Quantum computing with realistically noisy devices

By Emanuel Knill. Nature, 2004

1,123 citations recorded by the source corpus.

In theory, quantum computers offer a means of solving problems that would be intractable on conventional computers. Assuming that a quantum computer could be constructed, it would in practice be required to function with noisy devices called ‘gates’. These gates cause decoherence of the fragile quantum states that are central to the computer's operation. The goal of so-called ‘fault-tolerant quantum computing’ is therefore to compute accurately even when the error probability per gate (EPG) is high. Here we report a simple architecture for fault-tolerant quantum computing, providing evidence that accurate quantum computing is possible for EPGs as high as three per cent. Such EPGs have been experimentally demonstrated, but to avoid excessive resource overheads required by the necessary architecture, lower EPGs are needed. Assuming the availability of quantum resources comparable to the digital resources available in today's computers, we show that non-trivial quantum computations at EPGs of as high as one per cent could be implemented.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/5d1ac222556297a0a79eb0cc815a05600a168446

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Near-deterministic quantum teleportation and resource-efficient quantum computation using linear optics and hybrid qubits (2011, background): “In order to realize scalable quantum computation, the amount of noise per operation should be below a fault tolerant threshold [22–24].”
Fault-tolerant quantum computation with constant overhead (2013, background): “Asymptotically, this is a very favorable scaling of overhead (ratio of physical qubits to logical qubits), but in practice the constant factors hidden by the big-O notation are quite large, ranging from hundreds or thousands for the most efficient known protocols to billions for protocols maximally ”
Noise tailoring for scalable quantum computation via randomized compiling (2015, background): “The example with T = Pd that has been implicitly appealed to and described as “toggling the Pauli frame” previously [11] is a special case of the above technique when the hard gates are Clifford gates (which are defined to be the gates that map Pauli operators to Pauli operators under conjugation), ”
Quantum accuracy threshold for concatenated distance-3 codes (2005, background): “Finally we remark that, while our estimate of the quantum accuracy threshold is the best that has so far been rigorously proven, recent studies by Knill have found numerical evidence for a much higher value of the threshold [ 13 ].”
An addressable quantum dot qubit with fault-tolerant control-fidelity. (2014, methodology): “These long coherence times, in particular the dephasing time T ∗ 2 , lead to low control error rates and the high fidelities that will be required for large-scale, fault tolerant quantum computing[7, 8].”
Stim: a fast stabilizer circuit simulator (2021, methodology): “Instead, the noise can be accumulated into a Pauli frame stored alongside the simulation [23].”
An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation (2009, methodology): “There are two advantages to doing so [ 30, 39, 48 ].”
Towards fault-tolerant quantum computing with trapped ions (2008, background): “, it is believed that error thresholds ranging between 10 −4 and 10 −2 will be required—depending on the noise model and the computational overhead for realizing the quantum gate”
Optimal architectures for long distance quantum communication (2015, background): “The second and third generations both use QEC to correct operation errors, with error correction thresholds of approximately 1% 26 .”
Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer (2020, methodology): “These can be commuted to the end of the circuit, in a procedure known as modifying the Pauli frame [124].”
Contextuality supplies the ‘magic’ for quantum computation (2014, neutral): “Forming the exclusivity graph C of {P} and applying the results of refs 31 and 32 identifies the left-hand side of equation (15) as a witness for the contextuality of r.”
Linear optical quantum computing with photonic qubits (2005, methodology): “General fault-tolerant thresholds for quantum computing have been derived by Steane (2003) and Knill (2005), and here we address LOQC specific error correction and fault-tolerant thresholds.”
Quantum computational supremacy (2017, background): “The general theory of quantum fault-tolerance 37,38 allows quantum computations to be protected against a suﬃciently small amount of physically reasonable noise.”
Demonstration of fault-tolerant universal quantum gate operations (2021, result): “Quantum state tomography of the experimentally prepared logical magic state is shown compared with the theoretical values in equation (41) in Fig.”
Quantum error correction for quantum memories (2013, neutral): “We take a small stabilizer code C 6 [defined in Knill (2005)] with parity checks X 1 X 4 X 5 X 6 , X 1 X 2 X 3 X 6 , Z 1 Z 4 Z 5 Z 6 , and Z 1 Z 2 Z 3 Z 6 acting on six qubits.”
Performance and structure of single-mode bosonic codes (2017, methodology): “In other words, unlike the use of Pauli frames [102], we cannot just record the value of |mx | and keep the quantum information in this error space with a lower value for |mx |: Subsequent dephasing errors would lead to more laddering up and down in the spin space so the QEC conditions would no long”