The LINPACK benchmark reports the performance of a computer for solving a system of linear equations with dense random matrices. Although this task was not designed with a real application directly in mind, the LINPACK benchmark has been used to define the list of TOP500 supercomputers since the debut of the list in 1993. We propose that a similar benchmark, called the quantum LINPACK benchmark, could be used to measure the whole machine performance of quantum computers. The success of the quantum LINPACK benchmark should be viewed as the minimal requirement for a quantum computer to perform a useful task of solving linear algebra problems, such as linear systems of equations. We propose an input model called the RAndom Circuit Block-Encoded Matrix (RACBEM), which is a proper generalization of a dense random matrix in the quantum setting. The RACBEM model is efficient to be implemented on a quantum computer, and can be designed to optimally adapt to any given quantum architecture, with relying on a black-box quantum compiler. Besides solving linear systems, the RACBEM model can be used to perform a variety of linear algebra tasks relevant to many physical applications, such as computing spectral measures, time series generated by a Hamiltonian simulation, and thermal averages of the energy. We implement these linear algebra operations on IBM Q quantum devices as well as quantum virtual machines, and demonstrate their performance in solving scientific computing problems.
Quantum secure data transfer is an important topic for quantum cyber security. We propose a scheme to realize quantum secure data transfer in the basis of quantum secure direct communication (QSDC). In this proposal, the transmitted data is encoded in the pulse shape of a single optical qubit, which is emitted from a trapped atom owned by the sender and received by the receiver with another trapped atom. The encoding process can be implemented with high fidelity by controlling the time-dependent driving pulse on the trapped atom to manipulate the Rabi frequency in accordance with the target pu…
Recently, dimensionality testing of a quantum state has received extensive attention (Ac{í}n et al. Phys. Rev. Letts. 2006, Scarani et al. Phys. Rev. Letts. 2006). Security proofs of existing quantum information processing protocols rely on the assumption about the dimension of quantum states in which logical bits are encoded. However, removing such assumption may cause security loophole. In the present paper, we show that this is indeed the case. We choose two players' quantum private query protocol by Yang et al. (Quant. Inf. Process. 2014) as an example and show how one player can gain an u…
We have proposed and demonstrated a scalable and efficient scheme for programmable unitary operations in orbital angular momentum (OAM) domain. Based on matrix decomposition into diagonal and Fourier factors, arbitrary matrix operators can be implemented only by diagonal matrices alternately acting on orbital angular momentum domain and azimuthal angle domain, which are linked by Fourier transform. With numerical simulations, unitary matrices with dimensionality of 3*3 are designed and discussed for OAM domain. Meanwhile, the parallelism of our proposed scheme is also presented with two 3*3 ma…
We devise an all-optical scheme for the generation of entangled multimode photonic states encoded in temporal modes of light. The scheme employs a nonlinear down-conversion process in an optical loop to generate one- and higher-dimensional tensor network states of light. We illustrate the principle with the generation of two different classes of entangled tensor network states and report on a variational algorithm to simulate the ground-state physics of many-body systems. We demonstrate that state-of-the-art optical devices are capable of determining the ground-state properties of the spin-1/2…
One-step implementation of a multi-target-qubit controlled-phase gate with photonic qubits encoded via eigenstates of the photon-number parity operator
There is an increasing interest in Quantum Machine Learning (QML) models, how they work and for which applications they could be useful. There have been many different proposals on how classical data can be encoded and what circuit ansätze and measurement operators should be used to process the encoded data and measure the output state of an ansatz. The choice of the aforementioned operators plays a determinant role in the expressive power of the QML model. In this work we investigate how certain changes in the circuit structure change this expressivity. We introduce both numerical and analyti…
Hybrid qubits have recently drawn intensive attention in quantum computing. We here propose a method to implement a universal controlled-phase gate of two hybrid qubits via two three-dimensional (3D) microwave cavities coupled to a superconducting flux qutrit. For the gate considered here, the control qubit is a microwave photonic qubit (particle-like qubit), whose two logic states are encoded by the vacuum state and the single-photon state of a cavity, while the target qubit is a cat-state qubit (wave-like qubit), whose two logic states are encoded by the two orthogonal cat states of the othe…
Qubit measurements are central to quantum information processing. In the field of superconducting qubits, standard readout techniques are not only limited by the signal-to-noise ratio, but also by state relaxation during the measurement. In this work, we demonstrate that the limitation due to relaxation can be suppressed by using the many-level Hilbert space of superconducting circuits: in a multilevel encoding, the measurement is only corrupted when multiple errors occur. Employing this technique, we show that we can directly resolve transmon gate errors at the level of one part in $10^3.$ Ex…
We introduce a proposal to prepare spin-obit maximally discordant mixed states by a linear optical circuit, with quantum bits (qubits) encoded in the polarization and transverse mode degrees of freedom of photons. In particular, we discuss how to prepare non-balanced spin-orbit entangled states, applying this technique to obtain maximally discordant mixed states. We present a simulation of the optical circuit by using the Jones matrix formalism. We performed a study of entanglement, classical and quantum correlations. The results show excellent agreement with the underlying theory and open a n…
We propose a scheme to probabilistically generate Greenberger-Horne-Zeilinger (GHZ) states encoded on the path degree of freedom of three photons. These photons are totally independent from each other, having no direct interaction during the whole evolution of the protocol, which remarkably requires only linear optical devices to work, and two extra ancillary photons to mediate the correlation. The efficacy of the method, which has potential application in distribited quantum computation and multiparty quantum communication, is analyzed in comparison with similar proposals reported in the rece…
We present an in-depth analysis regarding the error resistance and optimization of our all-optical Bell measurement and ultrafast long-distance quantum communication scheme proposed in [arXiv:1503.06777]. In order to promote our previous proposal from loss- to fault-tolerance, we introduce a general and compact formalism that can also be applied to other related schemes (including non-all-optical ones such as [PRL 112, 250501]). With the help of this new representation we show that our communication protocol does not only counteract the inevitable photon loss during channel transmission, but i…
The realization of quantum computers and quantum Internet requires not only quantum gates and quantum memories, but also transistors at single-photon levels to control the flow of information encoded on single photons. Single-photon transistor (SPT) is an optical transistor in the quantum limit, which uses a single photon to open or block a photonic channel. In sharp contrast to all previous SPT proposals which are based on single-photon nonlinearities, here I present a novel design for a high-gain and high-speed (up to THz) SPT based on a linear optical effect - giant circular birefringence (…
Major obstacles against efficient long distance quantum communication are photon losses during transmission and the probabilistic nature of Bell measurement causing exponential scaling in time and resource with distance. To overcome these difficulties, while conventional quantum repeaters require matter-based operations with long-lived quantum memories, recent proposals have employed encoded multiple photons in entanglement, providing an alternative way for scalability. In pursuing scalable quantum communications, naturally arising questions are thus whether any ultimate limit exists in all-op…
Photonics is the platform of choice to build a modular, easy-to-network quantum computer operating at room temperature. However, no concrete architecture has been presented so far that exploits both the advantages of qubits encoded into states of light and the modern tools for their generation. Here we propose such a design for a scalable and fault-tolerant photonic quantum computer informed by the latest developments in theory and technology. Central to our architecture is the generation and manipulation of three-dimensional hybrid resource states comprising both bosonic qubits and squeezed v…
An $n\overset{p}{\mapsto}m$ random access code (RAC) is an encoding of $n$ bits into $m$ bits such that any initial bit can be recovered with probability at least $p$, while in a quantum RAC (QRAC), the $n$ bits are encoded into $m$ qubits. Since its proposal, the idea of RACs was generalized in many different ways, e.g. allowing the use of shared entanglement (called entanglement-assisted random access code, or simply EARAC) or recovering multiple bits instead of one. In this paper we generalize the idea of RACs to recovering the value of a given Boolean function $f$ on any subset of fixed si…
