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The estimation of low energies of many-body systems is a cornerstone of computational quantum sciences. Variational quantum algorithms can be used to prepare ground states on pre-fault-tolerant quantum processors, but their lack of convergence guarantees and impractical number of cost function estimations prevent systematic scaling of experiments to large systems. Alternatives to variational approaches are needed for large-scale experiments on pre-fault-tolerant devices. Here, we use a superconducting quantum processor to compute eigenenergies of quantum many-body systems on two-dimensional lattices of up to 56 sites, using the Krylov quantum diagonalization algorithm, an analog of the well-known classical diagonalization technique. We construct subspaces of the many-body Hilbert space using Trotterized unitary evolutions executed on the quantum processor, and classically diagonalize many-body interacting Hamiltonians within those subspaces. These experiments show that quantum diagonalization algorithms are poised to complement their classical counterpart at the foundation of computational methods for quantum systems., Comment: 25 pages, 13 figures

We describe Qiskit, a software development kit for quantum information science. We discuss the key design decisions that have shaped its development, and examine the software architecture and its core components. We demonstrate an end-to-end workflow for solving a problem in condensed matter physics on a quantum computer that serves to highlight some of Qiskit's capabilities, for example the representation and optimization of circuits at various abstraction levels, its scalability and retargetability to new gates, and the use of quantum-classical computations via dynamic circuits. Lastly, we discuss some of the ecosystem of tools and plugins that extend Qiskit for various tasks, and the future ahead.

Quantum computers are becoming practical for computing numerous applications. However, simulating quantum computing on classical computers is still demanding yet useful because current quantum computers are limited because of computer resources, hardware limits, instability, and noises. Improving quantum computing simulation performance in classical computers will contribute to the development of quantum computers and their algorithms. Quantum computing simulations on classical computers require long performance times, especially for quantum circuits with a large number of qubits or when simulating a large number of shots for noise simulations or circuits with intermediate measures. Graphical processing units (GPU) are suitable to accelerate quantum computer simulations by exploiting their computational power and high bandwidth memory and they have a large advantage in simulating relatively larger qubits circuits. However, GPUs are inefficient at simulating multi-shots runs with noises because the randomness prevents highly parallelization. In addition, GPUs have a disadvantage in simulating circuits with a small number of qubits because of the large overheads in GPU kernel execution. In this paper, we introduce optimization techniques for multi-shot simulations on GPUs. We gather multiple shots of simulations into a single GPU kernel execution to reduce overheads by scheduling randomness caused by noises. In addition, we introduce shot-branching that reduces calculations and memory usage for multi-shot simulations. By using these techniques, we speed up x10 from previous implementations.

To run large-scale algorithms on a quantum computer, error-correcting codes must be able to perform a fundamental set of operations, called logic gates, while isolating the encoded information from noise~\cite{Harper2019,Ryan-Anderson2021,Egan2021fault, Chen2022calibrated, Sundaresan2022matching, ryananderson2022implementing, Postler2022demonstration, GoogleAI2023}. We can complete a universal set of logic gates by producing special resources called magic states~\cite{Bravyi2005universal,Maier2013magic, Chamberland2022building}. It is therefore important to produce high-fidelity magic states to conduct algorithms while introducing a minimal amount of noise to the computation. Here, we propose and implement a scheme to prepare a magic state on a superconducting qubit array using error correction. We find that our scheme produces better magic states than those we can prepare using the individual qubits of the device. This demonstrates a fundamental principle of fault-tolerant quantum computing~\cite{Shor96}, namely, that we can use error correction to improve the quality of logic gates with noisy qubits. Additionally, we show we can increase the yield of magic states using adaptive circuits, where circuit elements are changed depending on the outcome of mid-circuit measurements. This demonstrates an essential capability we will need for many error-correction subroutines. Our prototype will be invaluable in the future as it can reduce the number of physical qubits needed to produce high-fidelity magic states in large-scale quantum-computing architectures., Comment: 19 pages, 13 figures, 3 tables, comments welcome; v2 - Updated draft including new appendices following peer review. Includes a section on injecting the encoded magic state into larger codes (explicitly studying the surface code, the heavy-hex code and the color code) and a numerical section interrogating the fault-tolerant properties of the circuit

We investigate an error mitigated tomographic approach to the quantum circuit cutting problem in the presence of gate and measurement noise. We explore two tomography specific error mitigation techniques; readout error mitigated conditional fragment tomography, which uses knowledge of readout errors on all cut and conditional qubit measurements in the tomography reconstruction procedure; and dominant eigenvalue truncation (DEVT), which aims to improve the performance of circuit cutting by performing truncation of the individual conditional tomography fragments used in the reconstruction. We find that the performance of both readout error mitigated tomography and DEVT tomography are comparable for circuit cutting in the presence of symmetric measurement errors. For gate errors our numerical results show that probability estimates for the original circuit obtained using DEVT outperforms general circuit cutting for measurement, depolarization and weakly biased Pauli noise models, but does not improve performance for amplitude damping and coherent errors, and can greatly decrease performance for highly biased Pauli noise. In cases where DEVT was effective, it as also found to improve performance of partial tomographic reconstruction using at least 50% of the full tomographic data with a conditional least-squares tomographic fitter, while linear inversion tomography with or without DEVT mitigation was found to perform poorly with with partial data., Comment: 15+2 pages, double column

We develop general purpose algorithms for computing and utilizing both the Dyson series and Magnus expansion, with the goal of facilitating numerical perturbative studies of quantum dynamics. To enable broad applications to models with multiple parameters, we phrase our algorithms in terms of multivariable sensitivity analysis, for either the solution or the time-averaged generator of the evolution over a fixed time-interval. These tools simultaneously compute a collection of terms up to arbitrary order, and are general in the sense that the model can depend on the parameters in an arbitrary time-dependent way. We implement the algorithms in the open source software package \qiskitdynamics{}, utilizing the JAX array library to enable just-in-time compilation, automatic differentiation, and GPU execution of all computations. Using a model of a single transmon, we demonstrate how to use these tools to approximate fidelity in a region of model parameter space, as well as construct perturbative robust control objectives. We also derive and implement Dyson and Magnus-based variations of the recently introduced Dysolve algorithm [Shillito et al., Physical Review Research, 3(3):033266] for simulating linear matrix differential equations. We show how the pre-computation step can be phrased as a multivariable expansion computation problem with fewer terms than in the original method. When simulating a two-transmon entangling gate on a GPU, we find the Dyson and Magnus-based solvers provide a speedup over traditional ODE solvers, ranging from roughly $2\times$ to $4\times$ for a solution and $10\times$ to $60\times$ for a gradient, depending on solution accuracy., Comment: Accepted version: Speedup results updated after rerunning simulations with updated packages, modified figures, and expanded discussions

Website fingerprinting (WF) is a well-know threat to users' web privacy. New internet standards, such as QUIC, include padding to support defenses against WF. Previous work only analyzes the effectiveness of defenses when users are behind a VPN. Yet, this is not how most users browse the Internet. In this paper, we provide a comprehensive evaluation of QUIC-padding-based defenses against WF when users directly browse the web. We confirm previous claims that network-layer padding cannot provide good protection against powerful adversaries capable of observing all traffic traces. We further demonstrate that such padding is ineffective even against adversaries with constraints on traffic visibility and processing power. At the application layer, we show that defenses need to be deployed by both first and third parties, and that they can only thwart traffic analysis in limited situations. We identify challenges to deploy effective WF defenses and provide recommendations to address them.

Credential stuffing attacks use stolen passwords to log into victim accounts. To defend against these attacks, recently deployed compromised credential checking (C3) services provide APIs that help users and companies check whether a username, password pair is exposed. These services however only check if the exact password is leaked, and therefore do not mitigate credential tweaking attacks - attempts to compromise a user account with variants of a user's leaked passwords. Recent work has shown credential tweaking attacks can compromise accounts quite effectively even when the credential stuffing countermeasures are in place. We initiate work on C3 services that protect users from credential tweaking attacks. The core underlying challenge is how to identify passwords that are similar to their leaked passwords while preserving honest clients' privacy and also preventing malicious clients from extracting breach data from the service. We formalize the problem and explore ways to measure password similarity that balance efficacy, performance, and security. Based on this study, we design "Might I Get Pwned" (MIGP), a new kind of breach alerting service. Our simulations show that MIGP reduces the efficacy of state-of-the-art 1000-guess credential tweaking attacks by 94%. MIGP preserves user privacy and limits potential exposure of sensitive breach entries. We show that the protocol is fast, with response time close to existing C3 services. We worked with Cloudflare to deploy MIGP in practice.

Proteins perform critical processes in all living systems: converting solar energy into chemical energy, replicating DNA, as the basis of highly performant materials, sensing and much more. While an incredible range of functionality has been sampled in nature, it accounts for a tiny fraction of the possible protein universe. If we could tap into this pool of unexplored protein structures, we could search for novel proteins with useful properties that we could apply to tackle the environmental and medical challenges facing humanity. This is the purpose of protein design. Sequence design is an important aspect of protein design, and many successful methods to do this have been developed. Recently, deep-learning methods that frame it as a classification problem have emerged as a powerful approach. Beyond their reported improvement in performance, their primary advantage over physics-based methods is that the computational burden is shifted from the user to the developers, thereby increasing accessibility to the design method. Despite this trend, the tools for assessment and comparison of such models remain quite generic. The goal of this paper is to both address the timely problem of evaluation and to shine a spotlight, within the Machine Learning community, on specific assessment criteria that will accelerate impact. We present a carefully curated benchmark set of proteins and propose a number of standard tests to assess the performance of deep learning based methods. Our robust benchmark provides biological insight into the behaviour of design methods, which is essential for evaluating their performance and utility. We compare five existing models with two novel models for sequence prediction. Finally, we test the designs produced by these models with AlphaFold2, a state-of-the-art structure-prediction algorithm, to determine if they are likely to fold into the intended 3D shapes., Comment: 9 pages, 5 figures

We introduce a Bayesian method for the estimation of single qubit errors in quantum devices, and use it to characterize these errors on three 27-qubit superconducting qubit devices. We self-consistently estimate up to seven parameters of each qubit's state preparation, readout, and gate errors, analyze the stability of these errors as a function of time, and demonstrate easily implemented approaches for mitigating different errors before a quantum computation experiment. On the investigated devices we find non-negligible qubit reset errors that cannot be parametrized as a diagonal mixed state, but manifest as a coherent phase of a superposition with a small contribution from the qubit's excited state. We are able to mitigate such errors by applying pre-rotations on the initialized qubits, which we demonstrate with multi-qubit entangled states. Our results demonstrate that Bayesian estimation can resolve small parameters - including those pertaining to quantum gate errors - with a high relative accuracy, at a lower measurement cost as compared with standard characterization approaches., Comment: v3 contains small corrections and clarifications

In clinical diagnostics and research involving histopathology, formalin fixed paraffin embedded (FFPE) tissue is almost universally favored for its superb image quality. However, tissue processing time (more than 24 hours) can slow decision-making. In contrast, fresh frozen (FF) processing (less than 1 hour) can yield rapid information but diagnostic accuracy is suboptimal due to lack of clearing, morphologic deformation and more frequent artifacts. Here, we bridge this gap using artificial intelligence. We synthesize FFPE-like images ,virtual FFPE, from FF images using a generative adversarial network (GAN) from 98 paired kidney samples derived from 40 patients. Five board-certified pathologists evaluated the results in a blinded test. Image quality of the virtual FFPE data was assessed to be high and showed a close resemblance to real FFPE images. Clinical assessments of disease on the virtual FFPE images showed a higher inter-observer agreement compared to FF images. The nearly instantaneously generated virtual FFPE images can not only reduce time to information but can facilitate more precise diagnosis from routine FF images without extraneous costs and effort., Comment: 24 pages, 6 figures, and 3 tables

Noise in existing quantum processors only enables an approximation to ideal quantum computation. However, these approximations can be vastly improved by error mitigation, for the computation of expectation values, as shown by small-scale experimental demonstrations. However, the practical scaling of these methods to larger system sizes remains unknown. Here, we demonstrate the utility of zero-noise extrapolation for relevant quantum circuits using up to 26 qubits, circuit depths of 60, and 1080 CNOT gates. We study the scaling of the method for canonical examples of product states and entangling Clifford circuits of increasing size, and extend it to the quench dynamics of 2-D Ising spin lattices with varying couplings. We show that the efficacy of the error mitigation is greatly enhanced by additional error suppression techniques and native gate decomposition that reduce the circuit time. By combining these methods, we demonstrate an accuracy in the approximate quantum simulation of the quench dynamics that surpasses the classical approximations obtained from a state-of-the-art 2-D tensor network method. These results reveal a path to a relevant quantum advantage with noisy, digital, quantum processors., Comment: 7 pages, 3 figures

The Domain Name System (DNS) is the foundation of a human-usable Internet, responding to client queries for host-names with corresponding IP addresses and records. Traditional DNS is also unencrypted, and leaks user information to network operators. Recent efforts to secure DNS using DNS over TLS (DoT) and DNS over HTTPS (DoH) have been gaining traction, ostensibly protecting traffic and hiding content from on-lookers. However, one of the criticisms of DoT and DoH is brought to bear by the small number of large-scale deployments (e.g., Comcast, Google, Cloudflare): DNS resolvers can associate query contents with client identities in the form of IP addresses. Oblivious DNS over HTTPS(ODoH) safeguards against this problem. In this paper we ask what it would take to make ODoH practical? We describe ODoH, a practical DNS protocol aimed at resolving this issue by both protecting the client's content and identity. We implement and deploy the protocol, and perform measurements to show that ODoH has comparable performance to protocols like DoH and DoT which are gaining widespread adoption, while improving client privacy, making ODoH a practical privacy enhancing replacement for the usage of DNS., Comment: 16 pages, 7 figures, Under submission and Presented at IETF 109 MAPRG

Variational Quantum Algorithms (VQAs) are a promising application for near-term quantum processors, however the quality of their results is greatly limited by noise. For this reason, various error mitigation techniques have emerged to deal with noise that can be applied to these algorithms. Recent work introduced a technique for mitigating expectation values against correlated measurement errors that can be applied to measurements of 10s of qubits. We apply these techniques to VQAs and demonstrate its effectiveness in improving estimates to the cost function. Moreover, we use the data resulting from this technique to experimentally characterize measurement errors in terms of the device connectivity on devices of up to 20 qubits. These results should be useful for better understanding the near-term potential of VQAs as well as understanding the correlations in measurement errors on large, near-term devices., Comment: 7 pages, 4 figures