We describe the encoding of multiple qubits per atom in trapped atom quantum processors and methods for performing both intra- and inter-atomic gates on participant qubits without disturbing the spectator qubits stored in the same atoms. We also introduce techniques for selective state preparation and measurement of individual qubits that leave the information encoded in the other qubits intact, a capability required for qubit quantum error correction. The additional internal states needed for polyqubit processing are already present in atomic processors, suggesting that the resource cost associated with this multiplicative increase in qubit number could be a good bargain in the short to medium term.
We describe the encoding of multiple qubits per atom in trapped atom quantum processors and methods for performing both intra- and inter-atomic gates on participant qubits without disturbing the spectator qubits stored in the same atoms. We also introduce techniques for selective state preparation and measurement of individual qubits that leave the information encoded in the other qubits intact, a capability required for qubit quantum error correction. The additional internal states needed for polyqubit processing are already present in atomic processors, suggesting that the resource cost associated with this multiplicative increase in qubit number could be a good bargain in the short to medium term.
Large-scale quantum information processors must be able to transport and maintain quantum information and repeatedly perform logical operations. Here, we show a combination of all of the fundamental elements required to perform scalable quantum computing through the use of qubits stored in the internal states of trapped atomic ions. We quantified the repeatability of a multiple-qubit operation and observed no loss of performance despite qubit transport over macroscopic distances. Key to these results is the use of different pairs of 9Be+ hyperfine states for robust qubit storage, readout, and gates, and simultaneous trapping of 24Mg+ "re-cooling" ions along with the qubit ions.
High quality, fully programmable quantum processors are available with small numbers (<1000) of qubits, and the scientific potential of these near-term machines is not well understood. If the small number of physical qubits precludes practical quantum error correction, how can these error-susceptible processors be used to perform useful tasks? We present a strategy for developing quantum error detection for certain gate imperfections that utilizes additional internal states and does not require additional physical qubits. Examples for adding error detection are provided for a universal gate set in the trapped-ion platform. Error detection can be used to certify individual gate operations against certain errors, and the irreversible nature of the detection allows a result of a complex computation to be checked at the end for error flags.
Information processing based on the laws of quantum mechanics promises to be a revolutionary new avenue in information technology. This emerging field of quantum information processing (QIP) is however challenged by the fragile nature of the quantum bits (qubits) in which quantum information is stored and processed. An error in even a single qubit makes the quantum processor go off-track, corrupting the calculation as a whole. Therefore, the chance for an erroneous outcome increases with the number of qubits in the processor. Large-scale QIP thus hinges on the ability to correct for these errors. Classical information processing often uses error correction algorithms to identify errors by checking whether information is consistent in multiple copies. This strategy is unfortunately not applicable to QIP as quantum states cannot be copied. Moreover, direct measurements on qubits collapse their quantum states, reducing them to classical information. Fortunately, the theory of quantum error correction (QEC) overcomes these complications by encoding quantum information in entangled states of many qubits and performing parity measurements to identify errors in the system without destroying the encoded information. Implementing these codes is challenging as it requires many qubits and quick interleaving of operations and measurements. Moreover, to not introduce more errors in the system than QEC can solve for, these operations and measurements need to be of sufficient fidelity and speed...
We propose encoding multiple qubits inside ions in existing trapped-ion quantum computers to access more qubits and to simplify circuits implementing standard algorithms. By using such `virtual' qubits, some inter-ion gates can be replaced by intra-ion gates, reducing the use of vibrational modes of the ion chain, leading to less noise. We discuss specific examples such as the Bernstein-Vazirani algorithm and random circuit sampling, using a small number of virtual qubits. Additionally, virtual qubits enable using larger number of data qubits for an error correcting code, and we consider the repetition code as an example. We also lay out practical considerations to be made when choosing states to encode virtual qubits in 137Ba+ ions, and for preparing states and performing measurements.
Quantum computing exists at the intersection of mathematics, physics, chemistry, and engineering; the main goal of quantum computing is the creation of devices and algorithms which use the properties of quantum mechanics to store, manipulate and measure information. There exist many families of algorithms, which, using non-classical logical operations, can outperform traditional, classical algorithms in terms of memory and processing requirements. In addition, quantum computing devices are fundamentally smaller than classical processors and memory elements; since the physical models governing their performance are applicable on all scales, as opposed to classical logic elements, whose underlying principles rely on the macroscopic nature of the device in question. \n \nQuantum algorithms, for the most part, are predicated on a theory of resources. It is often assumed that quantum computers can be placed in a precise fiducial state prior to computation, and that logical operations are perfect, inducing no error on the system which they affect. These assumptions greatly simplify algorithmic design, but are fundamentally unrealistic. In order to justify their use, it is necessary to develop a framework for using a large number of imperfect devices to simulate the action of a perfect device, with some acceptable probability of failure. This is the study of fault-tolerant quantum computing. In order to pursue this study effectively, it is necessary to understand the fundamental nature of generic quantum states and operations, as well as the means by which one can correct quantum errors. Additionally, it is important to attempt to minimize the use of computational resources in achieving error reduction and fault-tolerant computing. \n \nThis thesis is concerned with three projects related to the use of error-prone quantum systems to transmit and manipulate information. The first of these is concerned with the use of imperfectly-prepared states in error-correction routines. Using optimal quantum error correction, we are able to deduce a method of partially protecting encoded quantum information against preparation errors prior to encoding, using no additional qubits. The second of these projects details the search for entangled states which can be used to transmit classical information over quantum channels at a rate superior to classical states. The third of these projects concerns the transcoding of data from one quantum code into another using few ancillary resources. The descriptions of these projects are preceded by a brief introduction to representations of quantum states and channels, for completeness. \n \nThree techniques of general interest are presented in appendices. The first is an introduction to, and a minor advance in the development of optimal error correction codes. The second is a more efficient means of calculating the action of a quantum channel on a given state, given that the channel acts non-trivially only on a subsystem, rather than the entire system. Finally, we include documentation on a software package developed to aid the search for quantum transcoding operations.
Modularization promises to break down the design and implementation complexity of large scale quantum processors into smaller manageable subtasks. In this approach, quantum channels, realized for instance through physical rerouting of qubits or quantum teleportation, connect multiple modules. Each of those modules hosts a subset of qubits, e.g. multiple logical qubits, and provides quantum operations on them. In this work, we implement for the first time all logical operations required for modular fault-tolerant universal quantum computing with a non-Calderbank-Shor-Steane (CSS) code, the perfect [[5,1,3]] code, on a trapped-ion quantum computer. This code is the smallest quantum error-correcting (QEC) code capable of correcting any single-qubit error, making it a compact alternative to larger CSS codes. We demonstrate logical state teleportation and a full suite of fault-tolerant operations required for universal logical control, including logical state preparation, QEC with real-time feedback, logical measurements, magic-state preparation, logical entangling operations, and magic-state injection. Moreover, we characterize the logical spectator error picked up by idling logical qubits during quantum operations on distinct qubit registers and demonstrate a logical Pauli quantum process tomography that minimizes required sampling resources for logical tomography.