Phase-space-simulation method for quantum computation with magic states on qubits

Abstract

We propose a method for classical simulation of finite-dimensional quantum systems, based on sampling from a quasiprobability distribution, i.e., a generalized Wigner function. Our construction applies to all finite dimensions, with the most interesting case being that of qubits. For multiple qubits, we find that quantum computation by Clifford gates and Pauli measurements on magic states can be efficiently classically simulated if the quasiprobability distribution of the magic states is non-negative. This provides the so far missing qubit counterpart of the corresponding result [V. Veitch et al., New J. Phys. 14, 113011 (2012)] applying only to odd dimension. Our approach is more general than previous ones based on mixtures of stabilizer states. Namely, all mixtures of stabilizer states can be efficiently simulated, but for any number of qubits there also exist efficiently simulable states outside the stabilizer polytope. Further, our simulation method extends to negative quasiprobability distributions, where it provides amplitude estimation. The simulation cost is then proportional to a robustness measure squared. For all quantum states, this robustness is smaller than or equal to robustness of magic.

Measurement reduction in variational quantum algorithms

“…Then, in Sec. V we show that noncontextual Hamiltonians, defined in [41] (also studied in [42]), are reducible to commuting Hamiltonians under unitary partitioning. We close the paper with discussion and directions for future work.…”

Quasi-probability information in a coupled two-qubit system interacting non-linearly with a coherent cavity under intrinsic decoherence

“…Recently, the non-classicality and the quantum coherence were used to realize quantum computations 53 , 54 , quantum tomography 55 , quantum interference 56 as well as to implement large cat states in finite-temperature reservoir 57 .…”

Contextual Subspace Variational Quantum Eigensolver

“…A set of observables is noncontextual when it is possible to assign values to them simultaneously without contradiction [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. How can we determine if a set S of Pauli operators is noncontextual?…”

“…Because all terms in H nc can simultaneously be assigned definite values without contradiction we can introduce a phase space description of its eigenspaces [14,36]. The phase space points are the possible joint value assignments to a set of observables derived from S nc , which we describe below.…”