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Quantum computation, a completely different paradigm of computing, benefits from theoretically proven speed-ups for certain problems and opens up the possibility of exactly studying the properties of quantum systems. Yet, because of the inherent fragile nature of the physical computing elements, qubits, achieving quantum advantages over classical computation requires extremely low error rates for qubit operations as well as a significant overhead of physical qubits, in order to realize fault-tolerance via quantum error correction. However, recent theoretical work has shown that the accuracy of computation based off expectation values of quantum observables can be enhanced through an extrapolation of results from a collection of varying noisy experiments. Here, we demonstrate this error mitigation protocol on a superconducting quantum processor, enhancing its computational capability, with no additional hardware modifications. We apply the protocol to mitigate errors on canonical single- and two-qubit experiments and then extend its application to the variational optimization of Hamiltonians for quantum chemistry and magnetism. We effectively demonstrate that the suppression of incoherent errors helps unearth otherwise inaccessible accuracies to the variational solutions using our noisy processor. These results demonstrate that error mitigation techniques will be critical to significantly enhance the capabilities of near-term quantum computing hardware.

The execution of quantum circuits on real systems has largely been limited to those which are simply time-ordered sequences of unitary operations followed by a projective measurement. As hardware platforms for quantum computing continue to mature in size and capability, it is imperative to enable quantum circuits beyond their conventional construction. Here we break into the realm of dynamic quantum circuits on a superconducting-based quantum system. Dynamic quantum circuits involve not only the evolution of the quantum state throughout the computation, but also periodic measurements of a subset of qubits mid-circuit and concurrent processing of the resulting classical information within timescales shorter than the execution times of the circuits. Using noisy quantum hardware, we explore one of the most fundamental quantum algorithms, quantum phase estimation, in its adaptive version, which exploits dynamic circuits, and compare the results to a non-adaptive implementation of the same algorithm. We demonstrate that the version of real-time quantum computing with dynamic circuits can offer a substantial and tangible advantage when noise and latency are sufficiently low in the system, opening the door to a new realm of available algorithms on real quantum systems., 7 pages, 4 figures, plus supplement

In this work, we extend a multiqubit benchmarking technique known as the binned output generation (BOG) in order to discriminate between coherent and incoherent noise sources in the multiqubit regime. While methods exist to discriminate coherent from incoherent noise at the single and few-qubit level, these methods scale poorly beyond a few qubits or must make assumptions about the form of the noise. On the other end of the spectrum, system-level benchmarking techniques exist, but they fail to discriminate between coherent and incoherent noise sources. We experimentally verify the BOG against randomized benchmarking (RB) (the industry standard benchmarking technique) in the two-qubit regime, then apply this technique to a six-qubit linear chain, a regime currently inaccessible to RB. In this experiment, we inject an instantaneous coherent $Z$-type noise on each qubit and demonstrate that the measured coherent noise scales correctly with the magnitude of the injected noise, while the measured incoherent noise remains unchanged as expected. This demonstrates a robust technique to measure coherent errors in a variety of hardware.

The concept of quantum computing has inspired a whole new generation of scientists, including physicists, engineers, and computer scientists, to fundamentally change the landscape of information technology. With experimental demonstrations stretching back more than two decades, the quantum computing community has achieved a major milestone over the past few years: the ability to build systems that are stretching the limits of what can be classically simulated, and which enable cloud-based research for a wide range of scientists, thus increasing the pool of talent exploring early quantum systems. While such noisy near-term quantum computing systems fall far short of the requirements for fault-tolerant systems, they provide unique test beds for exploring the opportunities for quantum applications. Here, we highlight an IBM-specific perspective of the facets associated with these systems, including quantum software, cloud access, benchmarking quantum systems, error correction and mitigation in such systems, understanding the complexity of quantum circuits, and how early quantum applications can run on near-term quantum computers.

The interplay of bulk and boundary scattering is explored in a regime where quantum size effects modify mesoscopic transport in a degenerate Fermi liquid film of $^3$He on a rough surface. We discuss mass transport and the momentum relaxation time of the film in a torsional oscillator geometry within the framework of a quasiclassical theory that includes the experimentally determined power spectrum of the rough surface. The theory explains the anomalous temperature dependence of the relaxation rate observed experimentally. We model further studies on $^3$He confined in nanofluidic sample chambers with lithographically defined surface roughness. The improved understanding of surface roughness scattering can be extended to the analogous system of electrons in metals and suggests routes to improve the conductivity of thin metallic films., Comment: 6 pages, 1 figure

Nonreciprocal microwave devices play critical roles in high-fidelity, quantum-nondemolition (QND) measurement schemes. They impose unidirectional routing of readout signals and protect the quantum systems from unwanted noise originated by the output chain. However, cryogenic circulators and isolators are disadvantageous in scalable superconducting architectures because they use magnetic materials and strong magnetic fields. Here, we realize an active isolator formed by coupling two nondegenerate Josephson mixers in an interferometric scheme and driving them with phase-shifted, same-frequency pumps. By incorporating our Josephson-based isolator into a superconducting qubit setup, we demonstrate fast, high-fidelity, QND measurements of the qubit while providing 20 dB of protection within a bandwidth of 10 MHz against amplified noise reflected off the Josephson amplifier in the output chain. A moderate reduction of 35% is observed in T2E when the Josephson-based isolator is turned on. Such a moderate degradation can be mitigated by minimizing heat dissipation in the pump lines., Magnetic-based isolators are critical components for protecting qubits against noise in quantum setups but unsuitable for large processors. Here, Abdo et al. show good protection of a qubit in a high-fidelity quantum readout setup using a Josephson-based isolator devoid of magnetic materials.

Robust quantum computation requires encoding delicate quantum information into degrees of freedom that are hard for the environment to change. Quantum encodings have been demonstrated in many physical systems by observing and correcting storage errors, but applications require not just storing information; we must accurately compute even with faulty operations. The theory of fault-tolerant quantum computing illuminates a way forward by providing a foundation and collection of techniques for limiting the spread of errors. Here we implement one of the smallest quantum codes in a five-qubit superconducting transmon device and demonstrate fault-tolerant state preparation. We characterize the resulting code words through quantum process tomography and study the free evolution of the logical observables. Our results are consistent with fault-tolerant state preparation in a protected qubit subspace.

We present parity measurements on a five-qubit lattice with connectivity amenable to the surface code quantum error correction architecture. Using all-microwave controls of superconducting qubits coupled via resonators, we encode the parities of four data qubit states in either the $X$- or the $Z$-basis. Given the connectivity of the lattice, we perform full characterization of the static $Z$-interactions within the set of five qubits, as well as dynamical $Z$-interactions brought along by single- and two-qubit microwave drives. The parity measurements are significantly improved by modifying the microwave two-qubit gates to dynamically remove non-ideal $Z$ errors., Comment: 8 pages, 4 figures

Quantum computing holds the promise of a novel form of information processing in which data resides in quantum states. By exploiting superpositions and entanglement among these states, quantum logic operations are expected to far surpass conventional digital logic in certain classes of problems. To realize this prospect, we employ superconducting circuits at millikelvin temperatures. The nonlinearity of a Josephson tunnel junction enables a two-level quantum system, or qubit, with excitation energy in the microwave regime. Key recent advances in such devices are the demonstration of robust and simple multi-qubit gates, the integration of superconducting qubits into arrays of four or more, and gate fidelities reaching 99%. [1,2,3]

The resonator-induced phase (RIP) gate is a multi-qubit entangling gate that allows a high degree of flexibility in qubit frequencies, making it attractive for quantum operations in large-scale architectures. We experimentally realize the RIP gate with four superconducting qubits in a three-dimensional (3D) circuit-quantum electrodynamics architecture, demonstrating high-fidelity controlled-Z (CZ) gates between all possible pairs of qubits from two different 4-qubit devices in pair subspaces. These qubits are arranged within a wide range of frequency detunings, up to as large as 1.8 GHz. We further show a dynamical multi-qubit refocusing scheme in order to isolate out 2-qubit interactions, and combine them to generate a four-qubit Greenberger-Horne-Zeilinger state., Comment: 5 pages, 4 figures in main text with 9 pages 4 figures in the supplemental material

The ability to detect and deal with errors when manipulating quantum systems is a fundamental requirement for fault-tolerant quantum computing. Unlike classical bits that are subject to only digital bit-flip errors, quantum bits are susceptible to a much larger spectrum of errors, for which any complete quantum error-correcting code must account. Whilst classical bit-flip detection can be realized via a linear array of qubits, a general fault-tolerant quantum error-correcting code requires extending into a higher-dimensional lattice. Here we present a quantum error detection protocol on a two-by-two planar lattice of superconducting qubits. The protocol detects an arbitrary quantum error on an encoded two-qubit entangled state via quantum non-demolition parity measurements on another pair of error syndrome qubits. This result represents a building block towards larger lattices amenable to fault-tolerant quantum error correction architectures such as the surface code., The physical realization of a quantum computer requires built-in error-correcting codes that compensate the disruption of quantum information arising from noise. Here, the authors demonstrate a quantum error detection scheme for arbitrary single-qubit errors on a four superconducting qubit lattice.

The ability to perform fast, high-fidelity readout of quantum bits (qubits) is essential to the goal of building a quantum computer. However, coupling a fast measurement channel to a superconducting qubit typically also speeds up its relaxation via spontaneous emission. Here we use impedance engineering to design a filter by which photons may easily leave the resonator at the cavity frequency but not at the qubit frequency. We implement this broadband filter in both an on-chip and off-chip configuration., Comment: 5 pages, 3 figures

High-fidelity measurements are important for the physical implementation of quantum information protocols. Current methods for classifying measurement trajectories in superconducting qubit systems produce fidelities that are systematically lower than those predicted by experimental parameters. Here, we place current classification methods within the framework of machine learning algorithms and improve on them by investigating more sophisticated ML approaches. We find that non-linear algorithms and clustering methods produce significantly higher assignment fidelities that help close the gap to the fidelity achievable under ideal noise conditions. Clustering methods group trajectories into natural subsets within the data, which allows for the diagnosis of specific systematic errors. We find large clusters in the data associated with relaxation processes and show these are the main source of discrepancy between our experimental and achievable fidelities. These error diagnosis techniques help provide a concrete path forward to improve qubit measurements., Comment: 8 pages, 6 figures, submitted version

Quantum process tomography is a necessary tool for verifying quantum gates and diagnosing faults in architectures and gate design. We show that the standard approach of process tomography is grossly inaccurate in the case where the states and measurement operators used to interrogate the system are generated by gates that have some systematic error, a situation all but unavoidable in any practical setting. These errors in tomography can not be fully corrected through oversampling or by performing a larger set of experiments. We present an alternative method for tomography to reconstruct an entire library of gates in a self-consistent manner. The essential ingredient is to define a likelihood function that assumes nothing about the gates used for preparation and measurement. In order to make the resulting optimization tractable we linearize about the target, a reasonable approximation when benchmarking a quantum computer as opposed to probing a black-box function., 10 pages, 6 figures

We demonstrate enhanced relaxation and dephasing times of transmon qubits, up to ~ 60 \mu s by fabricating the interdigitated shunting capacitors using titanium nitride (TiN). Compared to lift-off aluminum deposited simultaneously with the Josephson junction, this represents as much as a six-fold improvement and provides evidence that previous planar transmon coherence times are limited by surface losses from two-level system (TLS) defects residing at or near interfaces. Concurrently, we observe an anomalous temperature dependent frequency shift of TiN resonators which is inconsistent with the predicted TLS model., Comment: 3 figures

We implement a complete randomized benchmarking protocol on a system of two superconducting qubits. The protocol consists of randomizing over gates in the Clifford group, which experimentally are generated via an improved two-qubit cross-resonance gate implementation and single-qubit unitaries. From this we extract an optimal average error per Clifford of 0.0936. We also perform an interleaved experiment, alternating our optimal two-qubit gate with random two-qubit Clifford gates, to obtain a two-qubit gate error of 0.0653. We compare these values with a two-qubit gate error of ~0.12 obtained from quantum process tomography, which is likely limited by state preparation and measurement errors., 4 figures plus supplementary material

We report a system where fixed interactions between non-computational levels make bright the otherwise forbidden two-photon 00 --> 11 transition. The system is formed by hand selection and assembly of two discrete component transmon-style superconducting qubits inside a rectangular microwave cavity. The application of a monochromatic drive tuned to this transition induces two-photon Rabi-like oscillations between the ground and doubly-excited states via the Bell basis. The system therefore allows all-microwave two-qubit universal control with the same techniques and hardware required for single qubit control. We report Ramsey-like and spin echo sequences with the generated Bell states, and measure a two-qubit gate fidelity of 90% (unconstrained) and 86% (maximum likelihood estimator)., 5 pages, 4 figures. V2: add supplemental material about the Schrieffer-Wolff transformation

We use quantum process tomography to characterize a full universal set of all-microwave gates on two superconducting single-frequency single-junction transmon qubits. All extracted gate fidelities, including those for Clifford group generators, single-qubit pi/4 and pi/8 rotations, and a two-qubit controlled-NOT, exceed 95% (98%), without (with) accounting for state preparation and measurement errors. Furthermore, we introduce a process map representation in the Pauli basis which is visually efficient and informative. This high-fidelity gate set serves as another critical building block towards scalable architectures of superconducting qubits for error correction schemes., Comment: 4 figures, 2 tables plus supplementary material

We report a superconducting artificial atom with a coherence time of ${T}_{2}^{*}=92$ $\ensuremath{\mu}$s and energy relaxation time ${T}_{1}=70$ $\ensuremath{\mu}$s. The system consists of a single Josephson junction transmon qubit on a sapphire substrate embedded in an otherwise empty copper waveguide cavity whose lowest eigenmode is dispersively coupled to the qubit transition. We attribute the factor of four increase in the coherence quality factor relative to previous reports to device modifications aimed at reducing qubit dephasing from residual cavity photons. This simple device holds promise as a robust and easily produced artificial quantum system whose intrinsic coherence properties are sufficient to allow tests of quantum error correction.

We demonstrate an all-microwave two-qubit gate on superconducting qubits which are fixed in frequency at optimal bias points. The gate requires no additional subcircuitry and is tunable via the amplitude of microwave irradiation on one qubit at the transition frequency of the other. We use the gate to generate entangled states with a maximal extracted concurrence of 0.88, and quantum process tomography reveals a gate fidelity of 81%.

Thin films of TiN were sputter-deposited onto Si and sapphire wafers with and without SiN buffer layers. The films were fabricated into RF coplanar waveguide resonators, and internal quality factor measurements were taken at millikelvin temperatures in both the many photon and single photon limits, i.e. high and low power regimes, respectively. At high power, internal quality factors ($Q_i$'s) higher than $10^7$ were measured for TiN with predominantly a (200)-TiN orientation. Films that showed significant (111)-TiN texture invariably had much lower $Q_i$'s, on the order of $10^5$. Our studies show that the (200)-TiN is favored for growth at high temperature on either bare Si or SiN buffer layers. However, growth on bare sapphire or Si(100) at low temperature resulted in primarily a (111)-TiN orientation. Ellipsometry and Auger measurements indicate that the (200)-TiN growth on the bare Si substrates is correlated with the formation of a thin, $\approx 2$ nm, layer of SiN during the pre-deposition procedure. In the single photon regime, $Q_i$ of these films exceeded $8\times10^5$, while thicker SiN buffer layers led to reduced $Q_i$'s at low power., Submitted to APL July 2010

We have observed millisecond-long coherent evolution of nuclear spins in a quantum wire at 1.2 K. Local, all-electrical manipulation of nuclear spins is achieved by dynamic nuclear polarization in the breakdown regime of the Integer Quantum Hall Effect combined with pulsed Nuclear Magnetic Resonance. The excitation thresholds for the breakdown are significantly smaller than what would be expected for our sample and the direction of the nuclear polarization can be controlled by the voltage bias. As a four-level spin system, the device is equivalent to two qubits., 5 pages, 5 figures

A high precision torsional oscillator has been used to study 3He films of thickness in the range 100 to 350 nm. In previous work we found that the films decoupled from the oscillator motion below 60 mK, in the Knudsen limit. This precluded observation of the superfluid transition. Here we report measurements using a torsional oscillator whose highly polished inner surfaces have been decorated with a low density of silver particles to act as random elastic scattering centres. This modification locks the normal film to the surface. A superfluid transition of the film is observed.

We characterize a superconducting qubit before and after embedding it along with its package in an absorptive medium. We observe a drastic improvement in the effective qubit temperature and over a tenfold improvement in the relaxation time up to 5.7 μs. Our results suggest the presence of external radiation inside the cryogenic apparatus can be a limiting factor for both qubit initialization and coherence. Calculations support the hypothesis that the relaxation is not limited by direct coupling of thermal photons to the qubit prior to embedding, but by dissipation arising from quasiparticle generation.

We demonstrate the use of anodic bonding to fabricate cells with characteristic size as large as 7 x 10 mm(2), with height of approximately 640 nm, and without any internal support structure. The cells were fabricated from Hoya SD-2 glass and silicon wafers, each with 3 mm thickness to maintain dimensional stability under internal pressure. Bonding was carried out at 350 degrees C and 450 V with an electrode structure that excluded the electric field from the open region. We detail fabrication and characterization steps and also discuss the design of the fill line for access to the cavity.