Questions tagged [quantum-state]

Quantum systems can mathematically be described by their 'quantum state'. When the system is closed/isolated, the state is 'pure' and can be written as a sum (i.e. 'superposition') of basis vectors. When the system is a subsystem of an open system, the state is instead usually 'mixed' and cannot be written as a pure state, so has to be written as a density matrix. Consider using the density-matrix tag when relevant

40 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
16
votes
0answers
510 views

Quantum machine learning after Ewin Tang

Recently, a series of research papers have been released (this, this and this, also this) that provide classical algorithms with the same runtime as quantum machine learning algorithms for the same ...
7
votes
1answer
124 views

On the distribution of the fidelity of a random product state with an arbitrary many-qubit state

Consider an arbitrary $n$-qubit state $\lvert \psi \rangle$. How much do we understand about the probability distribution of the fidelity of $\lvert \psi \rangle$ with a tensor product $\lvert \alpha \...
6
votes
0answers
82 views

Threshold and practical requirements for initial state preparation?

At the beginning of a quantum computational process we generally want to start in a perfectly known initial state, and evolve from there. This cannot be done perfectly, for fundamental reasons, but I ...
5
votes
0answers
89 views

Encoding bosonic degrees of freedom

A well-known way of encoding $N$ levels of a harmonic (bosonic) oscillator is as follows: \begin{equation} |n\rangle = |1\rangle^{\otimes n} \otimes |0\rangle^{\otimes N-n+1} \quad,\qquad ...
5
votes
0answers
110 views

How exactly is the stated composite state of the two registers being produced using the $R_{zz}$ controlled rotations?

This is a sequel to How are two different registers being used as "control"? I found the following quantum circuit given in Fig 5 (page 6) of the same paper i.e. Quantum Circuit Design for ...
3
votes
0answers
14 views

Deriving Bloch vector $dr$ from master equation

I am trying to derive the Bloch vector $dr$ for a measurement of a observable in any arbitrary direction $\theta$. For context this is the setup and derivation I have for continuous measurement along ...
3
votes
0answers
30 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 ...
3
votes
0answers
41 views

Understanding shared Bell states from quantum entanglement

I'm trying to understand an entanglement swapping derivation provided in this PDF (pages 2 - 3) I have several things about this process that I don't understand, and I was hoping someone could ...
3
votes
0answers
20 views

Synchronous Interactions Between Quantum and Macroscopic Systems

Synchronous Interactions Between Quantum and Macroscopic Systems Lester Ingber This project calculates synchronous quantum systems and macroscopic systems with well-defined interactions. I would ...
3
votes
0answers
76 views

How to implement the mixed quantum state fidelity in a quantum circuit?

Suppose we use Uhlmann-Josza fidelity $F(\rho, \sigma):=(\mathrm{tr}\sqrt{\sqrt{\rho}\sigma\sqrt{\rho}})^2$, can we construct a quantum circuit that help us to calculate the fidelity of two mixed ...
3
votes
0answers
24 views

Finding separable decompositions of bipartite X-states using the methodology of Li and Qiao

Two recent papers of Jun-Li Li and Cong-Feng Qiao (arXiv:1607.03364 and arXiv:1708.05336) present "practical schemes for the decomposition of a bipartite mixed state into a sum of direct products of ...
3
votes
0answers
32 views

Are X-state separability and PPT- probabilities the same for the two-qubit, qubit-qutrit, two-qutrit, etc. states?

On p. 3 of "Separability Probability Formulas and Their Proofs for Generalized Two-Qubit X-Matrices Endowed with Hilbert-Schmidt and Induced Measures" (https://arxiv.org/abs/1501.02289), it is ...
3
votes
0answers
34 views

Why does $x\sqrt{1-x^2}$ enhance the ability to approximate analytical functions in quantum circuit learning?

In this paper Quantum Circuit Learning they say that the ability of a quantum circuit to approximate a function can be enhanced by terms like $x\sqrt{1-x^2}$ ($x\in[-1,1])$. Given inputs $\{x,f(x)\}$, ...
3
votes
0answers
46 views

Can “experimental data from a quantum computer” be used to test separability probability conjectures?

An article entitled "Experimental data from a quantum computer verifies the generalize Pauli exclusion principle" by Scott E. Smart, David I. Schuster, and David A. Mazziotti has just appeared In the ...
3
votes
0answers
42 views

Why does state preparation of 'off the shelf' qubits not follow from the Born rule (Mermin)?

In Mermin's Quantum Computer Science, section 1.10 (Measurement gates and state preparation), Mermin writes that: This role of measurement gates in state preparation follows from the Born rule if ...
2
votes
0answers
18 views

Is quantum deletion via a partial randomization procedure possible?

The paper, Quantum deletion is possible via a partial randomization procedure claims that it is possible to bypass the no-deleting theorem by a procedure called R-deletion. But this seems to go ...
2
votes
0answers
22 views

Is there a measure similar to the Helstrom measurement which can distinguish between more than 2 pure quantum states?

My understanding is the Helstrom measurement distinguishes between 2 pure quantum states. Is there a measure similar to the Helstrom measurement which can distinguishes between more than 2 pure ...
2
votes
2answers
101 views

What is the probability of a single qubit state lying over the surface of Bloch sphere?

I want to compute the POVM $E_{(\theta, \phi)}$ of the measure which gives the probability of a qubit state lying over the surface of Bloch sphere, with angles $\theta, \phi$. How can I handle this? ...
2
votes
0answers
50 views

Please clarify the following orthogonal property (quantum anonymous voting)

I am a beginner at QC, currently going through a paper on Quantum Anonymous Voting. Please clarify the orthogonal property described in the following scenario. Consider $n$ voters $V_{0}, V_{1}, V_{2}...
2
votes
0answers
51 views

How to define initial state $\rvert \Psi(0) \rangle \equiv \rvert 1, -1 \rangle \otimes \rvert 0 \rangle_{\text{cav}} $ of a system in QuTiP?

Say, we have a $\require{mhchem}\ce{^87Rb}$ atom having an electric dipole transition on the $D_{1}$ line and we have two hyperfine ground states, one on $F = 1$ and one on $F = 2$ level. So, we take ...
2
votes
0answers
67 views

States of a qubit in a DC-SQUID

Does anybody of you know what are the two states $|0\rangle$ and $|1\rangle$ of a qubit in a DC-SQUID (2 Josephson junctions in a loop)?
2
votes
0answers
49 views

GHZ - measuring particles

I'm referring to an earlier question. It involves secret sharing based on the different measurement directions 3 people i.e Alice Bob and Charlie do. Now there is a block in the referred paper which ...
2
votes
0answers
50 views

Restoring an initial state after computation

Let me first tell my problem statement. Suppose I have a uniform superposition of states $$|A\rangle=\dfrac{1}{2^{9}}\sum_{i,j,k=0}^{2^6-1}|0\rangle^{\otimes 8}|i\rangle|j\rangle|k\rangle,$$ where $|0\...
2
votes
0answers
48 views

What interesting properties can I measure with a 1 qubit state?

I am playing with the IBM Q and I would like to know what interesting properties I can measure with only a 1 qubit state. This is because things like Bell's inequalities, concurrence, PPT criterion, ...
2
votes
0answers
20 views

Hamiltonian of the valence electron of Yb+ ion

Let's say I have chosen the valence electron of Yb+ as my qubit. I want to consider it's hyperfine structure as the two-level energy states. Are my following assumptions correct? If the magnetic ...
1
vote
0answers
30 views

Constructing and Measuring in an Arbitrary 3-qubit basis

As part of a Quantum Theory project I have "constructed" an arbitrary 3-qubit basis: $\left|B_0\right> =\left|000\right>$ $\left|B_1\right> = \frac{1}{\sqrt{2}}\cos(x)(\left|100\right> +...
1
vote
0answers
30 views

Are there different orderings of the fifteen SU(4) generators in common use?

I've recently performed certain analyses (Archipelagos of Total Bound and Free Entanglement) pertaining to eq. (50) in Separable Decompositions of Bipartite Mixed States , that is \begin{equation} ...
1
vote
0answers
64 views

Quantum operation involving permutation

Suppose I have the state $\frac{1}{2^l/2}\sum_{i=0}^{2^l-1}|0\rangle^{\otimes q}\otimes |i\rangle^{\otimes}|0\rangle_i^{\otimes l}$. I perform some unitary transformation between the registers $|i\...
1
vote
0answers
49 views

Implementing conditional operators in a quantum circuit

I have 4 states say $|00\rangle, |01\rangle,|10\rangle, |11\rangle$. I want to add the states in a manner such that $|a\rangle=|00\rangle\otimes|01\rangle\to |00\rangle\otimes|01\rangle$ and $|b\...
0
votes
2answers
38 views

How to switch bit in the quantum state?

I want to transform binary representation from one to other. Here, I have 2 registers one act as control register and another is target register with the same number of qubits $n$. Consider $n = 3$ ...
0
votes
0answers
38 views

How can I find the fidelity of preparation?

I want to know the fidelity (or error rate) of the preparation ($|0\rangle$) How can I have it?
0
votes
0answers
25 views

Affine Map of the Bloch sphere

I am referring to Equation (8.89) to (8.92) in Chapter 8 of "Quantum Computing and Information 10th Anniversary Edition" by Nielsen and Chuang. This section deals with the geometric picture of single ...
0
votes
0answers
54 views

deliver a quantum register to/from a function in qiskit

Can I create a function in qiskit which receive a quantum register as an argument, and/or returns a quantum register? In the example below, I created a quantum register, and a quantum circuit which ...
0
votes
0answers
32 views

Quantum state preference theory for economics

Game theory (Nash, 1950) and state preference theory (Arrow and Debreu, 1954) are fundamental models when learning about equilibrium in microeconomics. In equation form, state preference theory ...
0
votes
0answers
37 views

Implementing B92 protocol on IBM Qx

I wanted to implement the B92 protocol on IBM Qx. Implementing the protocol would require that a particular qubit should not be measured when using a particular base i.e. there should be no output at ...
0
votes
0answers
20 views

Change entangled far Qbit state without mesaure it

Hello I entangled with Qsharp a far QBit (Bob)to a 3 Qbit register that is also entangled to another marked qbit for a Grover search. When I look for the value 4 with Grover search the Bob qbit is ...
0
votes
0answers
66 views

Which state describes carrier transport through channel? A mixed state or a pure state?

A pure quantum state is a state which can be described by a single ket vector. A mixed quantum state is a statistical ensemble of pure states. When carriers transport from source to drain in a Field ...
0
votes
0answers
456 views

FPGA qubit simulation

This question is regarding the simulation of qubits, using FPGAs. My question is: how does using FPGAs to simulate qubits help us understand or give us an insight into how quantum computers could be ...
-1
votes
0answers
23 views

Can we use the process of recursion in predicting the future process?

Because while recursion we tend to find the possible result of a current problem by going into its future state through recursion and sometimes by means of through memorization. Then why can't we use ...
-2
votes
0answers
37 views

If one had a verifiable solution to P versus NP problem, how, and why, would one go about submitting it?

Asking for a friend. The exclusivity/elitism of the field (and the dominance-human hierarchy), as well as the outcomes of "exploitation of "discoveries" throughout history have friend leaning away ...