Quantum error correction (QEC) protects quantum information by encoding it redundantly, repeatedly measuring error syndromes and correcting the errors they reveal [1, 2, 3]. It works only if the physical operations are good enough, below the code’s threshold, and if errors stay local and uncorrelated. Every QEC cycle is a sequence of control tasks — entangling gates, measurements, resets, real-time decisions — so the quality of control decides whether encoding helps at all.

The control stack of a QEC cycle

  • Gates. The surface code needs only nearest-neighbour gates and tolerates errors near 1% per step [4]. Superconducting and neutral-atom processors have reached this regime [5, 6]. See Quantum gate synthesis.
  • Measurement. Syndrome readout must be fast and accurate, and must not disturb neighbouring qubits. Careful design of superconducting dispersive readout reached 98.25% fidelity in 48 ns [7]. Five qubits were read out in one multiplexed channel with 80 ns pulses [8]. Shaped measurement pulses empty the readout resonator quickly so that the next cycle can start [9].
  • Reset. Ancillas must return to the ground state after each measurement. An all-microwave protocol resets a transmon in under 500 ns with 0.2% residual excitation, without feedback [10].
  • Leakage. Population in non-computational levels is long-lived and mobile, which makes errors correlated in space and time. A reset protocol that removes leakage from all relevant levels lowered logical error rates and stabilized their suppression with system size [11]. See DRAG & leakage suppression.
  • Real-time decoding. Corrections must be decided faster than errors accumulate. Increasing the surface-code distance first improved logical performance modestly [12]. Later, distance-5 and distance-7 memories ran below threshold, suppressing the logical error by a factor of 2.14 per distance step and outliving their best physical qubit, with a real-time decoder [13]. Reconfigurable atom arrays have run logical circuits with up to 280 physical qubits [14]. See Control electronics & software stacks.

Optimizing codes and recoveries

Standard codes correct a fixed set of errors exactly. If the noise is known, encoding and recovery can be optimized for it, as a control problem on quantum channels. Iterative algorithms find optimal encodings and decodings for a given channel [15]. The optimal recovery for a given code is a semidefinite program [16]. Optimizing encoding and recovery together can make them robust to uncertainty in the noise [17]. See QCPOP & polynomial optimization for related convex methods.

QEC can also be continuous. Weak measurements and Hamiltonian feedback protect states between discrete correction cycles [18]. Reinforcement learning can discover feedback strategies of this kind [19], and a learning agent has acted in real time on a superconducting qubit [20]. See Measurement-based feedback and Reinforcement & machine learning for control.

Fault-tolerant operations

The ancillas used to detect errors are often noisier than the encoded qubit, and their errors must not spread to it.

  • Error detection can be made fault-tolerant to ancilla errors by using higher ancilla levels [21]. Gates can be made error-transparent, keeping the device’s tolerance to errors that occur before or during them [22]. On a cavity-encoded qubit, ancilla-induced errors were corrected in real time during the gate [23].
  • Noise bias is a resource. Cat qubits stabilized by two-photon dissipation show an exponential suppression of bit flips as the cat grows, at the price of a linear increase of phase flips [24]. Bias-preserving CX gates on such qubits raise the fault-tolerance threshold and reduce overhead [25].

Bosonic codes

A single oscillator can host an error-correctable qubit: cat codes [26, 27] or grid (GKP) codes [28, 29]. A GKP memory with parameters tuned by reinforcement learning outlived the best of its physical components by a factor of 2.27 [30]. Logical operations on such codes are designed by numerical optimal control of the cavity–ancilla system [31] or built from sequences of simpler operations [32]. See Bosonic & continuous-variable control and Reservoir engineering & dissipative preparation.

Limitations

  • Physical gate fidelities are a proxy. What matters is the logical error rate, which depends on correlations, leakage and the decoder, and these are rarely part of the control objective.
  • A large code needs thousands of calibrated pulses that drift. Calibration and recalibration have to be automated.
  • Feedback latency is set by electronics and decoders, not by the quantum hardware alone.