8 research outputs found
Combining Topological Hardware and Topological Software: Color Code Quantum Computing with Topological Superconductor Networks
We present a scalable architecture for fault-tolerant topological quantum
computation using networks of voltage-controlled Majorana Cooper pair boxes,
and topological color codes for error correction. Color codes have a set of
transversal gates which coincides with the set of topologically protected gates
in Majorana-based systems, namely the Clifford gates. In this way, we establish
color codes as providing a natural setting in which advantages offered by
topological hardware can be combined with those arising from topological
error-correcting software for full-fledged fault-tolerant quantum computing. We
provide a complete description of our architecture including the underlying
physical ingredients. We start by showing that in topological superconductor
networks, hexagonal cells can be employed to serve as physical qubits for
universal quantum computation, and present protocols for realizing
topologically protected Clifford gates. These hexagonal cell qubits allow for a
direct implementation of open-boundary color codes with ancilla-free syndrome
readout and logical -gates via magic state distillation. For concreteness,
we describe how the necessary operations can be implemented using networks of
Majorana Cooper pair boxes, and give a feasibility estimate for error
correction in this architecture. Our approach is motivated by nanowire-based
networks of topological superconductors, but could also be realized in
alternative settings such as quantum Hall-superconductor hybrids.Comment: 24 pages, 24 figure
The boundaries and twist defects of the color code and their applications to topological quantum computation
The color code is both an interesting example of an exactly solved topologically ordered phase of matter and also among the most promising candidate models to realize fault-tolerant quantum computation with minimal resource overhead. The contributions of this work are threefold. First of all, we build upon the abstract theory of boundaries and domain walls of topological phases of matter to comprehensively catalog the objects realizable in color codes. Together with our classification we also provide lattice representations of these objects which include three new types of boundaries as well as a generating set for all 72 color code twist defects. Our work thus provides an explicit toy model that will help to better understand the abstract theory of domain walls. Secondly, we discover a number of interesting new applications of the cataloged objects for quantum information protocols. These include improved methods for performing quantum computations by code deformation, a new four-qubit error-detecting code, as well as families of new quantum error-correcting codes we call stellated color codes, which encode logical qubits at the same distance as the next best color code, but using approximately half the number of physical qubits. To the best of our knowledge, our new topological codes have the highest encoding rate of local stabilizer codes with bounded-weight stabilizers in two dimensions. Finally, we show how the boundaries and twist defects of the color code are represented by multiple copies of other phases. Indeed, in addition to the well studied comparison between the color code and two copies of the surface code, we also compare the color code to two copies of the three-fermion model. In particular, we find that this analogy offers a very clear lens through which we can view the symmetries of the color code
which gives rise to its multitude of domain walls
Color-Code Quantum Computing with Topological Superconductor Networks
We present a scalable architecture for fault-tolerant topological quantum
computation using networks of voltage-controlled Majorana Cooper pair boxes
and topological color codes for error correction. Color codes have a set of
transversal gates which coincides with the set of topologically protected
gates in Majorana-based systems, namely, the Clifford gates. In this way, we
establish color codes as providing a natural setting in which advantages
offered by topological hardware can be combined with those arising from
topological error-correcting software for full-fledged fault-tolerant quantum
computing. We provide a complete description of our architecture, including
the underlying physical ingredients. We start by showing that in topological
superconductor networks, hexagonal cells can be employed to serve as physical
qubits for universal quantum computation, and we present protocols for
realizing topologically protected Clifford gates. These hexagonal-cell qubits
allow for a direct implementation of open-boundary color codes with ancilla-
free syndrome read-out and logical T gates via magic-state distillation. For
concreteness, we describe how the necessary operations can be implemented
using networks of Majorana Cooper pair boxes, and we give a feasibility
estimate for error correction in this architecture. Our approach is motivated
by nanowire-based networks of topological superconductors, but it could also
be realized in alternative settings such as quantum-Hall–superconductor
hybrids
Poking Holes and Cutting Corners to Achieve Clifford Gates with the Surface Code
The surface code is currently the leading proposal to achieve fault-tolerant quantum computation. Among its strengths are the plethora of known ways in which fault-tolerant Clifford operations can be performed, namely, by deforming the topology of the surface, by the fusion and splitting of codes, and even by braiding engineered Majorana modes using twist defects. Here, we present a unified framework to describe these methods, which can be used to better compare different schemes and to facilitate the design of hybrid schemes. Our unification includes the identification of twist defects with the corners of the planar code. This identification enables us to perform single-qubit Clifford gates by exchanging the corners of the planar code via code deformation. We analyze ways in which different schemes can be combined and propose a new logical encoding. We also show how all of the Clifford gates can be implemented with the planar code, without loss of distance, using code deformations, thus offering an attractive alternative to ancilla-mediated schemes to complete the Clifford group with lattice surgery
Reinforcement learning decoders for fault-tolerant quantum computation
Topological error correcting codes, and particularly the surface code, currently provide the most feasible road-map towards large-scale fault-tolerant quantum computation. As such, obtaining fast and flexible decoding algorithms for these codes, within the experimentally realistic and challenging context of faulty syndrome measurements, without requiring any final read-out of the physical qubits, is of critical importance. In this work, we show that the problem of decoding such codes can be naturally reformulated as a process of repeated interactions between a decoding agent and a code environment, to which the machinery of reinforcement learning can be applied to obtain decoding agents. While in principle this framework can be instantiated with environments modelling circuit level noise, we take a first step towards this goal by using deepQ learning to obtain decoding agents for a variety of simplified phenomenological noise models, which yield faulty syndrome measurements without including the propagation of errors which arise in full circuit level noise models
IRAK-M Expression in Tumor Cells Supports Colorectal Cancer Progression through Reduction of Antimicrobial Defense and Stabilization of STAT3
Colorectal cancer (CRC) is associated with loss of epithelial barrier integrity, which facilitates the interaction of the immunological microenvironment with the luminal microbiome, eliciting tumor-supportive inflammation. An important regulator of intestinal inflammatory responses is IRAK-M, a negative regulator of TLR signaling. Here we investigate the compartment-specific impact of IRAK-M on colorectal carcinogenesis using a mouse model. We demonstrate that IRAK-M is expressed in tumor cells due to combined TLR and Wnt activation. Tumor cell-intrinsic IRAK-M is responsible for regulation of microbial colonization of tumors and STAT3 protein stability in tumor cells, leading to tumor cell proliferation. IRAK-M expression in human CRCs is associated with poor prognosis. These results suggest that IRAK-M may be a potential therapeutic target for CRC treatment