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

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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 ...
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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 \...
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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 ...
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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 ...
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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 ...
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How do physical implementations of Z gate selectively affect $\lvert1\rangle $ basis vector?

The Pauli Z gate inverts the phase of $\lvert1\rangle $ while leaving $\lvert0\rangle$ unaffected. When I think about how $\lvert1\rangle $ and $\lvert0\rangle$ are physically realized, however, as ...
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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 ...
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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 ...
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72 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 ...
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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 ...
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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 ...
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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 $\{x,f(x)\}$, ...
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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 ...
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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 ...
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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}...
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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 ...
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Holevo quantity and mutual information

On this page, it is stated that the Holevo quantity is an upper bound to the accessible information of a quantum state. In the scenario where Alice encodes classical information into a quantum state ...
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64 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)?
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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 ...
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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\...
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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, ...
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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 ...
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59 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\...
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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\...
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How to encode a qubit in standard basis?

I wonder what the steps for encoding a qubit in a certain basis are (you can give your answer in terms of the standard basis for simplicity). Example and a little explanation about steps would be ...
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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 ...
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28 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 ...
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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 ...
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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 ...
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398 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 ...
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How to generate the following $n$-level $n$-particle singlet state?

$$\boxed{|S_{n}\rangle = \frac{1} {\sqrt{n!}} \sum_{S\in P_n^{n}} ( \,-1) \,^{\Gamma(S)}|s_{0}\rangle |s_{1}\rangle ....|s_{n-1}\rangle}$$ Here $P_n^{n}$ is the set of all permutations of $Z_n := \{0,...