Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

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What is the original reference for the Hadamard test?

The Hadamard test is a widely used routine in quantum computing to compute the real and imaginary part of expectation values of unitary operators. However, all papers I have come across in the literature that make use of the Hadamard test fail to…
bm442
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Estimate/determine Bures separability probabilities making use of corresponding Hilbert-Schmidt probabilities

For two-qubit states, represented by a $4\times 4$ density matrix, the generic state is described by 15 real parameters. For ease of calculation, it can help to consider restricted families of states, such as the "$X$"-states, where any matrix…
Paul B. Slater
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Why was Feynman hesitant about simulating fermions with a quantum computer?

Richard Feynman has a number of foundational publications from the early-mid 80's on quantum computing that I continue to read with awe and inspiration. As earlier discussed, the 1985 article "Quantum Mechanical Computers" is concerned with…
Mark Spinelli
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Categories and types of quantum inspired algorithms

I have a question concerning "quantum-inspired" algorithms. There seem to be several types of algorithms that fall into this category. Some examples are: Ewin's dequantized algorithms Tensor Networks A couple of optimization examples by…
sheesymcdeezy
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Quantum walk with binary tree

I’m trying to grok quantum walks, and would like to create an example that walks a perfect binary tree to find the one and only marked leaf node. Is this possible? If so, suppose the depth of the tree is five. Would that require a circuit with five…
JavaFXpert
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Can a quantum computer break quantum cryptography?

I’m not sure if this makes sense, but I know that there is quantum and post-quantum encryption, and I’m curious whether quantum computing can break a quantum encryption.
Gejolop
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Are there separable $\rho$ that cannot be decomposed with less than $\operatorname{rank}(\rho)^2$ pure product states?

In What separable $\rho$ only admit separable pure decompositions with more than $\mathrm{rank}(\rho)$ terms?, examples were given of separable states $\rho$ with separable decompositions requiring more than $\operatorname{rank}(\rho)$ components.…
glS
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Are qudit graph states well-defined for non-prime dimension?

Qudit graph states are $d$-dimension generalisations of qubit graph states such that each state is represented by a weighted graph $G$ (with no self-loops) such that each edge $(i, j)$ is assigned a weight $A_{i, j} = 0,\ldots,d-1$. The graph state…
SLesslyTall
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Is the controlled-Hadamard gate in the Clifford group?

Is the controlled-Hadamard gate a member of the Clifford group? I understand that Controlled Pauli gates are in the Clifford group. If controlled Hadamard is Clifford member, then is a controlled-SingleClifford also a member of the Clifford group ?
Isolated Information
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How many operations can a quantum computer perform per second?

I want to know what time complexity is considered efficient/inefficient for quantum computers. For this, I need to know how many operations a quantum computer can perform per second. Can anyone tell me how to calculate it and what factors it depends…
PiMan
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Implementing a CCCNOT gate using only Toffoli gates

A CCCNOT gate is a four-bit reversible gate that flips its fourth bit if and only if the first three bits are all in the state $1$. How would I implement a CCCNOT gate using Toffoli gates? Assume that bits in the workspace start with a particular…
chuster
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Quantum Walk: Why the need of adding "tail" nodes to the root?

As stated in the question, I have found in several papers (e.g. 1, 2) that in order to perform a quantum walk on a given tree it is necessary to add some nodes to the root $r$, say $r^{'}$ and $r^{"}$. Why are they needed? References: Farhi E.,…
FSic
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Why does (almost) every pair of Hamiltonians generate, through repeated commutation, the whole space of Hermitian matrices?

In [1], the problem of simulating a Hamiltonian using repeated applications of a different set of Hamiltonians is discussed. In particular, let $A$ and $B$ be a pair of Hermitian operators, and let $\mathcal L$ be the algebra generated from $A, B$…
glS
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Composing multiple quantum circuits in single quantum program in Qiskit

I was wondering if there is a way to compose a program with multiple quantum circuits without having the register reinitialized at $0$ for each circuit. Specifically, I would like run a second quantum circuit after running the first one, as in this…
asdf
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Rotating about the y- or z-axis of the Bloch sphere

In order to rotate about an axis of the Bloch sphere we ususally use pulses e.g. in trapped ion quantum computing or superconducting qubits. Let's say we have rotation around the x-axis. What do I have to change in order to be able to rotate around…
Quasar
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