# Upper bounds on fault tolerance thresholds of noisy Clifford-based quantum computers

@article{Plenio2008UpperBO, title={Upper bounds on fault tolerance thresholds of noisy Clifford-based quantum computers}, author={Martin Bodo Plenio and Shashank Virmani}, journal={New Journal of Physics}, year={2008}, volume={12}, pages={033012} }

We consider the possibility of adding noise to a quantum circuit to make it efficiently simulatable classically. In previous works, this approach has been used to derive upper bounds to fault tolerance thresholds—usually by identifying a privileged resource, such as an entangling gate or a non-Clifford operation, and then deriving the noise levels required to make it 'unprivileged'. In this work, we consider extensions of this approach where noise is added to Clifford gates too and then…

## 14 Citations

Upper Bounds on the Noise Threshold for Fault-Tolerant Quantum Computing

- Mathematics, Computer ScienceICALP
- 2008

New upper bounds on the tolerable level of noise in a quantum circuit are proved using a Pauli basis decomposition, finding that for p > 1 - Θ(1/√k), the output of any such circuit of large enough depth is essentially independent of its input, making the circuit useless.

The robustness of magic state distillation against errors in Clifford gates

- Computer Science, PhysicsQuantum Inf. Comput.
- 2013

The ability to perform magic state distillation with noisy gates leads us to conclude that this could be a realistic scheme for future small-scale quantum computing devices as fault-tolerance need only be used in the final steps of the protocol.

Resource optimization for fault-tolerant quantum computing

- Mathematics, Computer Science
- 2013

This thesis shows how to simplify universal encoded computation by using only transversal gates and standard error correction procedures, circumventing existing no-go theorems and finds that by using a special class of non-deterministic circuits, the cost of decomposition can be reduced by as much as a factor of four over state-of-the-art techniques, which typically use deterministic circuits.

A study of the robustness of magic state distillation against Clifford gate faults

- Mathematics
- 2012

Quantum error correction and fault-tolerance are at the heart of any scalable quantum computation architecture. Developing a set of tools that satisfy the requirements of faulttolerant schemes is…

Noise thresholds for higher-dimensional systems using the discrete Wigner function

- Physics
- 2011

For a quantum computer acting on $d$-dimensional systems, we analyze the computational power of circuits wherein stabilizer operations are perfect, and we allow access to imperfect nonstabilizer…

Quantum universality by state distillation

- Computer Science, PhysicsQuantum Inf. Comput.
- 2009

The range of single-qubit mixed states that are known to give universality is extended, by using a simple parity-checking operation, and certain practical stability characteristics are often required, and a stable distillation procedure is shown.

Towards fault-tolerant quantum computation with higher-dimensional systems

- Computer Science
- 2014

This thesis investigates the two main essential ingredients of many state-of-the-art fault-tolerant schemes, which are magic state distillation and topological error correction, and discovers a particular five-dimensional code that outperforms all known qubit codes.

Tight noise thresholds for quantum computation with perfect stabilizer operations.

- Physics, MedicinePhysical review letters
- 2009

It is proved that for all unitary single-qubit gates there exists a tight depolarizing noise threshold that determines whether the gate enables universal quantum computation or if the gate can be simulated by a mixture of Clifford gates.

Generalized state spaces and nonlocality in fault-tolerant quantum-computing schemes

- Physics
- 2011

We develop connections between generalized notions of entanglement and quantum computational devices where the measurements available are restricted, either because they are noisy and/or because by…

Nonlocality as a benchmark for universal quantum computation in Ising anyon topological quantum computers

- Physics
- 2012

An obstacle affecting any proposal for a topological quantum computer based on Ising anyons is that
quasiparticle braiding can only implement a finite (nonuniversal) set of quantum operations. The…

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