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… 
Upper Bounds on the Noise Threshold for Fault-Tolerant Quantum Computing
TLDR
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
TLDR
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
TLDR
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
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
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
  • B. Reichardt
  • Computer Science, Physics
    Quantum Inf. Comput.
  • 2009
TLDR
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
TLDR
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.
TLDR
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
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
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
...
1
2
...

References

SHOWING 1-10 OF 37 REFERENCES
Classical simulability, entanglement breaking, and quantum computation thresholds (11 pages)
We investigate the amount of noise required to turn a universal quantum gate set into one that can be efficiently modeled classically. This question is useful for providing upper bounds on
Bounding fault-tolerant thresholds for purification and quantum computation
In this paper, we place bounds on when it is impossible to purify a noisy two-qubit state if all the gates used in the purification protocol are subject to adversarial, local, independent noise. It
New Limits on Fault-Tolerant Quantum Computation
We show that quantum circuits cannot be made fault-tolerant against a depolarizing noise level of thetas = (6 - 2radic2)/7 ap 45%, thereby improving on a previous bound of 50% (due to Razborov,
Overhead and noise threshold of fault-tolerant quantum error correction
Fault-tolerant quantum error correction (QEC) networks are studied by a combination of numerical and approximate analytical treatments. The probability of failure of the recovery operation is
Quantum computing with realistically noisy devices
  • E. Knill
  • Computer Science, Medicine
    Nature
  • 2005
TLDR
This work reports a simple architecture for fault-tolerant quantum computing, providing evidence that accurate quantum computing is possible for EPGs as high as three per cent, and shows that non-trivial quantum computations at EPG’s of as low as one per cent could be implemented.
An upper bound on the threshold quantum decoherence rate
  • A. Razborov
  • Physics, Mathematics
    Quantum Inf. Comput.
  • 2004
TLDR
It is shown that if the decohereace rate η is greater than 1/2, then the authors can not even store a single qubit for more than logarithmic time.
Tight noise thresholds for quantum computation with perfect stabilizer operations.
TLDR
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.
Universal quantum computation with ideal Clifford gates and noisy ancillas (14 pages)
We consider a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state |0>, and qubit measurement in the computational basis.
Quantum Universality from Magic States Distillation Applied to CSS Codes
  • B. Reichardt
  • Physics, Computer Science
    Quantum Inf. Process.
  • 2005
TLDR
A sharp threshold is shown in the Hadamard “magic” direction of the Bloch sphere between those ρ allowing universal quantum computation, and those for which any calculation can be efficiently classically simulated.
Accuracy threshold for postselected quantum computation
TLDR
This proof provides a rigorous foundation for the scheme suggested by Knill, in which preparation circuits for ancilla states are protected by a concatenated error-detecting code and the preparation is aborted if an error is detected.
...
1
2
3
4
...