Indirect controllability of an arbitrary finite dimensional quantum system (N-dimensional qudit) through a quantum accessor is investigated. Here, The qudit is coupled to a quantum accessor which is modeled as a fully controllable spin chain with nearest neighbor (anisotropic) XY-coupling. The complete controllability of such indirect control system is investigated in detail. The general approach is applied to the indirect controllability of two and three dimensional quantum systems. For two and three dimensional systems, a simpler indirect control scheme is also presented.
Complete controllability of degenerate quantum system using quantum accessor modeled as a qubit chain with nearest neighborhood coupling is investigated. Sufficient conditions on the length of accessor and the way of coupling between controlled system and accessor are obtained. General approach to arbitrary finite system is presented and two and three level degenerate systems are investigated in detail.
This is the second one in our series of papers on indirect quantum control assisted by quantum accessor. In this paper we propose and study a new class of indirect quantum control(IDQC) scheme based on the initial states preparation of the accessor. In the present scheme, after the initial state of the accessor is properly prepared, the system is controlled by repeatedly switching on and off the interaction between the system and the accessor. This is different from the protocol of our first paper, where we manipulate the interaction between the controlled system and the accessor. We prove the…
A pure indirect control of quantum systems via quantum accessor is investigated. In this control scheme, we do not apply any external classical excitation fields on the controlled system and we control a quantum system via a quantum accessor and classical control fields control the accessor only. Complete controllability is investigated for arbitrary finite dimensional quantum systems and exemplified by 2 and 3 dimensional systems. The scheme exhibits some advantages; it uses less qubits in accessor and does not depend on the energy-level structure of the controlled system.
It is considered the indirect inter-qubit coupling in 1D chain of atoms with nuclear spins 1/2, which plays role of qubits in the quantum register. This chain of the atoms is placed by regular way in easy-axis 3D antiferromagnetic thin plate substrate, which is cleaned from the other nuclear spin containing isotopes. It is shown that the range of indirect inter-spin coupling may run to a great number of lattice constants both near critical point of quantum phase transition in antiferromagnet of spin-flop type (control parameter is external magnetic field) and/or near homogeneous antiferromagne…
We give analytical solutions for the time-optimal synthesis of entangling gates between indirectly coupled qubits 1 and 3 in a linear spin chain of three qubits subject to an Ising Hamiltonian interaction with equal coupling $J$ plus a local magnetic field acting on the intermediate qubit. The energy available is fixed, but we relax the standard assumption of instantaneous unitary operations acting on single qubits. The time required for performing an entangling gate which is equivalent, modulo local unitary operations, to the $\mathrm{CNOT}(1, 3)$ between the indirectly coupled qubits 1 and 3…
An NMR realization of a two-qubit quantum gate which processes quantum information indirectly via couplings to a spectator qubit is presented in the context of the Deutsch-Jozsa algorithm. This enables a successful comprehensive NMR implementation of the Deutsch-Jozsa algorithm for functions with three argument bits and demonstrates a technique essential for multi-qubit quantum computation.
Dynamical decoupling (DD) sequences were invented to eliminate the direct coupling between qubit and its environment. We further investigate the possibility of decoupling the indirect qubit-qubit interaction induced by a common environment, and sucessfully find simplified solutions that preserve the bipartite quantum states to arbitrary order. Through analyzing the exact dynamics of the controlled two-qubit density matrix, we have proven that applying independent Uhrig Dynamical Decoupling (UDD) on each qubit will effectively eliminate both the qubit- environment and indirect qubit-qubit coupl…
Hybrid quantum registers consisting of different types of qubits offer a range of advantages as well as challenges. The main challenge is that some types of qubits react only slowly to external control fields, thus considerably slowing down the information processing operations. One promising approach that has been tested in a number of cases is to use indirect control, where external fields are applied only to qubits that interact strongly with resonant excitation pulses. Here we use this approach to indirectly control the nuclear spins of an NV center, using microwave pulses to drive the ele…
Hybrid quantum registers, such as electron-nuclear spin systems, have emerged as promising hardware for implementing quantum information and computing protocols in scalable systems. Nevertheless, the coherent control of such systems still faces challenges. Particularly, the lower gyromagnetic ratios of the nuclear spins cause them to respond slowly to control fields, resulting in gate times that are generally longer than the coherence time of the electron spin. Here, we demonstrate a scheme for circumventing this problem by indirect control: We apply a small number of short pulses only to the …
A quantum mechanical system S is indirectly controlled when the control affects an ancillary system A and the evolution of S is modified through the interaction with A only. A study of indirect controllability gives a description of the set of states that can be obtained for S with this scheme. In this paper, we study the indirect controllability of quantum systems in the finite dimensional case. After discussing the relevant definitions, we give a general necessary condition for controllability in Lie algebraic terms. We present a detailed treatment of the case where both systems, S and A, ar…
We analytically investigate the role of entanglement in time-optimal state evolution as an appli- cation of the quantum brachistochrone, a general method for obtaining the optimal time-dependent Hamiltonian for reaching a target quantum state. As a model, we treat two qubits indirectly cou- pled through an intermediate qubit that is directly controllable, which represents a typical situation in quantum information processing. We find the time-optimal unitary evolution law and quantify residual entanglement by the two-tangle between the indirectly coupled qubits, for all possible sets of initia…
Performing measurements for high-weight operators has been a practical problem in quantum computation, especially for quantum codes in the stabilizer formalism. The conventional procedure of measuring a high-weight operator requires multiple pairwise unitary operations, which can be slow and prone to errors. We provide an alternative method to passively detect the value of a high-weight operator using only two-local interactions and single-qubit continuous measurements. This approach involves joint interactions between the system and continuously-monitored ancillary qubits. The measurement out…
We propose and demonstrate a protocol for high-fidelity indirect readout of trapped ion hyperfine qubits, where the state of a $^9\text{Be}^+$ qubit ion is mapped to a $^{25}\text{Mg}^+$ readout ion using laser-driven Raman transitions. By partitioning the $^9\text{Be}^+$ ground state hyperfine manifold into two subspaces representing the two qubit states and choosing appropriate laser parameters, the protocol can be made robust to spontaneous photon scattering errors on the Raman transitions, enabling repetition for increased readout fidelity. We demonstrate combined readout and back-action e…
We present a protocol for measuring the quadrature of a harmonic oscillator (HO). The HO is coupled to a qubit, with an interaction modulated by the qubit control and effectively proportional to the HO quadrature $I$. Repeated measurement of the qubit leads to gradually increasing information on the quadrature $I$, leading to squeezing. We derive an analytical formula for the quadrature variance, $(ΔI)^2 = 1/(1+4ϕ^2 s)$, with $ϕ$ the product of interaction strength and interaction time and $s$ the number of repetitions of the measurement. We discuss the robustness of this scheme against decohe…
We quantify the resources required for entangling two uncoupled spin qubits through an intermediate mesoscopic spin system (MSS) by indirect joint measurement. Indirect joint measurement benefits from coherent magnification of the target qubits' state in the collective magnetization of the MSS; such that a low-resolution collective measurement on the MSS suffices to prepare post-selected entanglement on the target qubits. A MSS consisting of two non-interacting halves, each coupled to one of the target qubits is identified as a geometry that allows implementing the magnification process with e…
Nielsen [quant-ph/0108020] showed that universal quantum computation is possible given quantum memory and the ability to perform projective measurements on up to 4-qubits. We describe an improved method that requires only 2-qubit measurements, which are both sufficient and necessary. We present a method to partially collapse the $C_k$-hierarchy in the indirect construction of unitary gates [Gottesman and Chuang, Nature, {\bf 402} 309 (1999)], and apply the method to find discrete universal sets of 2-qubit measurements.
We propose a mechanism of long-range coherent coupling between nuclear spins to be used as qubits in solid-state semiconductor-heterojunction quantum information processing devices. The coupling is via localized donor electrons which in turn interact with the two-dimensional electron gas. An effective two-spin interaction Hamiltonian is derived and the coupling strength is evaluated. We also discuss mechanisms of qubit decoherence and consider possibilities for gate control of the interaction between neighboring qubits. The resulting quantum computing scheme retains all the gate-control and me…
Universal quantum computation requires the implementation of arbitrary control operations on the quantum register. In most cases, this is achieved by external control fields acting selectively on each qubit to drive single-qubit operations. In combination with a drift Hamiltonian containing interactions between the qubits, this allows the implementation of any required gate operation. Here, we demonstrate an alternative scheme that does not require local control for all qubits: we implement one- and two-qubit gate operations on a set of target qubits indirectly, through a combination of gates …
We propose a method for entangling two non-interacting qubits by measuring their parity indirectly through an intermediate mesoscopic system. The protocol is designed to require only global control and course-grained collective measurement of the mesoscopic system along with local interactions between the target qubits and mesoscopic system. A generalization of the method measures the hamming weight of the qubits' state and probabilistically produces an entangled state by post-selecting on hamming weight one. Our technique provides a new design element that can be integrated into quantum proce…
We present protocols to generate quantum entanglement on nonlocal magnons in hybrid systems composed of yttrium iron garnet (YIG) spheres, microwave cavities and a superconducting (SC) qubit. In the schemes, the YIGs are coupled to respective microwave cavities in resonant way, and the SC qubit is placed at the center of the cavities, which interacts with the cavities simultaneously. By exchanging the virtual photon, the cavities can indirectly interact in the far-detuning regime. Detailed protocols are presented to establish entanglement for two, three and arbitrary $N$ magnons with reasonabl…
We demonstrate a scalable device architecture that facilitates indirect exchange between singlet-triplet spin qubits, mediated by an intermediate quantum state. The device comprises five quantum dots, which can be independently loaded and unloaded via tunneling to adjacent reservoirs, avoiding charge latch-up common in linear dot arrays. In a step towards realizing two-qubit entanglement based on indirect exchange, the architecture permits precise control over tunnel rates between the singlet-triplet qubits and the intermediate state. We show that by separating qubits by 1 um, the residual cap…
We theoretically study the superradiant phase transition (SPT) in an indirect Rabi model, where both a two-level system and a single mode bosonic field couple to an auxiliary bosonic field. We find that the indirect spin-field coupling induced by the virtual excitation of the auxiliary field can allow the occurrence of a SPT at a critical point, and the influence of the so-called $A^2$ term in the normal Rabi model is naturally avoided. In the large detuning regime, we present the analytical expression of quantum critical point in terms of the original system parameters. The critical atom-fiel…
The possibility of exchanging the quantum correlations and the non-local information between three qubits interact directly or indirectly via Dzyaloshinskii-Moriya (DM)is discussed. The initial state settings and the interaction strength represent control parameters on the exchanging phenomena. The non-local information that encoded on the different partitions doesn't exceed the initial one. It is shown that, the ability of DM interaction to generate entanglement is larger than that displayed for the dipole interaction. The possibility of maximizing the quantum correlations between the three q…
We first consider various methods for the indirect implementation of unitary gates. We apply these methods to rederive the universality of 4-qubit measurements based on a scheme much simpler than Nielsen's original construction [quant-ph/0108020]. Then, we prove the universality of simple discrete sets of 2-qubit measurements, again using a scheme simplifying the initial construction [quant-ph/0111122]. Finally, we show how to use a single 4-qubit measurement to achieve universal quantum computation, and outline a proof for the universality of almost all maximally entangling 4-qubit measuremen…
In this paper, we propose quantum circuits for runtime assertions, which can be used for both software debugging and error detection. Runtime assertion is challenging in quantum computing for two key reasons. First, a quantum bit (qubit) cannot be copied, which is known as the non-cloning theorem. Second, when a qubit is measured, its superposition state collapses into a classical state, losing the inherent parallel information. In this paper, we overcome these challenges with runtime computation through ancilla qubits, which are used to indirectly collect the information of the qubits of inte…
We propose a quantum-electrodynamics scheme for implementing the discrete-time, coined quantum walk with the walker corresponding to the phase degree of freedom for a quasi-magnon field realized in an ensemble of nitrogen-vacancy centres in diamond. The coin is realized as a superconducting flux qubit. Our scheme improves on an existing proposal for implementing quantum walks in cavity quantum electrodynamics by removing the cumbersome requirement of varying drive-pulse durations according to mean quasiparticle number. Our improvement is relevant to all indirect-coin-flip cavity quantum-electr…
Indirect control of qubits by a quantum actuator has been proposed as an appealing strategy to manipulate qubits that couple only weakly to external fields. While universal quantum control can be easily achieved when the actuator-qubit coupling is anisotropic, the efficiency of this approach is less clear. Here we analyze the time-efficiency of the quantum actuator control. We describe a strategy to find time-optimal control sequence by the quantum actuator and compare their gate times with direct driving, identifying regimes where the actuator control performs faster. As an example, we focus …
We introduce the quantum indirect estimation theory, which provides a general framework to address the problem of which ensemble averages can be estimated by means of an available set of measuring apparatuses, e. g. estimate the ensemble average of an observable by measuring other observable. A main ingredient in this approach is that of informationally complete (infocomplete in short) measurements, which allow to estimate the ensemble average of any arbitrary system operator, as for quantum tomography. This naturally leads to the more stringent concept of AB-informationally complete measureme…
We discuss definitions of the quantum efficiency for binary-outcome qubit detectors with imperfect fidelity, focusing on the subclass of quantum non-demolition detectors. Quantum efficiency is analyzed for several models of detectors, including indirect projective measurement, linear detector in binary-outcome regime, detector of the superconducting phase qubit, and detector based on tunneling into continuum.
A scheme for distributed quantum measurement that allows nondestructive or indirect Bell measurement was proposed by Gupta et al., (Int. J. Quant. Infor. \textbf{5} (2007) 627) and subsequently realized experimentally using an NMR-based three-qubit quantum computer by Samal et al., (J. Phys. B, \textbf{43} (2010) 095508). In the present work, a similar experiment is performed using the five-qubit super-conductivity-based quantum computer, which has been recently placed in cloud by IBM Corporation. The experiment confirmed that the Bell state can be constructed and measured in a nondestructive …
While quantum information processing by nuclear magnetic resonance (NMR) with small number of qubits is well established, implementation of lengthy computations have proved to be difficult due to decoherence/relaxation. In such circumstances, shallow circuits (circuits using parallel computation) may prove to be realistic. Parity and fanout gates are essential to create shallow circuits. In this article we implement inversion-on-equality gate, followed by parity gate and fanout gate in 3-qubit systems by NMR, using evolution under indirect exchange coupling Hamiltonian.
Hadamard spectroscopy has earlier been used to speed-up multi-dimensional NMR experiments. In this work we speed-up the two-dimensional quantum computing scheme, by using Hadamard spectroscopy in the indirect dimension, resulting in a scheme which is faster and requires the Fourier transformation only in the direct dimension. Two and three qubit quantum gates are implemented with an extra observer qubit. We also use one-dimensional Hadamard spectroscopy for binary information storage by spatial encoding and implementation of a parallel search algorithm.
This paper is a continuation of our previous paper [8], in which we have studied the dynamics of quantum correlations of two qubits embedded each into its own disordered multiconnected environment. We modeled the environment by random matrices of large size allowing for a possibility to describe meso- and even nanoenvironments. In this paper we also study the dynamics of quantum correlations of two qubits but embedded into a common environment which we also model by random matrices of large size. We obtain the large size limit of the reduced density matrix of two qubits. We then use an analog …
Indirect Indication of the KCBS-Type Quantum Contextuality by the CHSH-Bell Test
Faculty of Engineering and Natural Sciences, Sabanci University（萨贝里大学工程与自然科学学院）；Sabanci University（萨贝里大学）；International Centre for Theory of Quantum Technologies, University of Gdansk（格但斯克大学量子技术理论国际中心）；University of Gdansk（格但斯克大学）
We develop a theory of indirect measurements where a probe is able to read, in short interaction times, the quantum state of a remote system through an incoherent wall. The probe and the system can interact with an ancilla in an incoherent state but not directly among themselves and, nevertheless, the fast transfer of quantum information can be achieved with robustness. We exemplify our measurement scheme with a paradigmatic example of this tripartite problem: qubit-oscillator-qubit, and discuss different physical scenarios pointing out the associated advantages and limitations.
Theoretical study of the indirect coupling of nuclear spins (qubits) embedded into a mesoscopic ring and in a finite length quantum wire in a magnetic field is presented. It is found that the hyperfine interaction, via the conduction electrons, between nuclear spins exhibits sharp maxima as function of the magnetic field and nuclear spin positions. This phenomenon can be used for manipulation of qubits with almost atomic precision. Experimental feasibility and implications for quantum logics devices is discussed.
We combine elements of the 1998 quantum computing proposals by Privman, Vagner and Kventsel, and by Kane, with the new idea of nuclear-spin qubit interactions mediated indirectly via the bound outer electrons of impurity atoms whose nuclear spins 1/2 are the qubits. These electrons, in turn, interact via the two-dimensional electron gas in the quantum Hall effect regime. The resulting quantum computing scheme retains all the gate-control and measurement aspects of the proposal by Kane, but allows qubit spacing at distances of order 100 nm, attainable with the present-day semiconductor-heterost…
Quantum control of solid state qubits via Reinforcement Learning
Ulm University（乌尔姆大学）；Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR)（德国航空航天中心）；Center for Integrated Quantum Science and Technology (IQST) Ulm-Stuttgart, Germany（乌尔姆-斯图加特集成量子科学与技术中心）
Multi-level Random-Telegraph Noise Mitigation using a Single Spectator Qubit
University of Newcastle（纽卡斯尔大学）；Griffith University（格里菲斯大学）；Qian Xuesen Laboratory of Space Technology, China Academy of Space Technology（中国空间技术研究院钱学森空间技术实验室）；Mahidol University（玛希隆大学）
Coherent control and optical readout of the electron spin of the $^{29}$SiV$^{-}$ center in diamond has been demonstrated in literature, with exciting prospects for implementations as memory nodes and spin qubits. Nuclear spins may be even better suited for many applications in quantum information processing due to their long coherence times. Control of the $^{29}$SiV$^{-}$ nuclear spin using conventional NMR techniques is feasible, albeit at slow kilohertz rates due to the nuclear spin's low gyromagnetic ratio. In this work we theoretically demonstrate how indirect control using the electron …
We present a quantum CISC compiler and show how to assemble complex instruction sets in a scalable way. Enlarging the toolbox of universal gates by optimised complex multi-qubit instruction sets thus paves the way to fight decoherence for realistic settings. Compiling a quantum module into the machine code for steering a concrete quantum hardware device lends itself to be tackled by means of optimal quantum control. To this end, there are two opposite approaches: (i) one may use a decomposition into the restricted instruction set (RISC) of universal one- and two-qubit gates, which in turn have…
Quantum chaotic kicked top model is implemented experimentally in a two qubit system comprising of a pair of spin-1/2 nuclei using Nuclear Magnetic Resonance techniques. The essential nonlinear interaction was realized using indirect spin-spin coupling, while the linear kicks were realized using RF pulses. After a variable number of kicks, quantum state tomography was employed to reconstruct the single-qubit density matrices using which we could extract various measures such as von Neumann entropies, Husimi distributions, and Lyapunov exponents. These measures enabled the study of corresponden…
Diagonalization of the effective Hamiltonian describing an open quantum system is the usual method of tracking its exceptional points. Although, such a method is successful for tracking EPs in Markovian systems, it may be problematic in non-Markovian systems where a closed expression of the effective Hamiltonian describing the open system may not exist. In this work we provide an alternative method of tracking EPs in open quantum systems, using an experimentally measurable quantity, namely the effective decay rate of a qubit. The quantum system under consideration consists of two non-identical…
We study the efficiency of quantum tomographic reconstruction where the system under investigation (quantum target) is indirectly monitored by looking at the state of a quantum probe that has been scattered off the target. In particular we focus on the state tomography of a qubit through a one-dimensional scattering of a probe qubit, with a Heisenberg-type interaction. Via direct evaluation of the associated quantum Cramér-Rao bounds, we compare the accuracy efficiency that one can get by adopting entanglement-assisted strategies with that achievable when entanglement resources are not availab…
We describe a new scheme to interconvert stationary and photonic qubits which is based on indirect qubit-light interactions mediated by a mechanical resonator. This approach does not rely on the specific optical response of the qubit and thereby enables optical quantum interfaces for a wide range of solid state spin and charge based systems. We discuss the implementation of quantum state transfer protocols between distant nodes of a large scale network and evaluate the effect of the main noise sources on the resulting state transfer fidelities. For the specific examples of electronic spin qubi…
We demonstrate experimentally the creation and measurement of an entangled state between a microscopic two level system and a macroscopic superconducting resonator where their indirect interaction is mediated by an artificial atom, a superconducting persistent current qubit (PCQB). We show that the microscopic two level system, formed by a defect in an oxide layer, exhibits an order of magnitude longer dephasing time than the PCQB, while the dephasing time of the entangled states between the microscopic two level system and macroscopic superconducting resonator is significantly longer than the…
Estimating the dimension of an Hilbert space is an important component of quantum system identification. In quantum technologies, the dimension of a quantum system (or its corresponding accessible Hilbert space) is an important resource, as larger dimensions determine e.g. the performance of quantum computation protocols or the sensitivity of quantum sensors. Despite being a critical task in quantum system identification, estimating the Hilbert space dimension is experimentally challenging. While there have been proposals for various dimension witnesses capable of putting a lower bound on the …
We propose an effective scheme for manipulating quantum information stored in a superconducting nanocircuit. The Josephson qubits are coupled via their separate interactions with an information bus, a large current-biased Josephson junction treated as an oscillator with adjustable frequency. The bus is sequentially coupled to only one qubit at a time. Distant Josephson qubits without any direct interaction can be indirectly coupled with each other by independently interacting with the bus sequentially, via exciting/de-exciting vibrational quanta in the bus. This is a superconducting analog of …
Optimal control can be used to significantly improve multi-qubit gates in quantum information processing hardware architectures based on superconducting circuit quantum electrodynamics. We apply this approach not only to dispersive gates of two qubits inside a cavity, but, more generally, to architectures based on two-dimensional arrays of cavities and qubits. For high-fidelity gate operations, simultaneous evolutions of controls and couplings in the two coupling dimensions of cavity grids are shown to be significantly faster than conventional sequential implementations. Even under experimenta…
