The randomized benchmarking method yields estimates of the computationally relevant errors without relying on accurate state preparation and measurement. Since it involves long sequences of randomly chosen gates, it also verifies that error behavior is stable when used in long computations. (arXiv:0707.0963)
Questions tagged [randomised-benchmarking]
27 questions
23
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What is the intuition behind quantum t-designs?
I started reading about Randomized Benchmarking (this paper, arxiv version) and came across "unitary 2 design."
After some googling, I found that the Clifford group being a unitary 2 design is a specific case of "Quantum t-design."
I read the…
Blackwidow
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Purpose of using Fidelity in Randomised Benchmarking
Often, when comparing two density matrices, $\rho$ and $\sigma$ (such as when $\rho$ is an experimental implementation of an ideal $\sigma$), the closeness of these two states is given by the quantum state fidelity $$F =…
Mithrandir24601
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Why does the twirl of a quantum channel give a depolarizing channel?
I would like to understand in detail why the twirl of a quantum channel gives depolarizing channel, which is the starting point of randomized benchmarking. To be self-contained, let me set up the notation.
Let $\hat{U}$ denote a superoperator that…
fagd
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Physical meaning of twirling in Randomized Benchmarking
I was reading papers on Randomized Benchmarking, such as this and this.
(more specifically, equation 30 in the second paper)
It appears to be some kind of averaging but I would like to have a more intuitive and physical picture of what it actually…
Blackwidow
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8
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Two definitions of the Clifford group and their relation
Clifford groups are used in at least 3 places I've encountered so far in QIP:
A circuit that contains only Clifford operations, which are generated from CNOT, H and P, is sufficient for a wide variety of quantum circuits, as shown here.
Clifford…
Lior
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How to benchmark a quantum computer?
Using a simple puzzle game to benchmark quantum computers is the most clever approach I have seen so far.
The author of the aforementioned article, James, makes a nice analogy to buying a laptop ("more than just a single number when comparing") in…
user820789
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Is the "unitary twirling operation" physically realizable?
In this neat answer by Markus Heinrich, it is shown that twirling an arbitrary quantum channel $\Lambda$ over the unitary group $U(d)$ yields a depolarizing channel $\tilde{\Lambda}$ given by
$$
\tilde{\Lambda}(M) = \Pi_{U(d)}(\Lambda)(M) =…
Eric Kubischta
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What are well-known orthogonal 2-designs, other than the real Clifford group?
The paper Real Randomized Benchmarking (arXiv) makes use of the fact that the real Clifford group is an orthogonal 2-design on $ n $ qubits in order to do randomized benchmarking (in other words, it uses that fact that the real Clifford group is a…
Ian Gershon Teixeira
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Does Randomized Benchmarking characterize decoherence error?
In my understanding, Randomized Benchmarking (RB) generates a sequence of Clifford gates with different lengths and then characterizes the average error. Since RB is not sensitive to SPAM error, it doesn't characterize it.
My question is, does the…
peachnuts
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Could a new benchmark of quantum processors Q-Score by Atos be more useful than quantum volume?
A few days ago, Atos company published new benchmark for quantum computers. The benchmark is called Q-Score and it is defined as follows:
To provide a frame of reference for comparing performance scores and maintain uniformity, Q-score relies on a…
Martin Vesely
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What is the shortest-circuit-depth quantum-benchmarking algorithm?
An algorithm implementing a model whose results are known, and from the known results, the benchmarking of the device could be done. What is the currently known shortest circuit depth algorithm that has been used on a real device? An additional…
aimedaca
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How to do randomised benchmarking for non-Clifford gates on Qiskit?
For my summer research internship I'm looking to randomized benchmark (RB) non-Clifford gates for a single qubit. Since I found out that Qiskit ignis allows for the RB of Clifford gates, naturally I thought I'd start there. However, the Ignis RB…
Darren Ng
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Using XOR games to benchmark quantum computers
In an answer to a previous question, What exactly are Quantum XOR Games?, ahelwer states:
One application of xor games is self-testing: when running algorithms on an untrusted quantum computer, you can use xor games to verify that the computer…
user820789
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Why does the definition of a unitary t-design use tensor products?
A t-design $X$ is defined by the following equation
$$\frac{1}{|X|} \sum_{U \in X} U^{\otimes t} \otimes\left(U^*\right)^{\otimes t}=\int_{U(d)} U^{\otimes t} \otimes\left(U^*\right)^{\otimes t} d U$$
where the right hand side uses the Haar measure…
user1936752
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How can I get fidelity of a gate from randomized benchmarking?
I found (page 33) the method of finding fidelity from fit by "interleaved and reference decay" according to the sequence fidelity formula: $$F_{ref}=Ap_{ref}^{m}+B,$$
where $p_{ref}^{m}$ is sequence decay.
But if we look at the following…
Curious
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