Universal Fault-Tolerant Quantum Computing with Stabiliser Codes
- URL: http://arxiv.org/abs/2012.05260v2
- Date: Thu, 20 May 2021 03:55:17 GMT
- Title: Universal Fault-Tolerant Quantum Computing with Stabiliser Codes
- Authors: Paul Webster, Michael Vasmer, Thomas R. Scruby, and Stephen D.
Bartlett
- Abstract summary: Quantum computers should have both universal and fault-tolerant logic gates.
A number of no-go theorems constrain the ways in which a set of fault-tolerant logic gates can be universal.
We present a general framework for universal fault-tolerant logic with stabiliser codes.
We show how non-unitary implementations of logic gates provide a general approach to circumvent the no-go theorem.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The quantum logic gates used in the design of a quantum computer should be
both universal, meaning arbitrary quantum computations can be performed, and
fault-tolerant, meaning the gates keep errors from cascading out of control. A
number of no-go theorems constrain the ways in which a set of fault-tolerant
logic gates can be universal. These theorems are very restrictive, and
conventional wisdom holds that a universal fault-tolerant logic gate set cannot
be implemented natively, requiring us to use costly distillation procedures for
quantum computation. Here, we present a general framework for universal
fault-tolerant logic with stabiliser codes, together with a no-go theorem that
reveals the very broad conditions constraining such gate sets. Our theorem
applies to a wide range of stabiliser code families, including concatenated
codes and conventional topological stabiliser codes such as the surface code.
The broad applicability of our no-go theorem provides a new perspective on how
the constraints on universal fault-tolerant gate sets can be overcome. In
particular, we show how non-unitary implementations of logic gates provide a
general approach to circumvent the no-go theorem, and we present a rich
landscape of constructions for logic gate sets that are both universal and
fault-tolerant. That is, rather than restricting what is possible, our no-go
theorem provides a signpost to guide us to new, efficient architectures for
fault-tolerant quantum computing.
Related papers
- Universal transversal gates [0.0]
A long-standing challenge in quantum error correction is the infeasibility of universal gates, as shown by the Eastin-Knill theorem.
We obtain a necessary and sufficient condition for a quantum code to have universal gates and show that the Eastin-Knill no-go result is a special case that does not hold for a general error model.
arXiv Detail & Related papers (2024-10-09T16:34:47Z) - Demonstrating a universal logical gate set on a superconducting quantum processor [13.391691829693226]
We experimentally implement a logical CNOT gate along with arbitrary single-qubit rotation gates on distance-2 surface codes using the superconducting quantum processor Wuitkong.
We fault-tolerantly prepare logical Bell states and observe a violation of CHSH inequality, confirming the entanglement between logical qubits.
The demonstration of a universal logical gate set and the entangled logical states highlights significant aspects of FTQC on superconducting quantum processors.
arXiv Detail & Related papers (2024-05-15T02:04:34Z) - Experimental fault-tolerant code switching [1.9088985324817254]
We present the first experimental implementation of fault-tolerant code switching between two codes.
We construct logical circuits and prepare 12 different logical states which are not accessible in a fault-tolerant way within a single code.
Our results experimentally open up a new route towards deterministic control over logical qubits with low auxiliary qubit overhead.
arXiv Detail & Related papers (2024-03-20T16:40:57Z) - Toward Constructing a Continuous Logical Operator for Error-Corrected
Quantum Sensing [0.0]
Operations on logical qubits are only performed through universal gate sets consisting of finite-sized gates such as Clifford+T.
The Eastin-Knill theorem prevents a continuous signal from being both fault tolerant to local errors and transverse.
A protocol to design continuous logical z-rotations is proposed and applied to the Steane Code.
arXiv Detail & Related papers (2023-04-30T18:22:34Z) - 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) - Logical blocks for fault-tolerant topological quantum computation [55.41644538483948]
We present a framework for universal fault-tolerant logic motivated by the need for platform-independent logical gate definitions.
We explore novel schemes for universal logic that improve resource overheads.
Motivated by the favorable logical error rates for boundaryless computation, we introduce a novel computational scheme.
arXiv Detail & Related papers (2021-12-22T19:00:03Z) - 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) - Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems.
By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
arXiv Detail & Related papers (2021-08-03T17:49:09Z) - 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) - Using Quantum Metrological Bounds in Quantum Error Correction: A Simple
Proof of the Approximate Eastin-Knill Theorem [77.34726150561087]
We present a proof of the approximate Eastin-Knill theorem, which connects the quality of a quantum error-correcting code with its ability to achieve a universal set of logical gates.
Our derivation employs powerful bounds on the quantum Fisher information in generic quantum metrological protocols.
arXiv Detail & Related papers (2020-04-24T17:58:10Z)
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.