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In the framework of quantum computational tensor network [D. Gross and J. Eisert, Phys. Rev. Lett. {\bf98}, 220503 (2007)], which is a general framework of measurement-based quantum computation, the resource many-body state is represented…
We investigate relations between computational power and correlation in resource states for quantum computational tensor network, which is a general framework for measurement-based quantum computation. We find that if the size of resource…
We develop a generalized theory of quantum error correction (QEC) that applies to any linear map, in particular maps that are not completely positive (CP). This theory describes entanglement-assisted QEC for invertible noise maps, which we…
Quantum systems, in general, output data that cannot be simulated efficiently by a classical computer, and hence is useful for solving certain mathematical problems and simulating quantum many-body systems. This also implies, unfortunately,…
A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer. Unitary transformations can be performed by moving the excitations around each other. Measurements can be performed by joining excitations in…
We develop connections between generalised notions of entanglement and quantum computational devices where the measurements available are restricted, either because they are noisy and/or because by design they are only along Pauli…
Most research in quantum computing today is performed against simulations of quantum computers rather than true quantum computers. Simulating a quantum computer entails implementing all of the unitary operators corresponding to the quantum…
Transversal gates play an important role in the theory of fault-tolerant quantum computation due to their simplicity and robustness to noise. By definition, transversal operators do not couple physical subsystems within the same code block.…
We investigate quantum algorithms derived from tensor networks to simulate the static and dynamic properties of quantum many-body systems. Using a sequentially prepared quantum circuit representation of a matrix product state (MPS) that we…
By introducing an operator sum representation for arbitrary linear maps, we develop a generalized theory of quantum error correction (QEC) that applies to any linear map, in particular maps that are not completely positive (CP). This theory…
The most common error models for quantum computers assume the independence of errors on different qubits. However, most noise mechanisms have some correlations in space. We show how to improve quantum information processing for few-qubit…
Usual scenarios of fault-tolerant computation are concerned with the fault-tolerant realization of quantum algorithms that compute classical functions, such as Shor's algorithm for factoring. In particular, this means that input and output…
We show a similarity between two different classical simulation methods for measurement based quantum computation -- one relying on a low entanglement (tree tensor network) representation of the computer's state, and the other a tensor…
Tensor network theory and quantum simulation are respectively the key classical and quantum computing methods in understanding quantum many-body physics. Here, we introduce the framework of hybrid tensor networks with building blocks…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…
An interesting concept in quantum computation is that of global control (GC), where there is no need to manipulate qubits individually. One can implement a universal set of quantum gates on a one-dimensional array purely via signals that…
Quantum computation can be performed by encoding logical qubits into the states of two or more physical qubits, and controlling a single effective exchange interaction and possibly a global magnetic field. This "encoded universality"…
We present a theoretical framework for state-adaptive quantum error correction that bridges the gap between quantum computing and error correction paradigms. By incorporating knowledge of quantum states into the error correction process, we…
Quantum error correction provides a path to large-scale quantum computers, but is built on challenging assumptions about the characteristics of the underlying errors. In particular, the mathematical assumption of independent errors in…