You will now show that we can always convert quantum circuits with internal measurements into quantum circuits where all measurements occur at the end. This is nice because, as we know, a circuit without measurements just corresponds to multiplication by a unitary matrix. So suppose you have an n-qubit quantum circuit that does some internal measurements, and suppose the first measurement is at step t. It measures the state of the kth qubit in the standard basis and outputs a classical bit b = {0, 1} and the corresponding state collapses to the outcome. Now make two changes: 1. Introduce an (n + 1)st qubit to the circuit 2. Replace the measurement on qubit k by a CNOT gate whose control is the kth bit and the target bit is the new (n+1)st qubit. Solve the following: (i) Show that this exactly simulates the original circuit's operation. (ii) Explain how this gives a way of taking any quantum circuit and converting it into one where all measurements occur only at the final step. (The idea is that you want to be able to reproduce all the values output by the internal measurements in the circuit, using measurement gates that only happen at the end.)

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
icon
Related questions
Question
**Conversion of Quantum Circuits with Internal Measurements**

You will now show that we can always convert quantum circuits with internal measurements into quantum circuits where all measurements occur at the end. This is nice because, as we know, a circuit without measurements just corresponds to multiplication by a unitary matrix.

So suppose you have an \( n \)-qubit quantum circuit that does some internal measurements, and suppose the first measurement is at step \( t \). It measures the state of the \( k \)th qubit in the standard basis and outputs a classical bit \( b \in \{0, 1\} \) and the corresponding state collapses to the outcome.

Now make two changes:

1. Introduce an \( (n + 1) \)st qubit to the circuit.

2. Replace the measurement on qubit \( k \) by a CNOT gate whose control is the \( k \)th bit and the target bit is the new \( (n + 1) \)st qubit.

Solve the following:

(i) Show that this exactly simulates the original circuit’s operation.

(ii) Explain how this gives a way of taking any quantum circuit and converting it into one where all measurements occur only at the final step. (The idea is that you want to be able to reproduce all the values output by the internal measurements in the circuit, using measurement gates that only happen at the end.)
Transcribed Image Text:**Conversion of Quantum Circuits with Internal Measurements** You will now show that we can always convert quantum circuits with internal measurements into quantum circuits where all measurements occur at the end. This is nice because, as we know, a circuit without measurements just corresponds to multiplication by a unitary matrix. So suppose you have an \( n \)-qubit quantum circuit that does some internal measurements, and suppose the first measurement is at step \( t \). It measures the state of the \( k \)th qubit in the standard basis and outputs a classical bit \( b \in \{0, 1\} \) and the corresponding state collapses to the outcome. Now make two changes: 1. Introduce an \( (n + 1) \)st qubit to the circuit. 2. Replace the measurement on qubit \( k \) by a CNOT gate whose control is the \( k \)th bit and the target bit is the new \( (n + 1) \)st qubit. Solve the following: (i) Show that this exactly simulates the original circuit’s operation. (ii) Explain how this gives a way of taking any quantum circuit and converting it into one where all measurements occur only at the final step. (The idea is that you want to be able to reproduce all the values output by the internal measurements in the circuit, using measurement gates that only happen at the end.)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 4 images

Blurred answer
Knowledge Booster
Tunneling effect
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON