arXiv subjects

Liang Jiang

Publications and source records attributed to Liang Jiang.

At least 199 records · Page 11Linked to original sources

arXiv2021

New perspectives on covariant quantum error correction

Covariant codes are quantum codes such that a symmetry transformation on the logical system could be realized by a symmetry transformation on the physical system, usually with limited capability of performing quantum error correction (an important case being the Eastin--Knill theorem). The need for understanding the limits of covariant quantum error correction arises in various realms of physics including fault-tolerant quantum computation, condensed matter physics and quantum gravity. Here, we explore covariant quantum error correction with respect to continuous symmetries from the perspectives of quantum metrology and quantum resource theory, establishing solid connections between these formerly disparate fields. We prove new and powerful lower bounds on the infidelity of covariant quantum error correction, which not only extend the scope of previous no-go results but also provide a substantial improvement over existing bounds. Explicit lower bounds are derived for both erasure and depolarizing noises. We also present a type of covariant codes which nearly saturates these lower bounds.

quant-ph↗

arXiv2021

Quantum coding with low-depth random circuits

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 $D\ge 1$ spatial dimensions to generate quantum error-correcting codes. For random stabilizer codes and the erasure channel, we find strong evidence that a depth $O(\log N)$ random circuit is necessary and sufficient to converge (with high probability) to zero failure probability for any finite amount below the optimal erasure threshold, set by 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 ($D \to \infty$). 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 optimal threshold converge to zero with $N$. We find that the requisite depth scales like $O(\log N)$ only for dimensions $D \ge 2$, and that random circuits require $O(\sqrt{N})$ 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 additional stabilizers or gauge operators. With such targeted measurements, we can achieve sub-logarithmic depth in $D\ge 2$ 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.

quant-ph↗

arXiv2021

Quantum repeaters based on concatenated bosonic and discrete-variable quantum codes

We propose an architecture of quantum-error-correction-based quantum repeaters that combines 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 encoding the qubit in a single bosonic mode. On the second level we use a small discrete-variable code. Such an architecture has two important features. Firstly, errors on each of the two levels are corrected in repeaters of two different types. This enables for achieving performance needed in practical scenarios with a reduced cost with respect to an architecture for which all repeaters are the same. Secondly, the use of continuous-variable GKP code on the lower level generates additional analog information which enhances the error-correcting capabilities of the second-level code such that long-distance communication becomes possible with encodings consisting of only four or seven optical modes.

quant-ph↗

arXiv2021

Quantum control of bosonic modes with superconducting circuits

Bosonic modes have wide applications in various quantum technologies, such as optical photons for quantum communication, magnons in spin ensembles for quantum information storage and mechanical modes for reversible microwave-to-optical quantum transduction. There is emerging interest in utilizing bosonic modes for quantum information processing, with circuit quantum electrodynamics (circuit QED) as one of the leading architectures. Quantum information can be encoded into subspaces of a bosonic superconducting cavity mode with long coherence time. However, standard Gaussian operations (e.g., beam splitting and two-mode squeezing) are insufficient for universal quantum computing. The major challenge is to introduce additional nonlinear control beyond Gaussian operations without adding significant bosonic loss or decoherence. Here we review recent advances in universal control of a single bosonic code with superconducting circuits, including unitary control, quantum feedback control, driven-dissipative control and holonomic dissipative control. Various approaches to entangling different bosonic modes are also discussed.

quant-ph↗

arXiv2021

Resilience of quantum random access memory to generic noise

Quantum random access memory (QRAM)--memory which stores classical data but allows queries to be performed in superposition--is required for the implementation of numerous quantum algorithms. While naive implementations of QRAM are highly susceptible to decoherence and hence not scalable, it has been argued that the bucket brigade QRAM architecture [Giovannetti et al., Phys. Rev. Lett. 100 160501 (2008)] is highly resilient to noise, with the infidelity of a query scaling only logarithmically with the memory size. In prior analyses, however, this favorable scaling followed directly from the use of contrived noise models, thus leaving open the question of whether experimental implementations would actually enjoy the purported scaling advantage. In this work, we study the effects of decoherence on QRAM in full generality. Our main result is a proof that this favorable infidelity scaling holds for arbitrary error channels (including, e.g., depolarizing noise and coherent errors). Our proof identifies the origin of this noise resilience as the limited entanglement among the memory's components, and it also reveals that significant architectural simplifications can be made while preserving the noise resilience. We verify these results numerically using a novel classical algorithm for the efficient simulation of noisy QRAM circuits. Our findings indicate that QRAM can be implemented with existing hardware in realistically noisy devices, and that high-fidelity queries are possible without quantum error correction. Furthermore, we also prove that the benefits of the bucket-brigade architecture persist when quantum error correction is used, in which case the scheme offers improved hardware efficiency and resilience to logical errors.

quant-ph↗

arXiv2021

Engineering fast bias-preserving gates on stabilized cat qubits

Stabilized cat codes can provide a biased noise channel with a set of bias-preserving (BP) gates, which can significantly reduce the resource overhead for fault-tolerant quantum computing. All existing schemes of BP gates, however, require adiabatic quantum evolution, with performance limited by excitation loss and non-adiabatic errors during the adiabatic gates. In this work, we apply a derivative-based leakage suppression technique to overcome non-adiabatic errors, so that we can implement fast BP gates on Kerr-cat qubits with improved gate fidelity while maintaining high noise bias. When applied to concatenated quantum error correction, the fast BP gates can not only improve the logical error rate but also reduce resource overhead, which enables more efficient implementation of fault-tolerant quantum computing.

quant-ph↗

arXiv2021

Bootstrap Inference for Quantile Treatment Effects in Randomized Experiments with Matched Pairs

This paper examines methods of inference concerning quantile treatment effects (QTEs) in randomized experiments with matched-pairs designs (MPDs). Standard multiplier bootstrap inference fails to capture the negative dependence of observations within each pair and is therefore conservative. Analytical inference involves estimating multiple functional quantities that require several tuning parameters. Instead, this paper proposes two bootstrap methods that can consistently approximate the limit distribution of the original QTE estimator and lessen the burden of tuning parameter choice. Most especially, the inverse propensity score weighted multiplier bootstrap can be implemented without knowledge of pair identities.

econ.EM↗

arXiv2021

Photon-Number-Dependent Hamiltonian Engineering for Cavities

Cavity resonators are promising resources for quantum technology, while native nonlinear interactions for cavities are typically too weak to provide the level of quantum control required to deliver complex targeted operations. Here we investigate a scheme to engineer a target Hamiltonian for photonic cavities using ancilla qubits. By off-resonantly driving dispersively coupled ancilla qubits, we develop an optimized approach to engineering an arbitrary photon-number-dependent (PND) Hamiltonian for the cavities while minimizing the operation errors. The engineered Hamiltonian admits various applications including canceling unwanted cavity self-Kerr interactions, creating higher-order nonlinearities for quantum simulations, and designing quantum gates resilient to noise. Our scheme can be implemented with coupled microwave cavities and transmon qubits in superconducting circuit systems.

quant-ph↗

arXiv2021

Asymptotic theory of quantum channel estimation

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 is called the asymptotic QFI. Over the years, researchers found various types of upper bounds of the asymptotic QFI, but they were proven achievable only in several specific situations. It was known that the asymptotic QFI of an arbitrary quantum channel grows either linearly or quadratically with $N$. Here we show that a simple criterion can determine whether the scaling is linear or quadratic. In both cases, the asymptotic QFI and a quantum error correction protocol to achieve it are computable 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.

quant-ph↗

arXiv2021

Quantum limits of superresolution in a noisy environment

We analyze the ultimate quantum limit of resolving two identical sources in a noisy environment. We prove that in the presence of noise causing false excitation, such as thermal noise, the quantum Fisher information of arbitrary quantum states for the separation of the objects, which quantifies the resolution, always converges to zero as the separation goes to zero. Noisy cases contrast with a noiseless case where it has been shown to be nonzero for a small distance in various circumstances, revealing the superresolution. In addition, we show that false excitation on an arbitrary measurement, such as dark counts, also makes the classical Fisher information of the measurement approach to zero as the separation goes to zero. Finally, a practically relevant situation resolving two identical thermal sources, is quantitatively investigated by using the quantum and classical Fisher information of finite spatial mode multiplexing, showing that the amount of noise poses a limit on the resolution in a noisy system.

quant-ph↗

arXiv2021

Entanglement trimming in stabilizer formalism

Suppose in a quantum network, there are $n$ qubits hold by Alice, Bob and Charlie, denoted by systems $A$, $B$ and $C$, respectively. We require the qubits to be described by a stabilizer state and assume the system $A$ is entangled with the combined system $BC$. An interesting question to ask is when it is possible to transfer all the entanglement to system $A$ and $B$ by local operation on $C$ and classical communication to $AB$, namely \textit{entanglement trimming}. We find a necessary and sufficient condition and prove constructively for this entanglement trimming, which we name it as "the bigger man principle". This principle is then extended to qudit with square-free dimension and continuous variable stabilizer states.

quant-ph↗

arXiv2021

Autonomous quantum error correction and quantum computation

In this work, we present a general theoretical framework for the study of autonomously corrected quantum devices. First, we identify a necessary and sufficient revised version of the Knill-Laflamme conditions for the existence of an engineered Lindbladian providing protection against at most $c$ consecutive errors of natural dissipation, giving rise to an effective logical decoherence rate suppressed to order $c$. Moreover, we demonstrate that such engineered dissipation can be combined with generalized realizations of error-transparent Hamiltonians (ETH) in order to perform a quantum computation in the logical space while maintaining the same degree of suppression of decoherence. Finally, we introduce a formalism predicting with precision the emergent dynamics in the logical code space resulting from the interplay of natural, engineered dissipations sources and the generalized ETH.

quant-ph↗

arXiv2021

Charge-transfer effect on local lattice distortion in a HfNbTiZr high entropy alloy

It is often assumed that atoms are hard spheres in the estimation of local lattice distortion (LLD) in high-entropy alloys (HEAs). However, our study demonstrates that the hard sphere model misses the key effect, charge transfer among atoms with different electronegativities, in the understanding of the stabilization of severely-distorted HEAs. Through the characterization and simulations of the local structure of the HfNbTiZr HEA, we found that the charge transfer effect competes with LLD to significantly reduce the average atomic-size mismatch. Our finding may form the basis for the design of severely distorted, but stable HEAs.

cond-mat.mtrl-sci↗

arXiv2021

Single-shot number-resolved detection of microwave photons with error mitigation

Single-photon detectors are ubiquitous and integral components of photonic quantum cryptography, communication, and computation. Many applications, however, require not only detecting the presence of any photons, but distinguishing the number present with a single shot. Here, we implement a single-shot, high-fidelity photon number-resolving detector of up to 15 microwave photons in a cavity-qubit circuit QED platform. This detector functions by measuring a series of generalized parity operators which make up the bits in the binary decomposition of the photon number. Our protocol consists of successive, independent measurements of each bit by entangling the ancilla with the cavity, then reading out and resetting the ancilla. Photon loss and ancilla readout errors can flip one or more bits, causing nontrivial errors in the outcome, but these errors have a traceable form which can be captured in a simple hidden Markov model. Relying on the independence of each bit measurement, we mitigate biases in ensembles of measurements, showing good agreement with the predictions of the model. The mitigation improves the average total variation distance error of Fock states from $13.5\%$ to $1.1\%$. We also show that the mitigation is efficiently scalable to an $M$-mode system provided that the errors are independent and sufficiently small. Our work motivates the development of new algorithms that utilize single-shot, high-fidelity PNR detectors.

quant-ph↗

arXiv2020

Single-pixel Tracking and Imaging under Weak Illumination

Under weak illumination, tracking and imaging moving object turns out to be hard. By spatially collecting the signal, single pixel imaging schemes promise the capability of image reconstruction from low photon flux. However, due to the requirement on large number of samplings, how to clearly image moving objects is an essential problem for such schemes. Here we present a principle of single pixel tracking and imaging method. Velocity vector of the object is obtained from temporal correlation of the bucket signals in a typical computational ghost imaging system. Then the illumination beam is steered accordingly. Taking the velocity into account, both trajectory and clear image of the object are achieved during its evolution. Since tracking is achieved with bucket signals independently, this scheme is valid for capturing moving object as fast as its displacement within the interval of every sampling keeps larger than the resolution of the optical system. Experimentally, our method works well with the average number of detected photons down to 1.88 photons/speckle.

physics.optics↗

arXiv2020

Field-gradient measurement using a Stern-Gerlach atomic interferometer with butterfly geometry

Atomic interferometers have been studied as a promising device for precise sensing of external fields. Among various configurations, a particular configuration with a butterfly-shaped geometry has been designed to sensitively probe field gradients. We introduce a Stern-Gerlach (SG) butterfly interferometer by incorporating magnetic field in the conventional butterfly-shaped configuration. Atomic trajectories of the interferometer can be flexibly adjusted by controlling magnetic fields to increase the sensitivity of the interferometer, while the conventional butterfly interferometer using Raman transitions can be understood as a special case. We also show that the SG interferometer can keep high contrast against a misalignment in position and momentum caused by the field gradient.

quant-ph↗

arXiv2020

Multimode photon blockade

Interactions are essential for the creation of correlated quantum many-body states. While two-body interactions underlie most natural phenomena, three- and four-body interactions are important for the physics of nuclei [1], exotic few-body states in ultracold quantum gases [2], the fractional quantum Hall effect [3], quantum error correction [4], and holography [5, 6]. Recently, a number of artificial quantum systems have emerged as simulators for many-body physics, featuring the ability to engineer strong interactions. However, the interactions in these systems have largely been limited to the two-body paradigm, and require building up multi-body interactions by combining two-body forces. Here, we demonstrate a pure N-body interaction between microwave photons stored in an arbitrary number of electromagnetic modes of a multimode cavity. The system is dressed such that there is collectively no interaction until a target total photon number is reached across multiple distinct modes, at which point they interact strongly. The microwave cavity features 9 modes with photon lifetimes of $\sim 2$ ms coupled to a superconducting transmon circuit, forming a multimode circuit QED system with single photon cooperativities of $\sim10^9$. We generate multimode interactions by using cavity photon number resolved drives on the transmon circuit to blockade any multiphoton state with a chosen total photon number distributed across the target modes. We harness the interaction for state preparation, preparing Fock states of increasing photon number via quantum optimal control pulses acting only on the cavity modes. We demonstrate multimode interactions by generating entanglement purely with uniform cavity drives and multimode photon blockade, and characterize the resulting two- and three-mode W states using a new protocol for multimode Wigner tomography.

quant-ph↗

arXiv2020

Floquet Cavity Electromagnonics

Hybrid magnonics has recently attracted intensive attentions as a promising platform for coherent information processing. In spite of its rapid development, on-demand control over the interaction of magnons with other information carriers, in particular microwave photons in electromagnonic systems, has been long missing, significantly limiting the broad applications of hybrid magnonics. Here, we show that by introducing Floquet engineering into cavity electromagnonics, coherent control on the magnon-microwave photon coupling can be realized. Leveraging the periodic temporal modulation from a Floquet drive, our first-of-its-kind Floquet cavity electromagnonic system can manipulate the interaction between hybridized cavity electromagnonic modes on demand. Moreover, we demonstrate a new coupling regime in such systems: the Floquet ultrastrong coupling, where the Floquet splitting is comparable with or even larger than the level spacing of the two interacting modes, resulting in the breakdown of the rotating wave approximation. Our findings open up new directions for magnon-based coherent signal processing.

cond-mat.mes-hall↗