The complexity of NISQ

Abstract

The recent proliferation of NISQ devices has made it imperative to understand their power. In this work, we define and study the complexity class , which encapsulates problems that can be efficiently solved by a classical computer with access to noisy quantum circuits. We establish super-polynomial separations in the complexity among classical computation, , and fault-tolerant quantum computation to solve some problems based on modifications of Simon’s problems. We then consider the power of for three well-studied problems. For unstructured search, we prove that cannot achieve a Grover-like quadratic speedup over classical computers. For the Bernstein-Vazirani problem, we show that only needs a number of queries logarithmic in what is required for classical computers. Finally, for a quantum state learning problem, we prove that is exponentially weaker than classical computers with access to noiseless constant-depth quantum circuits.

Quantum Multi-Solution Bernoulli Search with Applications to Bitcoin's Post-Quantum Security

“…Extending such efforts to the hybrid-adversary landscape would offer fine-grained security assessments of post-quantum cryptosystems. Finally, in the context of complexity theory, the study of hybrid algorithms is further motivated by related models focusing on the interplay between classical computation and near-future quantum devices [CCHL22] and between circuit depth and quantum queries [SZ19, CM20, CCL23].…”

Which Options Exist for NISQ-Friendly Linear Response Formulations?

“…Still limited hardware-wise, it is believed that they have the potential, in due time, to revolutionize highperformance computing; especially, quantum chemistry has long been pointed out as an obvious area of application of quantum computing. 15−17 While fault-tolerant quantum computers are still in the making, the current paradigm to solve chemistry problems on near-term quantum hardware (commonly referred to as noisy intermediate-scale quantum, NISQ 18 ) is via a hybrid approach involving quantum and classical computers working in tandem. 19 The NISQ device is used to perform measurements of specific expectation values or density matrix elements, while the rest of the calculation is offloaded to the classical processors.…”

“…While fault-tolerant quantum computers are still in the making, the current paradigm to solve chemistry problems on near-term quantum hardware (commonly referred to as noisy intermediate-scale quantum, NISQ) is via a hybrid approach involving quantum and classical computers working in tandem . The NISQ device is used to perform measurements of specific expectation values or density matrix elements, while the rest of the calculation is offloaded to the classical processors.…”

Optimal depth and a novel approach to variational unitary quantum process tomography

“…Quantum tomography plays an essential role in the security assessment and characterization of channel and state evolution in noisy intermediate scale quantum (NISQ) devices [1,2]. A class of promising candidates, ranging from quantum deep neural networks (QDNN) [3], tensor networks [4], variational quantum circuit (VQC) [5,6], convex compressive algorithms [7][8][9] and quantum compilation algorithms [10], try to perform state and PT beyond the current classical computation capabilities.…”