:1910.11333v1 (submitted 23 Oct 2019): added URL for qFlex source code; added Erratum section; added Figure S41 comparing statistical and total uncertainty for log and linear XEB; new References [1,65]; miscellaneous updates for clarity and style consistency; miscellaneous typographical and formatting corrections.

/pdf/supplementary-information-for-quantum-supremacy-using-a-3tkhfafpzk.pdf

Supplementary information for "Quantum supremacy using a programmable superconducting processor"

The interaction of matter and light is one of the fundamental processes occurring in nature, and its most elementary form is realized when a single atom interacts with a single photon. Reaching this regime has been a major focus of research in atomic physics and quantum optics1 for several decades and has generated the field of cavity quantum electrodynamics2,3. Here we perform an experiment in which a superconducting two-level system, playing the role of an artificial atom, is coupled to an on-chip cavity consisting of a superconducting transmission line resonator. We show that the strong coupling regime can be attained in a solid-state system, and we experimentally observe the coherent interaction of a superconducting two-level system with a single microwave photon. The concept of circuit quantum electrodynamics opens many new possibilities for studying the strong interaction of light and matter. This system can also be exploited for quantum information processing and quantum communication and may lead to new approaches for single photon generation and detection.

https://arxiv.org/pdf/cond-mat/0407325.pdf

Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics

The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor1. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits2-7 to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 253 (about 1016). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one instance of a quantum circuit a million times-our benchmarks currently indicate that the equivalent task for a state-of-the-art classical supercomputer would take approximately 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy8-14 for this specific computational task, heralding a much-anticipated computing paradigm.

/pdf/quantum-supremacy-using-a-programmable-superconducting-5182kq634u.pdf

Quantum supremacy using a programmable superconducting processor

Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and instantaneously linked These predictions have been the topic of intense metaphysical debate ever since the theory's inception early last century However, supreme predictive power combined with direct experimental observation of some of these unusual phenomena leave little doubt as to its fundamental correctness In fact, without quantum mechanics we could not explain the workings of a laser, nor indeed how a fridge magnet operates Over the last several decades quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit these unique quantum properties? Today it is understood that the answer is yes Many research groups around the world are working towards one of the most ambitious goals humankind has ever embarked upon: a quantum computer that promises to exponentially improve computational power for particular tasks A number of physical systems, spanning much of modern physics, are being developed for this task---ranging from single particles of light to superconducting circuits---and it is not yet clear which, if any, will ultimately prove successful Here we describe the latest developments for each of the leading approaches and explain what the major challenges are for the future

Quantum Computing

Rydberg atoms with principal quantum number $n⪢1$ have exaggerated atomic properties including dipole-dipole interactions that scale as ${n}^{4}$ and radiative lifetimes that scale as ${n}^{3}$. It was proposed a decade ago to take advantage of these properties to implement quantum gates between neutral atom qubits. The availability of a strong long-range interaction that can be coherently turned on and off is an enabling resource for a wide range of quantum information tasks stretching far beyond the original gate proposal. Rydberg enabled capabilities include long-range two-qubit gates, collective encoding of multiqubit registers, implementation of robust light-atom quantum interfaces, and the potential for simulating quantum many-body physics. The advances of the last decade are reviewed, covering both theoretical and experimental aspects of Rydberg-mediated quantum information processing.

Quantum information with Rydberg atoms

We propose a realizable architecture using one-dimensional transmission line resonators to reach the strong-coupling limit of cavity quantum electrodynamics in superconducting electrical circuits. The vacuum Rabi frequency for the coupling of cavity photons to quantized excitations of an adjacent electrical circuit (qubit) can easily exceed the damping rates of both the cavity and qubit. This architecture is attractive both as a macroscopic analog of atomic physics experiments and for quantum computing and control, since it provides strong inhibition of spontaneous emission, potentially leading to greatly enhanced qubit lifetimes, allows high-fidelity quantum nondemolition measurements of the state of multiple qubits, and has a natural mechanism for entanglement of qubits separated by centimeter distances. In addition it would allow production of microwave photon states of fundamental importance for quantum communication.

https://arxiv.org/pdf/cond-mat/0402216.pdf

Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation

We have recently demonstrated that a superconducting quantum two-level system can be strongly coupled to a single microwave photon [1] The strong coupling between a quantum solid state circuit and an individual photon, analogous to atomic cavity quantum electrodynamics (CQED) [2], has previously been envisaged by many authors, see Ref 3 and references therein Our circuit quantum electrodynamics architecture [3], in which a superconducting charge qubit, the Cooper pair box [4], is coupled strongly to a coplanar transmission line resonator, has great prospects both for performing quantum optics experiments [5] in solids and for realizing elements for quantum information processing [6] with superconducting circuits [7] In this letter we present spectroscopic measurements which demonstrate the non-resonant (dispersive) strong coupling between a Cooper pair box and a coherent microwave field in a high quality cavity The quantum state of the Cooper pair box is controlled using resonant microwave radiation and is read out with a dispersive quantum non-demolition (QND) measurement [3, 8, 9] The interaction between the Cooper pair box and the measurement field containing n photons on average gives rise to a large ac-Stark shift of the qubit energy levels, analogous to the one observed in CQED [10] As a consequence of the strong coupling, quantum fluctuations in n induce a broadening of the transition line width, characterizing the back action of the measurement on the qubit

/pdf/ac-stark-shift-and-dephasing-of-a-superconducting-qubit-d1sddpwao0.pdf

ac Stark Shift and Dephasing of a Superconducting Qubit Strongly Coupled to a Cavity Field

Erratum: ac Stark Shift and Dephasing of a Superconducting Qubit Strongly Coupled to a Cavity Field [Phys. Rev. Lett. 94 , 123602 (2005)]

This chapter discusses the prospects for strong cavity quantum electrodynamics (cQED) with superconducting circuits. It propose that the combination of one-dimensional superconducting transmission line resonators, which confine their zero point energy to extremely small volumes, and superconducting charge qubits, which are electrically controllable qubits with large electric dipole moments, constitutes an interesting system to access the strong-coupling regime of cavity quantum electrodynamics. This combined system constitutes an advantageous architecture for the coherent control, entanglement, and readout of quantum bits for quantum computation and communication. Among the practical benefits of this approach are the ability to suppress radiative decay of the qubit while still allowing one-bit operations, a simple and minimally disruptive method for readout of single and multiple qubits, and the ability to generate tunable two-qubit entanglement over centimeter-scale distances. In the structures described in the chapter, the emission or absorption of a single photon by the qubit is tagged by a sudden large change in the resonator transmission properties making them potentially useful as single photon sources and detectors.

Ren-Shou Huang

Papers

Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics

Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation

ac Stark Shift and Dephasing of a Superconducting Qubit Strongly Coupled to a Cavity Field

Erratum: ac Stark Shift and Dephasing of a Superconducting Qubit Strongly Coupled to a Cavity Field [Phys. Rev. Lett. 94 , 123602 (2005)]

Course 16 - Prospects for Strong Cavity Quantum Electrodynamics with Superconducting Circuits