# Questions tagged [qudit]

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

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### Hadamard gate for qudit (dimesion 8)

I am using the code for generating the gates for qu8it The resultant gate is not unitary (and so not hermitian too). I am a bit confused with the result. Is it possible for a quantum gate to be non-...
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### Qudits in NISQ Devices: Benefits Beyond Dimensional Advantages?

It's clear from foundational research that qudits can provide an enhanced control of the Hilbert space over qubits, and I've encountered references that highlight improved robustness and noise ...
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### Is it possible to convert a qudit to a qubit?

I am trying to write a Qiskit code for a algorithm which uses qudits. I want to use qubits instead because $p$ value can go pretty high. Is it mathematically possible to convert qudit to qubit for ...
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### 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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### 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 ...
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### 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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### 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 ...
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### 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 ...
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### 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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### 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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### 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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### 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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### 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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### 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 ...
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### $n$ 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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### 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 ...
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### 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\...
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### 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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### How is quantum teleportation generalized to 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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?
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### 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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### 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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### 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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### How to show whether a bipartite high-dimensional 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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### 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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### 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 ...
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### 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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### 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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### 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 ...
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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 ...