Fault-tolerant quantum computing – from theory to practice

We work on various aspects of quantum error correction and fault tolerance. Our recent direction has been on reducing the gap between theoretical quantum error correction and fault tolerance ideas and their implementation in experiments. With the rapid development of quantum computing devices, we are beginning to have an inkling of what a quantum computer might look like, and the practical obstacles, to do with noise and scalability, are taking on concrete shapes. This is thus the right time to re-examine the often generic and abstract theoretical proposals for noise removal, in the light of recent experiments, for progress towards large-scale, useful quantum devices.

Below, we highlight some recent projects within the group.

Fault-tolerant embedding of circuits via  swap gates

HK Ng, with Entropica Labs (arXiv:2406.17044)

In near-term quantum devices, qubit connectivity remains limited by architectural constraints. A computational circuit with given connectivity requirements for multi-qubit gates has to be embedded in physical hardware with fixed connectivity. Long-distance gates have to be done by first routing the information together.

The simplest routing strategy uses swap gates to swap information carried by two unconnected qubits to connected ones. Ideal SWAPs just permute qubits; real SWAPs, however, can cause simultaneous errors on the qubits involved and spread errors across the circuit. General swap schemes can thus destroy fault-tolerant features carefully designed into the original circuit.

Here, we show that, by a simple restriction of allowed swap moves, we can embed an arbitrary circuit in a fault-tolerant manner.The embedded circuit will be noisier, but we show, in the examples of surface codes on heavy-hexagonal and hexagonal lattices, that the noise deterioration is not severe.

Our approach is easily incorporated into existing circuit compilation algorithms, and offers an immediate solution to implementing circuits on current hardware in a fault-tolerant manner.

Circuit-level fault tolerance of cat codes

LDH My, S Qin, and HK Ng, Quantum 9, 1810 (2025) [arXiv:2406.04157]

Bosonic codes, which encode quantum information in the infinite Hilbert space of a harmonic oscillator, are viable alternatives to conventional qubit codes. The family of rotationally symmetric bosonic (RSB) codesis capable of correcting for both photon loss and phase (i.e., rotation) errors, offering robustness against arbitrary physical errors at the base layer of encoding.

We extend the formalism of fault tolerance to RSB codes, and assess the performance of previously proposed teleportation-based error correction (EC) circuits [Grimsmo et al., 2020] for cat codes (a type of RSB codes), accounting for circuit-level noise, i.e., where every physical component of the circuit can be faulty. We find that the noise threshold is significantly worse than found in previous more idealised studies. Through our analysis, we identify crucial circuit settings, such as the choice of code order, the optimal waiting time between EC cycles, and the addition of squeezing to the code states, that improve the noise threshold by an order of magnitude, restoring the noise requirement to a level achievable with near-term quantum hardware.

Error correction in silicon-based spin-resonator systems

M Ma and HK Ng, with the groups of TS Koh & Bent Weber in NTU, and J Goh in A*STAR

Recent advances in coupling quantum-dots to superconducting (SC) resonatorsenable long-range gates between quantum-dot qubits, and present the intriguing possibility of implementing circuit-QED ideas in quantum-dot–resonator systems. We study how arbitrary bosonic resonator states can be prepared using a double-quantum-dot system as control, and investigate how computational operations can be performed on information carried by bosonic codes.

Double-quantum-dot—resonator system. Recent advances in coupling quantum-dots to superconducting (SC) resonatorsenable long-range gates between quantum-dot qubits, and present the intriguing possibility of implementing circuit-QED ideas in quantum-dot–resonator systems. We study how arbitrary bosonic resonator states can be prepared using a double-quantum-dot system as control, and investigate how computational operations can be performed on information carried by bosonic codes.

Simulating general noise nearly as cheaply as Pauli noise

M Myers II and Hui Khoon Ng (with various past group members)

Stabilizer simulation of Clifford quantum circuits – error-correction circuits, Clifford subroutines, etc. – on classical computers has played a central role in our understanding of circuit performance. The stabilizer description, however, restricts the accessible noise types one can incorporate into the simulation to only Pauli-type noise. More general noise, including coherent (or unitary) errors, are, however, known to have much more severe impact on circuit performance than Pauli noise; yet, such effects have been difficult to reproduce, much less investigate, in numerical simulations.

Here, through quasiprobability methods and variance-reduction techniques from importance sampling, we show how general noise can be simulated within the stabilizer formalism in reasonable time, opening the door to beyond-Pauli understanding of Clifford circuit performance. Among other examples, we present numerical results for the performance of the popular surface codes under circuit-level general noise, recovering the significant deterioration in the fault-tolerant threshold predicted by theoretical bounds for coherent errors but never before seen in numerical studies.

Noise-adapted fault tolerance

LDH My and HK Ng, with P Mandayam (IIT Madras) and A Jayashankar (TCG CREST)

Standard fault-tolerant (FT) schemes are designed with codes that correct arbitrary errors and assume no knowledge of the physical noise. Noise-adapted FT schemes, tailor-made to deal with the dominant noise in the device, may have lower resource overheads and less stringent thresholds. Here, we develop a full fault-tolerant quantum computing protocol for amplitude-damping (AD) noise, using Bacon-Shor codes. We describe a universal set of fault-tolerant encoded gadgets and estimate the noise thresholds below which our scheme leads to more accurate computation. This is the first example of a full FT scheme adapted to non-Pauli-type noise.

Our earlier article [PR Research 4, 023034 (2022)] details the protocol for the smallest instance of the 4-qubit code; the followup work [PR Research 7, 033275 (2025)] gives the generalization to higher-distance Bacon-Shor codes.

Reinforcement learning for real-time context-aware gate calibration

A Strauss, A Chatterjee, L Voss, and HK Ng

Quantum control has enabled significant improvements in gate fidelities. However, most methods do not provide dynamical and contextual (i.e., circuit-dependent) error robustness, critical for achieving physical error rates below the fault-tolerance threshold. Here, we present:
(1) a gate calibration procedure based on reinforcement learning (RL) tosuppress errors arising from a large collection of circuit contexts;
(2) a concrete use case showing how contextual and dynamical gate calibrations can successfully increase quantum circuit fidelity.​

Context-aware calibration: Agent is trained to learn how to cancel complex classical crosstalk noise over a layer of single-qubit gates by modifying the calibration of subsequent two-qubit gates.