Quantum information processing has the potential to substantially enhance how we learn from physical experiments, but coupling a quantum processor to an experimental sample introduces noise that can exponentially degrade learning even when the processor itself is fault-tolerant. In this work, we show that fault tolerance can nevertheless be leveraged to recover exponential speedups by embedding the unknown system into an arbitrarily high-distance quantum code with only constant error overhead and running a fault-tolerant learning algorithm. Using this $\textit{quantum uploading}$ procedure, we prove that both classical shadow tomography and the estimation of cubic observables can be performed exponentially faster than by any adaptive strategy that does not immediately upload the state into encoded memory. These separations hold even when the uploading stage is substantially noisier than the bare experimental interface. To prove them, we introduce the Heisenberg learning tree method, a flexible tool for obtaining learning lower bounds when the limited resource is not quantum replicas but an experimentally motivated constraint such as noise. We numerically illustrate the speedups in an astronomical imaging application, where quantum processing of individual uploaded photons locates an exoplanet obscured by a bright star using orders of magnitude fewer shots than unencoded baselines. Our results establish fault-tolerant quantum computation as a valuable tool for learning from quantum experiments.
Quantum information processing has the potential to substantially enhance how we learn from physical experiments, but coupling a quantum processor to an experimental sample introduces noise that can exponentially degrade learning even when the processor itself is fault-tolerant. In this work, we show that fault tolerance can nevertheless be leveraged to recover exponential speedups by embedding the unknown system into an arbitrarily high-distance quantum code with only constant error overhead and running a fault-tolerant learning algorithm. Using this quantum uploading procedure, we prove that both classical shadow tomography and the estimation of cubic observables can be performed exponentially faster than by any adaptive strategy that does not immediately upload the state into encoded memory. These separations hold even when the uploading stage is substantially noisier than the bare experimental interface. To prove them, we introduce the Heisenberg learning tree method, a flexible tool for obtaining learning lower bounds when the limited resource is not quantum replicas but an experimentally motivated constraint such as noise. We numerically illustrate the speedups in an astronomical imaging application, where quantum processing of individual uploaded photons locates an exoplanet obscured by a bright star using orders of magnitude fewer shots than unencoded baselines. Our results establish fault-tolerant quantum computation as a valuable tool for learning from quantum experiments.
We develop a framework for learning from noisy quantum experiments in which fault-tolerant devices access uncharacterized systems through noisy couplings. Introducing the complexity class NBQP ("noisy BQP''), we model noisy fault-tolerant quantum computers that cannot generally error-correct the oracle systems they query. Using this class, we prove that while noise can eliminate the exponential quantum learning advantages of unphysical, noiseless learners, a superpolynomial gap remains between NISQ and fault-tolerant devices. Turning to canonical learning tasks in noisy settings, we find that the exponential two-copy advantage for purity testing collapses under local depolarizing noise. Nevertheless, we identify a setting motivated by AdS/CFT in which noise-resilient physical structure restores this quantum learning advantage. We then analyze noisy Pauli shadow tomography, deriving lower bounds characterizing how instance size, quantum memory and noise jointly control sample complexity, and design algorithms with parametrically matching scalings. We study similar tradeoffs in quantum metrology, and show that the Heisenberg-limited sensitivity of existing error-correction-based protocols persists only up to a timescale inverse-polynomial in the error rate per probe qubit. Together, our results demonstrate that the primitives underlying quantum-enhanced experiments are fundamentally fragile to noise, and that realizing meaningful quantum advantages in future experiments will require interfacing noise-robust physical properties with available algorithmic techniques.
Quantum computation holds the promise of solving certain complex problems exponentially faster than classical computers. However, the high prevalent noise in current quantum devices impedes the accurate execution of even basic algorithms. This can be remedied by protecting quantum information with a quantum error-correcting code, where the logical information of an algorithmic qubit is spread across multiple physical qubits. Individual quantum errors are then located and corrected by the fault-tolerant measurement of multi-qubit stabilizer operators (parity checks). Unfortunately, error correction and fault tolerance both impose large demands on the qubit overhead: hundreds to thousands of physical qubits per logical qubit.
We reduce the spacetime cost of fault tolerance by redesigning key building blocks of an error-corrected quantum computer. First, we develop a combinatorial proof with flag fault tolerance that exponentially reduces the extra qubits needed to measure a stabilizer of any size, while tolerating one fault. We leverage these proofs to then design state preparation circuits for the Steane and Golay codes with 100% yield. Next, we improve error correction on a planar layout by showing that a distance-four code encoding six logical qubits protects information as well as the distance-five surface code, using one-tenth as many physical qubits. Finally, we optimize the time overhead of logical gates in surface code quantum computers by protecting measurement results with a classical code, cutting computation time by a factor of two to six. Our hardware-agnostic optimizations of fault tolerance overheads thus suggest new routes to advance the timeline of error-free quantum computing.
Learning unknown noise processes in quantum systems reveals their physical origin and informs error suppression, mitigation, and correction. Characterizing a general quantum process requires exponentially many parameters inferred from noncommuting measurements. Because these measurements cannot be performed simultaneously, the sample complexity grows exponentially. For Pauli channels, quantum memory and entangling operations can transform this task into measurements of commuting observables, reducing complexity exponentially. However, noise in these resources increases the overhead, leaving open whether any advantage remains in realistic devices. Here, we introduce error-mitigated entanglement-enhanced learning, analyze it theoretically, and demonstrate it experimentally. We quantify the noise-induced overhead, perform hypothesis testing with up to 64 qubits, and learn intrinsic noise in parallel-gate layers using up to 16 qubits of a superconducting processor. We show that noisy quantum memory provides a learning advantage, with a current experimental overhead of 1.33 ± 0.05 per qubit, below the no-entanglement lower bound of 2. The authors show that entanglement with noisy quantum memory can significantly speed up learning of quantum processes. With error mitigation, their method characterizes quantum noise at scale and outperforms entanglement-free approaches.
Data quality is an important factor in quantum computation, since quantum algorithms need high quality representations in order to run with low error rates. In addition, quantum algorithms benefit from different types of quantum data encodings that are tailored to specific applications. In order to improve data quality while maintaining data variety, this work applies fault tolerance techniques specific to different types of data encodings. Thus, fault tolerance improvements, aimed at reducing both noise and bias errors, are applied to two types of data encodings. The first type, angle encoding, benefits from an enhanced dynamic range representation. The second type, distribution encoding, is enhanced through the use of error correcting states. Our experiments encode classical data as a quantum state, apply noise simulations, and provide error analyses on the decoded data. Experimental results are assessed by comparing the post-processed output statistics to those of the original encodings and show improved accuracy through the inclusion of fault tolerance methods.
Quantum computation has the promise to solve problems that are not efficiently solvable by classical means. Yet, due to the fragile nature of quantum states, it is unavoidable that quantum systems are subject to decoherence, gate imperfections, and measurement errors. These problems stand as a major roadblock to the construction of large-scale fault-tolerant quantum computers. Conventional quantum error correction (QEC) codes, such as the surface code or Shor code, need to use an extensive amount of redundancy and classical control, which can be both computationally expensive and challenging to scale. In this context, we propose to investigate the use of machine learning (ML) techniques by realizing on-line identification, localization and correction of these quantum errors for fault-tolerant quantum computation by means of fault-tolerant quantum computing processes. Our model introduces a hybrids ML-QEC architecture that combines classical neural networks and decision-tree classifiers with quantum syndrome decoding. These models are trained on error syndromes produced using the approximation of common noise models (for example, depolarizing noise, dephasing and amplitude damping), simulated under different QEC schemes. The machine learning methods are trained with quantum error patterns and have a capability to rapidly infer where errors are likely to occur, as well as recommend correction operations with high confidence. As a result, the system reduces dramatically the delay and computational costs when compared to conventional decoding methods. There is also a self-adaptive learning module in the work, which recommences training on fresh quantum error distributions, meaning the system can adapt to changes in the environment (and also the decay of the hardware) as time progresses. The study further carries out ML predictions inside a real-time loop and cross-checks them with quantum state tomography and entanglement fidelity such as indicators. Experimental characterization on dedicated devices as well as noise models show that our ML-enhanced decoders reach higher fidelity and lower logical error rates compared to baseline decoders, especially in non-uniform or time-dependent noise. This work is a significant stride towards realizing practical fault-tolerant quantum computation by combining quantum error correction with the versatility and scalability of machine learning. With intelligent models to dictate learning, our proposed framework is able to eliminate a lot of trial-and-error manual processes in the conventional heuristic-based approach, and points to a potential path to achieve scalable quantum information processing platforms.
Quantum computation promises to revolutionize information processing by exploiting superposition and entanglement, enabling applications such as quantum simulation, combinatorial optimization, and secure quantum communication. Beyond individual processors, the quantum internet aims to connect quantum nodes through entanglement distribution, enabling distributed computation. However, quantum states are fragile: environmental interactions, imperfect gate operations, and measurement errors can quickly degrade encoded information. Reliable quantum computation therefore requires carefully designed quantum error-correcting codes and fault-tolerant protocols. Unlike classical redundancy schemes, quantum error correction must preserve delicate phase relationships and relies on indirect error detection through syndrome extraction with ancillary qubits, enabling error identification without collapsing encoded states. Topological codes, in particular, emerged early as the preferred choice for many architectures due to their planar structure, local interactions, and natural support for fault-tolerant logical operations. Color codes, for instance, allow transversal implementation of all Clifford gates, whereas non-Clifford operations require magic-state injection. More recent constructions, including quantum low-density parity-check codes, offer higher encoding rates and reduced resource overhead, but require long-range qubit connectivity and more complex protocols. Despite experimental progress, several challenges remain. Many platforms exhibit biased noise, motivating codes that exploit channel asymmetry. Real-time decoding remains a critical bottleneck, as fault-tolerant computation requires low-latency processing of rapidly generated syndrome data. Fault-tolerant logical state initialization also remains resource-intensive and scales poorly with code distance. Addressing these challenges, this thesis develops a unified framework spanning theory and experiment. It provides precise performance analysis of quantum error-correcting codes in the low physical error-rate regime, introduces codes tailored to biased noise, develops fast low-complexity decoding algorithms for real-time operation, and presents modular and efficient protocols for fault-tolerant state preparation of CSS codes. The latter is demonstrated experimentally through the preparation of a logical zero state of the Golay code on the Quantinuum H2 trapped-ion quantum computer.