Questions tagged [qudit]

For questions mainly related to qudits, the unit of quantum information in d-level quantum systems.

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1answer
102 views

What is the relation between a Fock state and a qudit?

What is the relation between a Fock state and a qudit? Is the Fock state $|n\rangle, n=0, 1, 2, ...$ a qudit having $d=\infty$?
6
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1answer
90 views

Uniformly distributed state in the Weyl basis

The Weyl basis (also known as Weyl-Heisenberg) is an orthonormal, unitary, and non-Hermitian basis for the Hilbert space of dimension $d$. The basis elements are given by $$ U_{ab} = \sqrt{\omega^{ab}}...
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1answer
85 views

Implementing quDit algorithms in Qiskit using quBit

How do you implement any $d$-dimensional qudit circuit in qiskit using qubits to simulate on an actual quantum computer?
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1answer
72 views

Why `cirq` needs `Qid` class instead of just `Qudit` class?

I am just wondering in what way cirq.Qid class generalizes qudits. From cirq.Qid documentation we read that it Identifies a ...
3
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1answer
80 views

Canonical construction of Logical Fourier Gate

For physical $d$-dimensional qudits we can define $$X= \sum_{i=0}^{d-1} |i+1\rangle \langle i |$$ and $$Z = \sum_{i=0}^{d-1} \omega^i |i\rangle \langle i |,$$ with $\omega=e^{2\pi i/d}$. The Fourier ...
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4answers
1k views

How does the NOT gate generalize beyond binary?

If we are working with qudits instead of qubits, how do the NOT and CNOT gates work? If the control state for a qubit system is $|1\rangle$, what is it for a $d$-ary qudit system, and why? For ...
6
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2answers
475 views

How to generalize the relationship HXH = Z for higher dimensions

Concerning the Hadamard gate and the Pauli $X$ and $Z$ gates for qubits, it is straightforward to show the following relationship via direct substitution: $$ HXH = Z.\tag{1}$$ And I would like to ...
4
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2answers
75 views

Is the column vector of a uniformly sampled random unitary matrix a uniformly sampled random state vector?

I am wondering if a random unitary matrix taken from a Haar measure (as in, it is uniformly sampled at random) can yield a uniformly sampled random state vector. In section 3 of this paper it says &...
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1answer
60 views

How does $U_f$ act on a qudit state in the Deutsch-Jozsa Algorithm

The problem starts with the given the input state $|\psi_{in} \rangle = |0 \rangle |1 \rangle$, I'm asked to calculate $|\psi'\rangle = H_d \otimes H_d |\psi_{in} \rangle$ where $H_d$ is the Hadamard ...
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0answers
38 views

Fault-tolerant qudit computation: advantage? [closed]

What are advantages of a fault-tolerant qudit computation compared with fault-tolerant quantum computation for qubits?
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1answer
117 views

Can a single qutrit in superposition be considered entangled?

Often in quantum computing the idea of quantum superposition is introduced well before the concept of entanglement. I suspect this may be because our conception of (classical) computing privileges ...
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0answers
44 views

How to simulate spin-1 systems with qiskit or on the IBMQ platform?

I am wondering how to simulate spin-1 systems with qiskit or on the IBMQ platform? I want to initialize a qudit (a spin-1 system), and then define the usual operations (such as Sx, Sy, and Sz) on the ...
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43 views

Find the qutrit analogue of certain qubit and ququart formulas of Li and Qiao for testing separability

In eqs. (33), (43)-(46), (56) of their paper, "Separable Decompositions of Bipartite Mixed States" https://arxiv.org/abs/1708.05336, Li and Qiao present a number of formulas pertinent to testing the ...
6
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1answer
173 views

$n$ qubit vs. a $d=2^n$ qudit states and measurements

The pure states of a qudit inhabit the $\mathbb{CP}(d-1)$ manifold. Is it true that the pure states of $n$ qubits live on the $\mathbb{CP}(2^n-1)$ manifold? If the answer to the first question is yes,...
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1answer
71 views

Explicit 16⨯16 matrix representations of two-qudit entanglement witnesses

I have a set of $16 \times 16$ two-qudit density matrices. I would like to study the bound-entanglement for this set, making use of entanglement witnesses for which explicit matrix representations are ...
3
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1answer
90 views

Computing with qutrits

I'm doing some calculations with qutrits and I need a unitary matrix $U$ that does the following: $$U|00\rangle = |12 \rangle - | 21\rangle $$ $$U|11\rangle = |20 \rangle - | 02\rangle $$ $$U|22\...
6
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0answers
156 views

Why can a point in anti-de Sitter space be modeled as a logical qutrit and how is its error correction done?

This isn't my area but the recent Quanta article How Space and Time Could Be a Quantum Error-Correcting Code struck me as interesting. They mention: In their paper[1] conjecturing that holographic ...
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2answers
409 views

Generalizing quantum teleportation for qudits

In an answer to a previous question, Generalization for n quantum teleportations, Craig Gidney states: The more complicated way to generalize teleportation is figuring out how to make it work on ...
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2answers
165 views

Time-bin encoding qudits

Time-bin encoding is a technique used in Quantum information science to encode a qubit of information on a photon. Wikipedia Is there a generalization for $n$-th level qudits?
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1answer
296 views

Graph state and maximally entangled state

How can I show that a multi-qudit graph state $|G\rangle$ is the maximally entangled state? What kind of measure of entanglement can be used to quantify the amount of entanglement in a given graph ...
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2answers
75 views

Combining Different Qunits

Has any work been done on quantum systems which use a combination of types of qunits (eg. using qubits & qutrits simultaneously)? If work has been done, what kind of work has been done? (eg. in ...
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2answers
198 views

Hilbert space to accurately represent 3x3 Rubik's Cube

What Hilbert space of dimension greater than 4.3e19 would be most convenient for working with the Rubik's Cube verse one qudit? The cardinality of the Rubik's Cube group is given by: Examples 66 ...
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2answers
368 views

Computing with Logical Qunits

What exactly is a logical (non-physical? error corrected?) qunit? Can quantum systems be built exclusively w/ logical qunits?
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1answer
201 views

Does local Clifford equivalence have a direct graphical representation for qudit graph states of non-prime dimension?

This question is a follow-up to the previous QCSE question: "Are qudit graph states well-defined for non-prime dimension?". From the question's answer, it appears that there is nothing wrong in ...
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3answers
2k views

Reverse Quantum Computing: How to unmeasure a qunit

After taking some measure, how can a qunit be "unmeasured"? Is unmeasurement (ie reverse quantum computing) possible?
9
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1answer
157 views

Are qudit graph states well-defined for non-prime dimension?

Qudit graph states are $d$-dimension generalisations of qubit graph states such that each state is represented by a weighted graph $G$ (with no self-loops) such that each edge $(i, j)$ is assigned a ...
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2answers
221 views

How to represent a qubyte?

I was not able to locate any visuals online. The visual I have in my head is a cube w/ bloch spheres as the eight vertices. I am also curious about a matrix representation, although I am not sure ...
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2answers
946 views

Difference between 3 qubits, 2 qutrits & 1 six level qunit

What is the difference between 3 qubits, 2 qutrits and a 6th level qunit? Are they equivalent? Why / why not? Can 6 classical bits be super-densely coded into each?
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2answers
850 views

How to show that an n-level system is entangled?

"How do I show that a two-qubit state is an entangled state?" includes an answer which references the Peres–Horodecki criterion. This works for $2\times 2$ and $2\times3$ dimensional cases; however, ...
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1answer
83 views

What are the differences between "$n$-th level e-bits" and "$n$-th level qunits"?

I have seen qubits, qutrits & entangled bits (e-bits) a decent amount. I have also seen qunits/qudits for n-th level qubits. What I am trying to wrap my head around is the differences between n-th ...
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2answers
242 views

Do any specific types of qudits other than qubits and qutrits have a name?

For example, has anyone seen something like: "quqrit" for a 4-level system[1], or "qupit" for a 5-level system[2] ? 1 From "quad" or "quart" since "tetra" would be qutrit, which is already a 3-level ...
7
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1answer
142 views

In qubit/qudit terms, where is the experimental limit between S=3/2 and 2·S=1/2?

This question is inspired by "What is the difference between a qudit system with d=4 and a two-qubit system?", as an experimental follow-up. Consider for illustration these two particular cases: ...
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5answers
2k views

What is the difference between a qudit system with d=4 and a two-qubit system?

I understand that a qudit is a quantum $d$-state system. If $d=4$, is this exactly the same as a two-qubit system, which also presents $4$ quantum states? The Hilbert space is the same, right? Are ...
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2answers
426 views

What is the most economical and preferred basis for the qudit?

In Classical Simulation of Quantum Error Correction in a Fibonacci Anyon Code, the authors state on page 2 in section I. Background, A. Topological model: We consider a system supporting nonabelian ...
3
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2answers
612 views

Is quantum computing limited to a superposition of only two states?

From Wikipedia: A qubit is a two-state quantum system [...] There are two possible outcomes for the measurement of a qubit — usually $0$ and $1$, like a bit. The difference is that whereas the state ...
8
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2answers
527 views

Are qutrits more robust to decoherence?

A string of $n$ qutrits has a state-space spanned by the $3^n$ different states $\lvert x \rangle $ for strings $x \in \{0,1,2\}^n$ (or $x \in \{-1,0,+1\}^n$, equivalently), while $n $ qubits can ...