Related papers: Clifford Gates by Code Deformation
We introduce a graphical representation of stabilizer states and translate the action of Clifford operators on stabilizer states into graph operations on the corresponding stabilizer-state graphs. Our stabilizer graphs are constructed of…
Fault-tolerant quantum computation is a basic problem in quantum computation, and teleportation is one of the main techniques in this theory. Using teleportation on stabilizer codes, the most well-known quantum codes, Pauli gates and…
Noncentrosymmetric superconductors with line nodes are expected to possess topologically protected flat zero-energy bands of surface states, which can be described as Majorana modes. We here investigate their fate if residual interactions…
Subsystem codes protect quantum information by encoding it in a tensor factor of a subspace of the physical state space. Subsystem codes generalize all major quantum error protection schemes, and therefore are especially versatile. This…
We propose a systematic and efficient quantum circuit composed solely of Clifford gates for simulating the ground state of the surface code model. This approach yields the ground state of the toric code in $\lceil…
Quantum codes are subspaces of the state space of a quantum system that are used to protect quantum information. Some common classes of quantum codes are stabilizer (or additive) codes, non-stabilizer (or non-additive) codes obtained from…
Flag verification techniques are useful in quantum error correction for detecting critical faults. Here we present an application of flag verification techniques to improving post-selected performance of near-term algorithms. We extend the…
Conventional quantum error correcting codes require multiple rounds of measurements to detect errors with enough confidence in fault-tolerant scenarios. Here I show that for suitable topological codes a single round of local measurements is…
We propose to represent both $n$--qubits and quantum gates acting on them as elements in the complex Clifford algebra defined on a complex vector space of dimension $2n.$ In this framework, the Dirac formalism can be realized in…
We develop a Clifford algebra approach for 3D Ising model. By utilizing some mathematical facts of the direct product of matrices and their trace, we expand the dimension of the transfer matrices V of the 3D Ising system by adding unit…
The color code is a topological quantum error-correcting code supporting a variety of valuable fault-tolerant logical gates. Its two-dimensional version, the triangular color code, may soon be realized with currently available…
We take initial steps towards a general framework for constructing logical gates in general quantum CSS codes. Viewing CSS codes as cochain complexes, we observe that cohomology invariants naturally give rise to diagonal logical gates. We…
We design flexible fault tolerant gate gadgets that allow the data and the ancilla to be encoded using different codes. By picking a stabilizer code for the ancilla we are able to perform both Clifford and non-Clifford gates fault…
Surface codes have emerged as promising candidates for quantum information processing. Building on the previous idea to realize the physical qubits of such systems in terms of Majorana bound states supported by topological semiconductor…
We translate the action of local Clifford operations on graph states into transformations on their associated graphs - i.e. we provide transformation rules, stated in purely graph theoretical terms, which completely characterize the…
Quantum error-correcting codes are essential to the implementation of fault-tolerant quantum computation. Homological products of classical codes offer a versatile framework for constructing quantum error-correcting codes with desirable…
We study the algebra of complex polynomials which remain invariant under the action of the local Clifford group under conjugation. Within this algebra, we consider the linear spaces of homogeneous polynomials degree by degree and construct…
Clifford codes can be understood as a generalization of stabilizer codes. To show the existence of a true Clifford code which is better than any stabilizer code is a well known open problem in the theory of Clifford codes. One of the main…
We consider geometric methods of ``rotating" the toric code in higher dimensions to reduce the qubit count. These geometric methods can be used to prepare higher dimensional toric code states using single shot techniques, and in turn these…
The inevitable presence of decoherence effects in systems suitable for quantum computation necessitates effective error-correction schemes to protect information from noise. We compute the stability of the toric code to depolarization by…