Efficient Classical Simulation of Quantum Circuits beyond the Stabilizer Formalism

Yongshan Ding, Frederic T. Chong

Selman Ipek, Atak Talay Yücel, Farzad Shahi +2 more

We introduce a novel tableau-based classical simulation method for quantum computation, formulated within the phase-space framework of the extended stabilizer theory of closed noncontextual operators. This method enables the efficient classical simulation of a broader class of quantum circuits beyond the stabilizer formalism. We identify additional families of input states that are efficiently simulatable within this framework, going beyond stabilizer states, and implement the simulator and benchmark its performance on basic quantum algorithms, including the hidden shift and Deutsch–Jozsa algorithms.

Michael Zurel, Arne Heimendahl

We present the generalization of the CNC formalism, based on closed and noncontextual sets of Pauli observables, to the setting of odd-prime-dimensional qudits. By introducing new CNC-type phase space point operators, we construct a quasiprobability representation for quantum computation which is covariant with respect to the Clifford group and positivity preserving under Pauli measurements, and whose nonnegative sector strictly contains the subtheory of quantum theory described by nonnegative Wigner functions. This allows for a broader class of magic state quantum circuits to be efficiently classically simulated than those covered by the stabilizer formalism and Wigner function methods.

Steven Sensarn

George F. Viamontes, Igor L. Markov, John P. Hayes

Patrick Rall

Verification of NISQ era quantum devices demands fast classical simulation of large noisy quantum circuits. We present an algorithm based on the stabilizer formalism that can efficiently simulate noisy stabilizer circuits. Additionally, the protocol can efficiently simulate a large set of multi-qubit mixed states that are not mixtures of stabilizer states. The existence of these 'bound states' was previously only known for odd-dimensional systems like qutrits. The algorithm also has the favorable property that circuits with depolarizing noise are simulated much faster than unitary circuits. This work builds upon a similar algorithm by Bennink et al. (Phys. Rev. A 95, 062337) and utilizes a framework by Pashayan et al. (Phys. Rev. Lett. 115, 070501).