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1500 questions
9
votes
2 answers
Fast way to check if two state vectors are equivalent up to Pauli operations
I'm looking for fast code, or a fast algorithm, for checking if a given state vector $A$ can be transformed into another state vector $B$ using only the Pauli operations $X$, $Y$, $Z$.
The naive strategy is to simply iterate through all $4^n$ ways…
Craig Gidney
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9
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1 answer
Quantum teleportation with moving Alice and Bob
I have questions regarding quantum teleportation, which keep confusing me.
Suppose Alice and Bob are in the same inertial frame $K$, and at time $t$ (in $K$) Alice teleports a quantum state to Bob. What I always hear is that this means that at time…
Tamás V
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9
votes
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Current limits on Grover search space
I was wondering why till date Grover search has been implemented only till 3 qubits (corresponding to size of database = 8). Refer this paper
The reason why I ask is that we have much larger sized quantum computers today. For eg IBM has 50 qubits,…
Maharshi Ray
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9
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What is the complexity of the quantum phase estimation in Grover's algorithm?
Suppose we are using GA (Grover's algorithm) such that we are given it has 2 or more solutions. The search space is of size $N$. We all know Grover's algorithm has, at worst, a time complexity proportional to $\sqrt{N}$.
Now assume we are using…
Learner
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9
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2 answers
Optimal strategy to a quantum state game
Consider the following game:
I flip a fair coin, and depending on the outcome (either heads/tails), I'll give you one of the following states:
$$|0\rangle \text{ or } \cos(x)|0\rangle + \sin(x)|1\rangle.$$
Here, $x$ is a known constant angle. But, I…
jjbid
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9
votes
2 answers
Why doesn't Deutsch-Jozsa Algorithm show that P ≠ BQP?
To my understanding, Deutsch-Jozsa algorithm solves a specific problem in constant time, using a fixed circuit depth, compared to a classical deterministic algorithm, which would require time exponential to the number of bits used to store the…
3yakuya
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9
votes
3 answers
Proof of optimality for CHSH game classical strategy
I'm aware that the optimality of the quantum strategy for the CHSH game is given by Tsirelson's bound, but presentations all skip over the (admittedly much less interesting) proof of the classical strategy's optimality.
In the CHSH game, we have two…
ahelwer
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9
votes
1 answer
Building Intuition for Relative Von Neumann Entropy
This is how I think about classical relative entropy: There is a variable that has distribution P, that is outcome $i$ has probability $p_i$ of occuring, but someone mistakes it to be of a distribution Q instead, so when outcome $i$ occurs, instead…
Mahathi Vempati
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9
votes
2 answers
Expected repetitions of the quantum part of Shor's algorithm
Shor's algorithm to factor a number $N$ goes as follows:
Pick a random value $b \in (0, N)$.
Use a specific quantum computation to a sample a value $v$ that should be close to $2^{m} k/p$ where $m$ is a precision parameter of the quantum…
Craig Gidney
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9
votes
2 answers
How much faster is “D-Wave Two” compared to its predecessor?
I don't have any specific task or algorithm in mind, so depending on how they were tested – Is there any research which shows just how the D-Wave Two computer was faster (in terms of computation performance) than its predecessor (D-Wave One)?
kenorb
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9
votes
1 answer
Quantum algorithms for problems outside NP
What is known about quatum algorithms for problems outside NP (eg NEXP-complete problems), both theoretically like upper & lower speedup bounds and various (im)possibility results, as well as concrete algorithms fro specific problems?
The reason I…
Daniel Mahler
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1 answer
Magic State Distillation Understanding Check
I'm currently trying to understand the T magic state distillation algorithm described in "Universal Quantum Computation with Ideal Clifford Gates and Noisy Ancillas" [1] (Section V starting on Page 6). I need to understand the basics of magic state…
Malcolm Regan
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9
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2 answers
How to obtain Y rotation with only X and Z rotations gates?
Let's say you have a system with which you can perform arbitrary rotations around the X and Z axis. How would you then be able to use these rotations to obtain an arbitrary rotation around the Y axis?
I have seen somewhere that rotation around an…
PhysicsMan
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9
votes
3 answers
Why is the state of multiple qubits given by their tensor product?
How did we derive that the state we get by $n$ qubits is their tensor product? You can use $n=2$ in the explanation for simplicity.
PiMan
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9
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2 answers
Shor's algorithm weaknesses & uniqueness of close rational
I'm working through a problem set, and am stuck on the following problem:
a) What can go wrong in Shor’s algorithm if Q (the dimension of the Quantum Fourier Transform) is not taken to be sufficiently large? Illustrate with an example.
b) What can…
Commutator
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