arXiv subjects

Stephan Eidenbenz

Publications and source records attributed to Stephan Eidenbenz.

At least 55 records · Page 3Linked to original sources

arXiv2024

Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions

Computational models are an essential tool for the design, characterization, and discovery of novel materials. Hard computational tasks in materials science stretch the limits of existing high-performance supercomputing centers, consuming much of their simulation, analysis, and data resources. Quantum computing, on the other hand, is an emerging technology with the potential to accelerate many of the computational tasks needed for materials science. In order to do that, the quantum technology must interact with conventional high-performance computing in several ways: approximate results validation, identification of hard problems, and synergies in quantum-centric supercomputing. In this paper, we provide a perspective on how quantum-centric supercomputing can help address critical computational problems in materials science, the challenges to face in order to solve representative use cases, and new suggested directions.

quant-ph↗

arXiv2024

Warm-Started QAOA with Aligned Mixers Converges Slowly Near the Poles of the Bloch Sphere

In order to boost the performance of the Quantum Approximate Optimization Algorithm (QAOA) to solve problems in combinatorial optimization, researchers have leveraged the solutions returned from classical algorithms in order to create a warm-started quantum initial state for QAOA that is biased towards "good" solutions. Cain et al. showed that if the classically-obtained solutions are mapped to the poles of the Bloch sphere, then vanilla QAOA with the standard mixer "gets stuck". If the classically-obtained solution is instead mapped to within some angle $θ$ from the poles of the Bloch sphere, creating an initial product state, then QAOA with optimal variational parameters is known to converge to the optimal solution with increased circuit depth if the mixer is modified to be "aligned" with the warm-start initial state. Leveraging recent work of Benchasattabuse et al., we provide theoretical lower bounds on the circuit depth necessary for this form of warm-started QAOA to achieve a desired change $Δλ$ in approximation ratio; in particular, we show that for small $θ$, the lower bound on the circuit depth roughly scales proportionally with $Δλ/θ$.

quant-ph↗

arXiv2024

The Better Solution Probability Metric: Optimizing QAOA to Outperform its Warm-Start Solution

This paper presents a numerical simulation investigation of the Warm-Start Quantum Approximate Optimization Algorithm (QAOA) as proposed by Tate et al. [1], focusing on its application to 3-regular Max-Cut problems. Our study demonstrates that Warm-Start QAOA consistently outperforms theoretical lower bounds on approximation ratios across various tilt angles, highlighting its potential in practical scenarios beyond worst-case predictions. Despite these improvements, Warm-Start QAOA with traditional parameters optimized for expectation value does not exceed the performance of the initial classical solution. To address this, we introduce an alternative parameter optimization objective, the Better Solution Probability (BSP) metric. Our results show that BSP-optimized Warm-Start QAOA identifies solutions at non-trivial tilt angles that are better than even the best classically found warm-start solutions with non-vanishing probabilities. These findings underscore the importance of both theoretical and empirical analyses in refining QAOA and exploring its potential for quantum advantage.

quant-ph↗

arXiv2024

Hierarchical Multigrid Ansatz for Variational Quantum Algorithms

Quantum computing is an emerging topic in engineering that promises to enhance supercomputing using fundamental physics. In the near term, the best candidate algorithms for achieving this advantage are variational quantum algorithms (VQAs). We design and numerically evaluate a novel ansatz for VQAs, focusing in particular on the variational quantum eigensolver (VQE). As our ansatz is inspired by classical multigrid hierarchy methods, we call it "multigrid" ansatz. The multigrid ansatz creates a parameterized quantum circuit for a quantum problem on $n$ qubits by successively building and optimizing circuits for smaller qubit counts $j < n$, reusing optimized parameter values as initial solutions to next level hierarchy at $j+1$. We show through numerical simulation that the multigrid ansatz outperforms the standard hardware-efficient ansatz in terms of solution quality for the Laplacian eigensolver as well as for a large class of combinatorial optimization problems with specific examples for MaxCut and Maximum $k$-Satisfiability. Our studies establish the multi-grid ansatz as a viable candidate for many VQAs and in particular present a promising alternative to the QAOA approach for combinatorial optimization problems.

quant-ph↗

arXiv2024

Quantum Approximate Optimization: A Computational Intelligence Perspective

Quantum computing is an emerging field on the multidisciplinary interface between physics, engineering, and computer science with the potential to make a large impact on computational intelligence (CI). The aim of this paper is to introduce quantum approximate optimization methods to the CI community because of direct relevance to solving combinatorial problems. We introduce quantum computing and variational quantum algorithms (VQAs). VQAs are an effective method for the near-term implementation of quantum solutions on noisy intermediate-scale quantum (NISQ) devices with less reliable qubits and early-stage error correction. Then, we explain Farhi et al.'s quantum approximate optimization algorithm (Farhi's QAOA, to prevent confusion). This VQA is generalized by Hadfield et al. to the quantum alternating operator ansatz (QAOA), which is a nature-inspired (particularly, adiabatic) quantum metaheuristic for approximately solving combinatorial optimization problems on gate-based quantum computers. We discuss connections of QAOA to relevant domains, such as computational learning theory and genetic algorithms, discussing current techniques and known results regarding hybrid quantum-classical intelligence systems. We present a schematic of how QAOA is constructed, and also discuss how CI techniques can be used to improve QAOA. We conclude with QAOA implementations for the well-known maximum cut, maximum bisection, and traveling salesperson problems, which can serve as templates for CI practitioners interested in using QAOA.

quant-ph↗

arXiv2024

Increasing the Measured Effective Quantum Volume with Zero Noise Extrapolation

Quantum Volume is a full-stack benchmark for near-term quantum computers. It quantifies the largest size of a square circuit which can be executed on the target device with reasonable fidelity. Error mitigation is a set of techniques intended to remove the effects of noise present in the computation of noisy quantum computers when computing an expectation value of interest. Effective quantum volume is a proposed metric that applies error mitigation to the quantum volume protocol in order to evaluate the effectiveness not only of the target device but also of the error mitigation algorithm. Digital Zero-Noise Extrapolation (ZNE) is an error mitigation technique that estimates the noiseless expectation value using circuit folding to amplify errors by known scale factors and extrapolating to the zero-noise limit. Here we demonstrate that ZNE, with global and local unitary folding with fractional scale factors, in conjunction with dynamical decoupling, can increase the effective quantum volume over the vendor-measured quantum volume. Specifically, we measure the effective quantum volume of four IBM Quantum superconducting processor units, obtaining values that are larger than the vendor-measured quantum volume on each device. This is the first such increase reported.

quant-ph↗

arXiv2024

A near-term quantum algorithm for solving linear systems of equations based on the Woodbury identity

Quantum algorithms for solving linear systems of equations have generated excitement because of the potential speed-ups involved and the importance of solving linear equations in many applications. However, applying these algorithms can be challenging. The Harrow-Hassidim-Lloyd algorithm and improvements thereof require complex subroutines suitable for fault-tolerant hardware such as Hamiltonian simulation, making it ill-suited to current hardware. Variational algorithms, on the other hand, involve expensive optimization loops, which can be prone to barren plateaus and local optima. We describe a quantum algorithm for solving linear systems of equations that avoids these problems. Our algorithm is based on the Woodbury identity, which analytically describes the inverse of a matrix that is a low-rank modification of another (easily-invertible) matrix. This approach only utilizes basic quantum subroutines like the Hadamard test or the swap test, so it is well-suited to current hardware. There is no optimization loop, so barren plateaus and local optima do not present a problem. The low-rank aspect of the identity enables us to efficiently transfer information to and from the quantum computer. This approach can produce accurate results on current hardware. As evidence of this, we estimate an inner product involving the solution of a system of more than 16 million equations with 2% error using IBM's Auckland quantum computer. To our knowledge, no system of equations this large has previously been solved to this level of accuracy on a quantum computer.

quant-ph↗

arXiv2024

Graph Neural Networks for Parameterized Quantum Circuits Expressibility Estimation

Parameterized quantum circuits (PQCs) are fundamental to quantum machine learning (QML), quantum optimization, and variational quantum algorithms (VQAs). The expressibility of PQCs is a measure that determines their capability to harness the full potential of the quantum state space. It is thus a crucial guidepost to know when selecting a particular PQC ansatz. However, the existing technique for expressibility computation through statistical estimation requires a large number of samples, which poses significant challenges due to time and computational resource constraints. This paper introduces a novel approach for expressibility estimation of PQCs using Graph Neural Networks (GNNs). We demonstrate the predictive power of our GNN model with a dataset consisting of 25,000 samples from the noiseless IBM QASM Simulator and 12,000 samples from three distinct noisy quantum backends. The model accurately estimates expressibility, with root mean square errors (RMSE) of 0.05 and 0.06 for the noiseless and noisy backends, respectively. We compare our model's predictions with reference circuits [Sim and others, QuTe'2019] and IBM Qiskit's hardware-efficient ansatz sets to further evaluate our model's performance. Our experimental evaluation in noiseless and noisy scenarios reveals a close alignment with ground truth expressibility values, highlighting the model's efficacy. Moreover, our model exhibits promising extrapolation capabilities, predicting expressibility values with low RMSE for out-of-range qubit circuits trained solely on only up to 5-qubit circuit sets. This work thus provides a reliable means of efficiently evaluating the expressibility of diverse PQCs on noiseless simulators and hardware.

quant-ph↗

arXiv2024

Probing Quantum Telecloning on Superconducting Quantum Processors

Quantum information can not be perfectly cloned, but approximate copies of quantum information can be generated. Quantum telecloning combines approximate quantum cloning, more typically referred as quantum cloning, and quantum teleportation. Quantum telecloning allows approximate copies of quantum information to be constructed by separate parties, using the classical results of a Bell measurement made on a prepared quantum telecloning state. Quantum telecloning can be implemented as a circuit on quantum computers using a classical co-processor to compute classical feed forward instructions using if statements based on the results of a mid-circuit Bell measurement in real time. We present universal, symmetric, optimal $1 \rightarrow M$ telecloning circuits, and experimentally demonstrate these quantum telecloning circuits for $M=2$ up to $M=10$, natively executed with real time classical control systems on IBM Quantum superconducting processors, known as dynamic circuits. We perform the cloning procedure on many different message states across the Bloch sphere, on $7$ IBM Quantum processors, optionally using the error suppression technique X-X sequence digital dynamical decoupling. Two circuit optimizations are utilized, one which removes ancilla qubits for $M=2, 3$, and one which reduces the total number of gates in the circuit but still uses ancilla qubits. Parallel single qubit tomography with MLE density matrix reconstruction is used in order to compute the mixed state density matrices of the clone qubits, and clone quality is measured using quantum fidelity. These results present one of the largest and most comprehensive NISQ computer experimental analyses on (single qubit) quantum telecloning to date. The clone fidelity sharply decreases to $0.5$ for $M > 5$, but for $M=2$ we are able to achieve a mean clone fidelity of up to $0.79$ using dynamical decoupling.

quant-ph↗

arXiv2024

Generating Hidden Markov Models from Process Models Through Nonnegative Tensor Factorization

Monitoring of industrial processes is a critical capability in industry and in government to ensure reliability of production cycles, quick emergency response, and national security. Process monitoring allows users to gauge the progress of an organization in an industrial process or predict the degradation or aging of machine parts in processes taking place at a remote location. Similar to many data science applications, we usually only have access to limited raw data, such as satellite imagery, short video clips, event logs, and signatures captured by a small set of sensors. To combat data scarcity, we leverage the knowledge of Subject Matter Experts (SMEs) who are familiar with the actions of interest. SMEs provide expert knowledge of the essential activities required for task completion and the resources necessary to carry out each of these activities. Various process mining techniques have been developed for this type of analysis; typically such approaches combine theoretical process models built based on domain expert insights with ad-hoc integration of available pieces of raw data. Here, we introduce a novel mathematically sound method that integrates theoretical process models (as proposed by SMEs) with interrelated minimal Hidden Markov Models (HMM), built via nonnegative tensor factorization. Our method consolidates: (a) theoretical process models, (b) HMMs, (c) coupled nonnegative matrix-tensor factorizations, and (d) custom model selection. To demonstrate our methodology and its abilities, we apply it on simple synthetic and real world process models.

cs.LG↗

arXiv2023

JuliQAOA: Fast, Flexible QAOA Simulation

We introduce JuliQAOA, a simulation package specifically built for the Quantum Alternating Operator Ansatz (QAOA). JuliQAOA does not require a circuit-level description of QAOA problems, or another package to simulate such circuits, instead relying on a more direct linear algebra implementation. This allows for increased QAOA-specific performance improvements, as well as improved flexibility and generality. JuliQAOA is the first QAOA package designed to aid in the study of both constrained and unconstrained combinatorial optimization problems, and can easily include novel cost functions, mixer Hamiltonians, and other variations. JuliQAOA also includes robust and extensible methods for learning optimal angles. Written in the Julia language, JuliQAOA outperforms existing QAOA software packages and scales well to HPC-level resources. JuliQAOA is available at https://github.com/lanl/JuliQAOA.jl.

quant-ph↗

arXiv2023

Provable bounds for noise-free expectation values computed from noisy samples

In this paper, we explore the impact of noise on quantum computing, particularly focusing on the challenges when sampling bit strings from noisy quantum computers as well as the implications for optimization and machine learning applications. We formally quantify the sampling overhead to extract good samples from noisy quantum computers and relate it to the layer fidelity, a metric to determine the performance of noisy quantum processors. Further, we show how this allows us to use the Conditional Value at Risk of noisy samples to determine provable bounds on noise-free expectation values. We discuss how to leverage these bounds for different algorithms and demonstrate our findings through experiments on a real quantum computer involving up to 127 qubits. The results show a strong alignment with theoretical predictions.

quant-ph↗

arXiv2023

LLVM Static Analysis for Program Characterization and Memory Reuse Profile Estimation

Profiling various application characteristics, including the number of different arithmetic operations performed, memory footprint, etc., dynamically is time- and space-consuming. On the other hand, static analysis methods, although fast, can be less accurate. This paper presents an LLVM-based probabilistic static analysis method that accurately predicts different program characteristics and estimates the reuse distance profile of a program by analyzing the LLVM IR file in constant time, regardless of program input size. We generate the basic-block-level control flow graph of the target application kernel and determine basic-block execution counts by solving the linear balance equation involving the adjacent basic blocks' transition probabilities. Finally, we represent the kernel memory accesses in a bracketed format and employ a recursive algorithm to calculate the reuse distance profile. The results show that our approach can predict application characteristics accurately compared to another LLVM-based dynamic code analysis tool, Byfl.

cs.SE↗

arXiv2023

BB-ML: Basic Block Performance Prediction using Machine Learning Techniques

Recent years have seen the adoption of Machine Learning (ML) techniques to predict the performance of large-scale applications, mostly at a coarse level. In contrast, we propose to use ML techniques for performance prediction at a much finer granularity, namely at the Basic Block (BB) level, which are single entry, single exit code blocks that are used for analysis by the compilers to break down a large code into manageable pieces. We extrapolate the basic block execution counts of GPU applications and use them for predicting the performance for large input sizes from the counts of smaller input sizes. We train a Poisson Neural Network (PNN) model using random input values as well as the lowest input values of the application to learn the relationship between inputs and basic block counts. Experimental results show that the model can accurately predict the basic block execution counts of 16 GPU benchmarks. We achieve an accuracy of 93.5% in extrapolating the basic block counts for large input sets when trained on smaller input sets and an accuracy of 97.7% in predicting basic block counts on random instances. In a case study, we apply the ML model to CUDA GPU benchmarks for performance prediction across a spectrum of applications. We use a variety of metrics for evaluation, including global memory requests and the active cycles of tensor cores, ALU, and FMA units. Results demonstrate the model's capability of predicting the performance of large datasets with an average error rate of 0.85% and 0.17% for global and shared memory requests, respectively. Additionally, to address the utilization of the main functional units in Ampere architecture GPUs, we calculate the active cycles for tensor cores, ALU, FMA, and FP64 units and achieve an average error of 2.3% and 10.66% for ALU and FMA units while the maximum observed error across all tested applications and units reaches 18.5%.

cs.LG↗

arXiv2023

Predicting Expressibility of Parameterized Quantum Circuits using Graph Neural Network

Parameterized Quantum Circuits (PQCs) are essential to quantum machine learning and optimization algorithms. The expressibility of PQCs, which measures their ability to represent a wide range of quantum states, is a critical factor influencing their efficacy in solving quantum problems. However, the existing technique for computing expressibility relies on statistically estimating it through classical simulations, which requires many samples. In this work, we propose a novel method based on Graph Neural Networks (GNNs) for predicting the expressibility of PQCs. By leveraging the graph-based representation of PQCs, our GNN-based model captures intricate relationships between circuit parameters and their resulting expressibility. We train the GNN model on a comprehensive dataset of PQCs annotated with their expressibility values. Experimental evaluation on a four thousand random PQC dataset and IBM Qiskit's hardware efficient ansatz sets demonstrates the superior performance of our approach, achieving a root mean square error (RMSE) of 0.03 and 0.06, respectively.

quant-ph↗

arXiv2023

Distributed Out-of-Memory NMF on CPU/GPU Architectures

We propose an efficient distributed out-of-memory implementation of the Non-negative Matrix Factorization (NMF) algorithm for heterogeneous high-performance-computing (HPC) systems. The proposed implementation is based on prior work on NMFk, which can perform automatic model selection and extract latent variables and patterns from data. In this work, we extend NMFk by adding support for dense and sparse matrix operation on multi-node, multi-GPU systems. The resulting algorithm is optimized for out-of-memory (OOM) problems where the memory required to factorize a given matrix is greater than the available GPU memory. Memory complexity is reduced by batching/tiling strategies, and sparse and dense matrix operations are significantly accelerated with GPU cores (or tensor cores when available). Input/Output (I/O) latency associated with batch copies between host and device is hidden using CUDA streams to overlap data transfers and compute asynchronously, and latency associated with collective communications (both intra-node and inter-node) is reduced using optimized NVIDIA Collective Communication Library NCCL based communicators. Benchmark results show significant improvement, from 32X to 76x speedup, with the new implementation using GPUs over the CPU-based NMFk. Good weak scaling was demonstrated on up to 4096 multi-GPU cluster nodes with approximately 25,000 GPUs when decomposing a dense 340 Terabyte-size matrix and an 11 Exabyte-size sparse matrix of density 10e-6.

cs.DC↗

arXiv2023

Quantum Volume in Practice: What Users Can Expect from NISQ Devices

Quantum volume (QV) has become the de-facto standard benchmark to quantify the capability of Noisy Intermediate-Scale Quantum (NISQ) devices. While QV values are often reported by NISQ providers for their systems, we perform our own series of QV calculations on 24 NISQ devices currently offered by IBM Q, IonQ, Rigetti, Oxford Quantum Circuits, and Quantinuum (formerly Honeywell). Our approach characterizes the performances that an advanced user of these NISQ devices can expect to achieve with a reasonable amount of optimization, but without white-box access to the device. In particular, we compile QV circuits to standard gate sets of the vendor using compiler optimization routines where available, and we perform experiments across different qubit subsets. We find that running QV tests requires very significant compilation cycles, QV values achieved in our tests typically lag behind officially reported results and also depend significantly on the classical compilation effort invested.

quant-ph↗

arXiv2023

High-Round QAOA for MAX $k$-SAT on Trapped Ion NISQ Devices

The Quantum Alternating Operator Ansatz (QAOA) is a hybrid classical-quantum algorithm that aims to sample the optimal solution(s) of discrete combinatorial optimization problems. We present optimized QAOA circuit constructions for sampling MAX $k$-SAT problems, specifically for $k=3$ and $k=4$. The novel $4$-SAT QAOA circuit construction we present uses measurement based uncomputation, followed by classical feed forward conditional operations. The QAOA circuit parameters for $3$-SAT are optimized via exact classical (noise-free) simulation, using HPC resources to simulate up to $20$ rounds on $10$ qubits. In order to explore the limits of current NISQ devices we execute these optimized QAOA circuits for random $3$-SAT test instances with clause-to-variable ratio $4$ on four trapped ion quantum computers: Quantinuum H1-1 (20 qubits), IonQ Harmony (11 qubits), IonQ Aria 1 (25 qubits), and IonQ Forte (30 qubits). The QAOA circuits that are executed include $n=10$ up to $p=20$, and $n=22$ for $p=1$ and $p=2$. The high round circuits use upwards of 9,000 individual gate instructions, making these some of the largest QAOA circuits executed on NISQ devices. Our main finding is that current NISQ devices perform best at low round counts (i.e., $p = 1,\ldots, 5$) and then -- as expected due to noise -- gradually start returning satisfiability truth assignments that are no better than randomly picked solutions as the number of QAOA rounds are further increased.

quant-ph↗