Superconducting qubits are leading candidates in the race to build a quantum computer capable of realizing computations beyond the reach of modern supercomputers. The superconducting qubit modality has been used to demonstrate prototype algorithms in the 'noisy intermediate scale quantum' (NISQ) technology era, in which non-error-corrected qubits are used to implement quantum simulations and quantum algorithms. With the recent demonstrations of multiple high fidelity two-qubit gates as well as operations on logical qubits in extensible superconducting qubit systems, this modality also holds promise for the longer-term goal of building larger-scale error-corrected quantum computers. In this brief review, we discuss several of the recent experimental advances in qubit hardware, gate implementations, readout capabilities, early NISQ algorithm implementations, and quantum error correction using superconducting qubits. While continued work on many aspects of this technology is certainly necessary, the pace of both conceptual and technical progress in the last years has been impressive, and here we hope to convey the excitement stemming from this progress.

We report infrared studies of the Landau level (LL) transitions in single layer graphene. Our specimens are density tunable and show in situ half-integer quantum Hall plateaus. Infrared transmission is measured in magnetic fields up to B=18 T at selected LL fillings. Resonances between hole LLs and electron LLs, as well as resonances between hole and electron LLs, are resolved. Their transition energies are proportional to sqrt[B], and the deduced band velocity is (-)c approximately equal to 1.1 x 10(6) m/s. The lack of precise scaling between different LL transitions indicates considerable contributions of many-particle effects to the infrared transition energies.

Detecting single-photon level signals—carriers of both classical and quantum information—is particularly challenging for low-energy microwave frequency excitations. Here we introduce a superconducting amplifier based on a Josephson junction transmission line. Unlike current standing-wave parametric amplifiers, this traveling wave architecture robustly achieves high gain over a bandwidth of several gigahertz with sufficient dynamic range to read out 20 superconducting qubits. To achieve this performance, we introduce a subwavelength resonant phase-matching technique that enables the creation of nonlinear microwave devices with unique dispersion relations. We benchmark the amplifier with weak measurements, obtaining a high quantum efficiency of 75% (70% including noise added by amplifiers following the Josephson amplifier). With a flexible design based on compact lumped elements, this Josephson amplifier has broad applicability to microwave metrology and quantum optics.

Using quantum devices supported by classical computational resources is a promising approach to quantum-enabled computation. One example of such a hybrid quantum-classical approach is the variational quantum eigensolver (VQE) built to utilize quantum resources for the solution of eigenvalue problems and optimizations with minimal coherence time requirements by leveraging classical computational resources. These algorithms have been placed among the candidates for first to achieve supremacy over classical computation. Here, we provide evidence for the conjecture that variational approaches can automatically suppress even non-systematic decoherence errors by introducing an exactly solvable channel model of variational state preparation. Moreover, we show how variational quantum-classical approaches fit in a more general hierarchy of measurement and classical computation that allows one to obtain increasingly accurate solutions with additional classical resources. We demonstrate numerically on a sample electronic system that this method both allows for the accurate determination of excited electronic states as well as reduces the impact of decoherence, without using any additional quantum coherence time or formal error correction codes.First conceived of by Richard Feynman [1], quantum computers have the potential to offer radical advances in solving important problems ranging from optimization and eigenvalue problems to materials design. One problem of particular recent interest is that of quantum chemistry, where quantum computers have the potential to offer an exponential speedup in the determination of physical and chemical properties [2][3][4]. This problem has received attention both because of its great practical utility, and because it is believed that it may be one of the first approaches to demonstrate the superiority of a quantum computer over currently available classical computers [5,6].Recently, there have been a number of advances in quantum chemistry on quantum computers both algorithmically and technologically. The original work utilized the quantum phase estimation algorithm [7-9] and analyzed the use of adiabatic state preparation in chemical problems. Since then, the cost of the quantum phase estimation procedure has been brought down dramatically through considerations of physical locality of interactions, chemical insights, and more general algorithmic enhancements [10][11][12][13][14]. Additionally, prototype implementations of many of these algorithms have now been verified in the lab on quantum technologies such as quantum photonics, ion traps, NMR computers, and nitrogen vacancies in diamond [15][16][17][18][19][20].While there have been significant developments in quantum hardware across a variety of platforms, many of these algorithms cannot be faithfully run on current or near-future technology. To combat this problem, a hybrid quantum classical approach was developed, with the the idea that quantum processors should only be * Corresponding author: jmcclean@lbl.gov FIG. 1. A cartoon sche...