Quantum computing represents an exciting frontier in the realm of information processing; it is a promising technology that may provide future advances in a wide range of fields, from quantum chemistry to optimization problems. This thesis discusses experimental results for several quantum algorithms performed on a programmable quantum computer consisting of a linear chain of five or seven trapped 171Yb+ atomic clock ions with long coherence times and high gate fidelities. We execute modular one- and two-qubit computation gates through Raman transitions driven by a beat note between counter-propagating beams from a pulsed laser. The system's individual addressing capability provides arbitrary single-qubit rotations as well as all possible two-qubit entangling gates, which are implemented using a pulse-segmentation scheme. The quantum computer can be programmed from a high-level interface to execute arbitrary quantum circuits, and comes with a toolbox of many important composite gates and quantum subroutines. We present experimental results for a complete three-qubit Grover quantum search algorithm, a hallmark application of a quantum computer with a well-known speedup over classical searches of an unsorted database, and report better-than-classical performance. The algorithm is performed for all 8 possible single-result oracles and all 28 possible two-result oracles. All quantum solutions are shown to outperform their classical counterparts. Performing parallel operations will be a powerful capability as deeper circuits on larger, more complex quantum computers present new challenges. Here, we perform a pair of 2-qubit gates simultaneously in a single chain of trapped ions. We employ a pre-calculated pulse shaping scheme that modulates the phase and amplitude of the Raman transitions to drive programmable high-fidelity 2-qubit entangling gates in parallel by coupling to the collective modes of motion of the ion chain. Ensuring the operation yields only spin-spin interactions between the desired pairs, with neither residual spin-motion entanglement nor crosstalk spin-spin entanglement, is a nonlinear constraint problem, and pulse solutions are found using optimization techniques. As an application, we demonstrate the quantum full adder using a depth-4 circuit requiring the use of parallel 2-qubit operations.
Quantum computing represents an exciting frontier in the realm of information processing; it is a promising technology that may provide future advances in a wide range of fields, from quantum chemistry to optimization problems. This thesis discusses experimental results for several quantum algorithms performed on a programmable quantum computer consisting of a linear chain of five or seven trapped 171Yb+ atomic clock ions with long coherence times and high gate fidelities. We execute modular one- and two-qubit computation gates through Raman transitions driven by a beat note between counter-propagating beams from a pulsed laser. The system's individual addressing capability provides arbitrary single-qubit rotations as well as all possible two-qubit entangling gates, which are implemented using a pulse-segmentation scheme. The quantum computer can be programmed from a high-level interface to execute arbitrary quantum circuits, and comes with a toolbox of many important composite gates and quantum subroutines. We present experimental results for a complete three-qubit Grover quantum search algorithm, a hallmark application of a quantum computer with a well-known speedup over classical searches of an unsorted database, and report better-than-classical performance. The algorithm is performed for all 8 possible single-result oracles and all 28 possible two-result oracles. All quantum solutions are shown to outperform their classical counterparts. Performing parallel operations will be a powerful capability as deeper circuits on larger, more complex quantum computers present new challenges. Here, we perform a pair of 2-qubit gates simultaneously in a single chain of trapped ions. We employ a pre-calculated pulse shaping scheme that modulates the phase and amplitude of the Raman transitions to drive programmable high-fidelity 2-qubit entangling gates in parallel by coupling to the collective modes of motion of the ion chain. Ensuring the operation yields only spin-spin interactions between the desired pairs, with neither residual spin-motion entanglement nor crosstalk spin-spin entanglement, is a nonlinear constraint problem, and pulse solutions are found using optimization techniques. As an application, we demonstrate the quantum full adder using a depth-4 circuit requiring the use of parallel 2-qubit operations.
Trapped atomic ion systems are currently the most advanced platform for quantum information processing. Their long coherence times, pristine state initialization and detection, and precisely controllable and versatile interactions make them excellent quantum systems for experiments in quantum computation and quantum simulation. One of the more promising schemes for quantum computing consists of performing single and multi-qubit quantum gates on qubits in a linear ion crystal. Some of the key challenges of scaling such a system are the individual addressing of arbitrary subsets of ions and controlling the growing complexity of motional mode interactions as the number of qubits increases or when the gates are performed faster. Traditional entangling quantum gates between ion qubits use laser pulses to couple the qubit states to the collective motion of the crystal, thereby generating a spin-spin interaction that can produce entanglement between selected qubits. The intrinsic limitations on the performance of gates using this method can be alleviated by applying optimally shaped pulses instead of pulses with constant amplitude. This thesis explains the theory behind this pulse shaping scheme and how it is implemented on a chain of Yb ions held in a linear radiofrequency `Paul' trap. Several experiments demonstrate the technique in chains of two, three, and five ions using various types of pulse shapes. A tightly focused individual addressing beam allows us to apply the entangling gates to a target pair of ions, and technical issues related to such tight focusing are discussed. Other advantages to the pulse shaping scheme include a robustness against detuning errors and the possibility of suppressing undesirable coupling due to optical spillover on neighboring ions. Combined with ion shuttling, we harness these features to perform sequential gates to different qubit pairs in order to create genuine tripartite entangled states and demonstrate the programmable quantum information processing capability of our system.
Abstract The circuit model of a quantum computer consists of sequences of gate operations between quantum bits (qubits), drawn from a universal family of discrete operations1. The ability to execute parallel entangling quantum gates offers efficiency gains in numerous quantum circuits2–4, as well as for entire algorithms—such as Shor’s factoring algorithm5—and quantum simulations6, 7. In circuits such as full adders and multiple-control Toffoli gates, parallelism can provide an exponential improvement in overall execution time through the divide-and-conquer technique8. More importantly, quantum gate parallelism is essential for fault-tolerant error correction of qubits that suffer from idle errors9, 10. However, the implementation of parallel quantum gates is complicated by potential crosstalk, especially between qubits that are fully connected by a common-mode bus, such as in Coulomb-coupled trapped atomic ions11, 12 or cavity-coupled superconducting transmons13. Here we present experimental results for parallel two-qubit entangling gates in an array of fully connected trapped 171Yb+ ion qubits. We perform a one-bit full-addition operation on a quantum computer using a depth-four quantum circuit4, 14, 15, where circuit depth denotes the number of runtime steps required. Our method exploits the power of highly connected qubit systems using classical control techniques and will help to speed up quantum circuits and achieve fault tolerance in trapped-ion quantum computers.
Over the past decade, the field of trapped ion quantum computing has emerged as one of the leaders in quantum information processing due the level of manipulation available and the long coherence times possible in the system. As this thesis will demonstrate, all of the necessary building blocks for a quantum computer have been exhibited in ion traps and small scale quantum algorithms have been implemented. In this trapped ion system, quantum bits consist of the first order magnetic field insensitive ground state hyperfine levels of 111Cd+. The qubits are manipulated via resonant and off-resonant coherent laser interactions. We experimentally realize Grover's quantum search algorithm over a 4 element database with n=2 trapped 111Cd+ ion qubits. One of the four states is marked, and with a single query it is recovered, on average, with 60% probability. This exceeds the performance of any possible classical search, which can only succeed with 50% probability following a single query. The algorithm consists of two Molmer-Sorensen entangling gates, that utilize bichromatic stimulated Raman transitions to create a spin dependent force, paired with several single-qubit rotations and near-perfect qubit measurements. The spectral arrangement of the Raman beams is tailored to suppress phase noise accumulation between gates. This suppression is critical for reliably performing consecutive operations during the algorithm. Additionally, this thesis discusses the possibility of combining trapped ions with trapped neutral atoms for the purpose studying ultra-cold charge exchange interactions. It may be possible to conceal quantum information, initially prepared in an ionic qubit, inside a pure nuclear spin qubit for the purpose of transportation and storage. As a first step, we present the laser-cooling and confinement of Cd atoms in a magneto-optical trap, and characterize the loading process from the background Cd vapor. The trapping laser drives the 1S0~rightarrow~1P1 transition at 229 nm in this two valence electron atom and also photoionizes atoms directly from the 1P1 state. This photoionization dominates other loss mechanisms and allows a direct measurement of the photoionization cross section.
Abstract Trapped-ion quantum computing can utilize all motional modes of the ion-crystal, to entangle multiple qubits simultaneously, enabling universal computation with multi-qubit gates supplemented by single-qubit rotations. Using multiple tones to drive each ion individually induces Ising-type interactions, forming a multi-qubit gate, where the coupling matrix of all ion pairs is fully controllable. This reduces the total gate count while maintaining high fidelity, as opposed to traditional methods that rely on a single type of two-qubit gate, such as the well-known Mølmer–Sørensen gate. However, scaling to large ion chains, individual addressing can be technically challenging in terms of optical delivery and signal generation. We explore global and semi-global drives combined with single-qubit flips and show that these can reproduce the full set of multi-qubit gates. Although optimizing the combination of single-qubit flips is a computationally hard problem, we propose an efficient scheme to implement any desired couplings in large ion chains, yielding a concatenation scheme that uses at most N / 2 multi-qubit gates, with N being the number of ions. In addition, we show that by using B < N independent semi-global fields, each driving a set of N / B ions, the number of maximal multi-qubit gates is reduced to approximately N 2 B 2 ( N − 1 ) . We show how to design the driving fields that support these schemes and investigate their properties. Our results pave the way for efficient implementations of quantum algorithms in large-scale trapped-ion quantum systems.
The Grover quantum search algorithm is a hallmark application of a quantum computer with a well-known speedup over classical searches of an unsorted database. Here, we report results for a complete three-qubit Grover search algorithm using the scalable quantum computing technology of trapped atomic ions, with better-than-classical performance. Two methods of state marking are used for the oracles: a phase-flip method employed by other experimental demonstrations, and a Boolean method requiring an ancilla qubit that is directly equivalent to the state marking scheme required to perform a classical search. We also report the deterministic implementation of a Toffoli-4 gate, which is used along with Toffoli-3 gates to construct the algorithms; these gates have process fidelities of 70.5% and 89.6%, respectively.
Trapped atomic ions are a promising medium for quantum computing, due to their long coherence times and potential for scalability. Current methods of entangling ions rely on addressing individual modes of motion within the trap and applying qubit state dependent forces with external fields. This approach can limit the speed of entangling gates and make them vulnerable to decoherence due to coupling to unwanted modes or ion heating. This thesis is directed towards demonstrating novel entanglement schemes which are not limited by the trap frequency, and can be made almost arbitrarily fast. Towards this goal, I report here on the first experiments using ultrafast laser pulses to control the internal and external states of a single trapped ion. I begin with experiments in ultrafast spin control, showing how a single laser pulse can be used to completely control both spin degrees of freedom of the ion qubit in tens of picoseconds. I also show how a train of weak pulses can be used to drive Raman transitions based on a frequency comb. I then discuss experiments using pulses to rapidly entangle the spin with the motion, and how careful spectral redistribution allows a single pulse to execute a spin-dependent momentum kick. Finally, I explain how these spin-dependent momentum kicks can be used in the future to create an ultrafast entangling gate. I go over how such a gate would work, and present experimentally realizable timing sequences which would create a maximally entangled state of two ions in a time faster than the period of motion in the trap.