Heisenberg spin chains can act as quantum wires transferring quantum states either perfectly or with high fidelity. Gaussian packets of excitations passing through dual rails can encode the two states of a logical qubit, depending on which rail is empty and which rail is carrying the packet. With extra interactions in one or between different chains, one can introduce interaction zones in arrays of such chains, where specific one or two qubit gates act on any qubit which passes through these interaction zones. Therefore universal quantum computation is made possible in a static way where no external control is needed. This scheme will then pave the way for a scalable way of quantum computation where specific hardwares can be connected to make large quantum circuits. Our scheme is an improvement of a recent scheme where we have achieved to borrow an idea from quantum electrodynamics to replace non-local interactions between spin chains with local interactions mediated by an ancillary chain.
We explicitly construct a quantum circuit which exactly generates random three-qubit states. The optimal circuit consists of three CNOT gates and fifteen single qubit elementary rotations, parametrized by fourteen independent angles. The explicit distribution of these angles is derived, showing that the joint distribution is a product of independent distributions of individual angles apart from four angles.
Theory-agnostic nonclassicality certification in an integrated photonic circuit
University of Gdańsk（格但斯克大学）；Griffith University（格里菲斯大学）；Sapienza Università di Roma（罗马大学）；Sparrow Quantum（麻雀量子）；Perimeter Institute for Theoretical Physics（理论物理柏拉图研究所）；Consiglio Nazionale delle Ricerche（意大利国家研究委员会）；Politecnico di Milano（米兰理工大学）
The cooling effects of a quantum LC circuit coupled inductively with an ensemble of artificial qubits are investigated. The particles may decay independently or collectively through their interaction with the environmental vacuum electromagnetic field reservoir. For appropriate bath temperatures and the resonator's quality factors, we demonstrate an effective cooling well below the thermal background. In particular, we found that for larger samples the cooling efficiency is better for independent qubits. However, the cooling process can be faster for collectively interacting particles.
We report a compact, scalable, quantum photonic integrated circuit realised by combining multiple, independent InGaAs/GaAs quantum-light-emitting-diodes (QLEDs) with a silicon oxynitride waveguide circuit. Each waveguide joining the circuit can then be excited by a separate, independently electrically contacted QLED. We show that the emission from neighbouring QLEDs can be independently tuned to degeneracy using the Stark Effect and that the resulting photon streams are indistinguishable. This enables on-chip Hong-Ou-Mandel-type interference, as required for many photonic quantum information p…
As the width and depth of quantum circuits implemented by state-of-the-art quantum processors rapidly increase, circuit analysis and assessment via classical simulation are becoming unfeasible. It is crucial, therefore, to develop new methods to identify significant error sources in large and complex quantum circuits. In this work, we present a technique that pinpoints the sections of a quantum circuit that affect the circuit output the most and thus helps to identify the most significant sources of error. The technique requires no classical verification of the circuit output and is thus a sca…
Superconducting circuits have emerged as a promising platform to build quantum processors. The challenge of designing a circuit is to compromise between realizing a set of performance metrics and reducing circuit complexity and noise sensitivity. At the same time, one needs to explore a large design space, and computational approaches often yield long simulation times. Here we automate the circuit design task using SCILLA, a software for automated discovery of superconducting circuits. SCILLA performs a parallelized, closed-loop optimization to design circuit diagrams that match pre-defined pr…
We prove that a classical computer can efficiently sample from the photon-number probability distribution of a Gaussian state prepared by using an optical circuit that is shallow and local. Our work generalizes previous known results for qubits to the continuous-variable domain. The key to our proof is the observation that the adjacency matrices characterizing the Gaussian states generated by shallow and local circuits have small bandwidth. To exploit this structure, we devise fast algorithms to calculate loop hafnians of banded matrices. Since sampling from deep optical circuits with exponent…
Small numbers of qubits are one of the primary constraints on the near-term deployment of advantageous quantum computing. To mitigate this constraint, techniques have been developed to break up a large quantum computation into smaller computations. While this work is sometimes called circuit knitting or divide and quantum we generically refer to it as circuit cutting (CC). Much of the existing work has focused on the development of more efficient circuit cutting schemes, leaving open questions on the limits of what theoretically optimal schemes can achieve. We develop bounds by breaking up pos…
Circuit locality from relativistic locality in scalar field mediated entanglement
Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, Austrian Academy of Sciences（维也纳量子光学与量子信息研究所）；Basic Research Community for Physics e.V.（基础物理社区协会）；Physics Department, Royal Holloway, University of London（伦敦大学皇家霍洛威学院物理系）；Quantum Group, Department of Computer Science, University of Oxford（牛津大学计算机科学系量子组）；Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna（维也纳大学物理学院量子科学与技术中心）；Research Platform TURIS, University of Vienna（维也纳大学TURIS研究平台）；Aix-Marseille University, Université de Toulon, CPT-CNRS（艾克斯-马赛大学，土伦大学，CPT-CNRS）；Department of Philosophy and the Rotman Institute of Philosophy, Western University（韦仕敦大学哲学系及罗特曼哲学研究所）；Perimeter Institute（珀尔默特研究所）
In this work, we study and improve two leading error mitigation techniques, namely Probabilistic Error Cancellation (PEC) and Zero-Noise Extrapolation (ZNE), for estimating the expectation value of local observables. For PEC, we introduce a new estimator that takes into account the light cone of the unitary circuit with respect to a target local observable. Given a fixed error tolerance, the sampling overhead for the new estimator can be several orders of magnitude smaller than the standard PEC estimators. For ZNE, we also use light-cone arguments to establish an error bound that closely captu…
Quantum computers are on the brink of surpassing the capabilities of even the most powerful classical computers. This naturally raises the question of how one can trust the results of a quantum computer when they cannot be compared to classical simulation. Here we present a verification technique that exploits the principles of measurement-based quantum computation to link quantum circuits of different input size, depth, and structure. Our approach enables consistency checks of quantum computations within a device, as well as between independent devices. We showcase our protocol by applying it…
Simulating quantum circuits with arbitrary local noise using Pauli Propagation
Ecole Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Freie Universität Berlin（柏林自由大学）；Dahlem Center for Complex Quantum Systems, Freie Universität Berlin（柏林自由大学达勒姆复杂量子系统中心）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
Recently Xue et al. [arXiv:1909.02196] demonstrated numerically that QAOA performance varies as a power law in the amount of noise under certain physical noise models. In this short note, we provide a deeper analysis of the origin of this behavior. In particular, we provide an approximate closed form equation for the fidelity and cost in terms of the noise rate, system size, and circuit depth. As an application, we show these equations accurately model the trade off between larger circuits which attain better cost values, at the expense of greater degradation due to noise.
Limitations of Noisy Geometrically Local Quantum Circuits
University of Maryland（马里兰大学）；Joint Center for Quantum Information & Computer Science, University of Maryland and NIST（马里兰大学与美国国家标准与技术研究院联合量子信息与计算中心）；IBM T. J. Watson Research Center（IBM托马斯·J·沃森研究中心）
In this Letter we give a method for constructing sets of simple circuits that can determine the spectrum of a partially transposed density matrix, without requiring either a tomographically complete POVM or the addition of noise to make the spectrum non-negative. These circuits depend only on the dimension of the Hilbert space and are otherwise independent of the state.
Currently available quantum computing hardware platforms have limited 2-qubit connectivity among their addressable qubits. In order to run a generic quantum algorithm on such a platform, one has to transform the initial logical quantum circuit describing the algorithm into an equivalent one that obeys the connectivity restrictions. In this work we construct a circuit synthesis scheme that takes as input the qubit connectivity graph and a quantum circuit over the gate set generated by $\{\text{CNOT},R_{Z}\}$ and outputs a circuit that respects the connectivity of the device. As a concrete appli…
Many-body phenomena far from equilibrium present challenges beyond reach by classical computational resources. Digital quantum computers provide a possible way forward but noise limits their use in the near-term. We propose a scheme to simulate and characterize many-body Floquetsystems hosting a rich variety of phases that operates with a shallow depth circuit. Starting from a "clean" periodic circuit that simulates the dynamical evolution of a Floquet system, we introduce quasi-periodicity to the circuit parameters to prevent thermalization by introducing many-body localization. By inspecting…
The surface code is a leading candidate quantum error correcting code, owing to its high threshold, and compatibility with existing experimental architectures. Bravyi et al. (2006) showed that encoding a state in the surface code using local unitary operations requires time at least linear in the lattice size $L$, however the most efficient known method for encoding an unknown state, introduced by Dennis et al. (2002), has $O(L^2)$ time complexity. Here, we present an optimal local unitary encoding circuit for the planar surface code that uses exactly $2L$ time steps to encode an unknown state…
Interconnecting clusters of qubits will be an essential element of scaling up future quantum computers. Operations between quantum processing units (QPUs) are usually significantly slower and costlier than those within a single QPU, so usage of the interconnect must be carefully managed. This is loosely analogous to the need to manage shared caches or memory in classical multi-CPU machines. Unlike classical clusters, however, quantum data is subject to the no-cloning theorem, which necessitates a rethinking of cache coherency strategies. Here, we consider a simple strategy of using EPR-mediate…
We prove that local random quantum circuits acting on n qubits composed of O(t^{10} n^2) many nearest neighbor two-qubit gates form an approximate unitary t-design. Previously it was unknown whether random quantum circuits were a t-design for any t > 3. The proof is based on an interplay of techniques from quantum many-body theory, representation theory, and the theory of Markov chains. In particular we employ a result of Nachtergaele for lower bounding the spectral gap of frustration-free quantum local Hamiltonians; a quasi-orthogonality property of permutation matrices; a result of Oliveira …
We study the distribution over measurement outcomes of noisy random quantum circuits in the low-fidelity regime. We show that, for local noise that is sufficiently weak and unital, correlations (measured by the linear cross-entropy benchmark) between the output distribution $p_{\text{noisy}}$ of a generic noisy circuit instance and the output distribution $p_{\text{ideal}}$ of the corresponding noiseless instance shrink exponentially with the expected number of gate-level errors, as $F=\text{exp}(-2sε\pm O(sε^2))$, where $ε$ is the probability of error per circuit location and $s$ is the numbe…
Magnetic flux tunability is an essential feature in most approaches to quantum computing based on superconducting qubits. Independent control of the fluxes in multiple loops is hampered by crosstalk. Calibrating flux crosstalk becomes a challenging task when the circuit elements interact strongly. We present a novel approach to flux crosstalk calibration, which is circuit model independent and relies on an iterative process to gradually improve calibration accuracy. This method allows us to reduce errors due to the inductive coupling between loops. The calibration procedure is automated and im…
We examine an unexplored quantum phenomenon we call oscillatory localization, where a discrete-time quantum walk with Grover's diffusion coin jumps back and forth between two vertices. We then connect it to the power dissipation of a related electric network. Namely, we show that there are only two kinds of oscillating states, called uniform states and flip states, and that the projection of an arbitrary state onto a flip state is bounded by the power dissipation of an electric circuit. By applying this framework to states along a single edge of a graph, we show that low effective resistance i…
The task of non-local quantum computation requires implementation of a unitary on $n$ qubits between two parties with only one round of communication, ideally with minimal pre-shared entanglement. We introduce a new protocol that makes use of the fact that port-based teleportation costs much less entanglement when done only on a small number of qubits at a time. Whereas previous protocols have entanglement cost independent of the unitary or scaling with its complexity, the cost of the new protocol scales with the non-locality of the unitary. Specifically, it takes the form $\sim n^{4V}$ with $…
The dynamical generation of complex correlations in quantum many-body systems is of renewed interest in the context of quantum chaos, where the out-of-time-ordered (OTO) correlation function appears as a convenient measure of scrambling. To detect the the transition from scrambling to many-body localization, the latter of which has limited dynamical complexity and is often classically simulatable, we develop both exact and approximate methods to compute OTO correlators for arbitrary universal quantum circuits. We take advantage of the mapping of quantum circuits to the dynamics of interacting …
This paper explores several aspects of the adiabatic quantum computation model. We first show a way that directly maps any arbitrary circuit in the standard quantum computing model to an adiabatic algorithm of the same depth. Specifically, we look for a smooth time-dependent Hamiltonian whose unique ground state slowly changes from the initial state of the circuit to its final state. Since this construction requires in general an n-local Hamiltonian, we will study whether approximation is possible using previous results on ground state entanglement and perturbation theory. Finally we will poin…
We propose a superconducting qubit circuit that can fully emulate a quantum vector spin-1/2, with an effective dipole moment having three independent components whose operators obey the commutation relations of a vector angular momentum in the computational subspace. Each component couples to an independently-controllable external bias, emulating the Zeeman effect due to a fictitious, vector magnetic field, and all three of these vector components remain relatively constant over a broad range of emulated total fields around zero. This capability, combined with established techniques for qubit …
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…
The maximum independent set (MIS) problem of graph theory using the quantum alternating operator ansatz is studied. We perform simulations on the Rigetti Forest simulator for the square ring, $K_{2,3}$, and $K_{3,3}$ graphs and analyze the dependence of the algorithm on the depth of the circuit and initial states. The probability distribution of observation of the feasible states representing maximum independent sets is observed to be asymmetric for the MIS problem, which is unlike the Max-Cut problem where the probability distribution of feasible states is symmetric. For asymmetric graphs it …
The butterfly velocity $v_B$ has been proposed as a characteristic velocity for information propagation in local systems. It can be measured by the ballistic spreading of local operators in time (or, equivalently, by out-of-time-ordered commutators). In general, this velocity can depend on the direction of spreading and, indeed, the asymmetry between different directions can be made arbitrarily large using arbitrarily deep quantum circuits. Nevertheless, in almost all examples of local time-independent Hamiltonians that have been examined thus far, this velocity is independent of the direction…
Recent works have demonstrated that large quantum circuits can be cut and decomposed into smaller clusters of quantum circuits with fewer qubits that can be executed independently on a small quantum computer. Classical post-processing then combines the results from each cluster to reconstruct the output of the original quantum circuit. However, the runtime for such hybrid quantum-classical algorithms is exponential in the number of cuts on a circuit. We propose Rotation-Inspired Circuit Cut Optimization (RICCO), an alternative method which reduces the post-processing overhead of circuit cuttin…
Parallel classical simulation of noisy shallow circuits: no quantum advantage in 1D
Technical University of Munich（慕尼黑工业大学）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与技术中心）；National University of Singapore（新加坡国立大学）；Centre for Quantum Technologies（量子技术中心）
Toward Optimal Circuit Depth for Geometrically Local Hamiltonian Simulation
Center on Frontiers of Computing Studies, School of Computer Science, Peking University（北京大学计算机科学学院前沿计算研究中心）；School of Physics, Peking University（北京大学物理学院）；School of Artificial Intelligence, Beijing Normal University（北京师范大学人工智能学院）；State Key Laboratory for Novel Software Technology, Nanjing University（南京大学软件新技术国家重点实验室）；Hefei National Laboratory（合肥国家实验室）；Mathematical Institute, University of Oxford（牛津大学数学研究所）
The study of quantum circuits composed of commuting gates is particularly useful to understand the delicate boundary between quantum and classical computation. Indeed, while being a restricted class, commuting circuits exhibit genuine quantum effects such as entanglement. In this paper we show that the computational power of commuting circuits exhibits a surprisingly rich structure. First we show that every 2-local commuting circuit acting on d-level systems and followed by single-qudit measurements can be efficiently simulated classically with high accuracy. In contrast, we prove that such st…
In this work we prove that the 5-qubit quantum error correcting code does not fix qubit independent errors, even assuming that the correction circuit does not introduce new errors. We say that a quantum code does not fix a quantum computing error if its application does not reduce the variance of the error. We also prove for qubit independent errors that if the correction circuit of the 5-qubit quantum code detects an error, the corrected state has central symmetry and, as a consequence, its variance is maximum. We have been able to obtain these results thanks to the high symmetry of the 5-qub…
We demonstrate the design of an integrated conditional quantum teleportation circuit and a readout circuit using a two-dimensional photonic crystal single chip. Fabrication and testing of the proposed quantum circuit can be accomplished with current or near future semiconductor process technology and experimental techniques. The readout part of our device, which has potential for independent use as an atomic interferometer, can also be used on its own or integrated with other compatible optical circuits to achieve atomic state detection. Further improvement of the device in terms of compactnes…
Finding ground states and low-lying excitations of a given Hamiltonian is one of the most important problems in many fields of physics. As a novel approach, quantum computing on Noisy Intermediate-Scale Quantum (NISQ) devices offers the prospect to efficiently perform such computations and may eventually outperform classical computers. However, current quantum devices still suffer from inherent quantum noise. In this work, we propose an error mitigation scheme suitable for parametric quantum circuits. This scheme is based on projecting a general quantum noise channel onto depolarization errors…
Dual-unitary quantum circuits can be used to construct 1+1 dimensional lattice models for which dynamical correlations of local observables can be explicitly calculated. We show how to analytically construct classes of dual-unitary circuits with any desired level of (non-)ergodicity for any dimension of the local Hilbert space, and present analytical results for thermalization to an infinite-temperature Gibbs state (ergodic) and a generalized Gibbs ensemble (non-ergodic). It is shown how a tunable ergodicity-inducing perturbation can be added to a non-ergodic circuit without breaking dual-unit…
