Simultaneously entangling gates for trapped-ion quantum computers

1. A method of performing simultaneous entangling gate operations in a trapped-ion quantum computer, comprising:

executing, by a processor in a digital computer, a software program that is stored in non-volatile memory of the digital computer, wherein the executed software program requires at least one computation to be performed, the at least one computation comprising:

selecting a gate duration value and a detuning frequency of pulses to be individually applied to a plurality of participating ions in a chain of trapped ions to simultaneously entangle a plurality of pairs of ions among the plurality of participating ions by one or more predetermined values of entanglement interaction, wherein

each of the trapped ions in the chain has two frequency-separated states defining a qubit, and

motional modes of the chain of trapped ions each have a distinct frequency;

determining amplitudes of the pulses, based on the selected gate duration value, the selected detuning frequency, and the frequencies of the motional modes of the chain of trapped ions;

generating the pulses having the determined amplitudes; and

applying the generated pulses to the plurality of participating ions for the selected gate duration value;

measuring population of qubit states of the ions in the chain of trapped ions, wherein the at least one computation further comprises:

processing quantum information corresponding to the qubit states of ions in the chain of trapped ions by the processor of the digital computer based on the measured population of the qubit states; and

generating a solution to a selected quantum algorithm based on the processed results of the quantum computations.

2. The method according to claim 1 , wherein the amplitudes are selected based on a condition where the trapped ions in the chain of trapped ions substantially return to their original positions and momentum values.

3. The method according to claim 2 , wherein the amplitudes are selected based on conditions where there is non-zero entanglement interaction between each of the plurality of pairs of ions that are to be entangled, and each pair of ions that are not to be entangled is decoupled.

4. The method according to claim 3 , wherein the one or more predetermined values of entanglement interaction are between zero and π/2.

5. The method according to claim 4 , wherein the amplitudes are selected based on a condition where power to be provided to the plurality of participating ions during the selected gate duration value is at a minimum.

6. The method according to claim 1 , wherein the amplitudes are selected based on conditions where there is non-zero entanglement interaction between each of the plurality of pairs of ions that are to be entangled, and each pair of ions that are not to be entangled is decoupled.

7. The method according to claim 6 , wherein the one or more predetermined values of entanglement interaction are between zero and π/2.

8. The method according to claim 6 , wherein the amplitudes are selected based on a condition where power to be provided to the plurality of participating ions during the selected gate duration value is at a minimum.

9. The method according to claim 1 , wherein determining the amplitudes comprises dividing the gate duration value into a plurality of time segments.

10. The method according to claim 1 ,

wherein the at least one computation further comprises:

selecting the quantum algorithm to be implemented on the chain of trapped ions;

compiling the selected quantum algorithm into a series of universal logic gates; and

translating the series of universal logic gates into pulses to apply to a plurality of participating ions in the chain of trapped ions.

11. A quantum computing system, comprising:

a chain of trapped ions, each of the trapped ions having two hyperfine states defining a qubit and an excited state;

one or more lasers configured to emit a laser beam that is split into two or more non-copropagating laser beams which are provided to each of the trapped ions, wherein the two or more non-copropagating laser beams are configured to cause Rabi flopping of each of the trapped ions between the two hyperfine states via the excited state; and

a controller comprising non-volatile memory having a number of instructions stored therein which, when executed by a processor of a digital computer, causes the quantum computing system to perform operations comprising:

select a gate duration value and a detuning frequency of one or more pulses to be individually applied to a plurality of participating ions in a chain of trapped ions to simultaneously entangle a plurality of pairs of ions among the plurality of participating ions by one or more predetermined values of entanglement interaction, wherein

each of the trapped ions has two frequency-separated states defining a qubit,

motional modes of the chain of trapped ions each have a distinct frequency, and

one of the plurality of pairs of ions comprises a first ion and a second ion;

determine amplitudes of the pulses, based on the selected gate duration value, the selected detuning frequency, and the frequencies of the motional modes of the chain of trapped ions, wherein the amplitudes are derived based on conditions for non-zero entanglement interaction between each of the plurality of pairs of ions that are to be entangled, decoupling between each pair of ions that are not to be entangled, and minimized power provided to the plurality of participating ions during the selected gate duration value;

generate the pulse comprising the determined amplitude and the detuning frequency;

apply the generated pulse to the first and second ions for the gate duration value;

measure population of qubit states of the ions in the chain of trapped ions;

process quantum information corresponding to the qubit states of ions in the chain of trapped ions by the processor of the digital computer based on the measured population of the qubit states; and

generate a solution to a selected quantum algorithm based on the processed results of the quantum computations.

12. The quantum computing system according to claim 11 , wherein

each of the trapped ions is 171 Yb+ having the 2 S 1/2 hyperfine states, and

the laser is a mode-locked laser at 355 nm.

13. The quantum computing system according to claim 11 , wherein the amplitudes are selected based on a condition where the trapped ions in the chain of trapped ions substantially return to their original positions and momentum values.

14. The quantum computing system according to claim 13 , wherein the amplitudes are selected based on conditions where there is non-zero entanglement interaction between each of the plurality of pairs of ions that are to be entangled, and each pair of ions that are not to be entangled is decoupled.

15. The quantum computing system according to claim 14 , wherein the one or more predetermined values of entanglement interaction are between zero and π/2.

16. The quantum computing system according to claim 15 , wherein the amplitudes are selected based on a condition where the power to be provided to the plurality of participating ions during the selected gate duration value is at a minimum.

17. The quantum computing system according to claim 11 , wherein the amplitudes are selected based on conditions where there is non-zero entanglement interaction between each of the plurality of pairs of ions that are to be entangled, and each pair of ions that are not to be entangled is decoupled.

18. The quantum computing system according to claim 17 , wherein the one or more predetermined values of entanglement interaction are between zero and π/2.

19. The quantum computing system according to claim 18 , wherein the amplitudes are selected based on a condition where the power to be provided to the plurality of participating ions during the selected gate duration value is at a minimum.

20. The quantum computing system according to claim 11 , wherein determining the amplitudes comprises dividing the gate duration value into a plurality of time segments.