Tenzan Araki

Abstract:

<jats:p>In contrast to monolithic devices, modular, networked quantum architectures are based on interconnecting smaller quantum hardware nodes using quantum communication links and offer a promising approach to scalability. Virtual distillation (VD) is a technique that can, under ideal conditions, suppress errors exponentially as the number of quantum state copies increases. However, additional gate operations required for VD introduce further errors, which may limit its practical effectiveness. In this work, we analyze three practical implementations of VD that correspond to edge cases that maximize space-time trade-offs. Specifically, we consider an implementation that minimizes the number of qubits but introduces significantly deeper quantum circuits and contrast it with implementations that parallelize the preparation of copies using additional qubits, including a constant-depth implementation. We rigorously characterize their circuit depth and gate count requirements and develop explicit architectures for implementing them in networked quantum systems—while also detailing implementations in early fault-tolerant quantum architectures. We numerically compare the performance of the three implementations under realistic noise characteristics of networked ion trap systems and conclude the following. First, VD effectively suppresses errors even for very noisy states. Second, the constant-depth implementation consistently outperforms the implementation that minimizes the number of qubits. Finally, the approach is highly robust to errors in remote entangling operations, with noise in local gates being the main limiting factor to its performance.</jats:p>

Abstract:

Estimating observable expectation values in eigenstates of quantum systems has a broad range of applications and is an area where early fault-tolerant quantum computers may provide practical quantum advantage. We develop a hybrid quantum-classical algorithm that enables the estimation of an arbitrary observable expectation value in an eigenstate, given an initial state is supplied that has dominant overlap with the targeted eigenstate – but may overlap with any other eigenstates. Our approach builds on, and is conceptually similar to purification-based error mitigation techniques; however, it achieves exponential suppression of algorithmic errors using only a single copy of the quantum state. The key innovation is that random time evolution is applied in the quantum computer to create an average mixed quantum state, which is then virtually purified with exponential efficacy. We prove rigorous performance guarantees and conclude that the complexity of our approach depends directly on the energy gap in the problem Hamiltonian and remarkably, can be compared to phase estimation combined with amplitude estimation in terms of its scaling with respect to a target precision. We demonstrate in a broad range of numerical simulations the applicability of our framework in near-term and early fault-tolerant settings. Furthermore, we demonstrate in a 100-qubit example that direct classical simulation of our approach enables the prediction of ground and excited state properties of quantum systems using tensor network techniques, which we recognize as a quantum-inspired classical approach.