Optical lattices with one atom on each site and interacting via cold controlled collisions provide an efficient way to entangle a large number of qubits with high fidelity. It has already been demonstrated experimentally that this approach is especially suited for the generation of cluster states [O. Mandel et al., Nature 425, 937 (2003)] which reduce the resource requirement for quantum computing to the ability to perform single-qubit rotations and qubit read out. In this paper, we describe how to implement these rotations in 1D and 2D optical lattices without having to address the atoms individually with a laser field.
The Leggett-Garg inequality holds for any macrorealistic system that is being measured noninvasively. A violation of the inequality can signal that a system does not conform to our primal intuition about the physical world. Alternatively, a violation can simply indicate that "clumsy" experimental technique led to invasive measurements. Here, we consider a recent Leggett-Garg test designed to try to rule out the mundane second possibility. We tailor this Leggett-Garg test to the IBM 5Q Quantum Experience system and find compelling evidence that qubit $Q_2$ of the system cannot be described by n…
A vital requirement for a quantum computer is the ability to locally address, with high fidelity, any of its qubits without affecting their neighbors. We propose an addressing method using composite sequences of laser pulses, which reduces dramatically the addressing error in a lattice of closely spaced atoms or ions, and at the same time significantly enhances the robustness of qubit manipulations. To this end, we design novel high-fidelity composite pulses for the most important single-qubit operations. In principle, this method allows one to beat the diffraction limit, for only atoms situat…
We propose a fast and efficient technique to create classes of highly entangled states of trapped ions, such as arbitrary Dicke states and superpositions of them, e.g. NOON states. The ions are initialized in the phonon ground state and are addressed globally with a composite pulse that is resonant with the first motional sideband. The technique operates on comparatively short time scales, as resonant interactions allow one to use the minimum laser pulse area. The number of single pulses from the composite sequence is equal to the number of ions, thus the implementation complexity grows only l…
Separate addressing of individual qubits is a challenging requirement for scalable quantum computation, and crosstalk between operations on neighboring qubits remains as a significant source of noise for current experimental implementation of multi-qubit platforms. We propose a scheme based on spatial refocusing from interference of several coherent laser beams to significantly reduce the crosstalk noise for any type of quantum gates. A general framework is developed for the spatial refocusing technique, in particular with practical Gaussian beams, and we show under typical experimental condit…
The establishment of a scalable scheme for quantum computing with addressable and long-lived qubits would be a scientific watershed, harnessing the laws of quantum physics to solve classically intractable problems. The design of many proposed quantum computational platforms is driven by competing needs: isolating the quantum system from the environment to prevent decoherence, and easily and accurately controlling the system with external fields. For example, neutral-atom optical-lattice architectures provide environmental isolation through the use of states that are robust against fluctuating …
Selective laser addressing of a single atom or atomic ion qubit can be improved using narrowband composite pulse sequences. We describe a Lie-algebraic technique to generalize known narrowband sequences and introduce new sequences related by dilation and rotation of sequence generators. Our method improves known narrowband sequences by decreasing both the pulse time and the residual error. Finally, we experimentally demonstrate these composite sequences using $^{40}$Ca$^+$ ions trapped in a surface-electrode ion trap.
The ability to individually manipulate the increasing number of qubits is one of the many challenges towards scalable quantum information processing with trapped ions. Using micro-mirrors fabricated with micro-electromechanical systems (MEMS) technology, we focus laser beams on individual ions in a linear chain and steer the focal point in two dimensions. We demonstrate sequential single qubit gates on multiple $^{171}$Yb$^+$ qubits and characterize the gate performance using quantum state tomography. Our system features negligible crosstalk to neighboring ions ($< 3\times 10^{-4}$), and switc…
We present a method for performing quantum state reconstruction on qubits and qubit registers in the presence of decoherence and inhomogeneous broadening. The method assumes only rudimentary single qubit rotations as well as knowledge of decoherence and loss mechanisms. We show that full state reconstruction is possible even in the case where single qubit rotations may only be performed imperfectly. Furthermore we show that for ensemble quantum computing proposals, quantum state reconstruction is possible even if the ensemble experiences inhomogeneous broadening and if only imperfect qubit man…
The ability to measure and reduce systematic errors in single-qubit logic gates is crucial when evaluating quantum computing implementations. We describe pulsed electron paramagnetic resonance (EPR) sequences that can be used to measure precisely even small systematic errors in rotations of electron-spin-based qubits. Using these sequences we obtain values for errors in rotation angle and axis for single-qubit rotations using a commercial EPR spectrometer. We conclude that errors in qubit operations by pulsed EPR are not limiting factors in the implementation of electron-spin based quantum com…
Individual addressing of qubits is essential for scalable quantum computation. Spatial addressing allows unlimited numbers of qubits to share the same frequency, whilst enabling arbitrary parallel operations. We demonstrate addressing of long-lived $^{43}\text{Ca}^+$ "atomic clock" qubits held in separate zones ($960μ$m apart) of a microfabricated surface trap with integrated microwave electrodes. Such zones could form part of a "quantum CCD" architecture for a large-scale quantum information processor. By coherently cancelling the microwave field in one zone we measure a ratio of Rabi frequen…
In a large scale trapped atomic ion quantum computer, high-fidelity two-qubit gates need to be extended over all qubits with individual control. We realize and characterize high-fidelity two-qubit gates in a system with up to 4 ions using radial modes. The ions are individually addressed by two tightly focused beams steered using micro-electromechanical system (MEMS) mirrors. We deduce a gate fidelity of 99.49(7)% in a two-ion chain and 99.30(6)% in a four-ion chain by applying a sequence of up to 21 two-qubit gates and measuring the final state fidelity. We characterize the residual errors an…
We present a way for implementing an n-qubit controlled-rotation gate with three-level superconducting qubit systems in cavity QED. The two logical states of a qubit are represented by the two lowest levels of each system while a higher-energy level is used for the gate implementation. The method operates essentially by preparing a $W$ state conditioned on the states of the control qubits, creating a single photon in the cavity mode, and then performing an arbitrary rotation on the states of the target qubit with assistance of the cavity photon. It is interesting to note that the basic operati…
One of the fundamental conditions for one-way quantum computation (1WQC) is the ability to make sequential measurements on isolated qubits that comprise the highly entangled resource for 1WQC, the cluster state. This has been a significant impediment in the implementation of 1WQC with ultracold atoms confined in optical lattices, because the width of the measuring lasers is generally much greater than the atomic (qubit) spacing. We demonstrate that deterministic 1WQC is nevertheless possible, with a polynomial increase in the number of operations, as long as the center of the beams can be posi…
A quantized fermion can be represented by a scalar particle encircling a magnetic flux line. It has the spinor structure which can be constructed from quantum gates and qubits. We have studied here the role of Berry phase in removing dynamical phase during one qubit rotation of a quantized fermion. The entanglement of two qubit inserting spin-echo to one of them results the change of Berry phase that can be considered as a measure of entanglement. Some effort is given to study the effect of noise on the Berry phase of spinor and their entangled states.
Exploring the symmetries underlying a previously proposed encryption scheme which relies on single-qubit rotations, we derive an improved upper bound on the maximum information that an eavesdropper might extract from all the available copies of the public key. Subsequently, the robustness of the scheme is investigated in the context of attacks that address each public-key qubit independently. The attacks under consideration make use of projective measurements on single qubits and their efficiency is compared to attacks that address many qubits collectively and require complicated quantum opera…
In a direct two-level qubit system, when the Rabi frequency is comparable to the resonance frequency, the rotating wave approximation is not appropriate. In this case, the Rabi oscillation is accompanied by another oscillation at twice the frequency of the driving field, the so called Bloch-Siegert oscillation (BSO), which depends on the initial phase of the driving field. This oscillation may restrict the precise rotation of a qubit made of direct two-level system. Here, we show that in case of an effectively two-level lambda system, the BSO is inherently negligible, implying a greater precis…
A crucial requirement for quantum information processing is the realization of multiple-qubit quantum gates. Here, we demonstrate an electron spin based all-electrical two-qubit gate consisting of single spin rotations and inter-dot spin exchange in a double quantum dot. A partially entangled output state is obtained by the application of the two-qubit gate to an initial, uncorrelated state. We find that the degree of entanglement is controllable by the exchange operation time. The approach represents a key step towards the realization of universal multiple qubit gates.
We discuss cryptographic applications of single-qubit rotations from the perspective of trapdoor one-way functions and public-key encryption. In particular, we present an asymmetric cryptosystem whose security relies on fundamental principles of quantum physics. A quantum public key is used for the encryption of messages while decryption is possible by means of a classical private key only. The trapdoor one-way function underlying the proposed cryptosystem maps integer numbers to quantum states of a qubit and its inversion can be infeasible by virtue of the Holevo's theorem.
We introduce a novel procedure for qubit rotation, alternative to the commonly used method of Rabi oscillations of controlled pulse area. It is based on the technique of Stimulated Raman Adiabatic Passage (STIRAP) and therefore it is robust against fluctuations of experimental parameters. Furthermore, our work shows that it is in principle possible to perform quantum logic operations via stimulated Raman adiabatic passage. This opens up the search for a completely new class of schemes to implement logic gates.
The rotation of subspaces by a chosen angle is a fundamental quantum computing operation, with applications in error correction and quantum algorithms such as the Quantum Approximate Optimization Algorithm, the Variational Quantum Eigensolver and the quantum singular value transformation. Such rotations are usually implemented at the hardware level via multiple-controlled-phase gates, which lead to large circuit depth when decomposed into one- and two-qubit gates. Here, we propose a fast, high-fidelity way to implement such operations via topological quantum walks, where a sequence of single-q…
We show how one can perform arbitrary rotation of any qubit, using delayed laser pulses through nonadiabatic evolution, i.e., via transitions among the adiabatic states. We use a double-Lambda scheme and use a set of control parameters such as detuning, ratio of pulse amplitudes, time-separation of two pulses for realizing different rotations of the qubit. We also investigate the effect of different kinds of chirping, namely linear chirping and hyperbolic tangent chirping. Our work using nonadiabatic evolution adds to the flexibility in the implementation of logic gate operations and show how …
Individual-qubit addressing is a prerequisite for many instances of quantum information processing. We demonstrate this capability on trapped-ion qubits with microwave near-fields delivered by electrode structures integrated into a microfabricated surface-electrode trap. We describe four approaches that may be used in quantum information experiments with hyperfine levels as qubits. We implement individual control on two 25Mg+ ions separated by 4.3 micrometer and find spin-flip crosstalk errors on the order of 10^(-3).
We propose and study ways speeding up of the entangling operations in the trapped ions system with high fidelity. First, we find a scheme to increase the speed of a two-qubit gate without the limitation of trap frequency, which was considered as the fundamental limit. Second, we study the fast gate scheme for entangling more than two qubits simultaneously. We apply the method of applying multiple frequency components on laser beams for the gate operations. In particular, in order to avoid infinite terms from the coupling to carrier transition, we focus on the phase-insensitive gate scheme here…
Trapped ions boast long coherence times and excellent gate fidelities, making them a useful platform for quantum information processing. Scaling to larger numbers of ion qubits in RF Paul traps demands great effort. Another technique for trapping ions is via a Penning trap where a 2D crystal of hundreds of ions is formed by controlling the rotation of the ions in the presence of a strong magnetic field. However, the rotation of the ion crystal makes single ion addressability a significant challenge. We propose a protocol that takes advantage of a deformable mirror to introduce AC Stark shift p…
We report the first experimental realization of single-qubit manipulation for single spinwaves stored in an atomic ensemble quantum memory. In order to have high-fidelity gate operations, we make use of stimulated Raman transition and controlled Lamor precession jointly. We characterize the gate performances with quantum state tomography and quantum process tomography, both of which imply that high-fidelity operations have been achieved. Our work complements the experimental toolbox of atomic-ensemble quantum memories by adding the capability of single-qubit manipulation, thus may have importa…
We study the fidelity of single qubit quantum gates performed with two-frequency laser fields that have a Gaussian or super Gaussian spatial mode. Numerical simulations are used to account for imperfections arising from atomic motion in an optical trap, spatially varying Stark shifts of the trapping and control beams, and transverse and axial misalignment of the control beams. Numerical results that account for the three dimensional distribution of control light show that a super Gaussian mode with intensity $I\sim e^{-2(r/w_0)^n}$ provides reduced sensitivity to atomic motion and beam misalig…
Crosstalk is a major concern in the implementation of large-scale quantum computation since it can degrade the performance of qubit addressing and cause gate errors. Finding the origin of crosstalk and separating contributions from different channels are essential prerequisites for figuring out crosstalk mitigation schemes. Here, by performing circuit analysis of two coupled floating transmon qubits, we demonstrate that, even if the stray coupling, e.g., between a qubit and the drive line of its nearby qubit, is absent, microwave crosstalk between qubits can still exist due to the presence of …
Due to their potential for long coherence times, dopant ions have long been considered promising candidates for scalable solid state quantum computing. However, the demonstration of two qubit operation has proven to be problematic, largely due to the difficulty of addressing closely spaced ions. Here we use optically active ions and optical frequency addressing to demonstrate a conditional phase shift between two qubits.
Trapped ions are one of the leading platforms for quantum information processing, exhibiting the highest gate and measurement fidelities of all contending hardware. In order to realize a universal quantum computer with trapped ions, independent and parallel control over the state of each qubit is necessary. The manipulation of individual qubit states in an ion chain via stimulated Raman transitions generally requires light focused on individual ions. In this manuscript, we present a novel, guided-light individual addressing system for hyperfine Ba$^+$ qubits. The system takes advantage of lase…
We describe, realize, and experimentally investigate a method to perform physical rotations of ion chains, trapped in a segmented surface Paul trap, as a building block for large scale quantum computational sequences. Control of trapping potentials is achieved by parametrizing electrode voltages in terms of spherical harmonic potentials. Voltage sequences that enable crystal rotations are numerically obtained by optimizing time-dependent ion positions and motional frequencies, taking into account the effect of electrical filters in our set-up. We minimize rotation-induced heating by expanding …
We explore the implementation of pseudo-random single-qubit rotations and multi-qubit pseudo-random circuits constructed only from Clifford gates and the T-gate, a phase rotation of pi/4. Such a gate set would be appropriate for computations performed in a fault tolerant setting. For single-qubit rotations the distribution of parameters found for unitaries constructed from Clifford plus T quickly approaches that of random rotations and require significantly fewer gates than the construction of arbitrary single-qubit rotations. For Clifford plus T pseudo-random circuits we find an exponential c…
When an off-resonant light field is coupled with atomic spins, its polarization can rotate depending on the direction of the spins via a Faraday rotation which has been used for monitoring and controlling the atomic spins. We observed Faraday rotation by an angle of more than 10 degrees for a single 1/2 nuclear spin of 171Yb atom in a high-finesse optical cavity. By employing the coupling between the single nuclear spin and a photon, we have also demonstrated that the spin can be projected or weakly measured through the projection of the transmitted single ancillary photon.
Any single-qubit unitary operation or quantum gate can be considered a rotation. Typical experimental implementations of single-qubit gates involve two or three fixed rotation axes, and up to three rotation steps. Here we show that, if the rotation axes can be tuned arbitrarily in a fixed plane, then two rotation steps are sufficient for implementing a single-qubit gate, and one rotation step is sufficient for implementing a state transformation. The results are relevant for "exchange-only" logical qubits encoded in three-spin blocks, which are important for universal quantum computation in de…
A frequently encountered source of systematic error in quantum computations is imperfections in the control pulses which are the classical fields that control qubit gate operations. From an analysis of the quantum mechanical time-evolution operator of the spin wavefunction, it has been demonstrated that composite pulses can mitigate certain systematic errors and an appealing geometric interpretation was developed for the design of error-suppressing composite pulses. Here we show that these same pulse sequences can be obtained within a quasi-classical framework. This raises the question of whet…
We show how an arbitrary qubit rotation can be teleported, albeit probabilistically, using 1 e-bit of entanglement and one classical bit. We use this to present a scheme for implementing quantum secret sharing. The scheme operates essentially by sending a "secret" rotated qubit of information to several users, who need to cooperate in order to recover the original qubit.
In this paper we utilize superoperator formalism to explore the entanglement evolution of four-qubit cluster states in a number of decohering environments. A four-qubit cluster state is a resource for the performance of an arbitrary single logical qubit rotation via measurement based cluster state quantum computation. We are specifically interested in the relationship between entanglement evolution and the fidelity with which the arbitrary single logical qubit rotation can be implemented in the presence of decoherence as this will have important experimental ramifications. We also note the exh…
We discuss the implementation of frequency selective rotations using sequences of hard pulses and delays. These rotations are suitable for implementing single qubit gates in Nuclear Magnetic Resonance (NMR) quantum computers, but can also be used in other related implementations of quantum computing. We also derive methods for implementing hard pulses in the presence of moderate off-resonance effects, and describe a simple procedure for implementing a hard 180 degree rotation in a two spin system. Finally we show how these two approaches can be combined to produce more accurate frequency selec…
A controlled qubit in a rotating frame opens new opportunities to probe fundamental quantum physics, such as geometric phases in physically rotating frames, and can potentially enhance detection of magnetic fields. Realising a single qubit that can be measured and controlled during physical rotation is experimentally challenging. In this work, we demonstrate quantum control of a single nitrogen-vacancy (NV) centre within a diamond rotated at 200,000rpm, a rotational period comparable to the NV spin coherence time $T_2$. We stroboscopically image individual NV centres that execute rapid circula…
The addressing of a particular qubit within a quantum register is a key prerequisite for scalable quantum computing. In general, executing a quantum gate with a single qubit, or a subset of qubits, affects the quantum states of all other qubits. This reduced fidelity of the whole quantum register could prevent the application of quantum error correction protocols and thus preclude scalability. We demonstrate addressing of individual qubits within a quantum byte (eight qubits) and measure the error induced in all non-addressed qubits (cross-talk) associated with the application of single-qubit …
We look for local unitary operators $W_1 \otimes W_2$ which would rotate all equally entangled two-qubit pure states by the same but arbitrary amount. It is shown that all two-qubit maximally entangled states can be rotated through the same but arbitrary amount by local unitary operators. But there is no local unitary operator which can rotate all equally entangled non-maximally entangled states by the same amount, unless it is unity. We have found the optimal sets of equally entangled non-maximally entangled states which can be rotated by the same but arbitrary amount via local unitary operat…
To date, individual addressing of ion qubits has relied primarily on local Rabi or transition frequency differences between ions created via electromagnetic field spatial gradients or via ion transport operations. Alternatively, it is possible to synthesize arbitrary local one-qubit gates by leveraging local phase differences in a global driving field. Here we report individual addressing of $^{40}$Ca$^+$ ions in a two-ion crystal using axial potential modulation in a global gate laser field. We characterize the resulting gate performance via one-qubit randomized benchmarking, applying differe…
We introduce a simple, widely applicable formalism for designing "error-divisible" two qubit gates: a quantum gate set where fractional rotations have proportionally reduced error compared to the full entangling gate. In current noisy intermediate-scale quantum (NISQ) algorithms, performance is largely constrained by error proliferation at high circuit depths, of which two-qubit gate error is generally the dominant contribution. Further, in many hardware implementations, arbitrary two qubit rotations must be composed from multiple two-qubit stock gates, further increasing error. This work intr…
The long coherence times and strong Coulomb interactions afforded by trapped ion qubits have enabled realizations of the necessary primitives for quantum information processing (QIP), and indeed the highest-fidelity quantum operations in any qubit to date. But while light delivery to each individual ion in a system is essential for general quantum manipulations and readout, experiments so far have employed optical systems cumbersome to scale to even a few tens of qubits. Here we demonstrate lithographically defined nanophotonic waveguide devices for light routing and ion addressing fully integ…
