The Complexity of NISQ

by   Sitan Chen, et al.

The recent proliferation of NISQ devices has made it imperative to understand their computational power. In this work, we define and study the complexity class , which is intended to encapsulate problems that can be efficiently solved by a classical computer with access to a NISQ device. To model existing devices, we assume the device can (1) noisily initialize all qubits, (2) apply many noisy quantum gates, and (3) perform a noisy measurement on all qubits. We first give evidence that ⊊⊊, by demonstrating super-polynomial oracle separations among the three classes, based on modifications of Simon's problem. 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 . For the Bernstein-Vazirani problem, we show that only needs a number of queries logarithmic in what is required for . Finally, for a quantum state learning problem, we prove that is exponentially weaker than classical computation with access to noiseless constant-depth quantum circuits.


page 4

page 42


Test of Quantumness with Small-Depth Quantum Circuits

Recently Brakerski, Christiano, Mahadev, Vazirani and Vidick (FOCS 2018)...

Oracle separations of hybrid quantum-classical circuits

An important theoretical problem in the study of quantum computation, th...

Learning Classical Readout Quantum PUFs based on single-qubit gates

Physical Unclonable Functions (PUFs) have been proposed as a way to iden...

On the Need for Large Quantum Depth

Near-term quantum computers are likely to have small depths due to short...

Introducing Structure to Expedite Quantum Search

We present a novel quantum algorithm for solving the unstructured search...

Robustness of Quantum Algorithms for Nonconvex Optimization

Recent results suggest that quantum computers possess the potential to s...

Communication Trade Offs in Intermediate Qudit Circuits

Quantum computing promises speedup of classical algorithms in the long t...

Please sign up or login with your details

Forgot password? Click here to reset