Episode 5

 I am currently running the code from the Coding with Qiskit Episode 5 tutorial. Should

see results by tomorrow morning. I am on ibm_brisbane because ibm_sherbrooke is on

maintenance.

Asked Merlin (ChatGPT4o) for a description of the set-up:

The provided Qiskit code defines a function `get_dynamic_CNOT_circuit(num_qubit)` that creates a quantum circuit with the purpose of implementing a dynamic CNOT operation over a 1D chain of nearest-neighbor qubits. Let's break down the setup and reasoning behind the circuit:

1. Initialization of Registers and Circuit:

   - A quantum register `qr` of size `num_qubit` is created. This includes:

     - The 0th qubit as the control.

     - The last qubit (`num_qubit - 1`) as the target.

     - Remaining qubits serve as ancillae for facilitating the operation.

   - Three classical registers are used:

     - `cr1` to store parity results for conditional X gates.

     - `cr2` to store parity results for conditional Z gates.

     - `cr3` for the final measurement results of the control and target qubits.

2. Preparation of the Control Qubit:

   - The control qubit (0th qubit) is initialized to the `+` state using a Hadamard gate (`qc.h(0)`).

3. **Entangling Control and First Ancilla:**

   - A CNOT gate entangles the control qubit with the first ancilla qubit (`qc.cx(0, 1)`).

4. Creation of Bell Pairs:

   - Bell pairs are created among ancilla qubits to facilitate interaction across the chain:

     - A series of Hadamard (`qc.h`) and CNOT gates (`qc.cx`) are applied on pairs of ancilla qubits.

5. Staggered Bell State Preparation:

   - Additional entanglement is created between alternating qubits, including the target qubit, using CNOT gates.

   - Another set of Hadamard gates is applied to complete these entanglements.

6. Measurement and Conditional Gates:

   - Measurements are performed on alternating ancilla qubits, storing results in classical registers `cr1` and `cr2`.

   - These measurement results are used to determine parities for conditional quantum gates:

     - The parity from `cr2` is used to apply a conditional Z gate on the control qubit.

     - The parity from `cr1` is used to apply a conditional X gate on the target qubit.

7. Final Measurements:

   - The state of the control qubit (0th qubit) and the target qubit are measured, with results recorded in `cr3`.

Reasoning:

The circuit essentially implements a non-standard CNOT operation where the control and target qubits are not adjacent but connected via a series of ancillae. The Bell pairs and conditional gates ensure that the operation can be translated across these ancillae, making use of the nearest-neighbor connectivity paradigm. This dynamic CNOT approach is useful for systems where long-range interactions need to be simulated via short-range entanglements and classical feedback.

What happens next; are there only 7 qubits for illustration, but actually 41 in the circuit?

In the provided code snippet, the purpose is to generate dynamic CNOT circuits with increasing numbers of qubits, starting from 7 qubits and going up to a maximum of 41 qubits (inclusive). Here's a breakdown of what happens next:

 Explanation of the Code

1. Initial Circuit Creation:

   - `qc = get_dynamic_CNOT_circuit(num_qubit=7)` creates a quantum circuit with exactly 7 qubits. This specific case serves as an illustration of how the circuit is formed with fewer qubits.

2. Setup for Multiple Circuits:

   - `max_num_qubit = 41` defines the maximum number of qubits.

   - `qc_list = []` initializes an empty list to store all the circuits generated.

   - `num_qubit_list = list(range(7, max_num_qubit + 1, 2))` creates a list of odd numbers starting from 7 up to 41 (inclusive). This means the circuits generated will have 7, 9, 11, ..., 41 qubits.

3. Loop to Generate Circuits:

   - `for num_qubit in num_qubit_list:` iterates through each number of qubits in `num_qubit_list`.

   - `qc_list.append(get_dynamic_CNOT_circuit(num_qubit))` calls the function to create a dynamic CNOT circuit for the current `num_qubit` and appends it to `qc_list`.

 Purpose of the Circuit Creation

- The function `get_dynamic_CNOT_circuit(num_qubit)` you've already looked at is called iteratively for each odd number of qubits from 7 to 41.

- This creates a series of circuits that demonstrate how the dynamic CNOT gate can be implemented for increasing qubit sizes, potentially useful for studying how the circuit scales and behaves as the number of qubits increases.

 Summary

Yes, while the initial example uses 7 qubits for demonstration purposes, the overall structure of the code is designed to generate quantum circuits with a variety of sizes, ending with 41 qubits. This allows for experimentation with various configurations, tests of quantum algorithms, and a better understanding of how circuit depth and complexity evolve with more qubits. 

What is the GHZ state?

                                                                         

                                                                                    

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Asked Perplexity Ai to summarize the paper on which this circuit is based:

Answer

The paper titled "Efficient Long-Range Entanglement using Dynamic Circuits" explores innovative methods for generating long-range entanglement in quantum systems through the use of dynamic circuits, which incorporate non-unitary operations and measurements.

Key Highlights:

Dynamic Circuits: The authors propose that dynamic circuits can surpass traditional unitary dynamics in efficiency when creating intricate entangled states. These circuits utilize measurements and conditional feed-forward operations, allowing for enhanced connectivity and state preparation in quantum devices.

Main Tasks:

CNOT Gate Teleportation: The study demonstrates the teleportation of a CNOT gate across up to 101 qubits by utilizing 99 mid-circuit measurement outcomes. This approach shows improved performance compared to conventional unitary methods.

GHZ State Preparation: The authors also focus on preparing Greenberger-Horne-Zeilinger (GHZ) states, providing a detailed error budget that outlines the challenges that need to be addressed to fully leverage dynamic circuits.

Future Implications: The findings suggest that dynamic circuits could play a crucial role in achieving long-range entanglement on large-scale quantum devices in the near future, potentially unlocking new capabilities in quantum computing.

This research indicates significant advancements in the field of quantum simulation and entanglement generation, highlighting the potential of dynamic circuits for practical applications in quantum technology.

Tell me more about the error budget.

Answer

The error budget in quantum computing refers to the detailed analysis and accounting of various error sources that can affect the performance of quantum systems. This concept is critical for understanding how different components contribute to overall logical error rates, especially in the context of quantum error correction (QEC).

Key Aspects of Error Budgets in Quantum Computing:

Components of Error Budgets:

Physical Errors: These include errors arising from gate operations, decoherence, and measurement inaccuracies. Each type of physical error has a distinct impact on the logical qubit's performance.

Error Suppression Factor: This factor quantifies how much the logical error rate can be reduced by increasing the size or distance of the error-correcting code. For instance, a higher distance code generally leads to better error suppression.

Dominant Error Sources:

Research shows that specific types of errors, such as controlled-Z (CZ) gate errors and data qubit decoherence during measurement, are often the most significant contributors to logical errors in quantum circuits. Understanding these dominant sources allows researchers to prioritize improvements in those areas.

Performance Thresholds:

Quantum error correction becomes effective only when the physical error rates are below a certain threshold. The error budget helps determine what improvements are necessary to achieve this threshold and thus make quantum computations feasible.

Estimation and Projections:

By simulating various scenarios with different physical error rates, researchers can estimate how much improvement is needed across different components to achieve desired logical performance levels. For example, projections may indicate that a 20% improvement in component performance is required to move below the error threshold.

Experimental Validation:

While theoretical models provide a framework for understanding error budgets, experimental validation is crucial. Researchers conduct tests with larger codes and longer durations to confirm that their projections hold true in practical scenarios.

Future Directions:

As quantum technologies evolve, continuous refinement of the error budget will be necessary to address new challenges and improve scalability. This includes developing more sophisticated QEC codes and optimizing existing quantum architectures.

In summary, an effective error budget is essential for advancing quantum computing technologies by identifying critical areas for improvement and guiding research efforts towards achieving fault-tolerant quantum systems.

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https://youtu.be/QDPtcwhpQkE?si=AHd_WSbvccYQbDk8