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1500 questions
6
votes
2 answers
Conditions for entangling $A$ with $C$ via an interaction on $AB$
I have three qubits in subsystems $A$, $B$, $C$. System $A$ initially contains some state $\rho_A$, and $BC$ contains a bipartite pure state $|\psi\rangle_{BC}$. I apply a unitary operation $U$ acting on $\mathcal{H}_A\otimes \mathcal{H}_B$ and then…
forky40
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6
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2 answers
Has it been proved that true post-quantum cryptography protocols exist?
Post-quantum cryptography is the development of cryptographic protocols that are not easily crackable using a fault-tolerance quantum computer. I know that NIST has a competition to find the best post-quantum cryptography algorithm, and some of the…
Mauricio
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6
votes
1 answer
If you had a 100 qubit fully fault-tolerant quantum computer, what would you do?
As quantum computers improve, eventually we may have error-corrected devices that have very low error rate. However, many applications (Shor's algorithm, quantum chemistry) appear to require thousands of error-corrected qubits, if not more. Are…
shixian105
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6
votes
2 answers
Are quantum channels bounded linear maps?
I've been reading about quantum channels from a couple of sources and have some doubts regarding some mathematical perspectives and properties of quantum channels. I've listed them below:
It is known that quantum channels map density operators on…
Peeveey
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6
votes
1 answer
Existence of Hamiltonians such that the time evolution unitary becomes identity
Can we always find a set of coefficients ${k_i}$ (where not every $k_i = 0$) for a given Hamiltonian $H = \sum k_i H_i$, such that the unitary operator becomes the identity operation: $e^{-iH} = e^{i\alpha}I$, where $\alpha$ is a real phase? The…
Hailey Han
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6
votes
1 answer
Would an ambient-pressure, room-temperature superconductor eliminate the need for a dil-fridge in transmon processors?
Although there are many competing designs for quantum computer architectures, a transmon-based superconducting qubit architecture is well-advanced enough to be "in the lead" across various metrics. But, transmon qubits use a dilution refrigerator…
Mark Spinelli
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6
votes
0 answers
Can we obfuscate the identity?
Motivated by Aaronson's call to find simple, verifiable proofs of quantumness, suppose we start off with a random polynomial-length circuit $U$ of, say, Hadamard+CCNOT (Toffoli) or CSWAP (Fredkin) gates, and attach $U^\dagger$ to it, can we then use…
Mark Spinelli
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6
votes
1 answer
We take the reciprocal $\lambda^{-1}$ of eigenvalues in HHL - but what's stopping us from raising them to a positive exponent $\lambda^m$?
The HHL algorithm generally can be thought of as diagonalizing our matrix $A$ with the quantum phase estimation algorithm, and applying a specific function $f(\lambda)=\lambda^{-1}$ to the eigenvalues so obtained by rotating an ancilla qubit and…
Mark Spinelli
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6
votes
3 answers
Why are rotations represented by exponentials of Pauli matrices?
I'm self-studying Quantum Computation from Nielsen and Chuang's book. In section 4.2 they discuss that for any unit vector $\hat n$, the rotation operator $R_{\hat n}(\theta) = \exp(-i\theta\hat n \cdot \vec\sigma/2)$ rotates the Bloch vector about…
slimmerikko
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6
votes
0 answers
Is amplitude estimation optimal?
Amplitude estimation requires $O(1/\epsilon)$ measurements if we want to estimate an amplitude to absolute precision $\epsilon$. Is this optimal? Why can't we do better than this?
I'm trying to see if there's an explanation in the literature but I'm…
confusion
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6
votes
1 answer
Can any channel be represented as $A\rho A^\dagger$ for some $A$?
Consider an arbitrary quantum operation defined by a series of Kraus operators $\sum_j K_j\rho K_j^\dagger$ over the density matrix of the system $\rho$. The operation might or might not be unitary, but the Kraus operators satisfy the completely…
Zarathustra
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6
votes
1 answer
Why is Grover's Algorithm considered to be a Quantum Walk?
I have heard it said that Grover's algorithm is (can be modeled as?) a Quantum Walk. In fact, one reason for their popularity is that QW are used in certain Quantum algorithms. I am trying to understand the connection between this algorithm and a…
Andreas132
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6
votes
1 answer
Universality with Toffoli + Hadamard
If I take the two gates Hadamard and Toffoli, then it is clear that I cannot simulate an arbitrary $n$ qubit unitary on $n$ qubits because both matrices are real, so there's no access to the complex space. However, I can simulate any $n$ qubit…
DaftWullie
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6
votes
0 answers
How to use Warm-Start QAOA in QisKit to solve non-convex QUBO problem?
I have a non-convex QUBO problem that I'd like to solve by warm-starting QAOA with a solution obtained from a continuous relaxation solution obtained by a classical algorithm. The specifics of the problem is shown below in the code.
I have 2…
underdog987
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6
votes
1 answer
Minimum-weight presentation for stabilizer group $S$ and logical Pauli group $N(S)/S$
Given some stabilizer group $S$ with presentation $\langle s_1, \dots, s_r \rangle$, what is known about finding a minimal-weight presentation for it? By this, I mean a new presentation $\langle s_1', \dots, s_r' \rangle$ such that $\sum_{j=1}^{r}…
Alex Townsend-Teague
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