The classical simulation of noisy quantum computers : a polyhedral approach

Jay Gambetta

Cihan Okay

Abstract Identifying the precise boundary between quantum and classical computational power is a central challenge in quantum computing. We introduce polyhedral classical simulators , a framework for classical simulation grounded in polyhedral geometry. This framework encompasses well-known methods such as the Gottesman–Knill algorithm, while extending naturally to more recent models including quantum computation with magic states and measurement-based quantum computation. The framework is compositional: The correctness of a simulation reduces to verifying a preservation property for the basic instruments of the model, from which the full adaptive simulation is assembled. Beyond unifying existing simulation methods, this provides a geometric roadmap for pushing the boundary of efficient classical simulation further.

Esteban Martínez-Vargas

I develop a theory of classicality from quantum systems. This theory stems from the study of classical and quantum stationary stochastic processes. The stochastic processes are characterized by polyhedral (classical) and semidefinite representative (quantum) cones. Based on a previous result by the author I expand the study of fixed points from quantum channels. I give a semidefinite program that characterizes a quantum channel separating into a core and a part that decays with many iterations. In general, the solution is non-separable in the space it is defined. I present a characterization of channels in terms of their fixed points for the separable case. A quantum simulation of a polyhedral cone can then be constructed.

Hansen S. Wu, Ribhu K. Kaul

We propose that scaling dimensions of d=3 conformal field theories can be studied on a system of qubits with near term quantum simulation platforms. Our proposal chooses couplings of quantum many-body problems on a polyhedral lattice at which the conformal state-operator correspondence can be observed most accurately in the spectrum. We validate our protocol on the Ising model where we extract the scaling dimensions of a number of scaling operators with a few percent accuracy from the spectrum of a system of just 20 qubits. The procedure makes only minor assumptions beyond general conformal invariance -- it may hence be applied widely. Requirements and challenges to realize this proposal on quantum computers are discussed. Our results demonstrate that for current or near term qubit platforms, three dimensional conformal field theories present a unique opportunity -- a forefront problem that is difficult on classical computers but may be solved through quantum simulation.

光祐 御手洗

Yongshan Ding, Frederic T. Chong