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Photonic synthetic materials provide an opportunity to explore the role of microscopic quantum phenomena in determining macroscopic material properties. There are, however, fundamental obstacles to overcome — in vacuum, photons not only lack mass, but also do not naturally interact with one another. Here, we review how the superconducting quantum circuit platform has been harnessed in the last decade to make some of the first materials from light. We describe the structures that are used to imbue individual microwave photons with matter-like properties such as mass, the nonlinear elements that mediate interactions between these photons, and quantum dynamic/thermodynamic approaches that can be used to assemble and stabilize strongly correlated states of many photons. We then describe state-of-the-art techniques to generate synthetic magnetic fields, engineer topological and non-topological flat bands and explore the physics of quantum materials in non-Euclidean geometries — directions that we view as some of the most exciting for this burgeoning field. Finally, we discuss upcoming prospects, and in particular opportunities to probe novel aspects of quantum thermalization and detect quasi-particles with exotic anyonic statistics, as well as potential applications in quantum information science. This Review Article surveys the physics of many-body quantum states formed by microwave photons in circuit quantum electrodynamics environments.

Precise means of characterizing analog quantum simulators are key to developing quantum simulators capable of beyond-classical computations. Here, we precisely estimate the free Hamiltonian parameters of a superconducting-qubit analog quantum simulator from measured time-series data on up to 14 qubits. To achieve this, we develop a scalable Hamiltonian learning algorithm that is robust against state-preparation and measurement (SPAM) errors and yields tomographic information about those SPAM errors. The key subroutines are a novel super-resolution technique for frequency extraction from matrix time-series, tensorESPRIT, and constrained manifold optimization. Our learning results verify the Hamiltonian dynamics on a Sycamore processor up to sub-MHz accuracy, and allow us to construct a spatial implementation error map for a grid of 27 qubits. Our results constitute an accurate implementation of a dynamical quantum simulation that is precisely characterized using a new diagnostic toolkit for understanding, calibrating, and improving analog quantum processors. Accurately estimating Hamiltonian parameters of a quantum system is crucial in the development of large-scale analog quantum simulators. Here, the authors develop and experimentally demonstrate an algorithm to robustly learn Hamiltonian parameters of bosonic systems undergoing dynamical evolution.

Helical Dirac fermion states in topological insulators could enable dissipation-free spintronics and robust quantum information processors. A study of the influence of disorder on these states shows that although they are resilient against backscattering by magnetic impurities, fluctuations caused by charge impurities could cause problems for such applications. Surfaces of topological insulators host a new class of states 1 with Dirac dispersion 2 , 3 , 4 and helical spin texture 5 . Potential quantum computing and spintronic applications using these states require manipulation of their electronic properties at the Dirac energy of their band structure by inducing magnetism or superconductivity through doping and the proximity effect 6 , 7 , 8 , 9 . Yet, the response of these states near the Dirac energy in their band structure to various perturbations has remained unexplored. Here we use spectroscopic mapping with the scanning tunnelling microscope to study their response to magnetic and non-magnetic bulk dopants in Bi 2 Te 3 and Bi 2 Se 3 . Far from the Dirac energy, helicity provides remarkable resilience to backscattering even in the presence of ferromagnetism. However, approaching the Dirac point, where the surface states’ wavelength diverges, bulk doping results in pronounced nanoscale spatial fluctuations of energy, momentum and helicity. Our results and their connection with similar studies of Dirac electrons in graphene 10 , 11 , 12 , 13 demonstrate that although backscattering and localization are absent for Dirac topological surface states, reducing charge defects is required for both tuning the chemical potential to the Dirac energy and achieving high electrical mobility for these novel states.

A foundational assumption of quantum error correction theory is that quantum gates can be scaled to large processors without exceeding the error-threshold for fault tolerance. Two major challenges that could become fundamental roadblocks are manufacturing high-performance quantum hardware and engineering a control system that can reach its performance limits. The control challenge of scaling quantum gates from small to large processors without degrading performance often maps to non-convex, high-constraint, and time-dynamic control optimization over an exponentially expanding configuration space. Here we report on a control optimization strategy that can scalably overcome the complexity of such problems. We demonstrate it by choreographing the frequency trajectories of 68 frequency-tunable superconducting qubits to execute single- and two-qubit gates while mitigating computational errors. When combined with a comprehensive model of physical errors across our processor, the strategy suppresses physical error rates by ~3.7× compared with the case of no optimization. Furthermore, it is projected to achieve a similar performance advantage on a distance-23 surface code logical qubit with 1057 physical qubits. Our control optimization strategy solves a generic scaling challenge in a way that can be adapted to a variety of quantum operations, algorithms, and computing architectures. Ensuring high-fidelity quantum gates while increasing the number of qubits poses a great challenge. Here the authors present a scalable strategy for optimizing frequency trajectories as a form of error mitigation on a 68-qubit superconducting quantum processor, demonstrating high single- and two-qubit gate fidelities.

Electronic states in disordered conductors on the verge of localization are predicted to exhibit critical spatial characteristics indicative of the proximity to a metal-insulator phase transition. We used scanning tunneling microscopy to visualize electronic states in Ga₁₋xMnxAs samples close to this transition. Our measurements show that doping-induced disorder produces strong spatial variations in the local tunneling conductance across a wide range of energies. Near the Fermi energy, where spectroscopic signatures of electron-electron interaction are the most prominent, the electronic states exhibit a diverging spatial correlation length. Power-law decay of the spatial correlations is accompanied by log-normal distributions of the local density of states and multifractal spatial characteristics.

Quantum cellular automata (QCA) evolve qubits in a quantum circuit depending only on the states of their neighborhoods and model how rich physical complexity can emerge from a simple set of underlying dynamical rules. The inability of classical computers to simulate large quantum systems hinders the elucidation of quantum cellular automata, but quantum computers offer an ideal simulation platform. Here, we experimentally realize QCA on a digital quantum processor, simulating a one-dimensional Goldilocks rule on chains of up to 23 superconducting qubits. We calculate calibrated and error-mitigated population dynamics and complex network measures, which indicate the formation of small-world mutual information networks. These networks decohere at fixed circuit depth independent of system size, the largest of which corresponding to 1,056 two-qubit gates. Such computations may enable the employment of QCA in applications like the simulation of strongly-correlated matter or beyond-classical computational demonstrations. The study of complexity in quantum systems is a fascinating topic, which however is still in its infancy, especially at the experimental level. Here, the authors report on the observation of “small-world” characteristics in the network of quantum correlations within chains of up to 23 superconducting qubits long.

Breaking down barriers Topological states have become the subject of much attention from condensed-matter physicists, as evidence accumulates to show that these states can be found on the surface of certain materials — in particular, bulk compounds called topological insulators. As a product of their topological nature, topological surface states are predicted to have the remarkable property of being robust against imperfections. This can allow, for example, the conduction of electronic currents without dissipation. Ali Yazdani and his team now report a tantalizing finding from scanning tunnelling microscope measurements — that topological surface states on antimony can be transmitted with high probability through naturally occurring barriers that stop other conventional surface states of common metals. The authors suggest that their findings indicate that topological surface states could be exploited in novel applications of nanoscale electronic devices. Topological surface states are a class of electronic states that might be of interest in quantum computing or spintronic applications. They are predicted to be robust against imperfections, but so far there has been no evidence that these states do transmit through naturally occurring surface defects. Here, scanning tunnelling microscopy has been used to show that topological surface states of antimony can be transmitted through naturally occurring barriers that block non-topological surface states of common metals. Topological surface states are a class of novel electronic states that are of potential interest in quantum computing or spintronic applications 1 , 2 , 3 , 4 , 5 , 6 , 7 . Unlike conventional two-dimensional electron states, these surface states are expected to be immune to localization and to overcome barriers caused by material imperfection 8 , 9 , 10 , 11 , 12 , 13 , 14 . Previous experiments have demonstrated that topological surface states do not backscatter between equal and opposite momentum states, owing to their chiral spin texture 15 , 16 , 17 , 18 . However, so far there is no evidence that these states in fact transmit through naturally occurring surface defects. Here we use a scanning tunnelling microscope to measure the transmission and reflection probabilities of topological surface states of antimony through naturally occurring crystalline steps separating atomic terraces. In contrast to non-topological surface states of common metals (copper, silver and gold) 19 , 20 , 21 , 22 , 23 , which are either reflected or absorbed by atomic steps, we show that topological surface states of antimony penetrate such barriers with high probability. This demonstration of the extended nature of antimony’s topological surface states suggests that such states may be useful for high current transmission even in the presence of atomic-scale irregularities—an electronic feature sought to efficiently interconnect nanoscale devices.

Practical quantum computing will require error rates well below those achievable with physical qubits. Quantum error correction 1 , 2 offers a path to algorithmically relevant error rates by encoding logical qubits within many physical qubits, for which increasing the number of physical qubits enhances protection against physical errors. However, introducing more qubits also increases the number of error sources, so the density of errors must be sufficiently low for logical performance to improve with increasing code size. Here we report the measurement of logical qubit performance scaling across several code sizes, and demonstrate that our system of superconducting qubits has sufficient performance to overcome the additional errors from increasing qubit number. We find that our distance-5 surface code logical qubit modestly outperforms an ensemble of distance-3 logical qubits on average, in terms of both logical error probability over 25 cycles and logical error per cycle ((2.914 ± 0.016)% compared to (3.028 ± 0.023)%). To investigate damaging, low-probability error sources, we run a distance-25 repetition code and observe a 1.7 × 10 −6 logical error per cycle floor set by a single high-energy event (1.6 × 10 −7 excluding this event). We accurately model our experiment, extracting error budgets that highlight the biggest challenges for future systems. These results mark an experimental demonstration in which quantum error correction begins to improve performance with increasing qubit number, illuminating the path to reaching the logical error rates required for computation. A study demonstrating increasing error suppression with larger surface code logical qubits, implemented on a superconducting quantum processor.

The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor 1 . 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 qubits 2 – 7 to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 2 53 (about 10 16 ). 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 supremacy 8 – 14 for this specific computational task, heralding a much-anticipated computing paradigm. Quantum supremacy is demonstrated using a programmable superconducting processor known as Sycamore, taking approximately 200 seconds to sample one instance of a quantum circuit a million times, which would take a state-of-the-art supercomputer around ten thousand years to compute.

Scalable quantum computing can become a reality with error correction, provided that coherent qubits can be constructed in large arrays 1 , 2 . The key premise is that physical errors can remain both small and sufficiently uncorrelated as devices scale, so that logical error rates can be exponentially suppressed. However, impacts from cosmic rays and latent radioactivity violate these assumptions. An impinging particle can ionize the substrate and induce a burst of quasiparticles that destroys qubit coherence throughout the device. High-energy radiation has been identified as a source of error in pilot superconducting quantum devices 3 – 5 , but the effect on large-scale algorithms and error correction remains an open question. Elucidating the physics involved requires operating large numbers of qubits at the same rapid timescales necessary for error correction. Here, we use space- and time-resolved measurements of a large-scale quantum processor to identify bursts of quasiparticles produced by high-energy rays. We track the events from their initial localized impact as they spread, simultaneously and severely limiting the energy coherence of all qubits and causing chip-wide failure. Our results provide direct insights into the impact of these damaging error bursts and highlight the necessity of mitigation to enable quantum computing to scale. Cosmic rays flying through superconducting quantum devices create bursts of excitations that destroy qubit coherence. Rapid, spatially resolved measurements of qubit error rates make it possible to observe the evolution of the bursts across a chip.