Entanglement and Quantum Error Correction with Superconducting Qubits
arXiv:1311.6759
Abstract
A quantum computer will use the properties of quantum physics to solve certain computational problems much faster than otherwise possible. One promising potential implementation is to use superconducting quantum bits in the circuit quantum electrodynamics (cQED) architecture. There, the low energy states of a nonlinear electronic oscillator are isolated and addressed as a qubit. These qubits are capacitively coupled to the modes of a microwave-frequency transmission line resonator which serves as a quantum communication bus. Microwave electrical pulses are applied to the resonator to manipulate or measure the qubit state. State control is calibrated using diagnostic sequences that expose systematic errors. Hybridization of the resonator with the qubit gives it a nonlinear response when driven strongly, useful for amplifying the measurement signal to enhance accuracy. Qubits coupled to the same bus may coherently interact with one another via the exchange of virtual photons. A two-qubit conditional phase gate mediated by this interaction can deterministically entangle its targets, and is used to generate two-qubit Bell states and three-qubit GHZ states. These three-qubit states are of particular interest because they redundantly encode quantum information. They are the basis of the quantum repetition code prototypical of more sophisticated schemes required for quantum computation. Using a three-qubit Toffoli gate, this code is demonstrated to autonomously correct either bit- or phase-flip errors. Despite observing the expected behavior, the overall fidelity is low because of decoherence. A superior implementation of cQED replaces the transmission-line resonator with a three-dimensional box mode, increasing lifetimes by an order of magnitude. In-situ qubit frequency control is enabled with control lines, which are used to fully characterize and control the system Hamiltonian.
Ph.D. thesis. 368 pages, 107 figures. Based in part on arXiv:1003.0142, arXiv:1003.2734, arXiv:1004.4323, arXiv:1004.4324, arXiv:1112.2621, and arXiv:1109.4948. Paper copies can be ordered from http://www.lulu.com/shop/search.ep?contributorId=1198976 . Please refer any questions, comments, or suggestions to mdreed at gmail dot com
References in corpus (39)
- Non-Abelian Anyons and Topological Quantum Computation
- Sideband Cooling Micromechanical Motion to the Quantum Ground State
- Strong dispersive coupling of a high finesse cavity to a micromechanical membrane
- Coupling Superconducting Qubits via a Cavity Bus
- Randomized Benchmarking of Quantum Gates
- Self-cooling of a micro-mirror by radiation pressure
- Resolving photon number states in a superconducting circuit
- Simple pulses for elimination of leakage in weakly nonlinear qubits
- Coherent Josephson qubit suitable for scalable quantum integrated circuits
- Superconducting qubit in waveguide cavity with coherence time approaching 0.1ms
- Demonstration of Entanglement of Electrostatically Coupled Singlet-Triplet Qubits
- Observation of Radiation Pressure Shot Noise on a Macroscopic Object
- Complete universal quantum gate set approaching fault-tolerant thresholds with superconducting qubits
- Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators
- Observation of quantum jumps in a superconducting artificial atom
- Realization of the quantum Toffoli gate with trapped ions
- Characterization of addressability by simultaneous randomized benchmarking
- Self-Consistent Quantum Process Tomography
- Single-shot qubit readout in circuit Quantum Electrodynamics
- Single-shot qubit readout in circuit Quantum Electrodynamics
- Millisecond charge-parity fluctuations and induced decoherence in a superconducting qubit
- Noiseless nonreciprocity in a parametric active device
- Demonstrating a Driven Reset Protocol of a Superconducting Qubit
- Process verification of two-qubit quantum gates by randomized benchmarking
- Feedback control of a solid-state qubit using high-fidelity projective measurement
- Process tomography of ion trap quantum gates
- Demonstration of entanglement-by-measurement of solid state qubits
- Initialization by measurement of a two-qubit superconducting circuit
- Low- and high-frequency noise from coherent two-level systems
- Randomized Benchmarking of Multi-Qubit Gates
- Improved Superconducting Qubit Readout by Qubit-Induced Nonlinearities
- Measurement based entanglement under conditions of extreme photon loss
- Threshold Error Penalty for Fault Tolerant Computation with Nearest Neighbour Communication
- Superconducting microfabricated ion traps
- Stabilizer quantum error correction toolbox for superconducting qubits
- Distributed quantum information processing with minimal local resources
- Experimental Monte Carlo Quantum Process Certification
- State of the art and prospects for quantum computing
- Measurement-based approach to entanglement generation in coupled quantum dots
Cited by in corpus (17)
- A Quantum Engineer's Guide to Superconducting Qubits
- To catch and reverse a quantum jump mid-flight
- Gatemon Benchmarking and Two-Qubit Operation
- An Experimental Microarchitecture for a Superconducting Quantum Processor
- Hardware for Dynamic Quantum Computing
- Active resonator reset in the nonlinear dispersive regime of circuit QED
- QubiC: An open source FPGA-based control and measurement system for superconducting quantum information processors
- Error analysis in suppression of unwanted qubit interactions for a parametric gate in a tunable superconducting circuit
- Simultaneous gates in frequency-crowded multilevel systems using fast, robust, analytic control shapes
- Perturbation impact of spectators on a cross-resonance gate in a tunable coupling superconducting circuit
- Filter Functions for Quantum Processes under Correlated Noise
- Mechanical Purcell Filters for Microwave Quantum Machines
- Mitigating information leakage in a crowded spectrum of weakly anharmonic qubits
- eQASM: An Executable Quantum Instruction Set Architecture
- An Introduction to Superconducting Qubits and Circuit Quantum Electrodynamics
- Generating time-domain linear cluster state by recycling superconducting qubits
- A practical guide for building superconducting quantum devices