The reliable resource estimation and benchmarking of quantum algorithms is a critical component of the development cycle of viable quantum applications for quantum computers of all sizes. Determining resource bottlenecks in algorithms, especially when resource intensive error correction protocols are required, is crucial to reduce the cost of implementing viable algorithms on actual quantum hardware.
The reliable resource estimation and benchmarking of quantum algorithms is a critical component of the development cycle of viable quantum applications for quantum computers of all sizes. Determining resource bottlenecks in algorithms, especially when resource intensive error correction protocols are required, is crucial to reduce the cost of implementing viable algorithms on actual quantum hardware.
Fault-tolerant quantum computation enables the deployment of practical quantum algorithms but incurs substantial overhead from error correction, making resource estimation a central concern. Beyond case-by-case analyses, existing quantum programming languages either require programmers to manipulate low-level hardware details, rendering fault-tolerant implementations cumbersome, or abstract away the underlying error-correction schemes, reducing the effectiveness of resource utilization and estimation.
To address these limitations while preserving programmability, we present a quantum programming language that enables efficient resource utilization, together with a resource-estimation framework for comprehensive resource analysis. Our framework features programmer-visible abstractions of error-correction schemes and cross-layer program-hardware analysis, allowing systematic exploration of resource trade-offs. We evaluate our approach on detailed fault-tolerant implementations of practical large-scale quantum algorithms, including components typically treated as black boxes in existing frameworks. The results demonstrate that our framework enables substantial resource savings while delivering detailed, fine-grained, and accurate resource estimates for fault-tolerant quantum programs.
Quantum algorithms are often represented in terms of quantum circuits operating on ideal (logical) qubits. However, the practical implementation of these algorithms poses significant challenges. Many quantum algorithms require a substantial number of logical qubits, and the inherent susceptibility to errors of quantum computers require quantum error correction. The integration of error correction introduces overhead in terms of both space (physical qubits required) and runtime (how long the algorithm needs to be run for). This paper addresses the complexity of comparing classical and quantum algorithms, primarily stemming from the additional quantum error correction overhead. We propose a comprehensive framework that facilitates a direct and meaningful comparison between classical and quantum algorithms. By acknowledging and addressing the challenges introduced by quantum error correction, our framework aims to provide a clearer understanding of the comparative performance of classical and quantum computing approaches. This work contributes to understanding the practical viability and potential advantages of quantum algorithms in real-world applications. We apply our framework to quantum cryptanalysis, since it is well known that quantum algorithms can break factoring and discrete logarithm based cryptography and weaken symmetric cryptography and hash functions. In order to estimate the real-world impact of these attacks, apart from tracking the development of fault-tolerant quantum computers it is important to have an estimate of the resources needed to implement these quantum attacks. This analysis provides state-of-the art snap-shot estimates of the realistic costs of implementing quantum attacks on these important cryptographic algorithms, assuming quantum fault-tolerance is achieved using surface code methods, and spanning a range of potential error rates. These estimates serve as a guide for gauging the realistic impact of these algorithms and for benchmarking the impact of future advances in quantum algorithms, circuit synthesis and optimization, fault-tolerance methods and physical error rates.
Quantum computing has made considerable progress in recent years in both software and hardware. But to unlock the power of quantum computers in solving problems that cannot be efficiently solved classically, quantum computing at scale is necessary. Unfortunately, quantum simulators suffer from their exponential complexity and, at the same time, the currently available quantum computing hardware is still rather limited (even if roadmaps make intriguing promises). Hence, in order to evaluate quantum computing applications, end-users are still frequently restricted to toy-size problem instances (which additionally often do not take error correction into account). This substantially hinders the development and assessment of real-world quantum computing applications. In this work, we demonstrate how to utilize Resource Estimation to improve this situation. We show how the current workflow (relying on simulation and/or execution) can be complemented with an estimation step, allowing that end-users (1) actually can consider real-world problem instances already today (also considering error correction schemes and correspondingly required hardware resources), (2) can start exploring possible optimizations of those instances across the entire design space, and (3) can incorporate hypotheses of hardware development trends to derive more informed and, thus, better design space parameters. Overall, this enables end-users already today to check out the promises of possible future quantum computing applications, even if the corresponding hardware to execute them is not available yet.
Quantum computing has made considerable progress in recent years in both software and hardware. But to unlock the power of quantum computers in solving problems that cannot be efficiently solved classically, quantum computing at scale is necessary. Unfortunately, quantum simulators suffer from their exponential complexity and, at the same time, the currently available quantum computing hardware is still rather limited (even if roadmaps make intriguing promises). Hence, in order to evaluate quantum computing applications, end-users are still frequently restricted to toy-size problem instances (which additionally often do not take error correction into account). This substantially hinders the development and assessment of real-world quantum computing applications. In this work, we demonstrate how to utilize Resource Estimation to improve this situation. We show how the current workflow (relying on simulation and/or execution) can be complemented with an estimation step, allowing that end-users (1) actually can consider real-world problem instances already today (also considering error correction schemes and correspondingly required hardware resources), (2) can start exploring possible optimizations of those instances across the entire design space, and (3) can incorporate hypotheses of hardware development trends to derive more informed and, thus, better design space parameters. Overall, this enables end-users already today to check out the promises of possible future quantum computing applications, even if the corresponding hardware to execute them is not available yet.
Quantum computing promises the ability to compute properties of quantum systems exponentially faster than classical computers. Quantum advantage is achieved when a practical problem is solved more efficiently on a quantum computer than on a classical computer. Demonstrating quantum advantage requires a powerful quantum computer with low error rates and an efficient quantum algorithm that has a useful application. Despite rapid progress in hardware development, we still lack useful applications that are feasible for the next generation of quantum computers. Here we argue that an exponential quantum advantage exists in producing numerical resource estimates of larger quantum algorithms by accurately measuring simulation errors. We provide a quantum algorithm for measuring simulation errors of Trotter-based algorithms. Our results indicate that this method will reduce runtimes of quantum algorithms by approximately three orders of magnitude for one-hundred qubit systems. We also predict that these reductions will increase with system size. The methods we propose require relatively few qubits and operations, meaning the next generation of quantum computers could compute simulation errors for classically intractable systems. Since the underlying computations that lead to reduced resource estimates are infeasible for classical computers, this task is a candidate for demonstrating practical quantum advantage.