Transcription
The state-of-the-art quantum computers of today are still much more error-prone than their classical counterparts. Errors and noise affect our quantum algorithm at each step, including quantum gate execution, cubit idling and readout, and more. This means that multi-step complicated algorithms may return results dominated by noise.
If we could correct practically all errors across many cubits, we would have a large-scale fault-tolerant quantum computer. That is the long-term goal. And the IBM quantum roadmap shows exactly how we'll get there. But what can we do to improve the fidelity of our quantum calculations and leverage the power of quantum computing today?
The answer is error suppression and error mitigation. These refer to a set of strategies for alleviating the impact of noise and imperfections in quantum hardware without requiring the full overhead of quantum error correction. In fact, even when fault-tolerant quantum computers emerge, we still fully expect them to incorporate some form of error mitigation.
In error suppression, you use knowledge about the undesirable effects of noise to introduce customization that can avoid the potential impacts on your circuit. This approach addresses errors at the level of gate control and compilation before any post-processing. These techniques often consist of altering or adding control signals to ensure that the processor returns the desired result.
Let's consider a specific phenomenon. Idle qubits can accumulate errors from environmental interactions or cross-talk interactions with neighboring qubits leading to dephasing or coherent shifts. Therefore, having qubits sit idle until the next pulse is applied may result in large error rates. To prevent this from happening, we can insert sequences of operations during those idle times. As long as those sequences amount to an identity, they don't affect the logical operation of the circuit. There are other considerations like ensuring that the gates you add anti-commute with the noise operation you want to suppress, but that's beyond the scope of this video. Different gate sequences will have different effects, and which sequence is better for each particular case remains an active area of research.
This procedure is known in the literature as dynamical decoupling. The simplest example is probably the insertion of two X gates on a qubit that would otherwise be idle like this. In practice, more complex sets of gates are often used like XY4 shown here. This process introduces additional gates, but much of the design effort occurs classically in advance. So the quantum overhead is often modest compared to other techniques.
A distinct but related form of error suppression is poly twirling. This method is implemented by randomly substituting noisy gates like two-qubit gates for logically equivalent ones made out of that original gate sandwiched between Pauli gates. This is done over several randomizations leading to an ensemble of circuits to execute instead of only the original one. Poly twirling does not reduce the total error but it reshapes the noise channel of the circuit into a Pauli channel eliminating coherent error terms and making it easier to model and mitigate. This has benefits when dealing for instance with coherent noise since over short times that tends to accumulate quadratically whereas Pauli noise accumulates linearly.
There are other benefits related to error mitigation techniques. While error suppression attempts to avoid the effects of noise, error mitigation attempts to fix the effects of noise after they occur. To achieve that, one can try to make the noise more predictable or even larger so that it can be later reversed more effectively.
One important method of error mitigation is zero-noise extrapolation or ZNE for short. This works by running a circuit in the presence of noise, amplifying that noise and then extrapolating back to approximate the zero-noise case. This requires running the circuit multiple times with different noise levels and it relies on our ability to scale quantum noise reliably enough for effective extrapolation.
Let's consider a concrete example in which you want to estimate the energy of a chemical system in a certain state. Let's call the energy E. We define an operator describing our energy and we make a quantum circuit that prepares a state that models the state of the chemical system. We could then use the estimator primitive to estimate this energy and we put that value here. Now we want to increase the noise in our circuit by a known factor without changing the logical effect of our circuit in the absence of noise.
One way of doing that is to introduce additional gates that cancel each other out. For example, assume a circuit contains a controlled-NOT or CNOT gate. This is a two-qubit gate that has a control and a target. If the control qubit is in the state one, we flip the state of the target qubit from 0 to 1 or 1 to 0 and we leave the control qubit unchanged. If the control qubit is in the state zero, we do nothing. There is some noise or error probability associated with this CNOT gate. To increase it by an approximately known factor, consider what happens if we replace our CNOT with three consecutive CNOT gates acting with the same control and target qubits. If the control qubit is in the zero state, nothing changes no matter how many CNOTs we add. If the control qubit is in the one state, then we flip the target state with the original CNOT. The remaining two CNOTs cancel each other out since they flip the target back to the original state and then apply a CNOT. Again, we keep the net logical operation unchanged while amplifying the noise level by inserting additional gate operations. This increases the noise level in a roughly predictable way. And in practice, the focus of noise amplification is often two-qubit gates since they generally contribute more errors than single-qubit gates. If we carry out similar processes throughout our circuit, we can amplify the overall noise level in the entire circuit.
Now we run this new circuit and get an estimation of our energy. Again, we plot this along with our first estimate, effectively plotting our energy estimates as a function of the noise factor. You have a result with factor 1 and a result with factor 3. You could keep going and collect more estimates with more noise factors. When you have enough data points, you can extrapolate that picture back to the zero-noise case. Recall that interpolation means estimating a value between two points that are known. We don't have a real data point at zero noise or with negative noise. So this process is extrapolation even though we're extrapolating downward to a lower noise level. This gives us an error-mitigated estimate of the result in the absence of noise. Zero-noise extrapolation.
There are other kinds of error suppression and mitigation and many subtleties to their implementation, but they all seek to reduce the effects of noise and yield higher fidelity results. All these methods come with caveats. Dynamical decoupling adds gates which can add single-gate errors. So there's a balancing act. ZNE adds gates and requires running a few different variations of your circuit in order to get an estimate of the error scaling. Clearly, error mitigation techniques like ZNE come with quantum overhead. You actually run more quantum gates and/or circuits. There's also a trade-off in error mitigation between accuracy and precision. That is, the distribution of outputs you get is centered better on the exact result, but its spread is wider. And ultimately, these methods will not eliminate all errors.
Finally, let's note that error mitigation is different from error correction. Error mitigation is often an approximate heuristic process that accepts that errors have occurred. Error correction, on the other hand, encodes logical information across many physical qubits and measures certain error syndromes, allowing the system to detect and correct errors without collapsing the logical information. That's all for now, but for more on error correction, see the links below. Thanks, and see you next time.