Understanding whether dissipation in an open quantum system is truly quantum is a question of both fundamental and practical interest. We consider a general model of n qubits subject to correlated Markovian dephasing, and present a sufficient conditi
on for when bath-induced dissipation can generate system entanglement and hence must be considered quantum. Surprisingly, we find that the presence or absence of time-reversal symmetry (TRS) plays a crucial role: broken TRS is required for dissipative entanglement generation. Further, simply having non-zero bath susceptibilities is not enough for the dissipation to be quantum. Our work also present an explicit experimental protocol for identifying truly quantum dephasing dissipation, and lays the groundwork for studying more complex dissipative systems and finding optimal noise mitigating strategies.
We show that entangled measurements provide an exponential advantage in sample complexity for Pauli channel estimation, which is both a fundamental problem and a practically important subroutine for benchmarking near-term quantum devices. The specifi
c task we consider is to learn the eigenvalues of an $n$-qubit Pauli channel to precision $varepsilon$ in $l_infty$ distance. We give an estimation protocol with an $n$-qubit ancilla that succeeds with high probability using only $O(n/varepsilon^{2})$ copies of the Pauli channel, while prove that any ancilla-free protocol (possibly with adaptive control and channel concatenation) would need at least $Omega(2^{n/3})$ rounds of measurement. We further study the advantages provided by a small number of ancillas. For the case that a $k$-qubit ancilla ($kle n$) is available, we obtain a sample complexity lower bound of $Omega(2^{(n-k)/3})$ for any non-concatenating protcol, and a stronger lower bound of $Omega(n2^{n-k})$ for any non-adaptive, non-concatenating protocol. The latter is shown to be tight by explicitly constructing a $k$-qubit-ancilla-assisted estimation protocol. We also show how to apply the ancilla-assisted estimation protocol to a practical quantum benchmarking task in a noise-resilient and sample-efficient manner, given reasonable noise assumptions. Our results provide a practically-interesting example for quantum advantages in property learning and also bring new insight for quantum benchmarking.
We use machine learning to classify rational two-dimensional conformal field theories. We first use the energy spectra of these minimal models to train a supervised learning algorithm. We find that the machine is able to correctly predict the nature
and the value of critical points of several strongly correlated spin models using only their energy spectra. This is in contrast to previous works that use machine learning to classify different phases of matter, but do not reveal the nature of the critical point between phases. Given that the ground-state entanglement Hamiltonian of certain topological phases of matter is also described by conformal field theories, we use supervised learning on R{e}yni entropies and find that the machine is able to identify which conformal field theory describes the entanglement Hamiltonian with only the lowest few R{e}yni entropies to a high degree of accuracy. Finally, using autoencoders, an unsupervised learning algorithm, we find a hidden variable that has a direct correlation with the central charge and discuss prospects for using machine learning to investigate other conformal field theories, including higher-dimensional ones. Our results highlight that machine learning can be used to find and characterize critical points and also hint at the intriguing possibility to use machine learning to learn about more complex conformal field theories.
Long-range correlated errors can severely impact the performance of NISQ (noisy intermediate-scale quantum) devices, and fault-tolerant quantum computation. Characterizing these errors is important for improving the performance of these devices, via
calibration and error correction, and to ensure correct interpretation of the results. We propose a compressed sensing method for detecting two-qubit correlated dephasing errors, assuming only that the correlations are sparse (i.e., at most s pairs of qubits have correlated errors, where s << n(n-1)/2, and n is the total number of qubits). In particular, our method can detect long-range correlations between any two qubits in the system (i.e., the correlations are not restricted to be geometrically local). Our method is highly scalable: it requires as few as m = O(s log n) measurement settings, and efficient classical postprocessing based on convex optimization. In addition, when m = O(s log^4(n)), our method is highly robust to noise, and has sample complexity O(max(n,s)^2 log^4(n)), which can be compared to conventional methods that have sample complexity O(n^3). Thus, our method is advantageous when the correlations are sufficiently sparse, that is, when s < O(n^(3/2) / log^2(n)). Our method also performs well in numerical simulations on small system sizes, and has some resistance to state-preparation-and-measurement (SPAM) errors. The key ingredient in our method is a new type of compressed sensing measurement, which works by preparing entangled Greenberger-Horne-Zeilinger states (GHZ states) on random subsets of qubits, and measuring their decay rates with high precision.
Efficient characterization of quantum devices is a significant challenge critical for the development of large scale quantum computers. We consider an experimentally motivated situation, in which we have a decent estimate of the Hamiltonian, and its
parameters need to be characterized and fine-tuned frequently to combat drifting experimental variables. We use a machine learning technique known as meta-learning to learn a more efficient optimizer for this task. We consider training with the nearest-neighbor Ising model and study the trained models generalizability to other Hamiltonian models and larger system sizes. We observe that the meta-optimizer outperforms other optimization methods in average loss over test samples. This advantage follows from the meta-optimizer being less likely to get stuck in local minima, which highly skews the distribution of the final loss of the other optimizers. In general, meta-learning decreases the number of calls to the experiment and reduces the needed classical computational resources.
Quantum systems are promising candidates for sensing of weak signals as they can provide unrivaled performance when estimating parameters of external fields. However, when trying to detect weak signals that are hidden by background noise, the signal-
to-noise-ratio is a more relevant metric than raw sensitivity. We identify, under modest assumptions about the statistical properties of the signal and noise, the optimal quantum control to detect an external signal in the presence of background noise using a quantum sensor. Interestingly, for white background noise, the optimal solution is the simple and well-known spin-locking control scheme. We further generalize, using numerical techniques, these results to the background noise being a correlated Lorentzian spectrum. We show that for increasing correlation time, pulse based sequences such as CPMG are also close to the optimal control for detecting the signal, with the crossover dependent on the signal frequency. These results show that an optimal detection scheme can be easily implemented in near-term quantum sensors without the need for complicated pulse shaping.
We reduce measurement errors in a quantum computer using machine learning techniques. We exploit a simple yet versatile neural network to classify multi-qubit quantum states, which is trained using experimental data. This flexible approach allows the
incorporation of any number of features of the data with minimal modifications to the underlying network architecture. We experimentally illustrate this approach in the readout of trapped-ion qubits using additional spatial and temporal features in the data. Using this neural network classifier, we efficiently treat qubit readout crosstalk, resulting in a 30% improvement in detection error over the conventional threshold method. Our approach does not depend on the specific details of the system and can be readily generalized to other quantum computing platforms.
