- NISQ value for scientific exploration - Commercially relevant applications need error correction and Fault-tolerant quantum computers ![[Pasted image 20240107155731.png]] ![[Pasted image 20240107155847.png]] ![[Pasted image 20240107160004.png]] On quantum error correction, specifically using a surface code, which is a way to **protect quantum information from errors.** In quantum computing, qubits (quantum bits) are used instead of classical bits. However, qubits are very susceptible to errors due to environmental noise and other factors. - **P_physical** is the error rate of physical qubits, which in this case is 0.001, meaning there is a 0.1% chance of an error occurring in a physical qubit. - **P_logical** is the targeted error rate after error correction is applied, which is much lower (10^-11), indicating a significantly reduced chance of errors in the processed quantum information. - **d** is the distance of the code, which determines how many errors can be corrected. It is calculated as the square root of **n**, the total number of physical qubits used per logical qubit. Here, **d = 19** means the system can correct errors spread out over 19 qubits. - **n = 361** tells us that 361 physical qubits are required to create one logical qubit with the desired low error rate. - **C** is a constant related to the surface code, and **P_threshold** is the threshold error rate, which is the maximum physical error rate allowed to still perform effective error correction. - The formula given shows how the logical error rate depends on these factors, aiming for a logical error rate much lower than the physical one. Ancilla qubits, which are additional qubits used for error syndrome measurement, meaning they help identify where errors might have occurred without disturbing the quantum information. The last part states that if the physical error rate improves to 10^-4, the required code distance **d** and the number of physical qubits **n** can be reduced, indicating a more efficient error correction (better error correction with fewer qubits). In essence, this is discussing the overhead or extra resources needed to achieve fault tolerance (the ability to correct errors) in a quantum computer ![[Pasted image 20240107160200.png]] Advancements in Quantum Error Correction (QEC), which are crucial for reliable quantum computing: 1. **Erasure conversion**: This means that if errors occur in predictable locations, they are easier to identify and correct. It's like knowing which part of a sentence tends to get misspelled and being extra vigilant in those parts. 2. **Biased noise**: This refers to the fact that not all errors are equal; some are more likely than others. By focusing on suppressing the most common errors, like bit flips (where a qubit accidentally switches from 0 to 1 or vice versa), and designing codes specifically to correct these, the system becomes more robust against errors that disrupt the quantum state's phase (phase flips). 3. **More efficient codes**: Developing error correction codes that require less overhead. This could mean using fewer additional qubits for error checking or having more straightforward ways to check for and correct errors. Using correlations between qubits that are not directly next to each other, could improve error detection and correction efficiency. 4. **Co-design**: This is about optimizing the relationship between the quantum hardware and the error correction codes. It's like making a glove that fits a hand perfectly — the error correction is tailored to the hardware's specifics, and vice versa, making the entire system more effective. Strategically optimising QEC, involves understanding the nature of errors, tailoring solutions to address the most significant issues, and integrating the error correction deeply with the hardware design for maximal efficiency. ### Erasure Conversions ![[Pasted image 20240107160225.png]] - **Erasure conversion**: A method where errors in a quantum computer are not just detected but announced (heralded) and occur at predictable locations within the circuit. Because their locations are known, they are easier to correct compared to random errors. - **Exiting the computational space**: Certain types of errors effectively remove the affected qubit from the set of qubits being used to perform computations, without affecting the overall quantum state. This is beneficial because it allows for the detection of errors without interfering with the integrity of the unaffected, or "coherent," qubits. - **Alkaline earth Rydberg atoms**: Research from Princeton and Caltech pertains to the use of these atoms in quantum computing. Rydberg atoms have highly excited states and can be used for quantum bits. The notation |1⟩ → |g⟩, not |1⟩ → |0⟩ suggests a preferred transition for error signalling, where |g⟩ might represent a special state used to indicate an error. - **Dual-rail superconducting qubit**: This is likely a type of qubit design where information is encoded in two separate physical paths or states, such as |01⟩ and |10⟩, which then transition to |00⟩ if an error is detected. The use of two transmons or resonators suggests that these qubits are designed using two parts that can each carry quantum information, enhancing the error detection capability. In summary, erasure conversion is a strategy to make quantum error correction more manageable by using special behaviors of quantum systems, such as predictable error locations and specific transitions, to detect and correct errors efficiently. The institutions mentioned are likely key players in the research and development of these quantum error correction techniques. ![[Pasted image 20240107162343.png]] When the phase errors dominate it's called Biased Noise. - **Biased noise**: In quantum computing, 'noise' refers to unwanted disturbances that cause errors. 'Biased' suggests that some errors occur more frequently than others. For instance, bit flips (where a qubit switches from 0 to 1 or vice versa) might happen more often than phase flips (where the phase of the qubit changes). - **Suppressing bit and phase flips**: physically suppressing bit flips (perhaps through improved hardware design or environmental shielding) and using error-correcting codes to handle phase flips. This implies that we can design our quantum systems and the operations (gates) on them to naturally resist certain types of errors while using algorithms to correct the others. - **Outer code**: 'repetition code' or 'asymmetric surface code' uses specific error-correcting codes. These are algorithms that repeat information across multiple qubits or use patterns in the qubits' arrangement to detect and correct errors without disturbing the correct information. ![[Pasted image 20240107163248.png]] #quantum