Quantum Lock using Quantum Phase Estimation and Phase Kickback

Implement a quantum lock with qubits and qudits for ASCII character passwords

First, let's define a unitary gate U such that all but one eigenvalue is 1. The only different eigenvalue will be -1 given by

|key〉:

U|key〉=-|key〉

Such gate is called a FlipSign:

FlipSign(n)|m〉=

- \| m 〉	ifm=n
\| m 〉	ifm≠n

where the input is n and the basis state is m.

Install the QuantumFramework paclet:

In[1]:=

PacletInstall["Wolfram/QuantumFramework"]

Load the paclet:

In[2]:=

Needs["Wolfram`QuantumFramework`"]

Load additional functions used for examples, explained in this Tech Note:

In[3]:=

Needs["Wolfram`QuantumFramework`ExampleRepository`"]

We can use "FlipSign" operator already designed in the Wolfram Quantum Framework:

In[4]:=

QuantumCircuitOperator["FlipSign"["01"]][QuantumState["01"]]["Formula"]

Out[4]=

-|01〉

In[5]:=

QuantumCircuitOperator["FlipSign"["01"]][QuantumState["10"]]["Formula"]

Out[5]=

|10〉

Use the quantum phase estimation as represented in the following circuit. Note that each step includes a label with the resultant state:

Out[6]=

We applied a phase kickback in the third step. This method will let us turn a global phase into a relative phase on a control wire. Since we are using a controlled FlipSign gate, it will act as the following:

|0〉|key〉+|1〉FlipSign|key〉->|0〉|key〉∓|1〉|key〉->|∓〉|key〉

At the end we apply the last Hadamard gate so we can distinguish if the key is correct or incorrect:

H|∓〉|key〉->|1〉|correctkey〉or|0〉|incorrectkey〉

Following the same circuit structure from the QPE subroutine, implement a quantum lock:

In[7]:=

quantumLock[key_String]:=QuantumCircuitOperator"H"{1},QuantumCircuitOperator{{"C","FlipSign"[key](Range[StringLength@key]+1),{1}}},"Label""

FlipSign

","H"{1},QuantumMeasurementOperator["Computational",{1}]

Generate a quantum lock with a binary password:

In[8]:=

lock=quantumLock["1010"];lock["Diagram"]

Out[8]=

Build a function to check if the key is correct:

In[9]:=

checkKey[lock_,key_String]:=Module[{result},result=lock[QuantumState["0"<>key]]["Mean"];If[MatchQ[result,1],"Correct key","Incorrect key, try again"]]

Try to open the quantum lock mechanism with an incorrect key:

In[10]:=

checkKey[lock,"1011"]

Out[10]=

Incorrect key, try again

Use the correct key to open the lock:

In[11]:=

checkKey[lock,"1010"]

Out[11]=

Correct key

Test every possible combination:

In[12]:=

allkeys=StringJoin/@MapAt[ToString[#]&,Tuples[{0,1},4],{All,All}];

In[13]:=

Dataset[#checkKey[lock,#]&/@allkeys]

Out[13]=

0000	Incorrect key, try again
0001	Incorrect key, try again
0010	Incorrect key, try again
0011	Incorrect key, try again
0100	Incorrect key, try again
0101	Incorrect key, try again
0110	Incorrect key, try again
0111	Incorrect key, try again
1000	Incorrect key, try again
1001	Incorrect key, try again
1010	Correct key
1011	Incorrect key, try again
1100	Incorrect key, try again
1101	Incorrect key, try again
1110	Incorrect key, try again
1111	Incorrect key, try again

We can use qudits to create a password for a quantum lock mechanism. Qudits, which are higher-dimensional quantum counterparts to classical bits, provide more combinations than classical bits binary passwords.

Expand the function definition by implementing a quantum lock for

different states:

In[14]:=

quantumLock[key_String,d_Integer]:=QuantumCircuitOperator"H"{1},QuantumCircuitOperator{{"C","FlipSign"[key,d](Range[StringLength@key]+1),{1}}},"Label""

FlipSign

","H"{1},QuantumMeasurementOperator["Computational",{1}]

Build a function to check if the key is correct:

Try to open the quantum lock mechanism with an incorrect key:

Open the lock with the correct key:

To create a quantum lock using qudits to represent ASCII characters, each character should be assigned to a unique combination of quantum states. For example, "00" could represent 'A', "01" for 'B', "10" for 'C', and "11" for 'D'. This method allows unique quantum states for all ASCII characters.

We can use the QuantumLockingMechanism function from the ExampleRepository context with any secret password:

Finally, you can test the lock mechanism:

External Links

Source Metadata

Citation:
- Quantum locking mechanism using quantum phase estimation and phase kickback for ASCII passwords
  by Sebastian Rodriguez
  Wolfram Community, STAFF PICKS, May 29, 2024
  https://community.wolfram.com/groups/-/m/t/3185554
- Motlagh, D. (2023, July 31). Building a quantum lock using phase kickback. https://pennylane.ai/qml/demos/tutorial_phase_kickback/

Publisher Information

Contributed by: Wolfram Research, Quantum Computation Framework Team

Wolfram Language Example Repository

Quantum Lock using Quantum Phase Estimation and Phase Kickback

External Links

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See Also

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