Quantum error correction (QEC) is vital for protecting quantum information against errors induced by quantum noise and decoherence, enabling fault-tolerant quantum computation. Here, we construct a SPICE-based classical emulator framework to simulate gate-based quantum error correction circuits, specifically designed to correct both bitflip and phase flip errors. In our framework, a collection of LC-oscillators emulates the process behavior quantum gates. Each quantum state is perfectly described by the phase and amplitude of each oscillator. Our framework is scalable to any quantum error correction system with any arbitrary number of qubits since each gate process is perfectly achieved. Here, we have successfully conducted simulations for an individual bit-flip correction circuit and Shor’s nine-bit error correcting quantum circuit, demonstrating the capability of our framework to effectively address and repair random bit-flip and phase flip errors in gate-based quantum computing circuits.
Quantum error correction (QEC) is vital for protecting quantum information against errors induced by quantum noise and decoherence, enabling fault-tolerant quantum computation. Here, we construct a SPICE-based classical emulator framework to simulate gate-based quantum error correction circuits, specifically designed to correct both bitflip and phase flip errors. In our framework, a collection of LC-oscillators emulates the process behavior quantum gates. Each quantum state is perfectly described by the phase and amplitude of each oscillator. Our framework is scalable to any quantum error correction system with any arbitrary number of qubits since each gate process is perfectly achieved. Here, we have successfully conducted simulations for an individual bit-flip correction circuit and Shor’s nine-bit error correcting quantum circuit, demonstrating the capability of our framework to effectively address and repair random bit-flip and phase flip errors in gate-based quantum computing circuits.
A circuit system consisting of LC-oscillators is mathematically shown to emulate quantum circuits. Here we develop a SPICE-based framework for emulating universal quantum gates (the phase-shift, the Hadamard, and the CNOT gates). To reconstruct each gate behavior, the inductors and capacitors are chosen and tuned precisely. Each quantum state is perfectly described by the phase and amplitude of each oscillator. In principle, our framework can simulate a quantum system with any arbitrary number of qubits since each gate process is perfectly achieved. Finally, we have simulated a quantum circuit with 3 qubits as input that consists of all the universal quantum gates. Our simulation result shows that our framework can classically emulate the result of any quantum circuit with an arbitrary number of qubits and quantum logic components.
Quantum technology is a new field of physics and engineering. In emerging areas like Quantum Cryptography, Quantum Computing etc, Quantum circuits play a key role. Quantum circuit is a model for Quantum computation, the computation process of Quantum gates are based on reversible logic. Encoder and Decoder are designed using Quantum gates, and synthesized in the QCAD simulator. Quantum error correction (QEC) is essential to protect quantum information from errors due to quantum noise and decoherence. It is also use to achieve fault-tolerant quantum computation that deals with noise on stored information, faulty quantum gates and faulty measurements.
Quantum systems operate using quantum bits (qubits), which are highly sensitive to external noises and disturbances and they are easily prone to errors. In the Noisy Intermediate-Scale Quantum (NISQ) era, these errors make difficult to build reliable, fault tolerant quantum circuits for real world deployment. This work provides an overview of need for Quantum Error Correction (QEC) in NISQ devices, as qubits commonly get affected by bit-flip, phase-flip, and combined errors that degrades system performance and examines Quantum Error Correction Code (QECC) techniques usage in communication, computation, and quantum multimedia applications such as image and video transmission. In addition, a simple three-qubit repetition circuit is introduced to demonstrate an error-mitigation approach. These findings, also show how QEC improves fidelity, reduces logical errors, and improves noise tolerance. The analysis also identifies challenges and outlines the future research direction aimed at achieving efficient and scalable fault tolerant quantum circuits.
Quantum systems operate using quantum bits (qubits), which are highly sensitive to external noises and disturbances and they are easily prone to errors. In the Noisy Intermediate-Scale Quantum (NISQ) era, these errors make difficult to build reliable, fault tolerant quantum circuits for real world deployment. This work provides an overview of need for Quantum Error Correction (QEC) in NISQ devices, as qubits commonly get affected by bit-flip, phase-flip, and combined errors that degrades system performance and examines Quantum Error Correction Code (QECC) techniques usage in communication, computation, and quantum multimedia applications such as image and video transmission. In addition, a simple three-qubit repetition circuit is introduced to demonstrate an error-mitigation approach. These findings, also show how QEC improves fidelity, reduces logical errors, and improves noise tolerance. The analysis also identifies challenges and outlines the future research direction aimed at achieving efficient and scalable fault tolerant quantum circuits.
Quantum error correction (QEC) is essential for realizing scalable quantum computation. However, when evaluating its benefits, most analyses assume idealized components, overlooking the imperfections inherent in realistic fault-tolerant (FT) implementations. In this paper, we investigate the performance of QEC schemes taking into account that quantum gates and measurements are themselves error-prone. We derive bounds for the failure probability of Shor-style FT-QEC schemes using limited structural information, such as the number of flag qubits and quantum gates. Our analysis separates and quantifies two key contributors to the failure rate: decoding errors and residual errors arising from circuit-level faults. The derived bounds highlight fundamental limitations in Shor-style FT-QEC performance and quantify how circuit imperfections degrade error correction capabilities, under the assumption of depolarizing noise.
Fault-tolerant quantum computation requires quantum error correction (QEC), and while the performance of various QEC codes has been well characterized under idealized noise conditions, it has not been sufficiently characterized by simulation under realistic noise conditions.In this paper, the performance of three basic QEC codes (3-qubit Bit-Flip, 3-qubit Phase-Flip and Shor's 9-qubit [[9,1,3]]) under simulated depolarizing noise, by using Qiskit Aer, is analyzed systematically in three stages.Stage 1 is a validation of all three implementations under ideal circumstances.Stage 2 tests for 6 different error rates of 0% to 5%, and runs 2048 shots per error rate.Stage 3 brings the analysis from stage 2 to 0% to 10%, but with an uncorrected baseline for comparison.Results verify that Shor's > Bit-Flip > Phase-Flip is consistent over practically relevant error rates.At 1% noise, within current IBM Quantum hardware range, all three codes achieve a logical fidelity of over 98.7%.An error rate of 7-8% is used to identify a cross-over threshold above which the simpler Bit-Flip code can match Shor's code in fidelity with only one-third the number of qubits.