Random Clifford circuits doped with non Clifford gates exhibit transitions to universal entanglement spectrum statistics[1] and quantum chaotic behavior. In [2] we proved that the injection of $O(n)$ non Clifford gates into a $n$-qubit Clifford circuit drives the transition towards the universal value of the purity fluctuations. In this paper, we show that doping a Clifford circuit with $O(n)$ single qubit non Clifford measurements is both necessary and sufficient to drive the transition to universal fluctuations of the purity.
The multiscale entanglement renormalization ansatz describes quantum many-body states by a hierarchical entanglement structure organized by length scale. Numerically, it has been demonstrated to capture critical lattice models and the data of the corresponding conformal field theories with high accuracy. However, a rigorous understanding of its success and precise relation to the continuum is still lacking. To address this challenge, we provide an explicit construction of entanglement-renormalization quantum circuits that rigorously approximate correlation functions of the massless Dirac confo…
Entanglement renormalization is a unitary real-space renormalization scheme. The corresponding quantum circuits or tensor networks are known as MERA, and they are particularly well-suited to describing quantum systems at criticality. In this work we show how to construct Gaussian bosonic quantum circuits that implement entanglement renormalization for ground states of arbitrary free bosonic chains. The construction is based on wavelet theory, and the dispersion relation of the Hamiltonian is translated into a filter design problem. We give a general algorithm that approximately solves this des…
We have studied the algebraic structure underlying the quantum circuits composed by $\cZ$ and $\Swap$ gates. Our results are applied to optimize the circuits and to understand the emergence of entanglement when a circuit acts on a fully factorized state.
Multipartite entanglement is of important resources for quantum communication and quantum computation. Our goal in this paper is to characterize general multipartite entangled states according to shallow quantum circuits. We firstly prove any genuinely multipartite entanglement on finite-dimensional spaces can be generated by using 2-layer shallow quantum circuit consisting of two biseparable quantum channels, which the smallest nontrivial circuit depth in the shallow quantum circuit model. We further propose a semi-device-independent entanglement model depending on the local connection abilit…
Entanglement is the defining characteristic of quantum mechanics. Bipartite entanglement is characterized by the von Neumann entropy. Entanglement is not just described by a number, however; it is also characterized by its level of complexity. The complexity of entanglement is at the root of the onset of quantum chaos, universal distribution of entanglement spectrum statistics, hardness of a disentangling algorithm and of the quantum machine learning of an unknown random circuit, and universal temporal entanglement fluctuations. In this paper, we numerically show how a crossover from a simple …
We show a similarity between two different classical simulation methods for measurement based quantum computation -- one relying on a low entanglement (tree tensor network) representation of the computer's state, and the other a tensor contraction method based on the topology of the graph state. We use this similarity to show that any quantum circuit that can be efficiently simulated via tensor contraction cannot produce much entanglement.
Electronic devices all around us contain classical control circuits. Such circuits consist of a network of controllers which can read and write signals to wires of the circuit with the goal to minimize the cost function of the circuit's output signal. Here, we propose the use of shared entanglement between controllers as a resource to improve the performance of otherwise purely classical control circuits. We study a well-known example from the classical control literature and demonstrate that allowing two controllers to share entanglement improves their ability to control. More precisely, we e…
We consider the entanglement manipulation capabilities of the universal covariant quantum cloner or quantum processor circuit for quantum bits. We investigate its use for cloning a member of a bipartite or a genuine tripartite entangled state of quantum bits. We find that for bipartite pure entangled states a nontrivial behavior of concurrence appears, while for GHZ entangled states a possibility of the partial extraction of bipartite entanglement can be achieved.
The entanglement in operator space is a well established measure for the complexity of the quantum many-body dynamics. In particular, that of local operators has recently been proposed as dynamical chaos indicator, i.e. as a quantity able to discriminate between quantum systems with integrable and chaotic dynamics. For chaotic systems the local-operator entanglement is expected to grow linearly in time, while it is expected to grow at most logarithmically in the integrable case. Here we study local-operator entanglement in dual-unitary quantum circuits, a class of "statistically solvable" quan…
Clifford circuits are insufficient for universal quantum computation or creating $t$-designs with $t\ge 4$. While the entanglement entropy is not a telltale of this insufficiency, the entanglement spectrum is: the entanglement levels are Poisson-distributed for circuits restricted to the Clifford gate-set, while the levels follow Wigner-Dyson statistics when universal gates are used. In this paper we show, using finite-size scaling analysis of different measures of level spacing statistics, that in the thermodynamic limit, inserting a single T $(π/8)$ gate in the middle of a random Clifford ci…
We study the growth of genuine multipartite entanglement in random quantum circuit models, which include random unitary circuit models and the random Clifford circuit. We find that for the random Clifford circuit, the growth of multipartite entanglement remains slower in comparison to the random unitary case. However, the final saturation value of multipartite entanglement is almost the same in both cases. The behavior is then compared to the genuine multipartite entanglement obtained in random matrix product states with a moderately high bond dimension. We then relate the behavior of multipar…
We consider the design of photonic circuits that make use of Ti:LiNbO$_{3}$ diffused channel waveguides for generating photons with various combinations of modal, spectral, and polarization entanglement. Down-converted photon pairs are generated via spontaneous optical parametric down-conversion (SPDC) in a two-mode waveguide. We study a class of photonic circuits comprising: 1) a nonlinear periodically poled two-mode waveguide structure, 2) a set of single-mode and two-mode waveguide-based couplers arranged in such a way that they suitably separate the three photons comprising the SPDC proces…
We consider the change of entanglement of formation $ΔE$ produced by the Hadamard-CNOT circuit on a general (pure or mixed) state $ρ$ describing a system of two qubits. We study numerically the probabilities of obtaining different values of $ΔE$, assuming that the initial state is randomly distributed in the space of all states according to the product measure recently introduced by Zyczkowski {\it et al.} [Phys. Rev. A {\bf 58} (1998) 883].
Random quantum circuit is a minimally structured model to study the entanglement dynamics of many-body quantum systems. In this paper, we considered a one-dimensional quantum circuit with noisy Haar-random unitary gates using density matrix operator and tensor contraction methods. It is shown that the entanglement evolution of the random quantum circuits is properly characterized by the logarithmic entanglement negativity. By performing exact numerical calculations, we found that, as the physical error rate is decreased below a critical value $p_c\approx 0.056$, the logarithmic entanglement ne…
One-dimensional quantum Gibbs states in constant circuit depth
Massachusetts Institute of Technology（麻省理工学院）；Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）；New York University（纽约大学）；University of Basel（巴塞尔大学）
We provide exact results for the dynamics of local-operator entanglement in quantum circuits with two-dimensional wires featuring ultralocal solitons, i.e. single-site operators which, up to a phase, are simply shifted by the time evolution. We classify all circuits allowing for ultralocal solitons and show that only dual-unitary circuits can feature moving ultralocal solitons. Then, we rigorously prove that if a circuit has an ultralocal soliton moving to the left (right), the entanglement of local operators initially supported on even (odd) sites saturates to a constant value and its dynamic…
We show that in a quantum system evolving unitarily under a stochastic quantum circuit the notions of irreversibility, universality of computation, and entanglement are closely related. As the state evolves from an initial product state, it gets asymptotically maximally entangled. We define irreversibility as the failure of searching for a disentangling circuit using a Metropolis-like algorithm. We show that irreversibility corresponds to Wigner-Dyson statistics in the level spacing of the entanglement eigenvalues, and that this is obtained from a quantum circuit made from a set of universal g…
Entanglement swapping, the process to entangle two particles without coupling them in any way, is one of the most striking manifestations of the quantum-mechanical nonlocal characteristic. Besides fundamental interest, this process has applications in complex entanglement manipulation and quantum communication. Here we report a high-fidelity, unconditional entanglement swapping experiment in a superconducting circuit. The measured concurrence characterizing the qubit-qubit entanglement produced by swapping is above 0.75, confirming most of the entanglement of one qubit with its partner is dete…
We present a theoretical proposal for a physical implementation of entanglement concentration and purification protocols for two-mode squeezed microwave photons in circuit quantum electrodynamics (QED). First, we give the description of the cross-Kerr effect induced between two resonators in circuit QED. Then we use the cross-Kerr media to design the effective quantum nondemolition (QND) measurement on microwave-photon number. By using the QND measurement, the parties in quantum communication can accomplish the entanglement concentration and purification of nonlocal two-mode squeezed microwave…
We study a limited set of optical circuits for creating near maximal polarisation entanglement {\em without} the usual large vacuum contribution. The optical circuits we consider involve passive interferometers, feed-forward detection, down-converters and squeezers. For input vacuum fields we find that the creation of maximal entanglement using such circuits is impossible when conditioned on two detected auxiliary photons. So far, there have been no experiments with more auxiliary photons. Thus, based on the minimum complexity of the circuits required, if near maximal polarisation entanglement…
In local quantum circuits with charge conservation, we initialize the system in random product states and study the dynamics of the Renyi entanglement entropy $R_α$. We rigorously prove that $R_α$ with Renyi index $α>1$ at time $t$ is $\le O(\sqrt{t\ln t})$ if the transport of charges is diffusive. Very recent numerical results of Rakovszky et al. show that this upper bound is saturated (up to the sub-logarithmic correction) in random local quantum circuits with charge conservation.
This paper reports 1.5-um band time-bin entanglement generation. We employed a spontaneous four-wave mixing process in a dispersion shifted fiber, with which correlated photon pairs with very narrow bandwidths were generated efficiently. To observe two-photon interference, we used planar lightwave circuit based interferometers that were operated stably without feedback control. As a result, we obtained coincidence fringes with 99 % visibilities after subtracting accidental coincidences, and successfully distributed entangled photons over 20-km standard single-mode fiber without any deteriorati…
Given an output wavefunction of a monitored quantum circuit consisting of both unitary gates and projective measurements, we ask whether two complementary subsystems are entangled or not. For Clifford circuits, we find that this question can be mapped to a certain classical error-correction problem where various entanglement measures can be explicitly computed from the recoverability. The dual classical code is constructed from spacetime patterns of out-of-time ordered correlation functions among local operators and measured Pauli operators in the past, suggesting that the volume-law entanglem…
We present an indirect two-qubit parity meter in planar circuit quantum electrodynamics, realized by discrete interaction with an ancilla and a subsequent projective ancilla measurement with a dedicated, dispersively coupled resonator. Quantum process tomography and successful entanglement by measurement demonstrate that the meter is intrinsically quantum non-demolition. Separate interaction and measurement steps allow commencing subsequent data qubit operations in parallel with ancilla measurement, offering time savings over continuous schemes.
We analyze a multiqubit circuit QED system in the regime where the qubit-photon coupling dominates over the system's bare energy scales. Under such conditions a manifold of low-energy states with a high degree of entanglement emerges. Here we describe a time-dependent protocol for extracting these quantum correlations and converting them into well-defined multipartite entangled states of noninteracting qubits. Based on a combination of various ultrastrong-coupling effects, the protocol can be operated in a fast and robust manner, while still being consistent with experimental constraints on sw…
On-chip integrated photonic circuits are crucial to further progress towards quantum technologies and in the science of quantum optics. Here we report precise control of single photon states and multi-photon entanglement directly on-chip. We manipulate the state of path-encoded qubits using integrated optical phase control based on resistive elements, observing an interference contrast of 98.2+/-0.3%. We demonstrate integrated quantum metrology by observing interference fringes with 2- and 4-photon entangled states generated in a waveguide circuit, with respective interference contrasts of 97.…
Whether noisy quantum devices without error correction can provide quantum advantage over classical computers is a critical issue of current quantum computation. In this work, the random quantum circuits, which are used as the paradigm model to demonstrate quantum advantage, are simulated with depolarizing noise on experiment relevant two-dimensional architecture. With comprehensive numerical simulation and theoretical analysis, we find that the maximum achievable operator entanglement entropy, which indicates maximal simulation cost, has area law scaling with the system size for constant nois…
Towards an experimental implementation of entanglement harvesting in superconducting circuits: effect of detector gap variation on entanglement harvesting
University of Waterloo（滑铁卢大学）；Perimeter Institute for Theoretical Physics（珀蒂默理论物理研究所）；ETH Zurich（苏黎世联邦理工学院）
We prepare two dimensional states generated by shallow circuits composed of (1) one layer of two-qubit CZ gate or (2) a few layers of two-qubit random Clifford gate. After measuring all of the bulk qubits, we study the entanglement structure of the remaining qubits on the one dimensional boundary. In the first model, we observe that the competition between the bulk X and Z measurements can lead to an entanglement phase transition between an entangled volume law phase and a disentangled area law phase. We numerically evaluate the critical exponents and generalize this idea to other qudit system…
Photonic chip based time-bin entanglement has attracted significant attention because of its potential for quantum communication and computation. Useful time-bin entanglement systems must be able to generate, manipulate and analyze entangled photons on a photonic chip for stable, scalable and reconfigurable operation. Here we report the first time-bin entanglement photonic chip that integrates time-bin generation, wavelength demultiplexing and entanglement analysis. A two-photon interference fringe with an 88.4% visibility is measured (without subtracting any noise), indicating the high perfor…
Conservation laws can constrain entanglement dynamics in isolated quantum systems, manifest in a slowdown of higher Rényi entropies. Here, we explore this phenomenon in a class of long-range random Clifford circuits with U$(1)$ symmetry where transport can be tuned from diffusive to superdiffusive. We unveil that the different hydrodynamic regimes reflect themselves in the asymptotic entanglement growth according to $S(t) \propto t^{1/z}$, where the dynamical transport exponent $z$ depends on the probability $\propto r^{-α}$ of gates spanning a distance $r$. For sufficiently small $α$, we show…
Quantum information protocols require various types of entanglement, such as Einstein-Podolsky-Rosen (EPR), Greenberger-Horne-Zeilinger (GHZ), and cluster states. In optics, on-demand preparation of these states has been realized by squeezed light sources, but such experiments require different optical circuits for different entangled states, thus lacking versatility. Here we demonstrate an on-demand entanglement synthesizer which programmably generates all these entangled states from a single squeezed light source. This is achieved by developing a loop-based circuit which is dynamically contr…
We construct entanglement renormalization schemes which provably approximate the ground states of non-interacting fermion nearest-neighbor hopping Hamiltonians on the one-dimensional discrete line and the two-dimensional square lattice. These schemes give hierarchical quantum circuits which build up the states from unentangled degrees of freedom. The circuits are based on pairs of discrete wavelet transforms which are approximately related by a "half-shift": translation by half a unit cell. The presence of the Fermi surface in the two-dimensional model requires a special kind of circuit archit…
Large-scale quantum information processing networks will most probably require the entanglement of distant systems that do not interact directly. This can be done by performing entangling gates between standing information carriers, used as memories or local computational resources, and flying ones, acting as quantum buses. We report the deterministic entanglement of two remote transmon qubits by Raman stimulated emission and absorption of a traveling photon wavepacket. We achieve a Bell state fidelity of 73 %, well explained by losses in the transmission line and decoherence of each qubit.
Institute for Advanced Study（高等研究院）；Tel-Aviv University（特拉维夫大学）
We consider information spreading measures in randomly initialized variational quantum circuits and introduce entanglement diagnostics for efficient variational quantum/classical computations. We establish a robust connection between entanglement measures and optimization accuracy by solving two eigensolver problems for Ising Hamiltonians with nearest-neighbor and long-range spin interactions. As the circuit depth affects the average entanglement of random circuit states, the entanglement diagnostics can identify a high-performing depth range for optimization tasks encoded in local Hamiltonian…
