Noise, Error Mitigation, and Fault Tolerance

Introduction

A quantum computer is not an ideal collection of perfectly controlled qubits. Physical qubits interact with their environment, control pulses are imperfect, measurement devices misclassify states, and finite experimental data produce statistical uncertainty. These effects are collectively called noise or errors. Managing them is one of the central engineering challenges of quantum computing.

Noise is especially damaging because quantum information is encoded in fragile amplitudes and relative phases. An error can change a computational-basis state, alter interference, destroy entanglement, or bias a measured result. Unlike classical bits, qubits cannot simply be copied for backup because of the no-cloning theorem. Quantum computing therefore requires specialized methods for characterizing, reducing, mitigating, and correcting errors.

This chapter distinguishes physical errors from statistical uncertainty, introduces basic noise models, explains practical error-mitigation methods, and develops the central ideas of quantum error correction and fault-tolerant computation.

Learning Objectives

After studying this chapter, you should be able to:

• distinguish decoherence, gate, readout, and sampling errors;
• describe common quantum noise channels and their effects;
• calculate simple error probabilities and sampling uncertainty;
• explain calibration, zero-noise extrapolation, probabilistic error cancellation, and measurement mitigation;
• describe quantum error-correcting codes, logical qubits, syndromes, and code distance;
• explain error thresholds and the requirements of fault-tolerant quantum computing;
• evaluate the limitations and practical trade-offs of mitigation and correction methods.

1. What Is a Quantum Error?

An ideal quantum circuit applies a sequence of unitary gates to an initial state and then measures selected qubits. A real experiment instead implements an imperfect quantum channel. If the intended operation is U but the physical operation is noisy, the actual transformation may be represented as a completely positive trace-preserving map, written conceptually as:

Here ρ is the density matrix describing the input state, 𝓔 is the physical noise process, and ρ′ is the resulting state. For an ideal operation, 𝓔(ρ) = UρU†. The density-matrix description is necessary because noise may produce mixed states, entanglement with an uncontrolled environment, or classical uncertainty.

A useful distinction is between physical error and estimation error. Physical error changes the state or operation. Estimation error occurs because a finite number of circuit executions, called shots, is used to estimate probabilities or expectation values. More shots reduce sampling uncertainty but do not automatically remove hardware noise.

1.1 Decoherence

Decoherence is the loss of quantum coherence caused by interaction with uncontrolled environmental degrees of freedom. Two characteristic times are commonly used:

• T₁, the energy-relaxation time, describes decay from |1⟩ toward |0⟩.
• T₂, the dephasing time, describes decay of phase coherence.

For many systems, T₂ cannot exceed approximately twice T₁, although the exact relationship depends on the mechanisms present. If pure dephasing has characteristic time Tφ, a common relation is:

Times are measured in units such as microseconds or milliseconds. This relation assumes Markovian exponential relaxation and dephasing and is a model rather than a universal law.

For energy relaxation, the excited-state population often follows:

where P₁(0) is the initial excited-state population and t is elapsed time. For pure exponential dephasing, an off-diagonal density-matrix element may decay approximately as:

The first process changes populations; the second primarily destroys phase information. In practice, both can occur simultaneously.

1.2 Gate and Control Errors

Gate errors arise when the implemented operation differs from the intended operation. Sources include inaccurate pulse amplitude, frequency detuning, phase error, pulse distortion, crosstalk between qubits, leakage outside the computational subspace, and unwanted coupling to neighboring devices.

A gate may be described by an average fidelity, but fidelity alone does not fully characterize the error. Two gates can have the same average fidelity while producing very different error patterns. Coherent over-rotations, for example, can accumulate systematically, whereas stochastic errors may behave more like random fluctuations.

If a rotation intended to be Rₓ(θ) is implemented as Rₓ(θ + δ), then δ is a coherent angle error. Repeating the operation can produce a systematic phase or population bias. Randomized compiling and carefully designed pulse sequences can sometimes convert coherent errors into more statistically manageable stochastic errors.

1.3 Readout Errors

Readout error occurs when the classical result reported by the measurement apparatus differs from the actual computational-basis state. For one qubit, a simple assignment matrix is:

Here p₀₁ is the probability of reporting 1 when the state is 0, and p₁₀ is the probability of reporting 0 when the state is 1. The matrix convention assumes probability vectors are columns and that the first row corresponds to reported 0.

For multiple qubits, a complete assignment matrix has 2ⁿ × 2ⁿ entries for n qubits. Direct calibration becomes expensive as n increases, so practical methods often use tensor-product approximations or locality assumptions.

1.4 Sampling Error

Suppose a measurement has probability p of producing outcome 1 and is repeated N independent times. The observed frequency p̂ is an estimator of p. Its standard deviation is:

This is the binomial standard deviation and assumes independent, identically distributed shots. The largest value occurs near p = 1/2, giving the conservative bound σ(p̂) ≤ 1/(2√N). Sampling error decreases only as the inverse square root of the number of shots. Consequently, reducing statistical uncertainty by a factor of 10 requires approximately 100 times as many shots.

2. Basic Noise Models

Noise models are simplified mathematical descriptions used for analysis, simulation, calibration, and algorithm design. A model is useful only within the conditions for which its assumptions are reasonable.

2.1 Bit-Flip and Phase-Flip Channels

A bit-flip channel applies the Pauli X operation with probability p and does nothing with probability 1 − p:

A phase-flip channel similarly applies Z with probability p:

A bit flip changes computational-basis values. A phase flip may not change measurement probabilities in the Z basis, but it changes interference and becomes observable after suitable basis changes.

2.2 Depolarizing Noise

A single-qubit depolarizing model is often written as:

In this parameterization, p is the total probability of applying one of the three nonidentity Pauli errors, with equal probability p/3 for each. Other literature uses p to denote a different shrinkage parameter, so the definition must always be checked before comparing results.

2.3 Amplitude Damping

Amplitude damping models energy relaxation. With relaxation probability γ during an operation or waiting period, the channel has Kraus operators:

and transforms the state according to:

The operators satisfy E₀†E₀ + E₁†E₁ = I, ensuring preservation of total probability. This model is non-unital: it tends to drive |1⟩ toward |0⟩ rather than mixing states symmetrically.

2.4 Correlated and Non-Markovian Noise

Simple models often assume independent errors at each gate and no memory. Real devices may violate these assumptions. Crosstalk creates correlations between qubits, while drift causes error rates to vary over time. Non-Markovian noise depends on previous interactions and may not be represented accurately by independent channels.

Correlations matter because many error-correction analyses assume locality and approximate independence. A low average error rate does not guarantee reliable computation if rare correlated events affect many qubits simultaneously.

3. Measuring and Characterizing Noise

Before improving a quantum device, engineers must determine what errors occur and how frequently. Important tools include:

• T₁ and T₂ measurements, which characterize relaxation and coherence;
• randomized benchmarking, which estimates average performance of gate sequences under specified assumptions;
• cycle benchmarking, which evaluates repeated implementations of a circuit cycle;
• process or gate-set tomography, which attempts to reconstruct operations but may require substantial data and careful statistical analysis;
• readout calibration, in which known basis states are prepared and measured repeatedly;
• noise spectroscopy, which investigates frequency-dependent environmental fluctuations.

No single metric is sufficient. A device may have good average gate fidelity but poor performance on a particular algorithm because of leakage, crosstalk, connectivity constraints, or coherent errors.

4. Error Mitigation

Error mitigation seeks to estimate the result that would have been obtained without noise, while operating on noisy hardware. It does not generally create a protected logical qubit and does not remove errors from each individual circuit execution. Instead, it uses additional experiments, classical computation, or carefully chosen circuit transformations.

4.1 Calibration and Circuit-Level Best Practice

The least expensive mitigation begins with good experimental practice:

1. calibrate qubit frequencies, pulse amplitudes, readout, and gate parameters;
2. minimize circuit depth and unnecessary qubit movement;
3. schedule operations to reduce idle time and crosstalk;
4. select qubits and couplers using recent calibration data;
5. repeat calibration checks because devices drift;
6. compare results with simulation and simple control experiments.

These actions reduce errors but cannot eliminate fundamental decoherence or all control imperfections.

4.2 Measurement-Error Mitigation

If the measured probability vector q is related to the ideal probability vector p by q = Mp, one may estimate p by applying an inverse or regularized inverse of M:

This equation assumes M is known accurately and invertible. Because statistical fluctuations can be greatly amplified by inversion, practical methods may use constrained or regularized estimation. Corrected probabilities can also become negative if an unconstrained inverse is applied to noisy data; such values are mathematical estimates, not physical probabilities, and require careful interpretation.

For a single qubit with symmetric assignment error r, the matrix is:

It is invertible when r ≠ 1/2. As r approaches 1/2, the determinant approaches zero and correction becomes unstable because the measurement contains very little information about the original state.

4.3 Zero-Noise Extrapolation

Zero-noise extrapolation estimates an observable at zero noise by evaluating it at several increased noise levels. Noise can be increased by stretching pulses, inserting identity-equivalent gate sequences, or other hardware-compatible transformations. If E(λ) is the measured expectation at noise scale λ and a chosen model is linear near λ = 0, a two-point extrapolation is:

Here λ₁ and λ₂ are distinct positive scale factors. The formula assumes the chosen noise-scaling procedure is sufficiently controlled and that E(λ) behaves approximately linearly over the interval. Higher-order fits may model curvature but require more data and can amplify statistical noise.

4.4 Probabilistic Error Cancellation

Probabilistic error cancellation represents an ideal operation as a signed combination of experimentally implementable noisy operations. Results from these operations are combined with possibly negative weights. In principle, this can cancel bias, but the sampling overhead can grow rapidly with circuit size and noise strength. It is therefore most useful for relatively small circuits and carefully characterized noise.

4.5 Symmetry Verification and Post-Selection

Many algorithms preserve a known symmetry, such as a fixed particle number or a stabilizer condition. Measurements violating that condition can be discarded or used to correct an estimate. This is called symmetry verification or post-selection. It can reduce certain errors but changes the sampling distribution and may discard a large fraction of data. It is valid only when the assumed symmetry genuinely applies to the ideal computation.

5. Quantum Error Correction

Error mitigation estimates ideal results from noisy data. Quantum error correction (QEC) instead encodes one logical qubit into multiple physical qubits so that errors can be detected and corrected without directly measuring the encoded quantum information.

5.1 The Encoding Principle

An error-correcting code defines a protected subspace called the codespace. Logical states |0_L⟩ and |1_L⟩ are distinct physical states involving several qubits. Ancillary qubits interact with the data qubits to measure syndromes—information about which error occurred—without revealing the logical amplitudes.

For example, a three-qubit bit-flip repetition code uses:

An arbitrary logical state α|0_L⟩ + β|1_L⟩ becomes α|000⟩ + β|111⟩. If one bit flip occurs, the majority value identifies the corrupted physical qubit. This code corrects one bit flip but does not protect against phase flips. It also illustrates why simply copying an unknown qubit is not allowed: the encoding is an entangling transformation, not independent cloning.

5.2 Stabilizers and Syndromes

Modern QEC commonly uses stabilizer codes. A stabilizer is an operator S for which valid code states satisfy:

Measuring stabilizer eigenvalues yields +1 or −1 syndrome information. The syndrome indicates whether the state has left the codespace and helps identify a recovery operation. It does not, ideally, reveal the logical coefficients α and β.

A code must distinguish errors that it intends to correct. If Eᵢ and Eⱼ are correctable errors and P is the projector onto the codespace, the quantum error-correction condition is:

where cᵢⱼ are scalar coefficients. This condition means that correctable errors do not leave distinguishable information about the logical state within the codespace. The equation applies to the selected set of errors and assumes an appropriate encoding and recovery operation.

5.3 Code Distance and Logical Errors

The distance d of a code is the minimum weight of a physical Pauli operator that acts nontrivially on the logical information while preserving the codespace. A code with distance d can correct up to:

arbitrary errors, where t is the number of correctable errors and ⌊·⌋ denotes the floor function. The statement assumes errors are within the code’s correction model and that recovery is implemented correctly.

Increasing d generally reduces the logical error rate when physical error rates are below threshold, but it also requires more qubits, more gates, more syndrome measurements, and more classical decoding.

5.4 Surface Codes and Other Architectures

The surface code is prominent because it uses local interactions on a two-dimensional layout and has relatively high tolerance to certain local error models. It encodes logical information in a lattice of data and measurement qubits. Repeated stabilizer measurements generate a history of syndromes that a classical decoder interprets.

Other codes include color codes, bosonic codes, concatenated codes, subsystem codes, and low-density parity-check quantum codes. Each involves trade-offs among physical connectivity, qubit overhead, gate requirements, decoding complexity, and tolerance to specific noise types.

6. Fault-Tolerant Quantum Computing

A computation is fault tolerant when errors occurring during state preparation, gates, measurement, storage, and error correction are prevented from causing uncontrolled logical failure. Fault tolerance is stronger than merely encoding the initial data: the entire computation, including syndrome extraction and recovery, must be protected.

6.1 The Threshold Concept

The threshold theorem states, informally, that under suitable assumptions—such as sufficiently local and weak noise, reliable state preparation and measurement, and an appropriate fault-tolerant construction—an arbitrarily long computation can be performed with bounded accuracy if the physical error rate is below a threshold p_th. The exact threshold depends on the code, architecture, decoder, noise model, and definition of error rate.

A simplified scaling model is:

Here p is a representative physical error rate, p_L is an estimated logical error rate per operation, d is code distance, and A is a hardware- and decoder-dependent constant. This is an illustrative asymptotic model, not a universal formula. Near threshold, finite-size effects and correlated errors can make the approximation inaccurate.

The central engineering requirement is not merely p < p_th. There must be sufficient margin below threshold to offset the large resource cost of encoding and repeated syndrome extraction.

6.2 Logical Gates and the Transversal Principle

A transversal gate acts independently across corresponding physical qubits of code blocks. Such operations limit the spread of a single physical fault, which makes them attractive for fault tolerance. However, no quantum error-correcting code supports a universal set of logical gates entirely transversally; this limitation is known as the Eastin–Knill theorem.

Universal fault-tolerant computation therefore uses additional techniques such as magic-state injection and distillation, lattice surgery, code deformation, or carefully designed non-transversal operations. Magic-state distillation consumes many noisy resource states to produce fewer high-fidelity states, often becoming a dominant resource cost in large fault-tolerant architectures.

6.3 The Fault-Tolerant Workflow

A practical fault-tolerant system requires:

1. preparation of encoded states;
2. repeated syndrome measurement;
3. classical decoding with low latency;
4. fault-tolerant logical gates;
5. logical measurement and state verification;
6. monitoring of leakage, drift, and correlated faults.

The quantum processor and classical control system therefore form an integrated hybrid architecture. A decoder that is mathematically powerful but too slow for real-time operation may be unsuitable for the hardware.

7. Worked Example: Relaxation and Sampling Uncertainty

Consider a qubit initially prepared in |1⟩ with T₁ = 80 μs. It is measured after t = 20 μs, assuming amplitude relaxation is the only relevant process.

Using:

we obtain:

Thus, the probability of still finding the qubit in |1⟩ is approximately 77.9%, and the relaxation probability is approximately 22.1%.

If the experiment is repeated N = 10,000 times and the true probability is p = 0.7788, the sampling standard deviation is:

The standard deviation is about 0.416 percentage points. This uncertainty is statistical; it does not represent an additional physical relaxation process.

8. Illustrative Case: Choosing a Strategy for a Noisy Variational Algorithm

Background. A research team runs a six-qubit variational algorithm on a superconducting processor. The circuit has moderate depth, uses repeated two-qubit gates, and estimates an energy from 50,000 shots per parameter setting.

Problem. The measured energy is consistently higher than a trusted small-system simulation. Calibration data show non-negligible readout asymmetry, while T₁ and T₂ vary across the device. The team cannot yet deploy a full logical code.

Analysis. The discrepancy may result from several sources: readout assignment error, decoherence during idle periods, two-qubit gate errors, parameter-dependent sampling fluctuations, and optimizer sensitivity to biased expectation values. Increasing shots alone will reduce sampling noise but will not remove systematic bias.

Approach. The team first recalibrates readout and constructs an assignment matrix for the measured qubits. It applies a validated, regularized measurement-mitigation procedure. It then uses circuit scheduling to shorten idle periods and selects qubits with better recent coherence data. For selected observables, it evaluates circuits at two or three controlled noise scales and applies zero-noise extrapolation. Each mitigation step is tested against calibration circuits with known answers. Confidence intervals are reported, and results are compared with unmitigated estimates.

Outcome. The corrected energy moves closer to the trusted simulation, but its variance increases and the extrapolated result is sensitive to the chosen fit. The team therefore reports both raw and mitigated values, includes uncertainty estimates, and avoids claiming fault-tolerant accuracy. The procedure improves present-day usefulness but does not provide the long-term reliability of a logical qubit.

Learning points. Error diagnosis should precede mitigation. Different errors require different interventions. Mitigation can trade bias for variance, and every correction method must be validated against assumptions about the noise.

9. Limitations, Governance, and Professional Practice

Error rates are not universal device properties. They depend on qubit choice, gate direction, circuit schedule, temperature, calibration age, and measurement basis. Reported performance should therefore specify the benchmark, noise conditions, confidence intervals, and data-collection procedure.

Mitigation can create misleading results if researchers select only favorable observables, discard inconvenient data without disclosure, or compare corrected results with ideal theory while omitting uncertainty. Reproducibility requires publishing circuit definitions, shot counts, calibration information where possible, mitigation settings, and statistical procedures.

Quantum error correction also raises resource and sustainability issues. Large fault-tolerant systems may require millions of physical qubits, extensive cryogenic infrastructure, high-speed electronics, and substantial energy consumption. Architecture decisions should consider total system cost, maintainability, supply-chain constraints, and safe operation—not only logical error rates.

Quantum technologies may eventually affect cryptography, scientific modeling, finance, and national security. Responsible development requires honest communication of current limitations, protection of experimental data, and avoidance of unsupported claims about quantum advantage.

10. Contemporary Directions

Current research is moving from isolated demonstrations toward complete error-managed workflows. Important directions include improved cryogenic control, leakage reduction, real-time decoders, biased-noise codes, bosonic error correction, bias-preserving gates, and hardware–software co-design. Machine learning is being investigated for calibration, pulse optimization, noise characterization, and decoding. However, a machine-learning method must be evaluated against independent test data and changing hardware conditions; it does not remove the need for physical understanding or fault-tolerant guarantees.

A practical development path is often:

1. characterize physical noise;
2. improve calibration and circuit design;
3. apply targeted mitigation to near-term workloads;
4. demonstrate repeated syndrome extraction;
5. observe decreasing logical error with increasing code distance;
6. scale toward universal fault-tolerant computation.

The key milestone for QEC is not simply observing a code in operation, but demonstrating that increasing code size lowers the logical error rate under well-defined conditions.

Chapter Summary

Quantum computations are affected by decoherence, imperfect gates, readout assignment errors, and finite-shot sampling uncertainty. Relaxation and dephasing are described using T₁ and T₂, while bit-flip, phase-flip, depolarizing, and amplitude-damping channels provide useful idealized noise models. Noise characterization requires multiple complementary benchmarks.

Error mitigation estimates ideal results from noisy experiments through calibration, measurement correction, zero-noise extrapolation, probabilistic error cancellation, and symmetry verification. These methods can reduce bias but often increase variance, sampling cost, or dependence on modeling assumptions.

Quantum error correction encodes logical qubits in multiple physical qubits and uses syndromes to detect errors without measuring logical amplitudes. Code distance determines the number of correctable errors under stated assumptions. Fault-tolerant computing protects state preparation, gates, storage, syndrome extraction, and measurement. When physical error rates are sufficiently below a code- and architecture-dependent threshold, increasing code distance can reduce logical error rates, although the resource overhead is substantial.

Key Terms

Decoherence: Loss of quantum coherence through interaction with the environment.

T₁ relaxation time: Characteristic time for energy relaxation from |1⟩ toward |0⟩.

T₂ coherence time: Characteristic time for decay of phase coherence.

Gate error: Difference between an intended quantum operation and its physical implementation.

Readout error: Misclassification of a qubit state by the measurement apparatus.

Sampling error: Statistical uncertainty caused by using a finite number of circuit shots.

Noise channel: A mathematical map describing the effect of noise on a quantum state.

Amplitude damping: Noise model for energy relaxation.

Depolarizing noise: Model applying nonidentity Pauli errors with specified probabilities.

Error mitigation: Estimation of ideal results from noisy experiments without full encoded correction.

Measurement-error mitigation: Correction of biased measurement probabilities using a calibrated assignment model.

Zero-noise extrapolation: Estimation of a zero-noise value from results obtained at increased noise levels.

Quantum error correction: Encoding and processing method that detects and corrects physical errors.

Logical qubit: An encoded qubit represented by multiple physical qubits.

Syndrome: Information indicating an error pattern without ideally revealing the logical state.

Stabilizer: Operator whose specified eigenvalue defines the codespace.

Code distance: Minimum weight of a logical operator that preserves the codespace while acting nontrivially on logical information.

Error threshold: Maximum physical error rate below which fault-tolerant scaling can, under assumptions, suppress logical errors.

Fault tolerance: Design of computation so that physical faults do not cause uncontrolled logical failure.

Magic-state distillation: Production of high-fidelity resource states for fault-tolerant non-Clifford gates.

Review Questions

5 Short Answer Questions

1. What is the difference between T₁ relaxation and T₂ dephasing?
2. Why does increasing the number of shots not remove gate errors?
3. What information does a quantum error-correction syndrome provide?
4. Define a logical qubit.
5. Why can measurement-error mitigation amplify statistical noise?

5 Long Answer Questions

1. Compare bit-flip, phase-flip, depolarizing, and amplitude-damping noise models.
2. Explain how zero-noise extrapolation works and identify its principal assumptions and limitations.
3. Describe the operation of a three-qubit bit-flip repetition code and explain what errors it fails to correct.
4. Explain code distance, the number of correctable errors, and the significance of the error threshold.
5. Describe the major components required for a fault-tolerant quantum computer.

3 Analytical / Application Questions

1. A qubit has T₁ = 100 μs and is measured 30 μs after preparation in |1⟩. Calculate the ideal survival probability using the exponential relaxation model. What additional information would be needed to predict the complete measurement distribution?
2. A six-qubit algorithm shows a stable energy bias after the number of shots is increased substantially. Propose a diagnostic sequence to determine whether readout, gate, decoherence, or model error is the main cause.
3. A proposed code has distance d = 5. Under the standard distance-based correction assumption, how many arbitrary physical errors can it correct? Explain why increasing distance can improve reliability but also increase implementation overhead.

Multiple Choice Questions with Answers

Question 1

Which process primarily describes loss of phase coherence without necessarily changing computational-basis populations?

A. Dephasing

B. Readout assignment

C. Shot sampling

D. Classical decoding

Correct Answer: A. Dephasing

Question 2

For independent measurements with probability p and N shots, which expression gives the binomial standard deviation of the observed frequency?

A. p/N

B. √[p(1 − p)/N]

C. N√p

D. p(1 − p)N

Correct Answer: B. √[p(1 − p)/N]

Question 3

What is the main purpose of a measurement assignment matrix?

A. To encode a logical qubit

B. To describe errors in reported measurement outcomes

C. To increase T₁

D. To implement a universal gate set

Correct Answer: B. To describe errors in reported measurement outcomes

Question 4

Which method estimates a zero-noise observable by measuring at several increased noise levels?

A. Zero-noise extrapolation

B. Amplitude damping

C. Syndrome extraction

D. Random sampling only

Correct Answer: A. Zero-noise extrapolation

Question 5

What does a quantum error-correction syndrome ideally reveal?

A. The amplitudes α and β of an unknown logical state

B. The complete classical algorithm input

C. Information about the physical error pattern

D. The exact future measurement result

Correct Answer: C. Information about the physical error pattern

Question 6

A code with distance d = 5 can correct how many arbitrary errors under the standard distance assumption?

A. 1

B. 2

C. 3

D. 5

Correct Answer: B. 2

Question 7

What is the role of T₁ in a relaxation model?

A. It characterizes energy relaxation

B. It measures readout asymmetry

C. It specifies code distance

D. It is the number of circuit shots

Correct Answer: A. It characterizes energy relaxation

Question 8

What condition is generally required for threshold-based fault-tolerant scaling?

A. Physical error rates must be sufficiently below a code-dependent threshold

B. All physical qubits must be error-free

C. Only readout errors may occur

D. The circuit must contain no entangling gates

Correct Answer: A. Physical error rates must be sufficiently below a code-dependent threshold

Question 9

Which statement best distinguishes error mitigation from quantum error correction?

A. Mitigation estimates improved results, while correction encodes information to detect and correct errors

B. Mitigation always eliminates every physical error

C. Correction requires only one physical qubit per logical qubit

D. They are identical terms for the same procedure

Correct Answer: A. Mitigation estimates improved results, while correction encodes information to detect and correct errors

Question 10

Why can simply increasing shots fail to solve a persistent bias in an experiment?

A. More shots increase gate noise directly

B. Sampling reduction does not remove systematic physical or readout errors

C. More shots prevent measurement

D. Sampling uncertainty is independent of shot count

Correct Answer: B. Sampling reduction does not remove systematic physical or readout errors