We developed a practical quantum advantage benchmarking framework that connects the accumulation of entropy in a quantum processing unit and the degradation of the solution to a target optimization problem. The benchmark is based on approximating from below the Gibbs states boundary in the energy-entropy space for the application of interest. We believe the proposed benchmarking technique creates a powerful bridge between hardware benchmarking and application benchmarking, while remaining hardware-agnostic. It can be extended to fault-tolerant scenarios and relies on computationally tractable numerics. We demonstrate its applicability on the problem of finding the ground state of the two-dimensional Fermi-Hubbard.
We developed a practical quantum advantage benchmarking framework that connects the accumulation of entropy in a quantum processing unit and the degradation of the solution to a target optimization problem. The benchmark is based on approximating from below the Gibbs states boundary in the energy-entropy space for the application of interest. We believe the proposed benchmarking technique creates a powerful bridge between hardware benchmarking and application benchmarking, while remaining hardware-agnostic. It can be extended to fault-tolerant scenarios and relies on computationally tractable numerics. We demonstrate its applicability on the problem of finding the ground state of the two-dimensional Fermi-Hubbard.
Almost half a century after the idea to solve problems using quantum systems first emerged, quantum computing has become a flourishing research field with a few hundreds of quantum machines deployed worldwide. Although large-scale fault-tolerant quantum devices are still believed to be several years or decades away, we already have access to those early machines, characterised by a limited number of qubits and operations that are prone to errors. This raises two important questions: can we already solve problems of commercial interest? If not, can we predict quantum utility? To answer these questions and guide the community towards practical quantum advantage, it is crucial to develop effective benchmarks. In this thesis, we propose to focus on entropy as a metric to benchmark quantum computers. A large class of errors during a quantum computation contributes to an increase in entropy of the system, such that an accumulation of entropy during a computation indicates a decrease in performance of the quantum computer. It is thus essential to monitor the entropy and understand how it relates to the degradation of the quantum device’s solution to problems of interest. In the first part of this thesis, as a proof of concept, we develop simple yet effective heuristic models for entropy accumulation in variational quantum circuits based on global depolarising noise, which we validate using numerical simulations. We then show how these toy models can be used to derive bounds on the circuit size beyond which quantum advantage is unattainable, by building on previous work. In a second part, we analyse entropy accumulation on an actual quantum computer based on superconducting qubits. This allows us to refine our heuristic model by highlighting the presence of entropy-decreasing noise. In particular, we study the combination of amplitude damping and depolarising noise in more detail as a potential explanation for experimental observations. Finally, we shift our focus to techniques for entropy estimation on actual quantum hardware, a key component used in the building of heuristic models for entropy accumulation. We analyse and compare existing methods and identify a gap in the literature, namely the lack of scalable single-copy techniques. We thus develop novel single-copy tools for entropy estimation, which trade off accuracy for scalability by bounding entropy. This section can serve as a good reference point for the research community in deciding which technique to choose in a specific context.
Assessing whether a noisy quantum device can potentially exhibit quantum advantage is essential for selecting practical quantum utility tasks that are not efficiently verifiable by classical means. For optimization, a prominent candidate for quantum advantage, entropy benchmarking provides insights based concomitantly on the specifics of the application and its implementation, as well as hardware noise. However, such an approach still does not account for finite-shot effects or for quantum error mitigation (QEM), a key near-term error suppression strategy that reduces estimation bias at the cost of increased sampling overhead. We address this limitation by developing a benchmarking framework that explicitly incorporates finite-shot statistics and the resource overhead induced by QEM. Our framework quantifies quantum advantage through the confidence that an estimated energy lies within an interval defined by the best-known classical upper and lower bounds. Using a proof-of-principle numerical study of the two-dimensional Fermi-Hubbard model at size 8×8, we demonstrate that the framework effectively identifies noise and shot-budget regimes in which the probabilistic error cancellation (PEC), a representative QEM method, is operationally advantageous, and potential quantum advantage is not hindered by finite-shot effects. Overall, our approach equips end-users with a framework based on lightweight numerics for assessing potential practical quantum advantage in optimization on near-future quantum hardware, in light of the allocated shot budget.
Understanding the limitations imposed by noise on current and next-generation quantum devices is a crucial step toward demonstrating practical quantum advantage. In this work, we investigate the accumulation of entropy density as a benchmark to monitor the performance of quantum processing units (QPUs). We provide a proof-of-principle demonstration of our methodology which entails developing simple heuristic models of how entropy accumulates, testing them against real QPU data, and finally using these models to determine a circuit volume threshold above which quantum advantage is unattainable. Monitoring entropy density not only offers an alternative approach that complements existing circuit-level benchmarking techniques, but, more importantly, it bridges the gap between circuit-level and application-level benchmarking protocols. In particular, our heuristic model of entropy accumulation allows us to outperform existing techniques that bound the circuit-size threshold for quantum advantage.
In order to quantify the relative performance of different test-bed quantum computing devices, it is useful to benchmark them using a common protocol. While some benchmarks rely on the performance of random circuits and are generic in nature, here we instead propose and implement a practical, application-based benchmark. In particular, our protocol calculates the energy of the ground state in the single-particle subspace of a one-dimensional (1D) Fermi Hubbard model, a problem which is efficient to solve classically. We provide a quantum ansatz for the problem that is provably able to probe the full single-particle subspace for a general-length 1D chain and scales efficiently in number of gates and measurements. Finally, we demonstrate and analyze the benchmark performance on superconducting and ion-trap test-bed hardware from three hardware vendors and with up to 24 qubits.
Motivated by recent breakthroughs in the development of spin-based quantum processing units based on exchange-only (EO) spin qubits, we provide a roadmap for the implementation of quantum algorithms on the EO platform, ranging from the NISQ to the fault-tolerant era. To provide an algorithm-driven perspective on the scaling of quantum chips, we consider a range of applications targeting different stages of hardware maturity and formulate requirements for a successful realization. We show that the compilation method Parity Twine perfectly complements the hardware's capabilities to perform tasks such as the quantum Fourier transform or QAOA. Furthermore, we describe an error detection technique native to Parity Twine, which EO qubits can leverage in a unique and advantageous way to improve algorithm performance. Finally, since both near-term algorithmic benchmarks and a long-term perspective can be found in digital quantum simulation, we specifically discuss the fermionic fast Fourier transform and the simulation of Fermi-Hubbard models. The latter is explicitly discussed in the context of quantum error correction and a partially fault-tolerant realization. By providing detailed resource estimates and identifying scaling bottlenecks on each level, our work offers a quantitative perspective on EO-based quantum computing and will inform future hardware design choices.
It is expected that the simulation of correlated fermions in chemistry and material science will be one of the first practical applications of quantum processors. Given the rapid evolution of quantum hardware, it is increasingly important to develop robust benchmarking techniques to gauge the capacity of quantum hardware specifically for the purpose of fermionic simulation. Here we propose using the one-dimensional Fermi-Hubbard model as an application benchmark for variational quantum simulations on near-term quantum devices. Since the one-dimensional Hubbard model is both strongly correlated and exactly solvable with the Bethe ansatz, it provides a reference ground state energy that a given device with limited coherence will be able to approximate up to a maximal size. The length of the largest chain that can be simulated provides an effective fermionic length. We use variational quantum eigensolver to approximate the ground state energy values of Fermi-Hubbard instances and show how the fermionic length benchmark can be used in practice to assess the performance of bounded-depth devices in a scalable fashion.