arXiv subjects

Ruslan Shaydulin

Publications and source records attributed to Ruslan Shaydulin.

At least 37 records · Page 2Linked to original sources

arXiv2025

Realization of a Quantum Streaming Algorithm on Long-lived Trapped-ion Qubits

Large classical datasets are often processed in the streaming model, with data arriving one item at a time. In this model, quantum algorithms have been shown to offer an unconditional exponential advantage in space. However, experimentally implementing such streaming algorithms requires qubits that remain coherent while interacting with an external data stream. In this work, we realize such a data-streaming model using Quantinuum Helios trapped-ion quantum computer with long-lived qubits that communicate with an external server. We implement a quantum pair sketch, which is the primitive underlying many quantum streaming algorithms, and use it to solve Hidden Matching, a problem known to exhibit a theoretical exponential quantum advantage in space. Furthermore, we compile the quantum streaming algorithm to fault-tolerant quantum architectures based on surface and bivariate bicycle codes and show that the quantum space advantage persists even with the overheads of fault-tolerance.

quant-ph↗

arXiv2025

Quantum Approximate Optimization Algorithm in Finite Size and Large Depth and Equivalence to Quantum Annealing

The quantum approximate optimization algorithm (QAOA) and quantum annealing are two of the most popular quantum optimization heuristics. While QAOA is known to be able to approximate quantum annealing, the approximation requires QAOA angles to vanish with the problem size $n$, whereas optimized QAOA angles are observed to be size-independent for small $n$ and constant in the infinite-size limit. This fact led to a folklore belief that QAOA has a mechanism that is fundamentally different from quantum annealing. In this work, we provide evidence against this by analytically showing that QAOA energy approximates that of quantum annealing under two conditions, namely that angles vary smoothly from one layer to the next and that the sum is bounded by a constant. These conditions are known to hold for near-optimal QAOA angles empirically. Our proof relies on a series expansion of QAOA energy in sum of angles, which we show converges to quantum annealing limit as QAOA depth grows for constant sum of angles even if angles do not vanish with problem size $n$. A corollary of our results is a quadratic improvement for the bound on depth required to compile Trotterized quantum annealing of the SK model in the average case.

quant-ph↗

arXiv2025

End-to-end quantum algorithms for tensor problems

We present a comprehensive end-to-end quantum algorithm for tensor problems, including tensor PCA and planted kXOR, that achieves potential superquadratic quantum speedups over classical methods. We build upon prior works by Hastings~(\textit{Quantum}, 2020) and Schmidhuber~\textit{et al.}~(\textit{Phys.~Rev.~X.}, 2025), we address key limitations by introducing a native qubit-based encoding for the Kikuchi method, enabling explicit quantum circuit constructions and non-asymptotic resource estimation. Our approach substantially reduces constant overheads through a novel guiding state preparation technique as well as circuit optimizations, reducing the threshold for a quantum advantage. We further extend the algorithmic framework to support recovery in sparse tensor PCA and tensor completion, and generalize detection to asymmetric tensors, demonstrating that the quantum advantage persists in these broader settings. Detailed resource estimates show that 900 logical qubits, $\sim 10^{15}$ gates and $\sim 10^{12}$ gate depth suffice for a problem that classically requires $\sim 10^{23}$ FLOPs. The gate count and depth for the same problem without the improvements presented in this paper would be at least $10^{19}$ and $10^{18}$ respectively. These advances position tensor problems as a candidate for quantum advantage whose resource requirements benefit significantly from algorithmic and compilation improvements; the magnitude of the improvements suggest that further enhancements are possible, which would make the algorithm viable for upcoming fault-tolerant quantum hardware.

quant-ph↗

arXiv2025

End-to-End Protocol for High-Quality QAOA Parameters with Few Shots

The quantum approximate optimization algorithm (QAOA) is a quantum heuristic for combinatorial optimization that has been demonstrated to scale better than state-of-the-art classical solvers for some problems. For a given problem instance, QAOA performance depends crucially on the choice of the parameters. While average-case optimal parameters are available in many cases, meaningful performance gains can be obtained by fine-tuning these parameters for a given instance. This task is especially challenging, however, when the number of circuit executions (shots) is limited. In this work, we develop an end-to-end protocol that combines multiple parameter settings and fine-tuning techniques. We use large-scale numerical experiments to optimize the protocol for the shot-limited setting and observe that optimizers with the simplest internal model (linear) perform best. We implement the optimized pipeline on a trapped-ion processor using up to 32 qubits and 5 QAOA layers, and we demonstrate that the pipeline is robust to small amounts of hardware noise. To the best of our knowledge, these are the largest demonstrations of QAOA parameter fine-tuning on a trapped-ion processor in terms of 2-qubit gate count.

quant-ph↗

arXiv2025

Non-Variational Quantum Random Access Optimization with Alternating Operator Ansatz

Solving hard optimization problems is one of the most promising application domains for quantum computers due to the ubiquity of such problems in industry and the availability of broadly applicable quantum speedups. However, the ability of near-term quantum computers to tackle industrial-scale optimization problems is limited by their size and the overheads of quantum error correction. Quantum Random Access Optimization (QRAO) has been proposed to reduce the space requirements of quantum optimization. However, to date QRAO has only been implemented using variational algorithms, which suffer from the need to train instance-specific variational parameters, making them difficult to scale. We propose and benchmark a non-variational approach to QRAO based on the Quantum Alternating Operator Ansatz (QAOA) for the MaxCut problem. We show that instance-independent ``fixed" parameters achieve good performance, removing the need for variational parameter optimization. Additionally, we evaluate different design choices, such as various mixers, initial states, and QRAO-specific implementations of the QAOA cost operator, and identify a strategy that performs well in practice. Our results pave the way for the practical execution of QRAO on early fault-tolerant quantum computers.

quant-ph↗

arXiv2025

Performance of Quantum Approximate Optimization with Quantum Error Detection

Quantum algorithms must be scaled up to tackle real-world applications. Doing so requires overcoming the noise present on today's hardware. The quantum approximate optimization algorithm (QAOA) is a promising candidate for scaling up, due to its modest resource requirements and documented asymptotic speedup over state-of-the-art classical algorithms for some problems. However, achieving better-than-classical performance with QAOA is believed to require fault tolerance. In this paper, we demonstrate a partially fault-tolerant implementation of QAOA using the $[[k+2,k,2]]$ ``Iceberg'' error detection code. We observe that encoding the circuit with the Iceberg code improves the algorithmic performance as compared to the unencoded circuit for problems with up to $20$ logical qubits on a trapped-ion quantum computer. Additionally, we propose and calibrate a model for predicting the code performance. We use this model to characterize the limits of the Iceberg code and extrapolate its performance to future hardware with improved error rates. In particular, we show how our model can be used to determine the necessary conditions for QAOA to outperform the Goemans-Williamson algorithm on future hardware. To the best of our knowledge, our results demonstrate the largest universal quantum computing algorithm protected by partially fault-tolerant quantum error detection on practical applications to date, paving the way towards solving real-world applications with quantum computers.

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↗

arXiv2025

Threshold for Fault-tolerant Quantum Advantage with the Quantum Approximate Optimization Algorithm

Optimization is often cited as a promising application of quantum computers. However, the low degree of provable quantum speedups has led prior rigorous end-to-end resource analyses to conclude that a quantum computer is unlikely to surpass classical state-of-the-art on optimization problems under realistic assumptions. In this work, we compile and analyze the Quantum Approximate Optimization Algorithm (QAOA) combined with Amplitude Amplification (AA) applied to random 8-SAT at the satisfiability threshold. Our compilation involves careful optimization of circuits for Hamiltonian simulation, which may be of independent interest. We use the analytical scaling of the time-to-solution for QAOA identified by PRX Quantum 5, 030348 (2024) and find that with QAOA depth $p=623$, QAOA+AA achieves a crossover with state-of-the-art classical heuristics at 179 variables and 14.99 hours of runtime when executed on a surface-code-based fault-tolerant quantum computer with 73.91 million physical qubits, a physical error rate of $10^{-3}$, and a $1~μ$s code cycle time. Notably, we allow the classical solver to be parallelized as long as its total energy consumption is equal to that required for decoding in the surface code. We further show that this restriction on classical solver energy consumption can be relaxed given optimistic but plausible reductions in physical error rates and fault-tolerance overheads, enabling a crossover of 2.94 hours using 8.88 million physical qubits against a classical solver running on a supercomputer with $725,760$ CPU cores. These findings support the hypothesis that large-scale fault-tolerant quantum computers will be useful for optimization.

quant-ph↗

arXiv2025

Certified randomness using a trapped-ion quantum processor

While quantum computers have the potential to perform a wide range of practically important tasks beyond the capabilities of classical computers, realizing this potential remains a challenge. One such task is to use an untrusted remote device to generate random bits that can be certified to contain a certain amount of entropy. Certified randomness has many applications but is fundamentally impossible to achieve solely by classical computation. In this work, we demonstrate the generation of certifiably random bits using the 56-qubit Quantinuum H2-1 trapped-ion quantum computer accessed over the internet. Our protocol leverages the classical hardness of recent random circuit sampling demonstrations: a client generates quantum "challenge" circuits using a small randomness seed, sends them to an untrusted quantum server to execute, and verifies the server's results. We analyze the security of our protocol against a restricted class of realistic near-term adversaries. Using classical verification with measured combined sustained performance of $1.1\times10^{18}$ floating-point operations per second across multiple supercomputers, we certify $71,313$ bits of entropy under this restricted adversary and additional assumptions. Our results demonstrate a step towards the practical applicability of today's quantum computers.

quant-ph↗

arXiv2025

Applications of Certified Randomness

Certified randomness can be generated with untrusted remote quantum computers using multiple known protocols, one of which has been recently realized experimentally. Unlike the randomness sources accessible on today's classical computers, the output of these protocols can be certified to be random under certain computational hardness assumptions, with no trust required in the hardware generating the randomness. In this perspective, we explore real-world applications for which the use of certified randomness protocols may lead to improved security and fairness. We identify promising applications in areas including cryptography, differential privacy, financial markets, and blockchain. Through this initial exploration, we hope to shed light on potential applications of certified randomness.

quant-ph↗

arXiv2024

Decomposition Pipeline for Large-Scale Portfolio Optimization with Applications to Near-Term Quantum Computing

Industrially relevant constrained optimization problems, such as portfolio optimization and portfolio rebalancing, are often intractable or difficult to solve exactly. In this work, we propose and benchmark a decomposition pipeline targeting portfolio optimization and rebalancing problems with constraints. The pipeline decomposes the optimization problem into constrained subproblems, which are then solved separately and aggregated to give a final result. Our pipeline includes three main components: preprocessing of correlation matrices based on random matrix theory, modified spectral clustering based on Newman's algorithm, and risk rebalancing. Our empirical results show that our pipeline consistently decomposes real-world portfolio optimization problems into subproblems with a size reduction of approximately 80%. Since subproblems are then solved independently, our pipeline drastically reduces the total computation time for state-of-the-art solvers. Moreover, by decomposing large problems into several smaller subproblems, the pipeline enables the use of near-term quantum devices as solvers, providing a path toward practical utility of quantum computers in portfolio optimization.

math.OC↗

arXiv2024

Parameter Setting Heuristics Make the Quantum Approximate Optimization Algorithm Suitable for the Early Fault-Tolerant Era

Quantum Approximate Optimization Algorithm (QAOA) is one of the most promising quantum heuristics for combinatorial optimization. While QAOA has been shown to perform well on small-scale instances and to provide an asymptotic speedup over state-of-the-art classical algorithms for some problems, fault-tolerance is understood to be required to realize this speedup in practice. The low resource requirements of QAOA make it particularly suitable to benchmark on early fault-tolerant quantum computing (EFTQC) hardware. However, the performance of QAOA depends crucially on the choice of the free parameters in the circuit. The task of setting these parameters is complicated in the EFTQC era by the large overheads, which preclude extensive classical optimization. In this paper, we summarize recent advances in parameter setting in QAOA and show that these advancements make EFTQC experiments with QAOA practically viable.

quant-ph↗

arXiv2024

Variational Quantum Algorithm Landscape Reconstruction by Low-Rank Tensor Completion

Variational quantum algorithms (VQAs) are a broad class of algorithms with many applications in science and industry. Applying a VQA to a problem involves optimizing a parameterized quantum circuit by maximizing or minimizing a cost function. A particular challenge associated with VQAs is understanding the properties of associated cost functions. Having the landscapes of VQA cost functions can greatly assist in developing and testing new variational quantum algorithms, but they are extremely expensive to compute. Reconstructing the landscape of a VQA using existing techniques requires a large number of cost function evaluations, especially when the dimension or the resolution of the landscape is high. To address this challenge, we propose a low-rank tensor-completion-based approach for local landscape reconstruction. By leveraging compact low-rank representations of tensors, our technique can overcome the curse of dimensionality and handle high-resolution landscapes. We demonstrate the power of landscapes in VQA development by showcasing practical applications of analyzing penalty terms for constrained optimization problems and examining the probability landscapes of certain basis states.

quant-ph↗

arXiv2024

The computational power of random quantum circuits in arbitrary geometries

Empirical evidence for a gap between the computational powers of classical and quantum computers has been provided by experiments that sample the output distributions of two-dimensional quantum circuits. Many attempts to close this gap have utilized classical simulations based on tensor network techniques, and their limitations shed light on the improvements to quantum hardware required to frustrate classical simulability. In particular, quantum computers having in excess of $\sim 50$ qubits are primarily vulnerable to classical simulation due to restrictions on their gate fidelity and their connectivity, the latter determining how many gates are required (and therefore how much infidelity is suffered) in generating highly-entangled states. Here, we describe recent hardware upgrades to Quantinuum's H2 quantum computer enabling it to operate on up to $56$ qubits with arbitrary connectivity and $99.843(5)\%$ two-qubit gate fidelity. Utilizing the flexible connectivity of H2, we present data from random circuit sampling in highly connected geometries, doing so at unprecedented fidelities and a scale that appears to be beyond the capabilities of state-of-the-art classical algorithms. The considerable difficulty of classically simulating H2 is likely limited only by qubit number, demonstrating the promise and scalability of the QCCD architecture as continued progress is made towards building larger machines.

quant-ph↗

arXiv2024

Evidence of Scaling Advantage for the Quantum Approximate Optimization Algorithm on a Classically Intractable Problem

The quantum approximate optimization algorithm (QAOA) is a leading candidate algorithm for solving optimization problems on quantum computers. However, the potential of QAOA to tackle classically intractable problems remains unclear. Here, we perform an extensive numerical investigation of QAOA on the low autocorrelation binary sequences (LABS) problem, which is classically intractable even for moderately sized instances. We perform noiseless simulations with up to 40 qubits and observe that the runtime of QAOA with fixed parameters scales better than branch-and-bound solvers, which are the state-of-the-art exact solvers for LABS. The combination of QAOA with quantum minimum finding gives the best empirical scaling of any algorithm for the LABS problem. We demonstrate experimental progress in executing QAOA for the LABS problem using an algorithm-specific error detection scheme on Quantinuum trapped-ion processors. Our results provide evidence for the utility of QAOA as an algorithmic component that enables quantum speedups.

quant-ph↗

arXiv2024

Parameter Setting in Quantum Approximate Optimization of Weighted Problems

Quantum Approximate Optimization Algorithm (QAOA) is a leading candidate algorithm for solving combinatorial optimization problems on quantum computers. However, in many cases QAOA requires computationally intensive parameter optimization. The challenge of parameter optimization is particularly acute in the case of weighted problems, for which the eigenvalues of the phase operator are non-integer and the QAOA energy landscape is not periodic. In this work, we develop parameter setting heuristics for QAOA applied to a general class of weighted problems. First, we derive optimal parameters for QAOA with depth $p=1$ applied to the weighted MaxCut problem under different assumptions on the weights. In particular, we rigorously prove the conventional wisdom that in the average case the first local optimum near zero gives globally-optimal QAOA parameters. Second, for $p\geq 1$ we prove that the QAOA energy landscape for weighted MaxCut approaches that for the unweighted case under a simple rescaling of parameters. Therefore, we can use parameters previously obtained for unweighted MaxCut for weighted problems. Finally, we prove that for $p=1$ the QAOA objective sharply concentrates around its expectation, which means that our parameter setting rules hold with high probability for a random weighted instance. We numerically validate this approach on general weighted graphs and show that on average the QAOA energy with the proposed fixed parameters is only $1.1$ percentage points away from that with optimized parameters. Third, we propose a general heuristic rescaling scheme inspired by the analytical results for weighted MaxCut and demonstrate its effectiveness using QAOA with the XY Hamming-weight-preserving mixer applied to the portfolio optimization problem. Our heuristic improves the convergence of local optimizers, reducing the number of iterations by 7.4x on average.

quant-ph↗

arXiv2024

Hardness of the Maximum Independent Set Problem on Unit-Disk Graphs and Prospects for Quantum Speedups

Rydberg atom arrays are among the leading contenders for the demonstration of quantum speedups. Motivated by recent experiments with up to 289 qubits [Ebadi et al., Science 376, 1209 (2022)] we study the maximum independent set problem on unit-disk graphs with a broader range of classical solvers beyond the scope of the original paper. We carry out extensive numerical studies and assess problem hardness, using both exact and heuristic algorithms. We find that quasi-planar instances with Union-Jack-like connectivity can be solved to optimality for up to thousands of nodes within minutes, with both custom and generic commercial solvers on commodity hardware, without any instance-specific fine-tuning. We also perform a scaling analysis, showing that by relaxing the constraints on the classical simulated annealing algorithms considered in Ebadi et al., our implementation is competitive with the quantum algorithms. Conversely, instances with larger connectivity or less structure are shown to display a time-to-solution potentially orders of magnitudes larger. Based on these results we propose protocols to systematically tune problem hardness, motivating experiments with Rydberg atom arrays on instances orders of magnitude harder (for established classical solvers) than previously studied.

quant-ph↗

arXiv2024

Alignment between Initial State and Mixer Improves QAOA Performance for Constrained Optimization

Quantum alternating operator ansatz (QAOA) has a strong connection to the adiabatic algorithm, which it can approximate with sufficient depth. However, it is unclear to what extent the lessons from the adiabatic regime apply to QAOA as executed in practice with small to moderate depth. In this paper, we demonstrate that the intuition from the adiabatic algorithm applies to the task of choosing the QAOA initial state. Specifically, we observe that the best performance is obtained when the initial state of QAOA is set to be the ground state of the mixing Hamiltonian, as required by the adiabatic algorithm. We provide numerical evidence using the examples of constrained portfolio optimization problems with both low ($p\leq 3$) and high ($p = 100$) QAOA depth. Additionally, we successfully apply QAOA with XY mixer to portfolio optimization on a trapped-ion quantum processor using 32 qubits and discuss our findings in near-term experiments.

quant-ph↗