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QND measurement

Quantum Nondemolition (QND) measurement, a fundamental idea in quantum physics, is turning out to be essential to creating reliable and fault-tolerant quantum computers. New developments demonstrate how QND methods can be used to view quantum systems without disturbing their sensitive states, which is an essential capacity for detecting and fixing mistakes that beset emerging quantum technologies.

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The Essential Difficulty of Quantum Measurement In the classical world, an object’s intrinsic features are typically unaffected by interaction, such as taking its temperature. The “stiffness” of the object permits observation without causing undue disturbance. But according to a basic principle of quantum mechanics, a quantum mechanical wave function is altered uncontrollable by observation. A significant obstacle to quantum computing, where data encoded in delicate quantum states needs to be maintained, is this inevitable disturbance, often referred to as quantum backaction.

Stiffening Wave Functions: The Revolution in QND In contrast to this conventional wisdom, scientists have shown that every wave function may be “stiffen” to survive observation without changing uncontrollably. Without the use of feedback or dissipation, this is mostly accomplished Hamiltonianly, which stabilises and holds the wave function motionless over an entire observation.

The fundamental process underlying QND measurement is a system’s self-Hamiltonian that is sufficiently strong. When a meter is connected to a quantum system through an operator, the measurement results are the expected values of the “stiff” eigenstates of the self-Hamiltonian of the system rather than the eigenvalues of that operator. Regardless of the measuring operator, the system is projected into one of these eigenstates following the measurement.

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Even if the self-Hamiltonian of the system and the measuring operator do not initially commute, this procedure, which frequently takes place under the rotating-wave approximation (RWA), guarantees that the interaction corresponds to a QND measurement. Decoding errors can be greatly aided by the fundamental understanding that the coupling to the environment is “renormalised,” which effectively broadcasts averaged information about “undefined” features of the wave function in a QND approach.

Applications: Going Beyond Conventional Measuring The following ground-breaking uses are made possible by this capacity to conduct non-perturbing measurements:

• Simultaneous Measurement of Non-Commuting Observables: Using a single copy of a quantum state, QND allows for the simultaneous measurement of expectation values of non-commuting observables. For example, meters can encode all observable expectation values of the locked eigenstate of a single qubit by locking it with a self-Hamiltonian. In contrast to the constraints of standard quantum measurement, this implies that information regarding attributes such as $\hat{\sigma}_x$, $\hat{\sigma}_y$, and $\hat{\sigma}_z$ can be obtained without erasing information in the others.
• Observing Entanglement Correlations: In a single copy of a composite system, like a two-qubit entangled state, QND may detect and quantify non-classical correlations. While the state itself is stable, the entangled state can be used to derive the mean values of non-commuting observables.
• Logical Readout in Quantum Error Correction (QEC): The main uses of QND are in logical readout and syndrome extraction for QEC. In “degenerate” quantum systems, where logical information is encoded in a degenerate subspace, this is especially important. For example, a powerful measurement of a quadrature would normally be a “demolition measurement,” destroying the coherent states in a Schrödinger-cat qubit, which uses coherent states to encode information and is stabilised as a degenerate ground-state manifold. Nonetheless, a QND qubit measurement is made possible even in cases where the measuring operator does not commute with the Hamiltonian of the system by treating the coupling as a perturbation, which renormalises the operator. QND measurement fidelities of about 99% have been made possible as a result. By calculating the mean photon number, this method may distinguish between several “error sectors” without disclosing the quantum information contained in the code words’ parity.

The Fault Tolerance and Knill-Laflamme Condition The validity of the Knill-Laflamme (KL) condition, a necessary and sufficient condition for quantum error correction, is one of the implications of QND. According to this condition, the code words will change in a way that can be decoded when environmental activity occurs if the environment is unable to read the logical information. According to the KL condition’s derivation inside the QND framework, the code words do not have to commute with the self-Hamiltonian or have eigenstates in order for the syndrome-measurement coupling that reveals mistakes in a QEC code to be effective. This implies that faults can be identified and described without compromising the confidentiality of the quantum data being safeguarded.

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The Function of QND in Stopping Leaks Recent developments in quantum error correction indirectly use the concepts of QND, even if they are not always referred to as such. For instance, “leakage” a significant cause of errors in quantum computers is successfully addressed by the Data Qubit Leakage Removal (DQLR) technique, which was successfully illustrated in a Nature Physics research published on October 5, 2023. Quantum information can leak into higher-energy states from a qubit’s two computational modes, causing correlated mistakes that can quickly weaken a quantum system.

As a “direct removal” technique, the DQLR approach can eliminate leakage from measure and data qubits without altering their computational states. This closely relates to the fundamental idea of QND measurement, which is to detect and fix a flaw (leak) without compromising the desired quantum state.

This discovery addressed a long-standing worry that this sneaky defect would prevent quantum systems with weak nonlinearity, such superconducting transmon qubits, from effectively implementing QEC at scale. DQLR decreased average leakage populations to around 10^-3 for data qubits and less than 10^-4 for measure qubits, hence reducing the lifespan of leakage and limiting its propagation. These low levels were maintained for numerous QEC cycles. This shows that QEC can maintain long-term stability, which is necessary for fault-tolerant quantum computers.

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Essentially, the future of quantum computing depends on the ability to carry out QND-like operations. The creation of scalable and dependable quantum processors is made possible by its ability to precisely and non-destructively interrogate quantum states, allowing for the discovery and rectification of mistakes without creating new ones.