In-Datacenter Performance Analysis of a Tensor Processing Unit

Many architects believe that major improvements in cost-energy-performance must now come from domain-specific hardware. This paper evaluates a custom ASIC---called a Tensor Processing Unit (TPU)---deployed in datacenters since 2015 that accelerates the inference phase of neural networks (NN). The heart of the TPU is a 65,536 8-bit MAC matrix multiply unit that offers a peak throughput of 92 TeraOps/second (TOPS) and a large (28 MiB) software-managed on-chip memory. The TPU's deterministic execution model is a better match to the 99th-percentile response-time requirement of our NN applications than are the time-varying optimizations of CPUs and GPUs (caches, out-of-order execution, multithreading, multiprocessing, prefetching, ...) that help average throughput more than guaranteed latency. The lack of such features helps explain why, despite having myriad MACs and a big memory, the TPU is relatively small and low power. We compare the TPU to a server-class Intel Haswell CPU and an Nvidia K80 GPU, which are contemporaries deployed in the same datacenters. Our workload, written in the high-level TensorFlow framework, uses production NN applications (MLPs, CNNs, and LSTMs) that represent 95% of our datacenters' NN inference demand. Despite low utilization for some applications, the TPU is on average about 15X - 30X faster than its contemporary GPU or CPU, with TOPS/Watt about 30X - 80X higher. Moreover, using the GPU's GDDR5 memory in the TPU would triple achieved TOPS and raise TOPS/Watt to nearly 70X the GPU and 200X the CPU.Comment: 17 pages, 11 figures, 8 tables. To appear at the 44th International Symposium on Computer Architecture (ISCA), Toronto, Canada, June 24-28, 201

Readout of a quantum processor with high dynamic range Josephson parametric amplifiers

We demonstrate a high dynamic range Josephson parametric amplifier (JPA) in which the active nonlinear element is implemented using an array of rf-SQUIDs. The device is matched to the 50 $\Omega$ environment with a Klopfenstein-taper impedance transformer and achieves a bandwidth of 250-300 MHz, with input saturation powers up to -95 dBm at 20 dB gain. A 54-qubit Sycamore processor was used to benchmark these devices, providing a calibration for readout power, an estimate of amplifier added noise, and a platform for comparison against standard impedance matched parametric amplifiers with a single dc-SQUID. We find that the high power rf-SQUID array design has no adverse effect on system noise, readout fidelity, or qubit dephasing, and we estimate an upper bound on amplifier added noise at 1.6 times the quantum limit. Lastly, amplifiers with this design show no degradation in readout fidelity due to gain compression, which can occur in multi-tone multiplexed readout with traditional JPAs.Comment: 9 pages, 8 figure

Measurement-Induced State Transitions in a Superconducting Qubit: Within the Rotating Wave Approximation

Superconducting qubits typically use a dispersive readout scheme, where a resonator is coupled to a qubit such that its frequency is qubit-state dependent. Measurement is performed by driving the resonator, where the transmitted resonator field yields information about the resonator frequency and thus the qubit state. Ideally, we could use arbitrarily strong resonator drives to achieve a target signal-to-noise ratio in the shortest possible time. However, experiments have shown that when the average resonator photon number exceeds a certain threshold, the qubit is excited out of its computational subspace, which we refer to as a measurement-induced state transition. These transitions degrade readout fidelity, and constitute leakage which precludes further operation of the qubit in, for example, error correction. Here we study these transitions using a transmon qubit by experimentally measuring their dependence on qubit frequency, average photon number, and qubit state, in the regime where the resonator frequency is lower than the qubit frequency. We observe signatures of resonant transitions between levels in the coupled qubit-resonator system that exhibit noisy behavior when measured repeatedly in time. We provide a semi-classical model of these transitions based on the rotating wave approximation and use it to predict the onset of state transitions in our experiments. Our results suggest the transmon is excited to levels near the top of its cosine potential following a state transition, where the charge dispersion of higher transmon levels explains the observed noisy behavior of state transitions. Moreover, occupation in these higher energy levels poses a major challenge for fast qubit reset

Overcoming leakage in scalable quantum error correction

Leakage of quantum information out of computational states into higher energy states represents a major challenge in the pursuit of quantum error correction (QEC). In a QEC circuit, leakage builds over time and spreads through multi-qubit interactions. This leads to correlated errors that degrade the exponential suppression of logical error with scale, challenging the feasibility of QEC as a path towards fault-tolerant quantum computation. Here, we demonstrate the execution of a distance-3 surface code and distance-21 bit-flip code on a Sycamore quantum processor where leakage is removed from all qubits in each cycle. This shortens the lifetime of leakage and curtails its ability to spread and induce correlated errors. We report a ten-fold reduction in steady-state leakage population on the data qubits encoding the logical state and an average leakage population of less than $1 \times 10^{-3}$ throughout the entire device. The leakage removal process itself efficiently returns leakage population back to the computational basis, and adding it to a code circuit prevents leakage from inducing correlated error across cycles, restoring a fundamental assumption of QEC. With this demonstration that leakage can be contained, we resolve a key challenge for practical QEC at scale.Comment: Main text: 7 pages, 5 figure

Suppressing quantum errors by scaling a surface code logical qubit

Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical qubits, where 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 in order for logical performance to improve with increasing code size. Here, we report the measurement of logical qubit performance scaling across multiple code sizes, and demonstrate that our system of superconducting qubits has sufficient performance to overcome the additional errors from increasing qubit number. We find our distance-5 surface code logical qubit modestly outperforms an ensemble of distance-3 logical qubits on average, both in terms of logical error probability over 25 cycles and logical error per cycle ($2.914\%\pm 0.016\%$ compared to $3.028\%\pm 0.023\%$). To investigate damaging, low-probability error sources, we run a distance-25 repetition code and observe a $1.7\times10^{-6}$ logical error per round floor set by a single high-energy event ($1.6\times10^{-7}$ when excluding this event). We are able to accurately model our experiment, and from this model we can extract error budgets that highlight the biggest challenges for future systems. These results mark the first experimental demonstration where quantum error correction begins to improve performance with increasing qubit number, illuminating the path to reaching the logical error rates required for computation.Comment: Main text: 6 pages, 4 figures. v2: Update author list, references, Fig. S12, Table I

Measurement-induced entanglement and teleportation on a noisy quantum processor

Measurement has a special role in quantum theory: by collapsing the wavefunction it can enable phenomena such as teleportation and thereby alter the "arrow of time" that constrains unitary evolution. When integrated in many-body dynamics, measurements can lead to emergent patterns of quantum information in space-time that go beyond established paradigms for characterizing phases, either in or out of equilibrium. On present-day NISQ processors, the experimental realization of this physics is challenging due to noise, hardware limitations, and the stochastic nature of quantum measurement. Here we address each of these experimental challenges and investigate measurement-induced quantum information phases on up to 70 superconducting qubits. By leveraging the interchangeability of space and time, we use a duality mapping, to avoid mid-circuit measurement and access different manifestations of the underlying phases -- from entanglement scaling to measurement-induced teleportation -- in a unified way. We obtain finite-size signatures of a phase transition with a decoding protocol that correlates the experimental measurement record with classical simulation data. The phases display sharply different sensitivity to noise, which we exploit to turn an inherent hardware limitation into a useful diagnostic. Our work demonstrates an approach to realize measurement-induced physics at scales that are at the limits of current NISQ processors

Non-Abelian braiding of graph vertices in a superconducting processor

Indistinguishability of particles is a fundamental principle of quantum mechanics. For all elementary and quasiparticles observed to date - including fermions, bosons, and Abelian anyons - this principle guarantees that the braiding of identical particles leaves the system unchanged. However, in two spatial dimensions, an intriguing possibility exists: braiding of non-Abelian anyons causes rotations in a space of topologically degenerate wavefunctions. Hence, it can change the observables of the system without violating the principle of indistinguishability. Despite the well developed mathematical description of non-Abelian anyons and numerous theoretical proposals, the experimental observation of their exchange statistics has remained elusive for decades. Controllable many-body quantum states generated on quantum processors offer another path for exploring these fundamental phenomena. While efforts on conventional solid-state platforms typically involve Hamiltonian dynamics of quasi-particles, superconducting quantum processors allow for directly manipulating the many-body wavefunction via unitary gates. Building on predictions that stabilizer codes can host projective non-Abelian Ising anyons, we implement a generalized stabilizer code and unitary protocol to create and braid them. This allows us to experimentally verify the fusion rules of the anyons and braid them to realize their statistics. We then study the prospect of employing the anyons for quantum computation and utilize braiding to create an entangled state of anyons encoding three logical qubits. Our work provides new insights about non-Abelian braiding and - through the future inclusion of error correction to achieve topological protection - could open a path toward fault-tolerant quantum computing

Legal Protection for the Individual Employee, 5th edition

This book is intended for courses on the individual rights of workers in the employment relationship, independent of courses on the law governing collective bargaining or employment discrimination. It can be used for one three credit survey course on employment law, or for two related courses on employment law and employee benefits, each of two credits. The book covers the full range of employment law subjects from the nature of the employment relationship, the definition of employee , pre-employment screening, individual employment contracts, the employment at-will doctrine, exceptions to the employment at–will doctrine, obligations of employees, monitoring and control of employees, the regulation of pay and hours of work (FLSA), state and federal regulation of workers compensation, unemployment compensation, the regulation of occupational safety and health (OSHA), state and federal regulation of unemployment compensation, and the regulation of employee benefits (ERISA).The book has been substantially updated from the last issue to facilitate teaching and to include such topics as: a separate chapter on the definition of employee , the Genetic Information Non-discrimination Act (GINA), employee privacy issues in the new information technology, the new restatement of employment law, and the Affordable Care Act (ACA). Where appropriate, the book presents interdisciplinary discussions of employment law problems from historical, sociological and economic perspectives. Efforts were also made to include relevant empirical evidence on important employment law questions. A recurring theme in the book, especially in the introductory chapter and the chapters on individual employment contracts and privacy, is the historical tension in the United States between legal ideologies of “free labor,” i.e., of the law as supporting a notion of labor that is free to contract for any employer imposed restraints or of the law as supporting a notion of labor that is free even from some unreasonable employer demands, with an eye towards equality and fairness. Another recurring theme in the book is when and how is it desirable to intervene in the labor market to address market failures to promote greater income equality, workplace health and safety, unemployment insurance, healthcare insurance and retirement income security.https://www.repository.law.indiana.edu/facbooks/1150/thumbnail.jp

Legal Protection for the Individual Employee, 5th edition

This book is intended for courses on the individual rights of workers in the employment relationship, independent of courses on the law governing collective bargaining or employment discrimination. It can be used for one three credit survey course on employment law, or for two related courses on employment law and employee benefits, each of two credits. The book covers the full range of employment law subjects from the nature of the employment relationship, the definition of employee , pre-employment screening, individual employment contracts, the employment at-will doctrine, exceptions to the employment at–will doctrine, obligations of employees, monitoring and control of employees, the regulation of pay and hours of work (FLSA), state and federal regulation of workers compensation, unemployment compensation, the regulation of occupational safety and health (OSHA), state and federal regulation of unemployment compensation, and the regulation of employee benefits (ERISA).The book has been substantially updated from the last issue to facilitate teaching and to include such topics as: a separate chapter on the definition of employee , the Genetic Information Non-discrimination Act (GINA), employee privacy issues in the new information technology, the new restatement of employment law, and the Affordable Care Act (ACA). Where appropriate, the book presents interdisciplinary discussions of employment law problems from historical, sociological and economic perspectives. Efforts were also made to include relevant empirical evidence on important employment law questions. A recurring theme in the book, especially in the introductory chapter and the chapters on individual employment contracts and privacy, is the historical tension in the United States between legal ideologies of “free labor,” i.e., of the law as supporting a notion of labor that is free to contract for any employer imposed restraints or of the law as supporting a notion of labor that is free even from some unreasonable employer demands, with an eye towards equality and fairness. Another recurring theme in the book is when and how is it desirable to intervene in the labor market to address market failures to promote greater income equality, workplace health and safety, unemployment insurance, healthcare insurance and retirement income security.https://www.repository.law.indiana.edu/facbooks/1150/thumbnail.jp

Legal Protection for the Individual Employee, 6th ed.

This book is intended for courses on the individual rights of workers in the employment relationship, independent of courses on the law governing collective bargaining or employment discrimination. It can be used for one three credit survey course on employment law, or for two related courses on employment law and employee benefits, each of two credits. The book covers the full range of employment law subjects from the nature of the employment relationship, the definition of employee , pre-employment screening, individual employment contracts, the employment at-will doctrine, exceptions to the employment at–will doctrine, obligations of employees, monitoring and control of employees, the regulation of pay and hours of work (FLSA), state and federal regulation of workers compensation, unemployment compensation, the regulation of occupational safety and health (OSHA), state and federal regulation of unemployment compensation, and the regulation of employee benefits (ERISA). The book has been substantially updated from the last issue. The first four chapters have been substantially rewritten to simplify the introductory discussion of the nature of the employment relationship and the recent changes that have occurred due to the adoption of new information technology and globalization. The book has also been updated to include more detailed discussions of the impact of the Affordable Care Act (ACA) and the legislative responses to the Covid-19 pandemic. Where appropriate, the book presents interdisciplinary discussions of employment law problems from historical, economic and industrial relations perspectives. All of these interdisciplinary discussions have been updated to reflect the most recent academic work. Efforts were also made to include relevant empirical evidence on the common practices of employers and important employment law questions. All of these empirical references have been updated to reflect the most recent available data. A recurring theme in the book, especially in the introductory chapter and the chapters on individual employment contracts and privacy, is the historical tension in the United States between legal ideologies of “free labor,” i.e., of the law as supporting a notion of labor that is free to contract for any employer imposed restraints or of the law as supporting a notion of labor that is free even from some unreasonable employer demands, with an eye towards equality and fairness. Another recurring theme in the book is when and how is it desirable to intervene in the labor market to address market failures to promote greater income equality, workplace health and safety, unemployment insurance, healthcare insurance, retirement income security and respect for human dignity.https://www.repository.law.indiana.edu/facbooks/1264/thumbnail.jp