Defining standard qubit gates for qutritsWhy is the decomposition of a qubit-qutrit Hamiltonian in terms of Pauli and Gell-Mann matrices not unique?How to apply single and two qubit gates to 2 qubits multiple times?The general form of unitary operations on a single qubitQutrit TeleportationWhat is the matrix for the operator that implements a function to tell the parity of its argument?Matrix representation and CX gateHow does quantum function parallelism work?What's the point of quantum gates being 'continuous'?How do you implement the gates for Grover's algorithm for more than 4 elements?Making a maximally mixed 2-qubit state in the IBM Q
Is my company merging branches wrong?
Is being an extrovert a necessary condition to be a manager?
How to use Screen Sharing if I don't know the remote Mac's IP address
How do you cope with rejection?
What causes a person to remain in this world as a ghost?
Why is there no current between two capacitors connected in series?
Was Tyrion always a poor strategist?
Does the fact that we can only measure the two-way speed of light undermine the axiom of invariance?
Salesforce bug enabled "Modify All"
Is there a word for pant sleeves?
How is dynamic resistance of a diode modeled for large voltage variations?
Removing Doubles Destroy Topology
Parse a C++14 integer literal
Existence of a model of ZFC in which the natural numbers are really the natural numbers
Why does an injection from a set to a countable set imply that set is countable?
How to draw with Tikz a chord parallel to AC that passes through a point?
Why use nominative in Coniugatio periphrastica passiva?
If you attack a Tarrasque while swallowed, what AC do you need to beat to hit it?
1950s or earlier book with electrical currents living on Pluto
pwaS eht tirsf dna tasl setterl fo hace dorw
Why is this python script running in background consuming 100 % CPU?
How would a physicist explain this starship engine?
Is there a way to generate a mapping graph like this?
Warped chessboard
Defining standard qubit gates for qutrits
Why is the decomposition of a qubit-qutrit Hamiltonian in terms of Pauli and Gell-Mann matrices not unique?How to apply single and two qubit gates to 2 qubits multiple times?The general form of unitary operations on a single qubitQutrit TeleportationWhat is the matrix for the operator that implements a function to tell the parity of its argument?Matrix representation and CX gateHow does quantum function parallelism work?What's the point of quantum gates being 'continuous'?How do you implement the gates for Grover's algorithm for more than 4 elements?Making a maximally mixed 2-qubit state in the IBM Q
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
$begingroup$
I am actually working on quantum computing with qutrits. I am trying to define standard qubit gates for qutrits. The CNOT gate for qubits is defined as follows: $$|x,yrangle to |x,y+x bmod 2rangle.$$
So the matrix is $$mathrmUCN =
beginpmatrix
1 & 0 & 0 & 0\
0 & 1 & 0 & 0\
0 & 0 & 0 & 1\
0 & 0 & 1 & 0
endpmatrix.$$
For the definition of the same type of gate for qutrit I am left with two choices:
$$|x,yrangle to |x,y+x bmod 3rangle$$
$$|x,yrangle to |x,y+2x bmod 3rangle$$
Does anyone know if one of the two is more common or more usually defined?
PS: I know that applying one two times is equivalent to apply the other one time.
quantum-gate qutrit
edited May 7 at 16:14
Sanchayan Dutta♦
7,12041658
asked May 7 at 14:08
Marco FalsoMarco Falso
184
$endgroup$
add a comment |
$begingroup$
I am actually working on quantum computing with qutrits. I am trying to define standard qubit gates for qutrits. The CNOT gate for qubits is defined as follows: $$|x,yrangle to |x,y+x bmod 2rangle.$$
So the matrix is $$mathrmUCN =
beginpmatrix
1 & 0 & 0 & 0\
0 & 1 & 0 & 0\
0 & 0 & 0 & 1\
0 & 0 & 1 & 0
endpmatrix.$$
For the definition of the same type of gate for qutrit I am left with two choices:
$$|x,yrangle to |x,y+x bmod 3rangle$$
$$|x,yrangle to |x,y+2x bmod 3rangle$$
Does anyone know if one of the two is more common or more usually defined?
PS: I know that applying one two times is equivalent to apply the other one time.
quantum-gate qutrit
edited May 7 at 16:14
Sanchayan Dutta♦
7,12041658
asked May 7 at 14:08
Marco FalsoMarco Falso
184
$endgroup$
$begingroup$
Hi, Marco. Welcome to Quantum Computing SE! It is preferable that you use MathJax to typeset your posts. Review How to write a good question?. I've edited the question on your behalf.
$endgroup$
– Sanchayan Dutta♦
May 7 at 16:18
$begingroup$
Hi Sanchayan, thanks a lot for the edit and the advice. I will make sure that I write a good question next time.
$endgroup$
– Marco Falso
May 7 at 16:21
add a comment |
$begingroup$
I am actually working on quantum computing with qutrits. I am trying to define standard qubit gates for qutrits. The CNOT gate for qubits is defined as follows: $$|x,yrangle to |x,y+x bmod 2rangle.$$
So the matrix is $$mathrmUCN =
beginpmatrix
1 & 0 & 0 & 0\
0 & 1 & 0 & 0\
0 & 0 & 0 & 1\
0 & 0 & 1 & 0
endpmatrix.$$
For the definition of the same type of gate for qutrit I am left with two choices:
$$|x,yrangle to |x,y+x bmod 3rangle$$
$$|x,yrangle to |x,y+2x bmod 3rangle$$
Does anyone know if one of the two is more common or more usually defined?
PS: I know that applying one two times is equivalent to apply the other one time.
quantum-gate qutrit
edited May 7 at 16:14
Sanchayan Dutta♦
7,12041658
asked May 7 at 14:08
Marco FalsoMarco Falso
184
$endgroup$
I am actually working on quantum computing with qutrits. I am trying to define standard qubit gates for qutrits. The CNOT gate for qubits is defined as follows: $$|x,yrangle to |x,y+x bmod 2rangle.$$
So the matrix is $$mathrmUCN =
beginpmatrix
1 & 0 & 0 & 0\
0 & 1 & 0 & 0\
0 & 0 & 0 & 1\
0 & 0 & 1 & 0
endpmatrix.$$
For the definition of the same type of gate for qutrit I am left with two choices:
$$|x,yrangle to |x,y+x bmod 3rangle$$
$$|x,yrangle to |x,y+2x bmod 3rangle$$
Does anyone know if one of the two is more common or more usually defined?
PS: I know that applying one two times is equivalent to apply the other one time.
quantum-gate qutrit
quantum-gate qutrit
edited May 7 at 16:14
Sanchayan Dutta♦
7,12041658
asked May 7 at 14:08
Marco FalsoMarco Falso
184
edited May 7 at 16:14
Sanchayan Dutta♦
7,12041658
asked May 7 at 14:08
Marco FalsoMarco Falso
184
edited May 7 at 16:14
Sanchayan Dutta♦
7,12041658
edited May 7 at 16:14
Sanchayan Dutta♦
7,12041658
edited May 7 at 16:14
Sanchayan Dutta♦
7,12041658
7,12041658
asked May 7 at 14:08
Marco FalsoMarco Falso
184
asked May 7 at 14:08
Marco FalsoMarco Falso
184
asked May 7 at 14:08
Marco FalsoMarco Falso
184
184
$begingroup$
Hi, Marco. Welcome to Quantum Computing SE! It is preferable that you use MathJax to typeset your posts. Review How to write a good question?. I've edited the question on your behalf.
$endgroup$
– Sanchayan Dutta♦
May 7 at 16:18
$begingroup$
Hi Sanchayan, thanks a lot for the edit and the advice. I will make sure that I write a good question next time.
$endgroup$
– Marco Falso
May 7 at 16:21
add a comment |
$begingroup$
Hi, Marco. Welcome to Quantum Computing SE! It is preferable that you use MathJax to typeset your posts. Review How to write a good question?. I've edited the question on your behalf.
$endgroup$
– Sanchayan Dutta♦
May 7 at 16:18
$begingroup$
Hi Sanchayan, thanks a lot for the edit and the advice. I will make sure that I write a good question next time.
$endgroup$
– Marco Falso
May 7 at 16:21
$begingroup$
Hi, Marco. Welcome to Quantum Computing SE! It is preferable that you use MathJax to typeset your posts. Review How to write a good question?. I've edited the question on your behalf.
$endgroup$
– Sanchayan Dutta♦
May 7 at 16:18
$begingroup$
Hi, Marco. Welcome to Quantum Computing SE! It is preferable that you use MathJax to typeset your posts. Review How to write a good question?. I've edited the question on your behalf.
$endgroup$
– Sanchayan Dutta♦
May 7 at 16:18
$begingroup$
Hi Sanchayan, thanks a lot for the edit and the advice. I will make sure that I write a good question next time.
$endgroup$
– Marco Falso
May 7 at 16:21
$begingroup$
Hi Sanchayan, thanks a lot for the edit and the advice. I will make sure that I write a good question next time.
$endgroup$
– Marco Falso
May 7 at 16:21
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Your first definition,
$$|x,yrangle to |x,y+x bmod 3rangle$$
is both more common and, IMO, easier to use. Especially as you point out that the second definition can be simulated by repeated application of the first. You can see the authors have used this version of the qutrit CNOT in
Construction of two qutrit entanglement by using magnetic resonance selective pulse sequences (Çorbaci et al., 2016) and in
Controlled Not (Cnot) Gate For Two Qutrit Systems, (KOCAKOÇ & TAPRAMAZ, 2018).
Additionally, you may want to consider the context of your qutrit gates. For example, section 2 of arXiv:1105.5485 first defines three versions of the qutrit X gate and then discusses what a controlled X would mean in these cases.
edited May 7 at 23:12
Sanchayan Dutta♦
7,12041658
answered May 7 at 16:44
Noah DNoah D
462
$endgroup$
$begingroup$
Thanks a lot for the articles. None of them uses the Hadamard gate I am using but at least I have some articles to relate to about computation with qutrits. I am convinced that X gate and Hadamard gate must change all the states and not be only extensions of the two dimensional ones.
$endgroup$
– Marco Falso
May 7 at 17:40
add a comment |
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "694"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fquantumcomputing.stackexchange.com%2fquestions%2f6087%2fdefining-standard-qubit-gates-for-qutrits%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Your first definition,
$$|x,yrangle to |x,y+x bmod 3rangle$$
is both more common and, IMO, easier to use. Especially as you point out that the second definition can be simulated by repeated application of the first. You can see the authors have used this version of the qutrit CNOT in
Construction of two qutrit entanglement by using magnetic resonance selective pulse sequences (Çorbaci et al., 2016) and in
Controlled Not (Cnot) Gate For Two Qutrit Systems, (KOCAKOÇ & TAPRAMAZ, 2018).
Additionally, you may want to consider the context of your qutrit gates. For example, section 2 of arXiv:1105.5485 first defines three versions of the qutrit X gate and then discusses what a controlled X would mean in these cases.
edited May 7 at 23:12
Sanchayan Dutta♦
7,12041658
answered May 7 at 16:44
Noah DNoah D
462
$endgroup$
$begingroup$
Thanks a lot for the articles. None of them uses the Hadamard gate I am using but at least I have some articles to relate to about computation with qutrits. I am convinced that X gate and Hadamard gate must change all the states and not be only extensions of the two dimensional ones.
$endgroup$
– Marco Falso
May 7 at 17:40
add a comment |
$begingroup$
Your first definition,
$$|x,yrangle to |x,y+x bmod 3rangle$$
is both more common and, IMO, easier to use. Especially as you point out that the second definition can be simulated by repeated application of the first. You can see the authors have used this version of the qutrit CNOT in
Construction of two qutrit entanglement by using magnetic resonance selective pulse sequences (Çorbaci et al., 2016) and in
Controlled Not (Cnot) Gate For Two Qutrit Systems, (KOCAKOÇ & TAPRAMAZ, 2018).
Additionally, you may want to consider the context of your qutrit gates. For example, section 2 of arXiv:1105.5485 first defines three versions of the qutrit X gate and then discusses what a controlled X would mean in these cases.
edited May 7 at 23:12
Sanchayan Dutta♦
7,12041658
answered May 7 at 16:44
Noah DNoah D
462
$endgroup$
$begingroup$
Thanks a lot for the articles. None of them uses the Hadamard gate I am using but at least I have some articles to relate to about computation with qutrits. I am convinced that X gate and Hadamard gate must change all the states and not be only extensions of the two dimensional ones.
$endgroup$
– Marco Falso
May 7 at 17:40
add a comment |
$begingroup$
Your first definition,
$$|x,yrangle to |x,y+x bmod 3rangle$$
is both more common and, IMO, easier to use. Especially as you point out that the second definition can be simulated by repeated application of the first. You can see the authors have used this version of the qutrit CNOT in
Construction of two qutrit entanglement by using magnetic resonance selective pulse sequences (Çorbaci et al., 2016) and in
Controlled Not (Cnot) Gate For Two Qutrit Systems, (KOCAKOÇ & TAPRAMAZ, 2018).
Additionally, you may want to consider the context of your qutrit gates. For example, section 2 of arXiv:1105.5485 first defines three versions of the qutrit X gate and then discusses what a controlled X would mean in these cases.
edited May 7 at 23:12
Sanchayan Dutta♦
7,12041658
answered May 7 at 16:44
Noah DNoah D
462
$endgroup$
Your first definition,
$$|x,yrangle to |x,y+x bmod 3rangle$$
is both more common and, IMO, easier to use. Especially as you point out that the second definition can be simulated by repeated application of the first. You can see the authors have used this version of the qutrit CNOT in
Construction of two qutrit entanglement by using magnetic resonance selective pulse sequences (Çorbaci et al., 2016) and in
Controlled Not (Cnot) Gate For Two Qutrit Systems, (KOCAKOÇ & TAPRAMAZ, 2018).
Additionally, you may want to consider the context of your qutrit gates. For example, section 2 of arXiv:1105.5485 first defines three versions of the qutrit X gate and then discusses what a controlled X would mean in these cases.
edited May 7 at 23:12
Sanchayan Dutta♦
7,12041658
answered May 7 at 16:44
Noah DNoah D
462
edited May 7 at 23:12
Sanchayan Dutta♦
7,12041658
edited May 7 at 23:12
Sanchayan Dutta♦
7,12041658
edited May 7 at 23:12
Sanchayan Dutta♦
7,12041658
7,12041658
answered May 7 at 16:44
Noah DNoah D
462
answered May 7 at 16:44
Noah DNoah D
462
answered May 7 at 16:44
Noah DNoah D
462
462
$begingroup$
Thanks a lot for the articles. None of them uses the Hadamard gate I am using but at least I have some articles to relate to about computation with qutrits. I am convinced that X gate and Hadamard gate must change all the states and not be only extensions of the two dimensional ones.
$endgroup$
– Marco Falso
May 7 at 17:40
add a comment |
$begingroup$
Thanks a lot for the articles. None of them uses the Hadamard gate I am using but at least I have some articles to relate to about computation with qutrits. I am convinced that X gate and Hadamard gate must change all the states and not be only extensions of the two dimensional ones.
$endgroup$
– Marco Falso
May 7 at 17:40
$begingroup$
Thanks a lot for the articles. None of them uses the Hadamard gate I am using but at least I have some articles to relate to about computation with qutrits. I am convinced that X gate and Hadamard gate must change all the states and not be only extensions of the two dimensional ones.
$endgroup$
– Marco Falso
May 7 at 17:40
$begingroup$
Thanks a lot for the articles. None of them uses the Hadamard gate I am using but at least I have some articles to relate to about computation with qutrits. I am convinced that X gate and Hadamard gate must change all the states and not be only extensions of the two dimensional ones.
$endgroup$
– Marco Falso
May 7 at 17:40
add a comment |
Thanks for contributing an answer to Quantum Computing Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fquantumcomputing.stackexchange.com%2fquestions%2f6087%2fdefining-standard-qubit-gates-for-qutrits%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
Hi, Marco. Welcome to Quantum Computing SE! It is preferable that you use MathJax to typeset your posts. Review How to write a good question?. I've edited the question on your behalf.
$endgroup$
– Sanchayan Dutta♦
May 7 at 16:18
$begingroup$
Hi Sanchayan, thanks a lot for the edit and the advice. I will make sure that I write a good question next time.
$endgroup$
– Marco Falso
May 7 at 16:21