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Science

Set, exchange, measure, repeat

Ian S. Osborne

Published Jun 18, 2020• 1 citation
Publisher

Abstract

Quantum Information Successful protocols for quantum information processing and quantum computation depend on the reliable storage and manipulation of the quantum state of a qubit. Qubits, however, are prone to errors because complete isolation from the environment is not possible. Methods for correcting these errors must also contend with the fact that direct measurement of a qubit destroys it. Xue et al. describe a repetitive quantum nondemolition method on a two-qubit system in which the state of the main qubit is mapped onto a second qubit that acts as an ancilla. Repeated measurement of the ancilla qubit allows the main qubit to be maintained and read out with higher fidelity. Such a protocol provides a route to robust quantum information processing in solid-state systems. Phys. Rev. X 10 , 021006 (2020).

DOI
10.1126/science.368.6497.1325-f

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Quantum Information
Successful protocols for quantum information processing and quantum computation depend on the reliable storage and manipulation of the quantum state of a qubit. Qubits, however, are prone to errors because complete isolation from the environment is not possible. Methods for correcting these errors must also contend with the fact that direct measurement of a qubit destroys it. Xue et al. describe a repetitive quantum nondemolition method on a two-qubit system in which the state of the main qubit is mapped onto a second qubit that acts as an ancilla. Repeated measurement of the ancilla qubit allows the main qubit to be maintained and read out with higher fidelity. Such a protocol provides a route to robust quantum information processing in solid-state systems.
Phys. Rev. X 10 , 021006 (2020).
High-fidelity qubit measurements play a crucial role in quantum computation, communication, and metrology. In recent experiments, it has been shown that readout fidelity can be improved by performing repeated quantum nondemolition (QND) readouts of a qubit's state through an ancilla. For a qubit encoded in a two-level system, the fidelity of such schemes is limited by the fact that a single error can destroy the information in the qubit. On the other hand, if a bosonic system is used, this fundamental limit can be overcome by utilizing higher levels such that a single error still leaves states distinguishable. In this work, we present a robust readout scheme which leverages both repeated QND readouts and higher-level encodings to asymptotically suppress the effects of mode relaxation and individual measurement infidelity. We calculate the measurement fidelity in terms of general experimental parameters, provide an information-theoretic description of the scheme, and describe its application to several encodings, including cat and binomial codes.
Quantum error correction is of crucial importance for fault-tolerant quantum computers.As an essential step toward the implementation of quantum error-correcting codes, quantum nondemolition measurements are needed to efficiently detect the state of a logical qubit without destroying it.Here we implement quantum nondemolition measurements in a Si/SiGe two-qubit system, with one qubit serving as the logical qubit and the other serving as the ancilla.Making use of a two-qubit controlled-rotation gate, the state of the logical qubit is mapped onto the ancilla, followed by a destructive readout of the ancilla.Repeating this procedure enhances the logical readout fidelity from 75.5 Æ 0.3% to 94.5 Æ 0.2% after 15 ancilla readouts.In addition, we compare the conventional thresholding method with an improved signal processing method called soft decoding that makes use of analog information in the readout signal to better estimate the state of the logical qubit.We demonstrate that soft decoding leads to a significant reduction in the required number of repetitions when the readout errors become limited by Gaussian noise, for instance, in the case of readouts with a low signal-to-noise ratio.These results pave the way for the implementation of quantum error correction with spin qubits in silicon.
Bits as well as qubits are affected by noise in transmission, the process of computation or even storage. We will refer to the error-prone area as a channel. The error is introduced by unwanted but unavoidable interaction with the rest of the world and needs to be corrected before the data can be reliable. Classically this is important in communication systems and there is a whole thriving field of study of classical error correction. In quantum systems, states are intrinsically so fragile that unless they are impossibly isolated from the rest of the world, errors or noise would make computation or communication using them infeasible. Fortunately, it was discovered early in the history of this subject that it is possible to encode qubits in special ways so as to make the information resilient to errors. The qubits are decoded at the end of the computation/communication (schematic of Figure 10.1).
Information processing based on the laws of quantum mechanics promises to be a revolutionary new avenue in information technology. This emerging field of quantum information processing (QIP) is however challenged by the fragile nature of the quantum bits (qubits) in which quantum information is stored and processed. An error in even a single qubit makes the quantum processor go off-track, corrupting the calculation as a whole. Therefore, the chance for an erroneous outcome increases with the number of qubits in the processor. Large-scale QIP thus hinges on the ability to correct for these errors. Classical information processing often uses error correction algorithms to identify errors by checking whether information is consistent in multiple copies. This strategy is unfortunately not applicable to QIP as quantum states cannot be copied. Moreover, direct measurements on qubits collapse their quantum states, reducing them to classical information. Fortunately, the theory of quantum error correction (QEC) overcomes these complications by encoding quantum information in entangled states of many qubits and performing parity measurements to identify errors in the system without destroying the encoded information. Implementing these codes is challenging as it requires many qubits and quick interleaving of operations and measurements. Moreover, to not introduce more errors in the system than QEC can solve for, these operations and measurements need to be of sufficient fidelity and speed...
Most quantum error-correcting codes are predicated on the assumption that there exists a reservoir of qubits in the state $|0\ensuremath{\rangle}$ which can be used as ancilla qubits to prepare multiqubit logical states. In this Brief Report, we examine the consequences of relaxing this assumption and propose a method to increase the fidelity produced by a given code when the ancilla qubits are initialized in mixed states, using the same number of qubits, at most doubling the number of gates when the recovery operation would already be implemented. The procedure implemented consists of altering the encoding operator to include the inverse of the unitary operation used to correct detected errors after decoding. This augmentation will be especially useful in quantum computing architectures that do not possess projective measurement, such as solid-state NMR quantum information processing.
Building reliable quantum computers requires protecting fragile quantum states from inevitable environmental noise and operational errors. While quantum error correction codes like the Steane [ ⁣[7,1,3] ⁣][\![7,1,3]\!][[7,1,3]] code provide elegant theoretical solutions, their practical success hinges critically on how we measure errors - a process called syndrome extraction. The challenge lies in the ancilla qubits used for measurement: when they fail, errors can cascade across the entire quantum system, destroying the very information we're trying to protect. We address this fundamental problem by implementing and comparing three sophisticated syndrome measurement strategies: Shor's cat-state approach, which distributes measurements across multiple entangled ancillas achieving 85-92% preparation success; Steane's encoded-ancilla method using complete error-corrected logical qubits reaching 97.8% syndrome fidelity; and a flexible unified framework that adapts strategies based on hardware capabilities. Through extensive simulations using IBM's Qiskit platform spanning randomized benchmarking and T-heavy circuits, we demonstrate that intelligent ancilla management improves error suppression by up to 2.4×\times× compared to standard approaches. Our implementations achieve logical error rates as low as 5.1×10−55.1 \times 10^{-5}5.1×10−5 under realistic noise conditions with physical error rates of 10−310^{-3}10−3, while maintaining near-unity logical fidelity (0.99997) even for deep circuits. The threshold analysis reveals robust performance across distance-3 to distance-13 codes with characteristic threshold curves showing exponential error suppression below the critical physical error rate. These results provide immediately deployable tools for near-term quantum devices and establish practical design principles for scaling toward fault-tolerant quantum computers.