We introduce Codex, a GPT language model finetuned on publicly available code from GitHub, and study its Python code-writing capabilities. A distinct production version of Codex powers GitHub Copilot. On HumanEval, a new evaluation set we release to measure functional correctness for synthesizing programs from docstrings, our model solves 28.8% of the problems, while GPT-3 solves 0% and GPT-J solves 11.4%. Furthermore, we find that repeated sampling from the model is a surprisingly effective strategy for producing working solutions to difficult prompts. Using this method, we solve 70.2% of our problems with 100 samples per problem. Careful investigation of our model reveals its limitations, including difficulty with docstrings describing long chains of operations and with binding operations to variables. Finally, we discuss the potential broader impacts of deploying powerful code generation technologies, covering safety, security, and economics.

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Harnessing techniques from analog signal processing, we establish a new path for large-scale quantum computation.

We describe and implement a family of entangling gates activated by radio-frequency flux modulation applied to a tunable transmon that is statically coupled to a neighboring transmon. The effect of this modulation is the resonant exchange of photons directly between levels of the two-transmon system, obviating the need for mediating qubits or resonator modes and allowing for the full utilization of all qubits in a scalable architecture. The resonance condition is selective in both the frequency and amplitude of modulation and thus alleviates frequency crowding. We demonstrate the use of three such resonances to produce entangling gates that enable universal quantum computation: one iSWAP gate and two distinct controlled Z gates. We report interleaved randomized benchmarking results indicating gate error rates of 6% for the iSWAP (duration 135ns) and 9% for the controlled Z gates (durations 175 ns and 270 ns), limited largely by qubit coherence.A central challenge in building a scalable quantum computer with superconducting qubits is the execution of high-fidelity, two-qubit gates within an architecture containing many resonant elements. As more elements are added, or as the multiplicity of couplings between elements is increased, the frequency space of the design becomes crowded and device performance suffers. In architectures composed of transmon qubits [1], there are two main approaches to implementing two-qubit gates. The first utilizes fixed-frequency qubits with static couplings where the two-qubit operations are activated by applying transverse microwave drives [2][3][4][5][6][7][8]. While fixedfrequency qubits generally have long coherence times, this architecture requires satisfying stringent constraints on qubit frequencies and anharmonicities [5,6,8] which requires some tunability to scale to many qubits [9]. The second approach relies on frequency-tunable transmons, and two-qubit gates are activated by tuning qubits into and out of resonance with a particular transition [10][11][12][13][14][15][16]. However, tunability comes at the cost of additional decoherence channels, thus significantly limiting coherence times [17]. In this approach the delivery of shaped unbalanced control signals poses a challenge [15]. Such gates are furthermore sensitive to frequency crowdingavoiding unwanted crossings with neighboring qubit energy levels during gate operations limits the flexibility and connectivity of the architecture.An alternative to these approaches is to modulate a circuit's couplings or energy levels at a frequency corresponding to the detuning between particular energy levels of interest [18][19][20][21][22][23][24][25][26]. This enables an entangling gate between a qubit and a single resonator [21,22], a qubit and many resonator modes [26], two transmon qubits coupled by a tunable mediating qubit [16,25], or two tunable transmons coupled to a mediating resonator [23,24].Building on these earlier results, we implement two entangling gates, iSWAP and controlled Z (CZ), between a flux-tunable transmon an...

Following the simple observation that the interconnection of a set of quantum optical input–output devices can be specified using structural mode VHSIC hardware description language, we demonstrate a computer-aided schematic capture workflow for modelling and simulating multi-component photonic circuits. We describe an algorithm for parsing circuit descriptions to derive quantum equations of motion, illustrate our approach using simple examples based on linear and cavity-nonlinear optical components, and demonstrate a computational approach to hierarchical model reduction.

A semiclassical simulation approach is presented for studying quantum noise in large-scale photonic circuits incorporating an ideal Kerr nonlinearity. A circuit solver is used to generate matrices defining a set of stochastic differential equations, in which the resonator field variables represent random samplings of the Wigner quasi-probability distributions. Although the semiclassical approach involves making a large-photon-number approximation, tests on one-and two-resonator circuits indicate satisfactory agreement between the semiclassical and full-quantum simulation results in the parameter regime of interest. The semiclassical model is used to simulate random errors in a largescale circuit that contains 88 resonators and hundreds of components in total, and functions as a 4-bit ripple counter. The error rate as a function of on-state photon number is examined, and it is observed that the quantum fluctuation amplitudes do not increase as signals propagate through the circuit, an important property for scalability.

In order to support near-term applications of quantum computing, a new compute paradigm has emerged-the quantum-classical cloud-in which quantum computers (QPUs) work in tandem with classical computers (CPUs) via a shared cloud infrastructure. In this work, we enumerate the architectural requirements of a quantum-classical cloud platform, and present a framework for benchmarking its runtime performance. In addition, we walk through two platform-level enhancements, parametric compilation and active qubit reset, that specifically optimize a quantumclassical architecture to support variational hybrid algorithms (VHAs), the most promising applications of near-term quantum hardware. Finally, we show that integrating these two features into the Rigetti Quantum Cloud Services (QCS) platform results in considerable improvements to the latencies that govern algorithm runtime. ‡ Current address: OpenAI,

We present squeezing and anti-squeezing spectra of the output from a degenerate optical parametric oscillator (OPO) network arranged in different coherent quantum feedback configurations. One OPO serves as a quantum plant, the other as a quantum controller. The addition of coherent feedback enables shaping of the output squeezing spectrum of the plant, and is found to be capable of pushing the frequency of maximum squeezing away from the optical driving frequency and broadening the spectrum over a wider frequency band. The experimental results are in excellent agreement with the developed theory, and illustrate the use of coherent quantum feedback to engineer the quantum-optical properties of the plant OPO output.