arXiv subjects

Salvatore Mandrà

Publications and source records attributed to Salvatore Mandrà.

At least 19 recordsLinked to original sources

arXiv2026

A Heuristic for Matrix Product State Simulation of Out-of-Equilibrium Dynamics of Two-Dimensional Quantum Spin Systems

Out-of-equilibrium dynamics of non-integrable Hamiltonian many-body quantum systems are characterized by highly entangled wave functions. Near-maximal entanglement arises in systems exhibiting thermalization or pre-thermalization, where the system converges to a steady state with a fixed energy density. Classical simulation of the time dependence of such wave functions requires exponential resources. However, typical computations aim to estimate expectation values of local operators and correlation functions to some expected precision. For thermalizing systems at sufficiently high energy densities, such computations can be done without storing the full wave function by instead simulating the evolution of the local operator, which requires significantly fewer resources. Nonetheless, constructing such resource-efficient classical algorithms remains a challenge for intermediate energy densities, where simulating both the wave function and operator evolution is costly. In this paper, we propose a heuristic approach to accelerate the convergence of Matrix Product State (MPS) simulations of expectation values, applicable across a broad range of energy densities. We estimate the desired observables by rescaling the MPS results at low bond dimensions with a factor that depends on the fidelity of the MPS wave function. Using this technique, we simulated the dynamics of the two-dimensional Transverse-Field Ising Model (TFIM) on a $7\times8$ grid with periodic boundary conditions, using a maximum bond dimension of $χ= 4096$ on a single A100 GPU, as well as the dynamics of the two-dimensional XY model on grids of size up to $9\times9$. We compare our TFIM results to similar simulations on a digital quantum processor [R. Haghshenas et al., Nature 653, 56 (2026)], demonstrating excellent agreement and confirming the predictive power of our method.

quant-ph↗

arXiv2025

Tensor networks for quantum computing

In the rapidly evolving field of quantum computing, tensor networks serve as an important tool due to their multifaceted utility. In this paper, we review the diverse applications of tensor networks and show that they are an important instrument for quantum computing. Specifically, we summarize the application of tensor networks in various domains of quantum computing, including simulation of quantum computation, quantum circuit synthesis, quantum error correction and mitigation, and quantum machine learning. Finally, we provide an outlook on the opportunities and the challenges of the tensor-network techniques.

quant-ph↗

arXiv2024

Generating Hard Ising Instances With Planted Solutions Using Post-Quantum Cryptographic Protocols

In this paper we present a novel method to generate hard instances with planted solutions based on the public-private McEliece post-quantum cryptographic protocol. Unlike other planting methods rooted in the infinite-size statistical analysis, our cryptographic protocol generates instances which are all hard (in cryptographic terms), with the hardness tuned by the size of the private key, and with a guaranteed unique ground state. More importantly, because of the private-public key protocol, planted solutions cannot be easily recovered by a direct inspection of the planted instances without the knowledge of the private key used to generate them, therefore making our protocol suitable to test and evaluate quantum devices without the risk of "backdoors" being exploited.

quant-ph↗

arXiv2024

Assessing and Advancing the Potential of Quantum Computing: A NASA Case Study

Quantum computing is one of the most enticing computational paradigms with the potential to revolutionize diverse areas of future-generation computational systems. While quantum computing hardware has advanced rapidly, from tiny laboratory experiments to quantum chips that can outperform even the largest supercomputers on specialized computational tasks, these noisy-intermediate scale quantum (NISQ) processors are still too small and non-robust to be directly useful for any real-world applications. In this paper, we describe NASA's work in assessing and advancing the potential of quantum computing. We discuss advances in algorithms, both near- and longer-term, and the results of our explorations on current hardware as well as with simulations, including illustrating the benefits of algorithm-hardware co-design in the NISQ era. This work also includes physics-inspired classical algorithms that can be used at application scale today. We discuss innovative tools supporting the assessment and advancement of quantum computing and describe improved methods for simulating quantum systems of various types on high-performance computing systems that incorporate realistic error models. We provide an overview of recent methods for benchmarking, evaluating, and characterizing quantum hardware for error mitigation, as well as insights into fundamental quantum physics that can be harnessed for computational purposes.

quant-ph↗

arXiv2021

HybridQ: A Hybrid Simulator for Quantum Circuits

Developing state-of-the-art classical simulators of quantum circuits is of utmost importance to test and evaluate early quantum technology and understand the true potential of full-blown error-corrected quantum computers. In the past few years, multiple theoretical and numerical advances have continuously pushed the boundary of what is classically simulable, hence the development of a plethora of tools which are often limited to a specific purpose or designed for a particular hardware (e.g. CPUs vs. GPUs). Moreover, such tools are typically developed using tailored languages and syntax, which makes it hard to compare results from, and create hybrid approaches using, different simulation techniques. To support unified and optimized use of these techniques across platforms, we developed HybridQ, a highly extensible platform designed to provide a common framework to integrate multiple state-of-the-art techniques to run on a variety of hardware. The philosophy behind its development has been driven by three main pillars: "Easy to Use", "Easy to Extend", and "Use the Best Available Technology". The powerful tools of HybridQ allow users to manipulate, develop, and extend noiseless and noisy circuits for different hardware architectures. HybridQ supports large-scale high-performance computing (HPC) simulations, automatically balancing workload among different processor nodes and enabling the use of multiple backends to maximize parallel efficiency. Everything is then glued together by a simple and expressive language that allows seamless switching from one technique to another as well as from one hardware to the next, without the need to write lengthy translations, thus greatly simplifying the development of new hybrid algorithms and techniques.

quant-ph↗

arXiv2021

Optimization and benchmarking of the thermal cycling algorithm

Optimization plays a significant role in many areas of science and technology. Most of the industrial optimization problems have inordinately complex structures that render finding their global minima a daunting task. Therefore, designing heuristics that can efficiently solve such problems is of utmost importance. In this paper we benchmark and improve the thermal cycling algorithm [Phys. Rev. Lett. 79, 4297 (1997)] that is designed to overcome energy barriers in nonconvex optimization problems by temperature cycling of a pool of candidate solutions. We perform a comprehensive parameter tuning of the algorithm and demonstrate that it competes closely with other state-of-the-art algorithms such as parallel tempering with isoenergetic cluster moves, while overwhelmingly outperforming more simplistic heuristics such as simulated annealing.

cond-mat.dis-nn↗

arXiv2021

Physics-Inspired Heuristics for Soft MIMO Detection in 5G New Radio and Beyond

Overcoming the conventional trade-off between throughput and bit error rate (BER) performance, versus computational complexity is a long-term challenge for uplink Multiple-Input Multiple-Output (MIMO) detection in base station design for the cellular 5G New Radio roadmap, as well as in next generation wireless local area networks. In this work, we present ParaMax, a MIMO detector architecture that for the first time brings to bear physics-inspired parallel tempering algorithmic techniques [28, 50, 67] on this class of problems. ParaMax can achieve near optimal maximum-likelihood (ML) throughput performance in the Large MIMO regime, Massive MIMO systems where the base station has additional RF chains, to approach the number of base station antennas, in order to support even more parallel spatial streams. ParaMax is able to achieve a near ML-BER performance up to 160x160 and 80x80 Large MIMO for low-order modulations such as BPSK and QPSK, respectively, only requiring less than tens of processing elements. With respect to Massive MIMO systems, in 12x24 MIMO with 16-QAM at SNR 16 dB, ParaMax achieves 330 Mbits/s near-optimal system throughput with 4--8 processing elements per subcarrier, which is approximately 1.4x throughput than linear detector-based Massive MIMO systems.

cs.NI↗

arXiv2020

Establishing the Quantum Supremacy Frontier with a 281 Pflop/s Simulation

Noisy Intermediate-Scale Quantum (NISQ) computers are entering an era in which they can perform computational tasks beyond the capabilities of the most powerful classical computers, thereby achieving "Quantum Supremacy", a major milestone in quantum computing. NISQ Supremacy requires comparison with a state-of-the-art classical simulator. We report HPC simulations of hard random quantum circuits (RQC), which have been recently used as a benchmark for the first experimental demonstration of Quantum Supremacy, sustaining an average performance of 281 Pflop/s (true single precision) on Summit, currently the fastest supercomputer in the World. These simulations were carried out using qFlex, a tensor-network-based classical high-performance simulator of RQCs. Our results show an advantage of many orders of magnitude in energy consumption of NISQ devices over classical supercomputers. In addition, we propose a standard benchmark for NISQ computers based on qFlex.

quant-ph↗

arXiv2019

A flexible high-performance simulator for verifying and benchmarking quantum circuits implemented on real hardware

Here we present qFlex, a flexible tensor network based quantum circuit simulator. qFlex can compute both exact amplitudes, essential for the verification of the quantum hardware, as well as low fidelity amplitudes, in order to mimic sampling from Noisy Intermediate-Scale Quantum (NISQ) devices. In this work, we focus on random quantum circuits (RQCs) in the range of sizes expected for supremacy experiments. Fidelity $f$ simulations are performed at a cost that is $1/f$ lower than perfect fidelity ones. We also present a technique to eliminate the overhead introduced by rejection sampling in most tensor network approaches. We benchmark the simulation of square lattices and Google's Bristlecone QPU. Our analysis is supported by extensive simulations on NASA HPC clusters Pleiades and Electra. For our most computationally demanding simulation, the two clusters combined reached a peak of 20 PFLOPS (single precision), i.e., $64\%$ of their maximum achievable performance, which represents the largest numerical computation in terms of sustained FLOPs and number of nodes utilized ever run on NASA HPC clusters. Finally, we introduce a novel multithreaded, cache-efficient tensor index permutation algorithm of general application.

quant-ph↗

arXiv2019

Feeding the multitude: A polynomial-time algorithm to improve sampling

A wide variety of optimization techniques, both exact and heuristic, tend to be biased samplers. This means that when attempting to find multiple uncorrelated solutions of a degenerate Boolean optimization problem a subset of the solution space tends to be favored while, in the worst case, some solutions can never be accessed by the used algorithm. Here we present a simple post-processing technique that improves sampling for any optimization approach, either quantum or classical. More precisely, starting from a pool of a few optimal configurations, the algorithm generates potentially new solutions via rejection-free cluster updates at zero temperature. Although the method is not ergodic and there is no guarantee that all the solutions can be found, fair sampling is typically improved. We illustrate the effectiveness of our method by improving the exponentially biased data produced by the D-Wave 2X quantum annealer [Phys. Rev. Lett. 118, 07052 (2017)], as well as data from three-dimensional Ising spin glasses. As part of the study, we also show that sampling is improved when sub-optimal states are included and discuss sampling at a finite fixed temperature.

cond-mat.dis-nn↗

arXiv2019

From Ansätze to Z-gates: a NASA View of Quantum Computing

For the last few years, the NASA Quantum Artificial Intelligence Laboratory (QuAIL) has been performing research to assess the potential impact of quantum computers on challenging computational problems relevant to future NASA missions. A key aspect of this research is devising methods to most effectively utilize emerging quantum computing hardware. Research questions include what experiments on early quantum hardware would give the most insight into the potential impact of quantum computing, the design of algorithms to explore on such hardware, and the development of tools to minimize the quantum resource requirements. We survey work relevant to these questions, with a particular emphasis on our recent work in quantum algorithms and applications, in elucidating mechanisms of quantum mechanics and their uses for quantum computational purposes, and in simulation, compilation, and physics-inspired classical algorithms. To our early application thrusts in planning and scheduling, fault diagnosis, and machine learning, we add thrusts related to robustness of communication networks and the simulation of many-body systems for material science and chemistry. We provide a brief update on quantum annealing work, but concentrate on gate-model quantum computing research advances within the last couple of years.

quant-ph↗

arXiv2019

Quantum Annealing Applied to De-Conflicting Optimal Trajectories for Air Traffic Management

We present the mapping of a class of simplified air traffic management (ATM) problems (strategic conflict resolution) to quadratic unconstrained boolean optimization (QUBO) problems. The mapping is performed through an original representation of the conflict-resolution problem in terms of a conflict graph, where nodes of the graph represent flights and edges represent a potential conflict between flights. The representation allows a natural decomposition of a real world instance related to wind-optimal trajectories over the Atlantic ocean into smaller subproblems, that can be discretized and are amenable to be programmed in quantum annealers. In the study, we tested the new programming techniques and we benchmark the hardness of the instances using both classical solvers and the D-Wave 2X and D-Wave 2000Q quantum chip. The preliminary results show that for reasonable modeling choices the most challenging subproblems which are programmable in the current devices are solved to optimality with 99% of probability within a second of annealing time.

quant-ph↗

arXiv2018

A deceptive step towards quantum speedup detection

There have been multiple attempts to design synthetic benchmark problems with the goal of detecting quantum speedup in current quantum annealing machines. To date, classical heuristics have consistently outperformed quantum-annealing based approaches. Here we introduce a class of problems based on frustrated cluster loops - deceptive cluster loops - for which all currently known state-of-the-art classical heuristics are outperformed by the D-Wave 2000Q quantum annealing machine. While there is a sizable constant speedup over all known classical heuristics, a noticeable improvement in the scaling remains elusive. These results represent the first steps towards a detection of potential quantum speedup, albeit without a scaling improvement and for synthetic benchmark problems.

quant-ph↗

arXiv2017

Patch-planting spin-glass solution for benchmarking

We introduce an algorithm to generate (not solve) spin-glass instances with planted solutions of arbitrary size and structure. First, a set of small problem patches with open boundaries is solved either exactly or with a heuristic, and then the individual patches are stitched together to create a large problem with a known planted solution. Because in these problems frustration is typically smaller than in random problems, we first assess the typical computational complexity of the individual patches using population annealing Monte Carlo, and introduce an approach that allows one to fine-tune the typical computational complexity of the patch-planted system. The scaling of the typical computational complexity of these planted instances with various numbers of patches and patch sizes is investigated and compared to random instances.

cond-mat.dis-nn↗

arXiv2017

The pitfalls of planar spin-glass benchmarks: Raising the bar for quantum annealers (again)

In an effort to overcome the limitations of random spin-glass benchmarks for quantum annealers, focus has shifted to carefully-crafted gadget-based problems whose logical structure has typically a planar topology. Recent experiments on these gadget problems using a commercially-available quantum annealer have demonstrated an impressive performance over a selection of commonly-used classical optimization heuristics. Here we show that efficient classical optimization techniques, such as minimum-weight perfect matching, can solve these gadget problems exactly and in polynomial time. We present approaches on how to mitigate this shortcoming of commonly-used benchmark problems based on planar logical topologies.

quant-ph↗

arXiv2017

A NASA Perspective on Quantum Computing: Opportunities and Challenges

In the last couple of decades, the world has seen several stunning instances of quantum algorithms that provably outperform the best classical algorithms. For most problems, however, it is currently unknown whether quantum algorithms can provide an advantage, and if so by how much, or how to design quantum algorithms that realize such advantages. Many of the most challenging computational problems arising in the practical world are tackled today by heuristic algorithms that have not been mathematically proven to outperform other approaches but have been shown to be effective empirically. While quantum heuristic algorithms have been proposed, empirical testing becomes possible only as quantum computation hardware is built. The next few years will be exciting as empirical testing of quantum heuristic algorithms becomes more and more feasible. While large-scale universal quantum computers are likely decades away, special-purpose quantum computational hardware has begun to emerge that will become more powerful over time, as well as some small-scale universal quantum computers.

quant-ph↗

arXiv2017

Exponentially-Biased Ground-State Sampling of Quantum Annealing Machines with Transverse-Field Driving Hamiltonians

We study the performance of the D-Wave 2X quantum annealing machine on systems with well-controlled ground-state degeneracy. While obtaining the ground state of a spin-glass benchmark instance represents a difficult task, the gold standard for any optimization algorithm or machine is to sample all solutions that minimize the Hamiltonian with more or less equal probability. Our results show that while naive transverse-field quantum annealing on the D-Wave 2X device can find the ground-state energy of the problems, it is not well suited in identifying all degenerate ground-state configurations associated to a particular instance. Even worse, some states are exponentially suppressed, in agreement with previous studies on toy model problems [New J. Phys. 11, 073021 (2009)]. These results suggest that more complex driving Hamiltonians are needed in future quantum annealing machines to ensure a fair sampling of the ground-state manifold.

quant-ph↗

arXiv2016

Strengths and weaknesses of weak-strong cluster problems: A detailed overview of state-of-the-art classical heuristics vs quantum approaches

To date, a conclusive detection of quantum speedup remains elusive. Recently, a team by Google Inc.~[V.~S.~Denchev {\em et al}., Phys.~Rev.~X {\bf 6}, 031015 (2016)] proposed a weak-strong cluster model tailored to have tall and narrow energy barriers separating local minima, with the aim to highlight the value of finite-range tunneling. More precisely, results from quantum Monte Carlo simulations, as well as the D-Wave 2X quantum annealer scale considerably better than state-of-the-art simulated annealing simulations. Moreover, the D-Wave 2X quantum annealer is $\sim 10^8$ times faster than simulated annealing on conventional computer hardware for problems with approximately $10^3$ variables. Here, an overview of different sequential, nontailored, as well as specialized tailored algorithms on the Google instances is given. We show that the quantum speedup is limited to sequential approaches and study the typical complexity of the benchmark problems using insights from the study of spin glasses.

quant-ph↗