Browsing by Subject "Quantum computing"

Ion traps are a leading candidate for scaling quantum computers. The component technologies can be difficult to integrate and manufacture. Experimental systems are also subject to mechanical drift creating a large maintenance overhead. A full system redesign with stability and scalability in mind is presented. The center of our approach is a compact cryogenic ion trap package (trap cryopackage). A surface trap is mounted to a modified ceramic pin grid array (CPGA) this is enclosed using a copper lid. The differentially pumped trap cryopackage has all necessary optical feedthroughs and an ion source (ablation target). The lid pressure is held at ultra-high vacuum (UHV) by cryogenic sorption pumping using carbon getter. We install this cryopackage into a commercial low-vibration closed-cycle cryostat which sits inside a custom monolithic enclosure. The system is tested and trapped ions are found to have common mode heating rate on the order of 10 quanta/s. The modular optical setup provides for a couterpropagating single qubit coherence time of 527 ms. We survey a population of FM two-qubit gates (gate times 120 μs - 450 μs) and find an average gate fidelity of 98\%. We study the gate survey with quantum Monte Carlo simulation and find that our two-qubit gate fidelity is limited by low frequency (30 Hz - 3 kHz) coherent electrical noise on our motional modes.

The challenge of building scalable quantum computer lies in striking appropriate balance between designing a reliable system architecture from large number of faulty computational resources and improving the physical quality of system components. The detailed investigation of performance variation with physics of the components and the system architecture requires adequate performance simulation tool. In this thesis we demonstrate a software tool capable of (1) mapping and scheduling the quantum circuit on a realistic quantum hardware architecture with physical resource constraints, (2) evaluating the performance metrics such as the execution time and the success probability of the algorithm execution, and (3) analyzing the constituents of these metrics and visualizing resource utilization to identify system components which crucially define the overall performance.

Using this versatile tool, we explore vast design space for modular quantum computer architecture based on trapped ions. We find that while success probability is uniformly determined by the fidelity of physical quantum operation, the execution time is a function of system resources invested at various layers of design hierarchy. At physical level, the number of lasers performing quantum gates, impact the latency of the fault-tolerant circuit blocks execution. When these blocks are used to construct meaningful arithmetic circuit such as quantum adders, the number of ancilla qubits for complicated non-clifford gates and entanglement resources to establish long-distance communication channels, become major performance limiting factors. Next, in order to factorize large integers, these adders are assembled into modular exponentiation circuit comprising bulk of Shor's algorithm. At this stage, the overall scaling of resource-constraint performance with the size of problem, describes the effectiveness of chosen design. By matching the resource investment with the pace of advancement in hardware technology, we find optimal designs for different types of quantum adders. Conclusively, we show that 2,048-bit Shor's algorithm can be reliably executed within the resource budget of 1.5 million qubits.

This thesis aims to present methods for characterizing and mitigating errors in quantum computers. We begin by providing a historical overview of computing devices and the evolution of quantum information. The basics of characterizing noise in quantum computers and the utilization of quantum control and error mitigation techniques to reduce the impact of noise on performance are also discussed. In the initial part of the thesis, we focus on a particularly detrimental type of time-dependent errors and derive theoretical limits of a closed-loop feedback based quantum control protocol for their mitigation. Two different protocols, one suitable for fault-tolerant systems and another for near-term devices, are presented and their performance is demonstrated through numerical simulations. Additionally, we explore the mitigation of coherent noise at the circuit level through the use of the hidden inverses protocol with results from experiments conducted at Duke University, Sandia National Laboratories, and IBM. Finally, we propose a scalable error characterization procedure for large quantum systems, which is tested through numerical simulations to highlight its sensitivity to various sources of noise. Crucially, this protocol does not require access to ideal classical simulation of quantum circuits unlike other benchmarks such as quantum volume or cross entropy benchmarks.

Quantum information science strives to leverage the quantum-mechanical nature of our universe in order to achieve large improvements in certain information processing tasks. Such tasks include quantum communications and fault-tolerant quantum computation. In this dissertation, we make contributions to both of these applications.

In deep-space optical communications, the mathematical abstraction of the binary phase shift keying (BPSK) modulated pure-loss optical channel is called the pure-state channel. It takes classical inputs and delivers quantum outputs that are pure (qubit) states. To achieve optimal information transmission, if classical error-correcting codes are employed over this channel, then one needs to develop receivers that collectively measure all output qubits in order to optimally identify the transmitted message. In general, it is hard to determine these optimal collective measurements and even harder to realize them in practice. So, current receivers first measure each qubit channel output and then classically post-process the measurements. This approach is sub-optimal. We investigate a recently proposed quantum algorithm for this task, which is inspired by classical belief-propagation algorithms, and analyze its performance on a simple $5$-bit code. We show that the algorithm makes optimal decisions for the value of each bit and it appears to achieve optimal performance when deciding the full transmitted message. We also provide explicit circuits for the algorithm in terms of standard gates. For deep-space optical communications, this suggests a near-term quantum advantage over the aforementioned sub-optimal scheme. Such a communication advantage appears to be the first of its kind.

Quantum error correction is vital to building a universal fault-tolerant quantum computer. An $[\![ n,k,d ]\!]$ quantum error-correcting code (QECC) protects $k$ information (or logical) qubits by encoding them into quantum states of $n > k$ physical qubits such that any undetectable error must affect at least $d$ physical qubits. In this dissertation we focus on stabilizer QECCs, which are the most widely used type of QECCs. Since we would like to perform universal (i.e., arbitrary) quantum computation on the $k$ logical qubits, an important problem is to determine fault-tolerant $n$-qubit physical operations that induce the desired logical operations. Our first contribution here is a systematic algorithm that can translate a given logical Clifford operation on a stabilizer QECC into all (equivalence classes of) physical Clifford circuits that realize that operation. We exploit binary symplectic matrices to make this translation efficient and call this procedure the Logical Clifford Synthesis (LCS) algorithm.

In order to achieve universality, a quantum computer also needs to implement at least one non-Clifford logical operation. We develop a mathematical framework for a large subset of diagonal (unitary) operations in the Clifford hierarchy, and we refer to these as Quadratic Form Diagonal (QFD) gates. We show that all $1$- and $2$-local diagonal gates in the hierarchy are QFD, and we rigorously derive their action on Pauli matrices. This framework of QFD gates includes many non-Clifford gates and could be of independent interest. Subsequently, we use the QFD formalism to characterize all $[\![ n,k,d ]\!]$ stabilizer codes whose code subspaces are preserved under the transversal action of $T$ and $T^{-1}$ gates on the $n$ physical qubits. The $T$ and $T^{-1}$ gates are among the simplest non-Clifford gates to engineer in the lab. By employing a ``reverse LCS'' strategy, we also discuss the logical operations induced by these physical gates. We discuss some important corollaries related to triorthogonal codes and the optimality of CSS codes with respect to $T$ and $T^{-1}$ gates. We also describe a few purely-classical coding problems motivated by physical constraints arising from fault-tolerance. Finally, we discuss several examples of codes and determine the logical operation induced by physical $Z$-rotations on a family of quantum Reed-Muller codes. A conscious effort has been made to keep this dissertation self-contained, by including necessary background material on quantum information and computation.

The framework of quantum field theory (QFT) underlies our modern understanding of both particle physics and condensed matter physics. Despite its importance, precise quantitative calculations in strongly-coupled theories in QFTs have generally only been possible through non-perturbative lattice Monte Carlo (MC) methods. Traditionally, such lattice MC methods proceed by starting from a lattice regularization of the continuum QFT of interest, which has the same (possibly infinite dimensional) local Hilbert space at each lattice site as the continuum QFT. In this thesis, we explore an alternative regularization where the local Hilbert space is also replaced by a smaller finite dimensional Hilbert space. Motivated by the appeal of such models for near-term quantum computers, we dub this approach qubit regularization. Using this approach, in this thesis, we present three main results. First, we develop a qubit-regularization for the O(N) nonlinear sigma model (NLSM) in D $\geq$ 3 spacetime dimensions. We show using numerical lattice calculations that the O(N ) qubit model lies in the correct universality class for N = 2, 4, 6, 8, and reproduces the universal physics of the O(N) Wilson-Fisher (WF) fixed point in D = 3 spacetime dimensions by computing some well-known critical exponents. Next, we explore sectors of large global charges of the O(N) WF conformal field theory (CFT) using the O(N) qubit model. This allows us to test the predictions of a recently proposed large-charge effective field theory (EFT) and extract the two leading low-energy constants (LECs) in the EFT. Performing computations for N = 2, 4, 6, 8, we are also able to quantitatively test predictions of a recent large-N analysis in the large-charge sectors. Finally, we show that our qubit approach can also be used to study the few-body physics of non-relativistic particles. In particular, we consider a system of two species of mass-imbalanced fermions in $1 + 1$ dimensions. We compute the ground state energies for a range of mass-imbalances and interaction strengths, and uncover some problems with recent results obtained from the Complex Langevin (CL) method for the same system.

Trapped ions provide a promising platform to build a practical quantum computer. Scaling the high performance of small systems to longer ion chains is a technical endeavor that benefits from both better hardware system design and gate-level control techniques. In this thesis, I discuss our work on building a small-scale trapped-ion quantum computing system that features stable laser beam control, low-crosstalk individual addressing and capability to implement high-fidelity multi-qubit gates.

We develop control techniques to extend the pack-leading fidelity of entangling gates in two-ion systems to longer chains. A major error source limiting entangling gate fidelities in ion chains is crosstalk between target and neighboring spectator qubits. We propose and demonstrate a crosstalk suppression scheme that eliminates all first-order crosstalk utilizing only local control of target qubits, as opposed to an existing scheme which requires control over all neighboring qubits. Using the scheme, we achieve a $99.5\%$ gate fidelity in a 5-ion chain. Complex quantum circuits can benefit from native multi-qubit gates such as the $N$-Toffoli gate, which substantially reduce the overhead cost from performing universal decomposition into single- and two-qubit gates. We take advantage of novel performance benefits of long ion chains to realize scalable Cirac-Zoller gates, which uses a simple pulse sequence to efficiently implement $N$-Toffoli gates. We demonstrate the Cirac-Zoller 3- and 4-Toffoli gates in a five-ion chain with higher fidelities than previous results using trapped ions. We also present the first experimental realization of a 5-Toffoli gate.

Trapped ion systems are the leading candidate for quantum information processing because many of the critical components have already been demonstrated. Scaling trapped ion systems to large numbers of ions is currently believed possible, but much work remains to prove it. Microfabricated surface ion traps are increasing in popularity for their ease of mass production and their ability to manipulate individual ions and interact arbitrary pairs of ions. Even with the advent of scalable ion traps, detection of an individual ion trapped in a high vacuum poses a challenge. The internal state of the ion chosen for a quantum bit can be measured via exposure to a probe beam that causes one state to scatter light (a "bright" state), but not the other state (a "dark" state). In free space, a single ion acts like a point source that emits in all directions; a standard two inch lens system can only collect about 2% of the light emitted by the ion. Poor light collection results in a high error rate and slow determination of the internal state of the ion. Fast, high fidelity state detection is necessary for quantum error correction and loophole-free Bell experiments at short (less than 100\,km) distances, and high efficiency collection is necessary to rapidly interconnect separate quantum computers. We demonstrate state detection fidelities of 99%, 99.856(8)% and 99.915(7) % which correspond to detection times of 10.5, 28.1 and 99.8 us, respectively.

Atomic ions trapped in microfabricated surface traps can be utilized as a physical platform with which to build a quantum computer. They possess many of the desirable characteristics of such a device, including high fidelity state preparation and readout, universal logic gates, and long coherence times, and can be readily entangled with each other through photonic interconnects. The use of optical cavities integrated with trapped ion qubits as a photonic interface presents the possibility for order of magnitude improvements in performance in several key areas for their use in quantum computation. The first part of this thesis describes the design and fabrication of a novel surface trap for integration with an optical cavity. The trap is custom made on a highly reflective mirror surface and includes the capability of moving the ion trap location along all three trap axes with nanometer scale precision. The second part of this thesis demonstrates the suitability of small microcavities formed from laser ablated, fused silica substrates with radii of curvature in the 300-500 micron range for use with the mirror trap as part of an integrated ion trap cavity system. Quantum computing applications for such a system include dramatic improvements in the photon entanglement rate of up to 10 kHz, the qubit measurement time down to 1 microsecond, and the qubit measurement error rate down to the 1e-5 range. The final part of this thesis describes a performance simulator for exploring the physical resource requirements and performance demands to scale a quantum computer to sizes capable of implementing quantum algorithms beyond the limits of classical computation.

In this dissertation we will discuss methods for creating error-robust logical qubits which have been optimized for trapped ion quantum computers. We will cover the basic building blocks of quantum information and develop an understanding of the standard techniques for building fault-tolerant quantum computers through the use of quantum error correcting codes. We will then focus on trapped ion systems, although many of the errors we consider also occur in other hardware implementations.

The majority of this dissertation is concerned with taking advantage of the structure found in experimental errors to maximize system performance. Using numerical simulation, we study the interplay of structured error models and quantum error correction. We then cover optimizations to the standard quantum error correction framework, both through gate compilation and code design, to correct coherent gate overrotation and dephasing errors. The latter section will also include experiments run on a quantum computer at the University of Maryland which verify the effectiveness of our ideas. We will end with a discussion of a method for quantum error detection in near-term systems by extending the flag gadget framework often used in quantum error correction.

Through this body of work we hope to provide evidence for the value, within the context of quantum error correction, of detailed understanding of our physical systems. Oftentimes, codes and protocols are designed without actual implementation in mind. While these studied often produce useful results, more effective methods can sometimes be found when the physics is kept in mind. Our hope is that this dissertation motivates further study of the physical error processes present in quantum computing architectures, as well as development of novel methods to correct them.