A new scheme is proposed which will permit electron spin resonance pulse techniques to be used to realize a quantum computer with a 100 qbits, or more. The computation is performed on effective pure states which correspond to off-diagonal blocks of the density matrix. Described is a scheme which very efficiently performs the preparation stage and which permits ``pseudo-projective measurement'' to be made on the output. With such measurements all members of the ensemble remain coherent.
We propose a parallel quantum computing mode for ensemble quantum computer. In this mode, some qubits can be in pure states while other qubits in mixed states. It enables a single ensemble quantum computer to perform $"$single-instruction-multi-data" type of parallel computation. In Grover's algorithm and Shor's algorithm, parallel quantum computing can provide additional speedup. In addition, it also makes a fuller use of qubit resources in an ensemble quantum computer. As a result, some qubits discarded in the preparation of an effective pure state in the Schulman-Varizani, and the Cleve-DiV…
We show that differently constructed ensembles having the same density matrix may be physically distinguished by observing fluctuations of some observables. An explicit expression for fluctuations of an observable in an ensemble is given. This result challenges Peres's fundamental postulate and seems to be contrary to the widely-spread belief that ensembles with the same density matrix are physically identical. This leads us to suggest that the current liquid NMR quantum computing is truly quantum-mechanical in nature.
Incorporating protection against quantum errors into adiabatic quantum computing (AQC) is an important task due to the inevitable presence of decoherence. Here we investigate an error-protected encoding of the AQC Hamiltonian, where qubit ensembles are used in place of qubits. Our Hamiltonian only involves total spin operators of the ensembles, offering a simpler route towards error-corrected quantum computing. Our scheme is particularly suited to neutral atomic gases where it is possible to realize large ensemble sizes and produce ensemble-ensemble entanglement. We identify a critical ensembl…
We propose to encode quantum information in rotational excitations in a molecular ensemble. Using a stripline cavity field for quantum state transfer between the molecular ensemble and a Cooper pair box two-level system, our proposal offers a linear scaling of the number of qubits in our register with the number of rotationally excited states available in the molecules.
The question of the generation of random mixed states is discussed, aiming for the computation of probabilistic characteristics of composite finite dimensional quantum systems. Particularly, we consider the generation of the random Hilbert-Schmidt and Bures ensembles of qubit and qutrit pairs and compute the corresponding probabilities to find a separable state among the states of a fixed rank.
We propose an effective realization of a complete set of elementary quantum gates in the solid-state quantum computer based on the multi-atomic coherent (MAC-) ensembles in the QED cavity. Here, we use the two-ensemble qubit encoding and swapping-based operations that together provide implementation of any encoded single-qubit operation by three elementary gates and the encoded controlled-NOT operation is performed in a single step. This approach simplifies a physical realization of universal quantum computing and adds the immunity to a number of errors. We also demonstrate that the proposed a…
Atomic ensembles, comprising clouds of atoms addressed by laser fields, provide an attractive system for both the storage of quantum information, and the coherent conversion of quantum information between atomic and optical degrees of freedom. In a landmark paper, Duan et al. (DLCZ) [1] showed that atomic ensembles could be used as nodes of a quantum repeater network capable of sharing pairwise quantum entanglement between systems separated by arbitrarily large distances. In recent years, a number of promising experiments have demonstrated key aspects of this proposal [2-7]. Here, we describe …
Searching a marked item or several marked items from an unsorted database is a very difficult mathematical problem. Using classical computer, it requires $O(N=2^n)$ steps to find the target. Using a quantum computer, Grover's algorithm uses $O(\sqrt{N=2^n})$ steps. In NMR ensemble computing, Brushweiler's algorithm uses $\log N$ steps. In this Letter, we propose an algorithm that fetches marked items in an unsorted database directly. It requires only a single query. It can find a single marked item or multiple number of items.
We propose an ensemble algorithm, which provides a new approach for evaluating and summing up a set of function samples. The proposed algorithm is not a quantum algorithm, insofar it does not involve quantum entanglement. The query complexity of the algorithm depends only on the scaling of the measurement sensitivity with the number of distinct spin sub-ensembles. From a practical point of view, the proposed algorithm may result in an exponential speedup, compared to known quantum and classical summing algorithms. However in general, this advantage exists only if the total number of function s…
In this paper we provide an operational method to detect multipartite entanglement in ensemble-based quantum computing. This method is based on the concept of entanglement witness. We decompose the entanglement witness for each class of multipartite entanglement into nonlocal operations in addition to local measurements. Individual single qubit measurements are performed simultaneously, hence complete detection of entanglement is performed in a single run experiment. This approach is particularly important for experiments where it is operationally difficult to prepare several copies of an unkn…
Experimental NMR implementations of the Deutsch-Josza quantum algorithm based on pesudo-pure spin states exhibit an exponential sensitivity scaling with the number of qubits. By employing truly mixed spin states in spin Liouville space, where molecules with different nuclear spin configurations represent different input states, the Deutsch-Josza problem can be solved by single function evaluation without sensitivity loss concomitant with increase of the number of bits.
Recently a new form of quantum memory has been proposed. The storage medium is an ensemble of electron spins, coupled to a stripline cavity and an ancillary readout system. Theoretical studies suggest that the system should be capable of storing numerous qubits within the ensemble, and an experimental proof-of-concept has already been performed. Here we show that this minimal architecture is not limited to storage but is in fact capable of full quantum processing by employing measurement-based entanglement. The technique appears to be remarkably robust against the anticipated dominant error ty…
Recently, we have shown that for conditions under which the so-called light-shift imbalance induced blockade (LSIIB) occurs, the collective excitation of an ensemble of a multi-level atom can be treated as a closed two level system. In this paper, we describe how such a system can be used as a quantum bit (qubit) for quantum communication and quantum computing. Specifically, we show how to realize a C-NOT gate using the collective qubit and an easily accessible ring cavity, via an extension of the so-called Pellizzari scheme. We also describe how multiple, small-scale quantum computers realize…
We propose a new physical approach for encoding and processing of quantum information in ensembles of multi-level quantum systems, where the different bits are not carried by individual particles but associated with the collective population of different internal levels. One- and two-bit gates are implemented by collective internal state transitions taking place in the presence of an excitation blockade mechanism which restricts the population of each internal state to the values zero and unity. 10-20 bit quantum computers can be built via this scheme in single trapped clouds of ground state a…
The proposal for quantum computing with rare-earth-ion qubits in inorganic crystals makes use of the inhomogeneous broadening of optical transitions in the ions to associate individual qubits with ions responding to radiation in selected frequency channels. We show that a class of Gaussian composite pulses and complex sech pulses provide accurate qubit pi-rotations, which are at the same time channel selective on a 5 MHz frequency scale and tolerant to 0.5 MHz deviations of the transition frequency of ions within a single channel. Rotations in qubit space of arbitrary angles and phases are pro…
We analyse the possibility to create two-mode spin squeezed states of two separate spin ensembles by inverting the spins in one ensemble and allowing spin exchange between the ensembles via a near resonant cavity field. We investigate the dynamics of the system using a combination of numerical and analytic calculations, and we obtain squeezing for a wide range of parameters. We also investigate the transfer of the squeezing properties to the cavity field and to an output mode from the cavity. Finally, we investigate how the squeezing is affected by effects of inhomogeneities which would be pre…
We propose a method to achieve strong coupling between a spin ensemble and a large Josephson junctions (LJJ). Then, the strong coupling between two spin ensembles can be induced by a LJJ. A non-adiabatic holonomic single-qubit quantum gates is realized. Moreover, with the dispersive interaction between the spin ensembles and the LJJ, the high-fidelity two-qubit phase gate can be implemented with two spin ensembles within an operation time 0.41 ns and $π$ phase-swap gate can be realized within an operation time 103.11 ns with a high fidelity greater than 99%.
We propose to encode a register of quantum bits in different collective electron spin wave excitations in a solid medium. Coupling to spins is enabled by locating them in the vicinity of a superconducting transmission line cavity, and making use of their strong collective coupling to the quantized radiation field. The transformation between different spin waves is achieved by applying gradient magnetic fields across the sample, while a Cooper Pair Box, resonant with the cavity field, may be used to carry out one- and two-qubit gate operations.
Single spin detection is a key objective in the field of metrology. There have been many experimental and theoretical investigations for the spin detection based on the use of probe spins. A probe spin shows the precession due to dipole-dipole interaction from a target spin, and measurement results of the probe spin allow us to estimate the state of the target spin. Here, we investigate performance of single-spin detection when using an ensemble of probe spins. Even though the ensemble of probe spins inevitably induces projection noise that could hinder the signal from the target spin, optimiz…
We propose a general method to maximize the fidelity of writing, storage and reading of quantum information (QI) in a spectrally inhomogeneous spin ensemble used as quantum memory. The method is based on preselecting the optimal spectral portion of the ensemble by a judiciously designed pulse. It allows drastic improvement of quantum memory realized by spin ensembles that store QI from a resonator or an optical beam.
The quantum nature of bulk ensemble NMR quantum computing --the center of recent heated debate, is addressed. Concepts of the mixed state and entanglement are examined, and the data in a 2 qubit liquid NMR quantum computation are analyzed. It is pointed out that the key problem in the current debate is the understanding of entanglement in a mixed state system. The following points are concluded in this Letter: 1)Density matrix describes the "state" of an average particle in an ensemble. It can not describe the state of an individual particle in an ensemble in detail; 2) Entanglement is a prope…
We propose a simple heralded amplification scheme for small rotations of the collective spin of an ensemble of particles. Our protocol makes use of two basic primitives for quantum memories, namely partial mapping of light onto an ensemble, and conversion of a collective spin excitation into light. The proposed scheme should be realizable with current technology, with potential applications to atomic clocks and magnetometry.
We report coherent coupling between two macroscopically separated nitrogen-vacancy electron spin ensembles in a cavity quantum electrodynamics system. The coherent interaction between the distant ensembles is directly detected in the cavity transmission spectrum by observing bright and dark collective multiensemble states and an increase of the coupling strength to the cavity mode. Additionally, in the dispersive limit we show transverse ensemble-ensemble coupling via virtual photons.
We propose a method to achieve quantum supremacy using ensembles of qubits, using only spin squeezing, basis rotations, and Fock state measurements. Each ensemble is assumed to be controllable only with its total spin. Using a repeated sequence of random basis rotations followed by squeezing, we show that the probability distribution of the final measurements quickly approaches a Porter-Thomas distribution. We show that the sampling probability can be related to a #P-hard problem with a complexity scaling as $(N+1)^M$, where $N$ is the number of qubits in an ensemble and $ M $ is the number of…
Inspired by recent developments in the control and manipulation of quantum dot nuclear spins, which allow for the transfer of an electron spin state to the surrounding nuclear-spin ensemble for storage, we propose a quantum repeater scheme that combines individual quantum dot electron spins and nuclear-spin ensembles, which serve as spin-photon interfaces and quantum memories respectively. We consider the use of low-strain quantum dots embedded in high-cooperativity optical microcavities. Quantum dot nuclear-spin ensembles allow for the long-term storage of entangled states, and heralded entan…
Inhomogeneously broadened spin ensembles play an important role in present-day implementation of hybrid quantum processing architectures. When coupled to a resonator such an ensemble may serve as a multi-mode quantum memory for the resonator field, and by employing spin-refocusing techniques the quantum memory time can be extended to the coherence time of individual spins in the ensemble. In the present paper we investigate such a memory protocol capable of storing an unknown resonator-field state, and we examine separately the various constituents of the protocol: the storage and read-out par…
We study a hybrid nano-mechanical system coupled to a spin ensemble as a quantum simulator to favor a quantum interference effect, the electromagnetically induced transparency (EIT). This system consists of two nano-mechanical resonators (NAMRs), each of which coupled to a nuclear spin ensemble. It could be regarded as a crucial element in the quantum network of NAMR arrays coupled to spin ensembles. Here, the nuclear spin ensembles behave as a long-lived transducer to store and transfer the NAMRs' quantum information. This system shows the analog of EIT effect under the driving of a probe mic…
We consider the optical generation and verification of entanglement in atomic ensembles under non-uniform interaction between the ensemble and an optical mode. We show that for a wide range of parameters a system of non-uniformly coupled atomic spins can be described as an ensemble of uniformly coupled spins with a reduced effective atom-light coupling and a reduced effective atom number, with a reduction factor of order unity given by the ensemble-mode geometry. This description is valid even for complex entangled states with arbitrary phase-space distribution functions as long as the detecti…
Entangled many body systems have recently attracted significant attention in various contexts. Among them, spin squeezed atoms and ions have raised interest in the field of precision measurements, as they allow to overcome quantum noise of uncorrelated particles. Precise quantum state engineering is also required as a resource for quantum computation, and spin squeezing can be used to create multi-partite entangled states. Two-mode spin squeezed systems have been used for elementary quantum communication protocols. Until now spin squeezing has been always achieved via generation of entanglemen…
When the dynamics of a spin ensemble are expressible solely in terms of symmetric processes and collective spin operators, the symmetric collective states of the ensemble are preserved. These many-body states, which are invariant under particle relabeling, can be efficiently simulated since they span a subspace whose dimension is linear in the number of spins. However, many open system dynamics break this symmetry, most notably when ensemble members undergo identical, but local, decoherence. In this paper, we extend the definition of symmetric collective states of an ensemble of spin-1/2 parti…
Spin counting via projection noise measurement of mesoscopic solid-state spin ensemble
ETH Zurich（苏黎世联邦理工学院）；JILA, National Institute of Standards and Technology and the University of Colorado, Boulder（美国科罗拉多大学博尔德分校与美国国家标准与技术研究院联合成立的JILA实验室）
We study the dynamical stability of the entanglement between the two spin ensembles in the presence of an environment. For a comparative study, we consider the two cases: a single spin ensemble, and two ensembles linearly coupled to a bath, respectively. In both circumstances, we assume the validity of the Markovian approximation for the bath. We examine the robustness of the state by means of the growth of the linear entropy which gives a measure of the purity of the system. We find out macroscopic entangled states of two spin ensembles can stably exist in a common bath. This result may be ve…
We consider how to measure collective spin states of an atomic ensemble based on the recent multi-pass approaches for quantum interface between light and atoms. We find that a scheme with two passages of a light pulse through the atomic ensemble is efficient to implement the homodyne tomography of the spin state. Thereby, we propose to utilize optical pulses as a phase-shifter that rotates the quadrature of the spins. This method substantially simplifies the geometry of experimental schemes.
We investigate numerically a single-pulse implementation of a quantum Control-Not (CN) gate for an ensemble of Ising spin systems at room temperature. For an ensemble of four-spin ``molecules'' we simulate the time-evolution of the density matrix, for both digital and superpositional initial conditions. Our numerical calculations confirm the feasibility of implementation of quantum CN gate in this system at finite temperature, using electromagnetic $π$-pulse.
This dissertation studies spin squeezing, entanglement and decoherence in large ensembles of cold, trapped alkali atoms with hyperfine spin f interacting with optical fields. Restricting the state of each atom to a qutrit embedded in the 2f+1 dimensional hyperfine spin enables us to efficiently model the coherent and dissipative dynamics of the ensemble. This formalism also allows us to explore the effects of local control on the internal hyperfine spins of the atoms. State preparation using such control increases the entangling power of the atom-light interface for f>1/2. Subsequent control o…
Electron and nuclear spins have good coherence times and an ensemble of spins is a promising candidate for a quantum memory. By employing holographic techniques via field gradients a single ensemble may be used to store many bits of information. Here we present a coherent memory using a pulsed magnetic field gradient, and demonstrate the storage and retrieval of up to 100 weak 10 GHz coherent excitations in collective states of an electron spin ensemble. We further show that such collective excitations in the electron spin can then be stored in nuclear spin states, which offer coherence times …
Long-lived quantum memories are essential components of a long-standing goal of remote distribution of entanglement in quantum networks. These can be realized by storing the quantum states of light as single-spin excitations in atomic ensembles. However, spin states are often subjected to different dephasing processes that limit the storage time, which in principle could be overcome using spin-echo techniques. Theoretical studies have suggested this to be challenging due to unavoidable spontaneous emission noise in ensemble-based quantum memories. Here we demonstrate spin-echo manipulation of …
Quantum spin dephasing is caused by inhomogeneous coupling to the environment, with resulting limits to the measurement time and precision of spin-based sensors. The effects of spin dephasing can be especially pernicious for dense ensembles of electronic spins in the solid-state, such as for nitrogen-vacancy (NV) color centers in diamond. We report the use of two complementary techniques, spin bath control and double quantum coherence, to enhance the inhomogeneous spin dephasing time ($T_2^*$) for NV ensembles by more than an order of magnitude. In combination, these quantum control techniques…
We study the evolution of an inverted spin ensemble coupled to a cavity. The inversion itself presents an inherent instability of the system; however, the inhomogeneous broadening of spin-resonance frequencies presents a stabilizing mechanism, and a stability criterion is derived. The detailed behavior of mean values and variances of the spin components and of the cavity field is accounted for under both stable and unstable conditions.
To establish an applicable system for advanced quantum information processing between light and atoms, we have demonstrated the quantum non-demolition (QND) measurement with a collective spin of cold ytterbium atoms (171Yb), and observed 1.8 (-1.5, +2.4) dB spin squeezing. Since a 171Yb atom has only a nuclear spin of 1/2 in the ground state, the system is the simplest spin ensemble and robust against decoherence. We used very short pulses with the width of 100 ns, so the interaction time became much shorter than the decoherence time, which is important for multi-step quantum information proce…
We propose a multi-mode quantum memory protocol able to store the quantum state of the field in a microwave resonator into an ensemble of electronic spins. The stored information is protected against inhomogeneous broadening of the spin ensemble by spin-echo techniques resulting in memory times orders of magnitude longer than previously achieved. By calculating the evolution of the first and second moments of the spin-cavity system variables for realistic experimental parameters, we show that a memory based on NV center spins in diamond can store a qubit encoded on the |0> and |1> Fock states …
We study the excitation dynamics of an inhomogeneously broadened spin ensemble coupled to a single cavity mode. The collective excitations of the spin ensemble can be described in terms of generalized spin waves and, in the absence of the cavity, the free evolution of the spin ensemble can be described as a drift in the wave number without dispersion. In this article we show that the dynamics in the presence of coupling to the cavity mode can be described solely by a modified time evolution of the wave numbers. In particular, we show that collective excitations with a well- defined wave number…
In large ensembles of identical atoms or spins, the interaction with a mode of the electromagnetic radiation field concentrates in a single superradiant degree of freedom with a collectively enhanced coupling. Given a controllable inhomogeneous broadening, such ensembles may be used for multi-mode storage of quantum states of the radiation field with applications in quantum communication networks and quantum computers. In this paper we analyze how the width and shape of the inhomogeneous broadening influence the collective enhancement and the dynamics of the cavity-ensemble system with focus o…
We analyze the magnetic dipole coupling of an ensemble of spins to a superconducting microwave stripline structure, incorporating a Josephson junction based transmon qubit. We show that this system is described by an embedded Jaynes-Cummings model: in the strong coupling regime, collective spin-wave excitations of the ensemble of electrons pick up the nonlinearity of the cavity mode, such that the two lowest eigenstates of the coupled spin-wave + microwave-cavity + Josephson-junction system define a hybrid two-level system. The proposal described here enables the use of spin ensembles as qubit…
Quantum squeezing and entanglement of spins can be used to improve the sensitivity in quantum metrology. Here we propose a scheme to create collective coupling of an ensemble of spins to mechanical vibrational mode actuated by an external magnetic field. We find an evolution time where the mechanical motion decouples from the spins, and the accumulated geometric phase yields a squeezing of $5.9~\text{dB}$ for $20$ spins. We also show the creation of a Greenberger-Horne-Zeilinger spin state for $20$ spins with a fidelity of $\sim 0.62$ at cryogenic temperature. The numerical simulations show th…
We experimentally demonstrate quantum machine learning using NMR based on a framework of quantum reservoir computing. Reservoir computing is for exploiting natural nonlinear dynamics with large degrees of freedom, which is called a reservoir, for a machine learning purpose. Here we propose a concrete physical implementation of a quantum reservoir using controllable dynamics of a nuclear spin ensemble in a molecular solid. In this implementation, we demonstrate learning of nonlinear functions with binary or continuous variable inputs with low mean squared errors. Our implementation and demonstr…
We describe how sideband cooling techniques may be applied to large spin ensembles in magnetic resonance. Using the Tavis-Cummings model in the presence of a Rabi drive, we solve a Markovian master equation describing the joint spin-cavity dynamics to derive cooling rates as a function of ensemble size. Our calculations indicate that the coupled angular momentum subspaces of a spin ensemble containing roughly $10^{11}$ electron spins may be polarized in a time many orders of magnitude shorter than the typical thermal relaxation time. The described techniques should permit efficient removal of …
We apply optimal control techniques to an inhomogeneous spin ensemble coupled to a cavity. A general procedure is proposed for designing the control strategies. We numerically show the extent to which optimal control fields robust against system uncertainties help enhancing the sensitivity of the detection process. The parameters of the numerical simulations are taken from recent Electron Spin Resonance experiments. The low and high cooperativity regimes are explored.
We present a Dicke state preparation scheme which uses global control of $N$ spin qubits: our scheme is based on the standard phase estimation algorithm, which estimates the eigenvalue of a unitary operator. The scheme prepares a Dicke state non-deterministically by collectively coupling the spins to an ancilla qubit via a $ZZ$-interaction, using $\ceil*{\log_2 N} + 1$ ancilla qubit measurements. The preparation of such Dicke states can be useful if the spins in the ensemble are used for magnetic sensing: we discuss a possible realization using an ensemble of electronic spins located at diamon…
We introduce tqix.pis, a library of tqix, for quantum dynamics simulation of spin ensembles. The library emulates a dynamic process by a quantum circuit, including initializing a quantum state, executing quantum operators, and measuring the final state. It utilizes collective processes in spin ensembles to reduce the dimension from exponentially to quadratically with the number of particles, i.e., the quantum state spans in Dicke basis. It also facilitates the simulation time with multi-core processors and Graphics Processing Units. The library is thus applicable for the simulation of ensemble…
We study the properties of a two-body random matrix ensemble for distinguishable spins. We require the ensemble to be invariant under the group of local transformations and analyze a parametrization in terms of the group parameters and the remaining parameters associated with the "entangling" part of the interaction. We then specialize to a spin chain with nearest neighbour interactions and numerically find a new type of quantum phase transition related to the strength of a random external field i.e. the time reversal breaking one body interaction term.
We present a simple model which allows us to explain the physical nature of the oscillating entropy. We consider an ensemble of qubits interacting with thermal two-level systems. The entropy of the qubits oscillates between zero and the value of entropy of the thermal systems. We show that the oscillations of the entropy can be clearly explained by the precession of the real or effective spins of the qubits.
We study the interaction between a superconducting cavity and a spin ensemble. The response of a cavity mode is monitored while simultaneously the spins are driven at a frequency close to their Larmor frequency, which is tuned to a value much higher than the cavity resonance. We experimentally find that the effective damping rate of the cavity mode is shifted by the driven spins. The measured shift in the damping rate is attributed to the retarded response of the cavity mode to the driven spins. The experimental results are compared with theoretical predictions and fair agreement is found.
Quantum non-demolition (QND) measurement of collective variables by off-resonant optical probing has the ability to create entanglement and squeezing in atomic ensembles. Until now, this technique has been applied to real or effective spin one-half systems. We show theoretically that the build-up of Raman coherence prevents the naive application of this technique to larger spin atoms, but that dynamical decoupling can be used to recover the ideal QND behavior. We experimentally demonstrate dynamical decoupling by using a two-polarization probing technique. The decoupled QND measurement achieve…
The one-dimensional homonuclear periodic array of nuclear spins I = 1/2, owing to hyperfine interaction of nuclear spins with electronic magnetic moments in antiferromagnetic structure, is considered. The neighbor nuclear spins in such array are opposite oriented and have resonant frequencies determined by hyperfine interaction constant, applied magnetic field value and interaction with the left and right nuclear neighbor spins. The resonant frequencies difference of nuclear spins, when the neighbor spins have different and the same states, is used to control the spin dynamics by means of sele…
