Error mitigation for universal gates on encoded qubits
- URL: http://arxiv.org/abs/2103.04915v2
- Date: Tue, 12 Oct 2021 15:48:03 GMT
- Title: Error mitigation for universal gates on encoded qubits
- Authors: Christophe Piveteau, David Sutter, Sergey Bravyi, Jay M. Gambetta,
Kristan Temme
- Abstract summary: We show how to implement Clifford+T circuits with a number of T-gates inversely proportional to the physical noise rate.
We argue that such circuits can be out of reach for state-of-the-art classical simulation algorithms.
- Score: 5.774786149181392
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The Eastin-Knill theorem states that no quantum error correcting code can
have a universal set of transversal gates. For CSS codes that can implement
Clifford gates transversally it suffices to provide one additional non-Clifford
gate, such as the T-gate, to achieve universality. Common methods to implement
fault-tolerant T-gates like magic state distillation generate a significant
hardware overhead that will likely prevent their practical usage in the
near-term future. Recently methods have been developed to mitigate the effect
of noise in shallow quantum circuits that are not protected by error
correction. Error mitigation methods require no additional hardware resources
but suffer from a bad asymptotic scaling and apply only to a restricted class
of quantum algorithms. In this work, we combine both approaches and show how to
implement encoded Clifford+T circuits where Clifford gates are protected from
noise by error correction while errors introduced by noisy encoded T-gates are
mitigated using the quasi-probability method. As a result, Clifford+T circuits
with a number of T-gates inversely proportional to the physical noise rate can
be implemented on small error-corrected devices without magic state
distillation. We argue that such circuits can be out of reach for
state-of-the-art classical simulation algorithms.
Related papers
- Theory of quantum error mitigation for non-Clifford gates [0.0]
Quantum error mitigation techniques mimic noiseless quantum circuits by running several related noisy circuits.
How well such techniques work is thought to depend strongly on how noisy the underlying gates are.
This paper generalizes these techniques to non-Clifford gates.
arXiv Detail & Related papers (2024-03-27T17:36:35Z) - Logical Gates and Read-Out of Superconducting Gottesman-Kitaev-Preskill Qubits [0.0]
In superconducting circuits, all the required two-qubit gates can be implemented with a single piece of hardware.
We analyze the error-spreading properties of GKP Clifford gates and describe how a modification in the decoder can reduce the gate infidelity by multiple orders of magnitude.
arXiv Detail & Related papers (2024-03-04T19:00:04Z) - Pseudo Twirling Mitigation of Coherent Errors in non-Clifford Gates [0.0]
We introduce, analyzes, and experimentally demonstrate a technique called Pseudo Twirling' to address coherent errors in general gates and circuits.
We experimentally showcase that integrating pseudo twirling with a quantum error mitigation method called Adaptive KIK' enables the simultaneous mitigation of both noise and coherent errors in non-Clifford gates.
arXiv Detail & Related papers (2024-01-17T08:14:59Z) - Implementing fault-tolerant non-Clifford gates using the [[8,3,2]] color
code [0.0]
We observe improved performance for encoded circuits implementing non-Clifford gates.
Our results illustrate the potential of using codes with quantum gates to implement non-trivial algorithms.
arXiv Detail & Related papers (2023-09-15T18:00:02Z) - Fast Flux-Activated Leakage Reduction for Superconducting Quantum
Circuits [84.60542868688235]
leakage out of the computational subspace arising from the multi-level structure of qubit implementations.
We present a resource-efficient universal leakage reduction unit for superconducting qubits using parametric flux modulation.
We demonstrate that using the leakage reduction unit in repeated weight-two stabilizer measurements reduces the total number of detected errors in a scalable fashion.
arXiv Detail & Related papers (2023-09-13T16:21:32Z) - Transversal Injection: A method for direct encoding of ancilla states
for non-Clifford gates using stabiliser codes [55.90903601048249]
We introduce a protocol to potentially reduce this overhead for non-Clifford gates.
Preliminary results hint at high quality fidelities at larger distances.
arXiv Detail & Related papers (2022-11-18T06:03:10Z) - Software mitigation of coherent two-qubit gate errors [55.878249096379804]
Two-qubit gates are important components of quantum computing.
But unwanted interactions between qubits (so-called parasitic gates) can degrade the performance of quantum applications.
We present two software methods to mitigate parasitic two-qubit gate errors.
arXiv Detail & Related papers (2021-11-08T17:37:27Z) - Finding the disjointness of stabilizer codes is NP-complete [77.34726150561087]
We show that the problem of calculating the $c-disjointness, or even approximating it to within a constant multiplicative factor, is NP-complete.
We provide bounds on the disjointness for various code families, including the CSS codes,$d codes and hypergraph codes.
Our results indicate that finding fault-tolerant logical gates for generic quantum error-correcting codes is a computationally challenging task.
arXiv Detail & Related papers (2021-08-10T15:00:20Z) - Engineering fast bias-preserving gates on stabilized cat qubits [64.20602234702581]
bias-preserving gates can significantly reduce resource overhead for fault-tolerant quantum computing.
In this work, we apply a derivative-based leakage suppression technique to overcome non-adiabatic errors.
arXiv Detail & Related papers (2021-05-28T15:20:21Z) - Fault-tolerant Coding for Quantum Communication [71.206200318454]
encode and decode circuits to reliably send messages over many uses of a noisy channel.
For every quantum channel $T$ and every $eps>0$ there exists a threshold $p(epsilon,T)$ for the gate error probability below which rates larger than $C-epsilon$ are fault-tolerantly achievable.
Our results are relevant in communication over large distances, and also on-chip, where distant parts of a quantum computer might need to communicate under higher levels of noise.
arXiv Detail & Related papers (2020-09-15T15:10:50Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.