20
That doesn't scale well. After a moderately long calculation you're basically left with the maximally mixed state or whatever fixed point your noise has. To scale to arbitrary long calculations you need to correct errors before they become too big.
Here's some short calculation for the intuition given above. Consider the simple white noise model (...
13
As an addition to Nat's answer, it's worth mentioning that 'noise' is a specific concept1 in quantum computing. This answer will use Preskill's lecture notes as a basis.
In essence, noise is indeed considered to be something that could be described as 'thermal noise', although it should be noted that it is an interaction with a thermal environment causing ...
12
If the error rate were low enough, you could run a computation a hundred times and take the most common answer. For instance, this would work if the error rate were low enough that the expected number of errors per computation was something very small — which means that how well this strategy works would depend on how long and complicated a computation ...
11
Unfortunately for analog computation it turns out that when realistic assumptions about the presence of noise in analog computers are made, their power disappears in all known instances; they cannot efficiently solve problems which are not solvable on a Turing machine.
"Noise" appears to be used in the general sense of non-idealities in a signal:
In ...
10
Throughout this answer, the norm of a matrix $A$, $\left\lVert A\right\rVert$ will be taken to be the spectral norm of $A$ (that is, the largest singular value of $A$). The solovay-Kitaev theorem states that approximating a gate to within an error $\epsilon$ requires $$\mathcal O\left(\log^c\frac 1\epsilon\right)$$ gates, for $c<4$ in any fixed number of ...
9
There is no specific paper for this, though information on the model can be found in the Qiskit Aer API documentation and is based on the research of IBMQ quantum computing group. As examples you can read some of the following papers for more information about errors in IBMQ devices:
arXiv:1410.6419 -- The Methods section at the end has a summary of gate ...
8
As far as I’m aware, the surface code is still regarded as the best. With an assumption of all elements failing with equal probability (and doing so in a certain way) it has a threshold of around 1%.
Note that the paper you linked to doesn’t have a 3D surface code. It is the decoding problem that is 3D, due to tracking changes to the 2D lattice over time. ...
8
The answer to noise (and any source of error, really) in quantum computations is quantum error correction: You choose an encoding such that discretized errors correspond not only to invalid encodings but also uniquely determine what kind of error must have occured. This is not possible for all errors but with reasonable error models (such as single qubit ...
7
This can be done using the 'Aer' component of Qiskit. The properties information can be turned into a noise model using
from qiskit.providers.aer import noise
properties = device.properties()
noise_model = noise.device.basic_device_noise_model(properties)
basis_gates = noise_model.basis_gates
This can then be supplied to the execute() method, as is ...
6
A channel $\Phi$ is said to be degradable if there exists another channel $\Xi$ such that $\Xi\Phi$ is complementary to $\Phi$.
The idea here is as follows. Suppose $\Phi$ is a channel and $\Psi$ is complementary to $\Phi$. If $\Phi$ is applied to a state $\rho$, then the output of the channel is $\Phi(\rho)$ (of course), while $\Psi(\rho)$ represents ...
6
How do we prevent quantum noise in a quantum computer?
Well, technically the answer is (at least for most systems): we use ridiculously low temperatures (much colder than space), we shield everything (or at least as much as possible) out, that might introduce any noise (radio waves, such as phone signals or light, magnetic fields, ...), we do everything to ...
6
There are several ways that you could realise the depolarising map $
\mathcal N_p(\rho) = (1\!-\!p)\:\!\rho + p \!\!\:\cdot\!\tfrac{1}{2}\mathbf 1$ map on a quantum computer — including an idealised quantum computer, in which waiting around for the noise to do the work for you would not be an available method.$\def\ket#1{\lvert#1\rangle}$
We start ...
6
The errors that are described by the Master equation are continuous errors. The action of error correction is to discretize those errors.
For example, dephasing noise can be described by the Master equation. The net effect is that an initial state $\rho$ is transformed into
$$
\rho\mapsto (1-p)\rho+pZ\rho Z,
$$
where $p$ is a function of time.
However, ...
6
(1) Both filters and attenuators are used
Let me just start by saying that non-attenuating filters have not been completely ruled out by people working in the design of cold quantum computers. I will use quotes from three papers, all from 2018, to support this point.
Paper #1: Distinguishing coherent and thermal photon noise in a circuit QED system
"...
5
I believe that the Centre for Engineered Quantum Systems, School of Physics, The University of Sydney and the Center for Theoretical Physics, Massachusetts Institute of Technology use of a tensor network decoder of Bravyi, Suchara and Vargo (BSV), to achieve the highest error correction threshold to date.
In their whitepaper from last December, "Ultrahigh ...
5
I'm going to go for an intuitive answer here, as requested. Let's s go in steps:
Your input is (often?) classical, so up to that point we're good.
Then you start doing quantum operations and achieve, for example, quantum superpositions between different states. Here you're right, you cannot look to check if you're doing OK, and that indeed is a problem, or ...
5
frequency (GHz): The frequency(energy) associated with the transition between the qubit's ground state ($|0\rangle$) and first excited state ($|1\rangle$).
readout error: The probability of preparing a $|0\rangle$($|1\rangle$) and measuring a $|1\rangle$($|0\rangle$), ie., of having an error in your readout
single qubit U2 error rate: The average error per ...
5
Optimization level 0 does not perform 1 qubit gate optimization and it will send 2 X gates (well 2 U3 gates after it unrolls to the basis set). You can see the passes optimization level 0 runs here: https://github.com/Qiskit/qiskit-terra/blob/master/qiskit/transpiler/preset_passmanagers/level0.py It will only map the circuit to the device and unroll the ...
5
Noise effects introduce classical uncertainty in what the underlying state is. A mixed state is a statistical ensemble of several quantum states $|\psi_i\rangle$ (not necessarily orthogonal), with respective probabilities $p_i$.
With the state vector you can represent pure states, not mixed ones. Instead, with the density operator you can represent both pure ...
5
As a first note: the (uncontrolled) transition of $|1\rangle$ to $|0\rangle$ is generally not referred to as dephasing but as relaxation. The noise-process that involves (spontaneous) relaxation is also called the amplitude damping channel.
Now, if you have a system which has a finite temperature, meaning that there is some energy in the system, the reverse ...
5
The 2-norm difference typically isn't particularly physical. So no, this is most likely not the right distance. What you want from a physical point of view is a distance measure which measures the maximal distance between the two channels on any possible input (possibly on a larger system), such as the diamond norm.
Note that the fact that "norms are ...
4
One simple way to do it is by defining a composite gate, like this:
class MyGateThenDepolarize(cirq.SingleQubitGate):
def _decompose_(self, qubits):
q = qubits[0]
return [MyGate.on(q), cirq.depolarize(p).on(q)]
If you want a depolarizing gate on every qubit at the end of every moment, you can do a noisy simulation:
cirq.sample(circuit, ...
4
Yes you can: When you build a noise model the noise is defined with respect to the name or label of gate objects, so you can use the labelto create multiple versions of a single gate but reference different errors in a noise model (NB: the transpiler strips away label information when it unrolls a gate not in the basis gates set).
Selective noise on ...
4
For amplitude damping, $\gamma$ is something like $e^{-\Delta t/T_1}$ where $\Delta t$ is how long the Kraus operator is supposed to act. But be very careful, Kraus evolution assumes your system has no initial correlations, that every qubit interacts with identical baths and that every qubit is identical. All the assumptions are most likely violated and so ...
4
According to so-called threshold theorem, it is possible to get rid of errors in quantum computation with arbitrary precision. However, there is an assumption that you have enough qubits.
To ilustrate the idea, you can encode one qubit $|q\rangle=\alpha|0\rangle+\beta|1\rangle$ with more qubits, for example $|q\rangle=\alpha|0000\rangle+\beta|1111\rangle$ ...
4
Quantum channels are foremost, linear operators. So given a basis for the Hilbert-Schmidt operator space (for example the states $\{|0\rangle\langle 0|,|0\rangle\langle 1|,|1\rangle\langle 0|,|1\rangle\langle 1|\}$ that you've chosen above), where density matrices reside, it acts linearly on the basis elements. Perhaps, the easiest way to see it is to write ...
4
For any quantum error correcting code, it is possible to construct a channel which introduces errors that the code cannot correct. However, the key point is that such channels are highly adversarial and not at all representative of any physically reasonable error mechanism.
An easy way to construct such adversarial noise is to build it from the logical ...
4
As Adam Zalcman has stated in his answer, channels whose Kraus operators are proportional to unitary operators are called mixed-unitary channels (or, alternatively, random unitary channels).
Every mixed-unitary channel is unital (meaning that it maps the identity operator to itself), so if you want a channel that is not mixed unitary, just pick any non-...
4
The standard noisy approach is not to try to determine the presence of an eavesdropper as such, but to create a final key where, even if there is an eavesdropper, you can still be confident that the eavesdropper has negligible information about the key. So you aren't trying to distinguish between noise and eavesdropping, but pessimistically assuming that ...
3
noise should average itself out.
Noise doesn't perfectly average itself out. That's the Gambler's Fallacy. Even though noise tends to meander back and forth, it still accumulates over time.
For example, if you generate N fair coin flips and sum them up, the expected magnitude of the difference from exactly $N/2$ heads grows like $O(\sqrt N)$. That's ...
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