Bootstrapping the Future: From Resource Estimation to Quantum Advantage

Quantum Algorithms That Work

A central problem in quantum computing is the development of domain-specific algorithms that enable real scientific and economic contributions. Quantum algorithms in numerous domains such as finance, chemistry, physics, and biology are being developed with the intention of achieving quantum advantage, i.e. to derive deeper insights relative to established algorithms on classical machines. But these algorithms are typically evaluated through simulation and/or testing on small devices (e.g. < 100 qubits), calling into question the robustness of their affordances as quantum systems scale. System-level challenges have traditionally complicated the economic potential of quantum computing, but significant advances in system fault-tolerance, qubit numbers, and ecosystem standardization show tremendous promise. Developments in this realm have received the lion’s share of media attention and are likely driving the investing surge into quantum technology. Nevertheless, following the influx of capital and drive to deploy intermediate quantum systems, the technology’s ultimate value will be determined by its real-world utility, enabled by domain-specific algorithms that scale alongside the systems that host them.

The Prototype Paradox

Effective domain-specific algorithms face a significant challenge: Researchers need to design for a system architecture that has yet to mature, in a manner that outperforms all existing classical solutions. With the anticipated deployment of quantum cloud computing, on-device testing to validate performance should enable more experimentation and faster validation. That being said, near-term quantum computers, regardless of physical modality, operate within a paradigm of error mitigation (as opposed to elimination), and utilize extensive corrective measures such as noise suppression and cancellation techniques, circuit knitting, and variational algorithms. This ensemble of approaches entails a hybrid quantum-classical computing system and imposes a significant amount of computational overhead. Performance on these near-term systems therefore bears little resemblance to that of future fault-tolerant systems, which are expected to have orders of magnitude greater capacity. Quantum simulation, as an alternative to on-device testing, is similarly bottlenecked by limited near-term quantum and classical computing capacity. Algorithms optimized for near-term noisy devices and their computationally efficient methods may be ill-suited to large, fault-tolerant systems, and emerging algorithms that appear untenable on current hardware may be ignored in lieu of classical solutions. These limitations may lead to a scenario in which fault-tolerant hardware is developed, but a lack of corresponding advancement in quantum software delays real-world achievements and punishes investors.

Resource Estimation

To address this issue, Resource Estimation (RE) has been proposed as a complementary method to on-device testing and simulation that can indicate the physical and logical requirements of quantum algorithms, particularly those that exceed the capacity of current hardware. While RE can characterize requirements for near-term noisy quantum computers, it can more importantly provide estimates for future fault-tolerant systems. Notable resource estimation tools include the Azure Quantum Resource Estimator, Google Quantum Algorithm Translator, Zapata BenchQ, and MIT pyLIQTR. Roughly speaking, these tools work in the following manner:

1. Use quantum instruction set architectures to translate high-level code into a logical representation.
2. Transform the logical representation into a low-level physical representation.
3. Estimate runtime under specific parameters such as the number of T gates and corresponding T factories (a bottleneck in quantum architecture), and the number of logical qubits and corresponding physical qubits.

These parameters describe the circuit in terms of its depth (gates/factories) and width (qubits), as in circuit complexity theory, with the added abstraction of logical to physical qubits to account for the cost of error correction. These estimates can provide stakeholders with a better understanding of how quantum computing will actually perform by 2030 and beyond.

Limitations

While RE is certainly useful, the methodology currently has two aspects that limit its generalizability and predictive power:

Specificity of Results

Estimates are technology and context dependent. Because tools rely on intermediate representations and instruction sets, their results pertain to the capabilities of specific physical modalities that are in constant flux. Estimates are also influenced by error budget parameters (specific to application). Exploring the impact of these parameters in a quantum chemistry simulation on a hypothetical fault-tolerant device, Quetschlich et al. varied operation speed (time regime), error rate, and factory number to obtain physical qubit estimates ranging from 6.04 million (non-Majorana) to 1.30 million (Majorana). Furthermore, varying the number of factories reduced physical qubit requirement to 1.08 million (Majorana), though with a significant increase in runtime.

Ancillary Code Limitations

Resource estimates may misrepresent true requirements for the following reasons:

• A source of computational overhead that may inflate the resource estimate is the error correction method. Current RE tools rely on surface code for correcting errors resulting from environmental noise and qubit decoherence. As surface code is potentially less efficient than other methods, estimates incorporating this form of error correction may be significantly higher than necessary.
• Initial state preparation is a computation necessary prior to simulating phenomena in a field such as quantum chemistry. The initial state and iterative optimizations incur computational cost that may significantly inflate estimates on near-term systems or may not be adequately included in fault-tolerant ones. Despite the efficiency of the actual simulation algorithms, preparing the initial state might incur so much overhead that quantum advantage could evaporate, particularly if the state is initialized on a hybrid classical-quantum system. In this vein, research skeptical of quantum advantage in chemistry has experimentally demonstrated that the states prepared by the variational quantum eigensolver, an algorithm for near-term systems, does not exhibit the time complexity necessary to achieve quantum advantage in that application. Further, the authors go on to argue that a reliance on state preparation in even advanced algorithms for fault-tolerant machines, such as phase estimation, will similarly dilute quantum advantage. Resource estimates such as those by Quetschlich et al., derived through qubitization and phase estimation, may not fully account for the computational cost of initial state preparation into their estimate. Together, surface code and initial state preparation dramatically affect current resource estimates.

Conclusion

It is important to note that the absence of evidence for quantum advantage in one area does not diminish its likelihood elsewhere, such as in finance, and that such advantage can only be demonstrated or disproven on a case-by-case basis. Additionally, more efficient error correction and initial state preparation methods could be developed as quantum computing scales, causing physical estimates to decrease significantly. Nevertheless, RE is useful for estimating algorithm performance on near-term systems and for setting the upper-bound for fault-tolerant system requirements (if costs such as initial state preparation are included). Researchers can use RE to compare algorithm performance within the limitations of ancillary code to develop better algorithms for future systems, and for stakeholders, it represents the best estimate of what will be possible under the future paradigm. Download here to read the full article.

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