A method performed by one or more classical computers , comprising: transforming a n-qubit quantum computation of the form C 2 M ( a,Z i ) C 1 exp(i φZ i ) C 0 |0〉 ⊗ n , where C k are Clifford operators and the exponentials represent single qubit rotations, to a sequence of exponentials and measurements of the form M ( a, P 2 ) exp( iφP 1 )|0〉 ⊗n , in which P 1 and P 2 are multiple qubit Pauli operators, and M ( a, P 2 ) = ( I + a P)/2 denotes measurement of the multiple qubit Pauli operator P 2 with outcome a = ±1, where I is the identity matrix, where P 1 = C 0 † Z i 1 C 0 , P 2 = C 1 C 0 † M a Z i 2 C 1 C 0 ; constructing a tree ( V , E ) with root node r ∈ V , the tree describing a 2D grid of qubits, in which each vertex in V describes a qubit in the 2D grid, and vertices describing nearest neighbor qubits in the 2D grid are connected by an edge in E ; and configuring a quantum computer comprising the 2D grid of qubits to implement the sequence of exponentials and measurements using: one qubit measurements and one qubit Clifford unitaries, either (A) controlled Z-gates or (B) two qubit measurements on nearest neighbor qubits described by vertices in V connected by an edge in E , (A) or (B) being used to perform multi-target Controlled-Z gates, and each Clifford C and C † such that CZ r C † = P being constructed using multi-target Controlled-Z gates, single qubit rotations that are only performed on the qubit described by the root node r . transforming a n-qubit quantum computation of the form C 2 M ( a,Z i ) C 1 exp(i φZ i ) C 0 |0〉 ⊗ n , where C k are Clifford operators and the exponentials represent single qubit rotations, to a sequence of exponentials and measurements of the form M ( a, P 2 ) exp( iφP 1 )|0〉 ⊗n , in which P 1 and P 2 are multiple qubit Pauli operators, and M ( a, P 2 ) = ( I + a P)/2 denotes measurement of the multiple qubit Pauli operator P 2 with outcome a = ±1, where I is the identity matrix, where P 1 = C 0 † Z i 1 C 0 , P 2 = C 1 C 0 † M a Z i 2 C 1 C 0 ; constructing a tree ( V , E ) with root node r ∈ V , the tree describing a 2D grid of qubits, in which each vertex in V describes a qubit in the 2D grid, and vertices describing nearest neighbor qubits in the 2D grid are connected by an edge in E ; and configuring a quantum computer comprising the 2D grid of qubits to implement the sequence of exponentials and measurements using: one qubit measurements and one qubit Clifford unitaries, either (A) controlled Z-gates or (B) two qubit measurements on nearest neighbor qubits described by vertices in V connected by an edge in E , (A) or (B) being used to perform multi-target Controlled-Z gates, and each Clifford C and C † such that CZ r C † = P being constructed using multi-target Controlled-Z gates, single qubit rotations that are only performed on the qubit described by the root node r . one qubit measurements and one qubit Clifford unitaries, either (A) controlled Z-gates or (B) two qubit measurements on nearest neighbor qubits described by vertices in V connected by an edge in E , (A) or (B) being used to perform multi-target Controlled-Z gates, and each Clifford C and C † such that CZ r C † = P being constructed using multi-target Controlled-Z gates, single qubit rotations that are only performed on the qubit described by the root node r . <EOS>