Quantum Computation and Communication in Bosonic Systems
arXiv:2103.09445
Abstract
Quantum computation and communication are important branches of quantum information science. However, noise in realistic quantum devices fundamentally limits the utility of these quantum technologies. A conventional approach towards large-scale and fault-tolerant quantum information processing is to use multi-qubit quantum error correction (QEC), that is, to encode a logical quantum bit (or a logical qubit) redundantly over many physical qubits such that the redundancy can be used to detect errors. The required resource overhead associated with the use of conventional multi-qubit QEC schemes, however, is too high for these schemes to be realized at scale with currently available quantum devices. Recently, bosonic (or continuous-variable) quantum error correction has risen as a promising hardware-efficient alternative to multi-qubit QEC schemes. In this thesis, I provide an overview of bosonic QEC and present my contributions to the field. Specifically, I present the benchmark and optimization results of various single-mode bosonic codes against practically relevant excitation loss errors. I also demonstrate that fault-tolerant bosonic QEC is possible by concatenating a single-mode bosonic code with a multi-qubit error-correcting code. Moreover, I discuss the fundamental aspects of bosonic QEC using the framework of quantum communication theory. In particular, I present improved bounds on important communication-theoretic quantities such as the quantum capacity of bosonic Gaussian channels. Furthermore, I provide explicit bosonic error correction schemes that nearly achieve the fundamental performance limit set by the quantum capacity. I conclude the thesis with discussions on the importance of non-Gaussian resources for continuous-variable quantum information processing.
arXiv comment294 pages, 41 figures, 8 tables. Based on arXiv:1708.05010, arXiv:1801.07271, arXiv:1811.06988, arXiv:1903.12615, arXiv:1908.03579. This thesis was written in February, 2020. Only a few typos have been fixed since then
References in corpus (108)
- Gaussian Quantum Information
- Charge insensitive qubit design derived from the Cooper pair box
- Surface codes: Towards practical large-scale quantum computation
- Quantum Teleportation is a Universal Computational Primitive
- Encoding a qubit in an oscillator
- Improved Simulation of Stabilizer Circuits
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- General Benchmarks for Quantum Repeaters
- Fundamental Limits of Repeaterless Quantum Communications
- Quantum Error Correction for Quantum Memories
- Quantum Resource Theories
- Quantum Computing with Very Noisy Devices
- Quantum computation over continuous variables
- The capacity of the noisy quantum channel
- Topological Quantum Distillation
- A simple formula for the average gate fidelity of a quantum dynamical operation
- Quantum data processing and error correction
- On the impossibility of distilling Gaussian states with Gaussian operations
- Confining the state of light to a quantum manifold by engineered two-photon loss
- Quantum measurements and the Abelian Stabilizer Problem
- Macroscopically distinct quantum superposition states as a bosonic code for amplitude damping
- New class of quantum error-correcting codes for a bosonic mode
- Quantum codes on a lattice with boundary
- Fault-Tolerant Measurement-Based Quantum Computing with Continuous-Variable Cluster States
- Quantum computing with nearest neighbor interactions and error rates over 1%
- Magic state distillation with low overhead
- Repeated Quantum Error Detection in a Surface Code
- Quantum Communication With Zero-Capacity Channels
- A No-Go Theorem for Gaussian Quantum Error Correction
- Performance and structure of single-mode bosonic codes
- Quantum Channel Capacity of Very Noisy Channels
- Low-distance Surface Codes under Realistic Quantum Noise
- Hardware-efficient autonomous quantum error correction
- Effective operator formalism for open quantum systems
- The sphere packing problem in dimension 24
- Symmetrised Characterisation of Noisy Quantum Processes
- Tracking Photon Jumps with Repeated Quantum Non-Demolition Parity Measurements
- On-demand quantum state transfer and entanglement between remote microwave cavity memories
- Quantum error correction with only two extra qubits
- Bosonic Quantum Codes for Amplitude Damping
- Cavity State Manipulation Using Photon-Number Selective Phase Gates
- Ultrahigh Error Threshold for Surface Codes with Biased Noise
- Quantum Capacities of Bosonic Channels
- Fault-tolerant bosonic quantum error correction with the surface-GKP code
- Universal Control of an Oscillator with Dispersive Coupling to a Qubit
- Fault-tolerant quantum error detection
- All-Gaussian universality and fault tolerance with the Gottesman-Kitaev-Preskill code
- Improved quantum capacity bounds of Gaussian loss channels and achievable rates with Gottesman-Kitaev-Preskill codes
- Coherent oscillations inside a quantum manifold stabilized by dissipation
- One-mode Bosonic Gaussian channels: a full weak-degradability classification
- All-optical generation of states for "Encoding a qubit in an oscillator"
- Entangling Bosonic Modes via an Engineered Exchange Interaction
- Degenerate Quantum Codes for Pauli Channels
- Quantum Error Correction with the Toric-GKP Code
- Generating Grid States From Schrödinger Cat States without Post-Selection
- Effective fault-tolerant quantum computation with slow measurements
- Improved magic states distillation for quantum universality
- Single-Mode Displacement Sensor
- Fault-tolerant quantum computation with few qubits
- Encoding a Qubit into a Cavity Mode in Circuit-QED using Phase Estimation
- Capacity Theorems for Quantum Multiple Access Channels: Classical-Quantum and Quantum-Quantum Capacity Regions
- Fault-tolerant thresholds for the surface code in excess of 5% under biased noise
- Operator-sum Representation for Bosonic Gaussian Channels
- Error-transparent operations on a logical qubit protected by quantum error correction
- Analog quantum error correction with encoding a qubit into an oscillator
- Optimum Quantum Error Recovery using Semidefinite Programming
- Cat codes with optimal decoherence suppression for a lossy bosonic channel
- Non-Gaussian and Gottesman-Kitaev-Preskill state preparation by photon catalysis
- Iterative Optimization of Quantum Error Correcting Codes
- Unbounded number of channel uses are required to see quantum capacity
- Coping with qubit leakage in topological codes
- Degradability of Bosonic Gaussian channels
- Encoding an oscillator into many oscillators
- Intracity quantum communication via thermal microwave networks
- Gaussian bosonic synergy: quantum communication via realistic channels of zero quantum capacity
- Pair-cat codes: autonomous error-correction with low-order nonlinearity
- Achievable rates for the Gaussian quantum channel
- Direct characteristic-function tomography of quantum states of the trapped-ion motional oscillator
- Approximate Degradable Quantum Channels
- Encoding qubits into oscillators with atomic ensembles and squeezed light
- New lower bounds on the non-zero capacity of Pauli Channels
- Engineering bilinear mode coupling in circuit QED: Theory and experiment
- Constructing finite dimensional codes with optical continuous variables
- Preparing encoded states in an oscillator
- Dephrasure channel and superadditivity of coherent information
- Fault-tolerant preparation of approximate GKP states
- Sequential modular position and momentum measurements of a trapped ion mechanical oscillator
- Universal Quantum Computing with Arbitrary Continuous-Variable Encoding
- Narrow Bounds for the Quantum Capacity of Thermal Attenuators
- Modular Bosonic Subsystem Codes
- Equivalence of approximate Gottesman-Kitaev-Preskill codes
- Energy-constrained private and quantum capacities of quantum channels
- Fault-Tolerant Quantum Computing in the Pauli or Clifford Frame with Slow Error Diagnostics
- Path-Independent Quantum Gates with Noisy Ancilla
- Private and Quantum Capacities of More Capable and Less Noisy Quantum Channels
- Degeneracy-preserving quantum non-demolition measurement of parity-type observables for cat-qubits
- Qudit-Basis Universal Quantum Computation using Interactions
- Dissipative Universal Lindbladian Simulation
- Implementation-independent sufficient condition of the Knill-Laflamme type for the autonomous protection of logical qudits by strong engineered dissipation
- Hardware-Efficient Bosonic Quantum Error-Correcting Codes Based on Symmetry Operators
- Generating continuous variable quantum codewords in the near-field atomic lithography
- Handling Leakage with Subsystem Codes
- Realizing modular quadrature measurements via a tunable photon-pressure coupling in circuit-QED
- Activation of quantum capacity of Gaussian channels
- Tracking Quantum Error Correction
- Quantum Error Correction with the GKP Code and Concatenation with Stabilizer Codes
- Conditional channel simulation
- Algorithmic complexity of quantum capacity