Most Popular

1500 questions
8
votes
2 answers

Apply readout error mitigation to mid-circuit measurement

I'm trying to construct a quantum circuit with 3 mid-circuit measurements, here's an example: qrz = QuantumRegister(2,'q') crz = ClassicalRegister(3,'c') qc = QuantumCircuit(qrz,crz) for i in range (3): qc.append(qc1(...),[0,1]). # qc1 is…
8
votes
1 answer

What are spin-coherent states?

Trying to understand the paper; https://arxiv.org/pdf/1702.02577.pdf and ran into "spin-coherent" states. I wonder those are.
John Parker
  • 1,181
  • 6
  • 15
8
votes
2 answers

What is the square root of the NOT gate?

I have encountered different matrix of operator "the Square Root of NOT gate". For example, the matrix is specified here: $\sqrt {NOT} = \frac{1}{2}\left( {\begin{array}{*{20}{c}} {1 + i}&{1 - i}\\ {1 - i}&{1 + i} \end{array}} \right)$ And here a…
alexhak
  • 481
  • 4
  • 11
8
votes
1 answer

How exactly does Simon's algorithm solve the Simon's problem?

Problem Statement: We are given a $2-1$ function $f:\{0,1\}^{n}\to\{0,1\}^{n}$ such that: there is a secret string $s\in\{0,1\}^{n}$ such that: $f(x)=f(x\oplus s)$. Challenge: find $s$. Simon's algorithm says: Set up a random superposition…
8
votes
1 answer

Definition of a NISQ device with respect to qubit counts and error rates

How do we define whether a device is a noisy intermediate-scale quantum (NISQ) device with respect to number of qubits and their error rates? Does it make sense to do this? I believe I once saw a definition of a NISQ device as one with on the order…
Greenstick
  • 1,086
  • 8
  • 23
8
votes
3 answers

In the adiabatic version of Grover's algorithm, how is the Hamiltonian constructed?

X-posted on physics.stackexchange In quantum computation, there is a famous algorithm to search a marked item in an unstructured database called Grover's algorithm. It achieves a quadratic speedup over the best possible classical algorithm. On the…
8
votes
1 answer

Do global phases matter when a gate is converted into a controlled gate?

Let's say that we have a unitary matrix M such that: $$ M = e^{i\pi/8}\begin{pmatrix} 1 & 0 \\ 0 & e^{i\pi/12} \\ \end{pmatrix} $$ If we were to apply this unitary matrix to the state $|1\rangle$, we would get: $$ M|1\rangle\ =\…
8
votes
1 answer

Can we get access to the second-lowest eigenstate?

I'd like to know if there's anything that can be said about whether and when we can efficiently prepare a state corresponding to the second-lowest eigenvalue $|\lambda_1\rangle$ of a given Hamiltonian, or in any other way learn what this energy…
8
votes
0 answers

Requirements for Achieving a Quantum Speedup

We usually talk about the power of a quantum computer by examining the separation between sets of gates that we know we can efficiently simulate on a classical computer (i.e. problems in the class BPP), and universal gate sets which, by definition,…
DaftWullie
  • 62,671
  • 4
  • 55
  • 140
8
votes
4 answers

Computing $e^x$ on a quantum computer

Does anyone know how to make a quantum circuit to compute exponentials where the exponent can be a fraction? To be more precise, I'm looking for a fixed point quantum arithmetic circuit that does the following: $$|\vec{x}\rangle|\vec{0}\rangle…
sheesymcdeezy
  • 2,021
  • 8
  • 27
8
votes
2 answers

What's the POVM corresponding to single-qubit state tomography?

Let $\rho$ be a single-qubit state. A standard way to characterise $\rho$ is to measure the expectation values of the Pauli matrices, that is, to perform projective measurements in the three mutually unbiased bases corresponding to the Pauli…
glS
  • 27,510
  • 7
  • 37
  • 125
8
votes
3 answers

Can I find the axis of rotation for any single-qubit gate?

Suppose I have an arbitrary qiskit $U_3$ gate: $U_3(\theta,\phi,\lambda)$. Is there a way I can find which axis the gate is rotating around? In other words, given any real numbers $\theta,\phi,\lambda$, can I find the vector $\hat n = (n_x,n_y,n_z)$…
ZR-
  • 2,408
  • 9
  • 24
8
votes
3 answers

If a Hamiltonian is quadratic in the ladder operator, why is its time evolution linear in the ladder operator?

How can one show that $\hat{U}^\dagger\hat{a}\hat{U}$ (with $\hat{U} =e^{-i\hat{H}t}$) involves only linear orders of the ladder operator, when $H$ is the general quadratic Hamiltonian $(\hat{H} = \alpha (\hat{a}^\dagger)^2+ \beta…
8
votes
0 answers

What are examples of zero capacity quantum channels with Choi rank less than $d$?

All the currently known examples of quantum channels with zero quantum capacity are either PPT or anti-degradable. These notions can be conveniently defined in terms of the Choi matrix of the given channel: A channel is said to be PPT if its Choi…
8
votes
2 answers

How can one argue that the $S$-gate is Clifford while $T$-gate is not?

How can one argue that $S$-gate is Clifford while $T$-gate is not?
heromano
  • 545
  • 2
  • 10