Liang Jiang

Recently, several quantum benchmarking algorithms have been developed to characterize noisy quantum gates on today's quantum devices. A well-known issue in benchmarking is that not everything about quantum noise is learnable due to the existence of gauge freedom, leaving open the question of what information about noise is learnable and what is not, which has been unclear even for a single CNOT gate. Here we give a precise characterization of the learnability of Pauli noise channels attached to Clifford gates, showing that learnable information corresponds to the cycle space of the pattern transfer graph of the gate set, while unlearnable information corresponds to the cut space. This implies the optimality of cycle benchmarking, in the sense that it can learn all learnable information about Pauli noise. We experimentally demonstrate noise characterization of IBM's CNOT gate up to 2 unlearnable degrees of freedom, for which we obtain bounds using physical constraints. In addition, we give an attempt to characterize the unlearnable information by assuming perfect initial state preparation. However, based on the experimental data, we conclude that this assumption is inaccurate as it yields unphysical estimates, and we obtain a lower bound on state preparation noise.

Abstract The quantum Fisher information (QFI), as a function of quantum states, measures the amount of information that a quantum state carries about an unknown parameter. The (entanglement-assisted) QFI of a quantum channel is defined to be the maximum QFI of the output state assuming an entangled input state over a single probe and an ancilla. In quantum metrology, people are interested in calculating the QFI of N identical copies of a quantum channel when N\rightarrow\infty, which we call the asymptotic QFI. It was known that the asymptotic QFI grows either linearly or quadratically with N. Here we obtain a simple criterion that determines whether the scaling is linear or quadratic. In both cases, the asymptotic QFI and a quantum error correction protocol to achieve it are solvable via a semidefinite program. When the scaling is quadratic, the Heisenberg limit, a feature of noiseless quantum channels, is recovered. When the scaling is linear, we show the asymptotic QFI is still in general larger than N times the single-channel QFI and furthermore, sequential estimation strategies provide no advantage over parallel ones. For details, see arXiv: 2003.10559.

Abstract Random quantum circuits have played a central role in establishing the computational advantages of near-term quantum computers over their conventional counterparts. Here, we use ensembles of low-depth random circuits with local connectivity in D spatial dimensions to generate quantum error-correcting codes. For random stabilizer codes and the erasure channel, we find strong evidence that a depth O(logN) random circuit is necessary and sufficient to converge (with high probability) to zero failure probability for any finite amount below the channel capacity for any D. Previous results on random circuits have only shown that O(N^1/D) depth suffices or that O(log^3 N) depth suffices for all-to-all connectivity. We then study the critical behavior of the erasure threshold in the so-called moderate deviation limit, where both the failure probability and the distance to the channel capacity converge to zero with N. We find that the requisite depth scales like O(log N) only for dimensions D=2, and that random circuits require O(N^1/2) depth for D=1. Finally, we introduce an "expurgation" algorithm that uses quantum measurements to remove logical operators that cause the code to fail by turning them into either additional stabilizers or into gauge operators in a subsystem code. With such targeted measurements, we can achieve sub-logarithmic depth in D=2 spatial dimensions below capacity without increasing the maximum weight of the check operators. We find that for any rate beneath the capacity, high-performing codes with thousands of logical qubits are achievable with depth 4-8 expurgated random circuits in D=2 dimensions. These results indicate that finite-rate quantum codes are practically relevant for near-term devices and may significantly reduce the resource requirements to achieve fault tolerance for near-term applications.

Abstract Quantum communication is an important branch of quantum information science, promising unconditional security to classical communication and providing the building block of a future large-scale quantum network. Noise in realistic quantum communication channels imposes fundamental limits on the communication rates of various quantum communication tasks. It is therefore crucial to identify or bound the quantum capacities of a quantum channel. Here, we consider Gaussian channels that model energy loss and thermal noise errors in realistic optical and microwave communication channels and study their various quantum capacities in the energy-constrained scenario. We provide improved lower bounds to various energy-constrained quantum capacities of these fundamental channels and show that higher communication rates can be attained than previously believed. Specifically, we show that one can boost the transmission rates of quantum information and private classical information by using a correlated multi-mode thermal state instead of the single-mode thermal state of the same energy.

Continuous-variable quantum key distribution (CV QKD) using optical coherent detectors is practically favorable due to its low implementation cost, flexibility of wavelength division multiplexing, and compatibility with standard coherent communication technologies. However, the security analysis and parameter estimation of CV QKD are complicated due to the infinite-dimensional latent Hilbert space. Also, the transmission of strong reference pulses undermines the security and complicates the experiments. In this work, we tackle these two problems by presenting a time-bin-encoding CV protocol with a simple phase-error-based security analysis valid under general coherent attacks. With the key encoded into the relative intensity between two optical modes, the need for global references is removed. Furthermore, phase randomization can be introduced to decouple the security analysis of different photon-number components. We can hence tag the photon number for each round, effectively estimate the associated privacy using a carefully designed coherent-detection method, and independently extract encryption keys from each component. Simulations manifest that the protocol using multi-photon components increases the key rate by two orders of magnitude compared to the one using only the single-photon component. Meanwhile, the protocol with four-intensity decoy analysis is sufficient to yield tight parameter estimation with a short-distance key-rate performance comparable to the best Bennett-Brassard-1984 (BB84) implementation.

We propose a novel strategy of using the Gottesman-Kitaev-Preskill (GKP) code in a two-way repeater architecture with multiplexing. The crucial feature of the GKP code that we make use of, is the fact that GKP qubits easily admit deterministic two-qubit gates, hence allowing for deterministic entanglement swapping. Furthermore, thanks to the availability of the analog information generated during the measurement of the GKP qubits, we can design better entanglement swapping procedures between the multiplexed elementary links. To boost the loss-resilience of our encoded qubits, we consider a concatenation of the GKP code with the discrete variable [[7,1,3]] code which has already proven effective in the context of quantum repeater schemes. We find that our architecture allows for high-rate near-deterministic end-to-end entanglement generation with much larger repeater spacing than for the previously considered error-correction based repeater schemes.

We propose a novel architecture of quantum-error-correction-based quantum repeaters that combines the techniques used in discrete and continuous variable quantum information. Specifically, we propose to encode the transmitted qubits in a concatenated code consisting of two levels. On the first level we use a continuous variable GKP code which encodes the qubit in a single bosonic mode. On the second level we use a small discrete variable code, encoding a logical qubit in as few as seven physical qubits. Such an architecture introduces two major novelties which allow us to make efficient use of resources. Firstly, our architecture makes use of two types of quantum repeaters: the simpler GKP repeaters that need to only be able to store and correct errors on a single GKP qubit and more powerful but more costly multi-qubit repeaters that additionally can correct errors on the higher level. We find that the combination of using the two types of repeaters enables us to achieve performance needed in practical scenarios with a significantly reduced cost with respect to an architecture based solely on multiqubit repeaters. Secondly the use of continuous variable GKP code on the lower level has the advantage of providing us with the information about the success probability of the specific GKP correction round. This analog information, unique to bosonic codes, provides significant boost in performance when used to correct second level errors in the multi-qubit repeaters.