Quantum Computer Architecture

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Questions and Answers

What is the name of the subarchitecture mentioned in the given diagram?

LEE.name Suberchitecture

What is the purpose of inserting SWAP gates in the circuit mapping?

To satisfy the restricted connectivity of the architecture

What is the initial step in determining a suitable mapping for the circuits that cannot be perfectly mapped to the architecture?

Choosing an initial layout

What is the significance of considering the circuits that cannot be perfectly mapped to the architecture?

To find a suitable mapping for those circuits Signup and view all the answers

What is the page number mentioned in the given diagram?

6 Signup and view all the answers

What is the total number of zeros shown in the binary representation in the diagram?

7 Signup and view all the answers

What is the purpose of building an interaction graph out of all gates for each circuit in the given quantum computer architecture?

To determine if the circuit can be mapped to the architecture A without adding any SWAP gates Signup and view all the answers

What is a necessary condition for two qubits to natively interact on architecture A?

They must be directly connected by a vertical or horizontal line. Signup and view all the answers

Why is it important to consider the architecture of a quantum computer when designing a quantum circuit?

Because it determines which qubits can interact and how the circuit can be mapped to the available hardware Signup and view all the answers

What is the purpose of SWAP gates in the context of quantum circuit mapping?

To move qubits around to enable interactions that are not natively supported by the architecture Signup and view all the answers

How can we determine which pairs of qubits can natively interact on architecture A?

By looking at the connections between qubits in the architecture diagram Signup and view all the answers

What is the significance of the interaction graph in determining if a circuit can be mapped to architecture A?

It helps determine if the circuit's qubit interactions can be natively implemented on the architecture Signup and view all the answers

What is the goal of Problem 5 in verifying the equivalence of circuits G and G'?

To show that both circuits act the same on all possible computational basis states. Signup and view all the answers

What is the significance of |i Í = |000Í, ..., |111Í in Problem 5?

These represent all possible computational basis states. Signup and view all the answers

What is the minimal cost for realizing G?

The question does not provide enough information to determine the minimal cost. Signup and view all the answers

What is the purpose of simplifying the circuit in Problem 5?

To make it easier to verify the equivalence of the circuits. Signup and view all the answers

How many credits is Problem 5 worth?

14 credits. Signup and view all the answers

What does the notation |i Í represent in Problem 5?

A computational basis state. Signup and view all the answers

What is the cost of applying a single CNOT gate in the circuit G?

10 Signup and view all the answers

What is the cost of applying a single-qubit gate in the circuit G?

1 Signup and view all the answers

Identify the single-qubit gate that can be replaced by a combination of `X`, `Y`, and `Z` gates.

H Signup and view all the answers

What is the cost of applying the gate sequence `H X` on a qubit?

2 Signup and view all the answers

What is the cost of applying the gate sequence `Z H` on a qubit?

2 Signup and view all the answers

What is the gate sequence that can replace `S X S†`?

© Signup and view all the answers

What is the gate sequence that can replace `S Y S†`?

Y Signup and view all the answers

What is the gate sequence that can replace `S Z S†`?

S† Signup and view all the answers

How does the CNOT gate affect the target qubit when the control qubit is in the state |1Í?

The CNOT gate flips the state of the target qubit. Signup and view all the answers

What output is produced by the gate configuration for the input state |100Í?

|111Í becomes the output. Signup and view all the answers

Describe the output for the input state |011Í when passed through the discussed quantum gates.

|1011 becomes the output. Signup and view all the answers

Which input state yields the output |001Í in the given mapping?

|000Í produces the output |001Í. Signup and view all the answers

What is the result of input |101Í in the provided quantum gate configuration?

|1111711 becomes the output. Signup and view all the answers

Explain the output of the configuration for the input state |110Í.

|11117 is the resulting output. Signup and view all the answers

What transformation occurs to |001Í according to the mapping shown?

|000Í transforms to |001Í. Signup and view all the answers

For the input |010Í, what is the resulting output after applying the gates?

|10107 becomes the output. Signup and view all the answers

What can you infer about the behavior of the gate for the input state |111Í?

|110071100711 becomes the output. Signup and view all the answers

If the input state is |000Í, what output does it initially yield in the context of the CNOT gate?

|000 becomes the output with no change. Signup and view all the answers

Study Notes

Problem 4: Compilation of Quantum Circuits

The problem considers a quantum computer architecture A with qubits Q0, Q1, Q2, Q3, Q4, and Q5.
The architecture allows native interaction between certain pairs of qubits.

Native Interactions

The pairs of qubits that can natively interact on this architecture are: (1, 3), (2, 5), and (0, 2).

Mappable Circuits

The circuits that can be mapped to the architecture A without adding any SWAP gates are:
- Circuit with gates on q3, q2, q1, and q0.
- Circuit with gates on q2, q1, q0, and q3.

Circuit Mapping

To map a circuit to the architecture, an interaction graph is built out of all gates for each circuit, and then fitted to the architecture.
If a circuit cannot be perfectly mapped, an initial layout is chosen, and SWAP gates are inserted to satisfy the restricted connectivity.

Simplifying Quantum Circuits

The goal is to simplify a given quantum circuit G as much as possible using certain quantum circuit identities.
The identities include:
- I = HXH
- X = HYH
- Y = HZH
- Z = HXH
- SXS† = XSS†
- SYS† = YSY†
- SZS† = ZSZ†
The cost of realizing the circuit is calculated, with CNOT gates costing 10 and single-qubit gates costing 1.

Problem 5: Verification of Quantum Circuits

The problem involves verifying the equivalence of two circuits G and GÕ by showing that they act the same on all possible computational basis states.
The CNOT gate flips the state of the target qubit whenever the control qubit is in state |1Í.

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Description

This quiz assesses your understanding of quantum circuits and their compilation. It involves identifying pairs of qubits that can natively interact in a given quantum computer architecture.