Stabilized entangling operations in a quantum computing system

A quantum computing system, comprising:

• a quantum processor comprising a plurality of physical qubits, wherein each of the physical qubits comprises a trapped ion;
• a classical computer configured to:
• compute a first control pulse and a second control pulse to be applied to a pair of trapped ions in a plurality of trapped ions in a quantum processor, each of the plurality of trapped ions having two frequency-separated states defining a qubit, wherein the computing of the first and second control pulses comprises:
• computing first Fourier coefficients of a first pulse function of the first control pulse and second Fourier coefficients of a second pulse function of the second control pulse based on a condition for closure of phase space trajectories and a condition for stabilization of phase-space closure;
• computing a first linear combination of the computed first Fourier coefficients and a second linear combination of the computed second Fourier coefficients based on a condition for non-zero degree of entanglement, a condition for stabilization of the degree of entanglement, and a condition for minimized power;
• and
• computing the first pulse function based on the computed first linear combination of the computed first Fourier coefficients, and the second pulse function based on the computed second linear combination of the computed second Fourier coefficients;
• and
• a system controller configured to:
• apply the first control pulse having the computed first pulse function to a first trapped ion of a pair of trapped ions, and the second control pulse having the computed second pulse function to a second trapped ion of the pair of trapped ions.

A quantum computing system comprising non-volatile memory having a number of instructions stored therein which, when executed by one or more processors, causes the quantum computing system to perform operations comprising:

• computing, by a classical computer, a first control pulse and a second control pulse to be applied to a pair of trapped ions in a plurality of trapped ions in a quantum processor, each of the plurality of trapped ions having two frequency-separated states defining a qubit, wherein the computing of the first and second control pulses comprises:
• computing first Fourier coefficients of a first pulse function of the first control pulse and second Fourier coefficients of a second pulse function of the second control pulse based on a condition for closure of phase space trajectories and a condition for stabilization of phase-space closure;
• computing a first linear combination of the computed first Fourier coefficients and a second linear combination of the computed second Fourier coefficients based on a condition for non-zero degree of entanglement, a condition for stabilization of the degree of entanglement, and a condition for minimized power;
• and
• computing the first pulse function based on the computed first linear combination of the computed first Fourier coefficients, and the second pulse function based on the computed second linear combination of the computed second Fourier coefficients;
• and
• applying, by a system controller, the first control pulse having the computed first pulse function to a first trapped ion of a pair of trapped ions, and the second control pulse having the computed second pulse function to a second trapped ion of the pair of trapped ions.