Many coherence transfer experiments in Nuclear Magnetic Resonance Spectroscopy, involving network of coupled spins, use temporary spin-decoupling to produce desired effective Hamiltonians. In this paper, we show that significant time can be saved in producing an effective Hamiltonian, if spin-decoupling is avoided. We provide time optimal pulse sequences for producing an important class of effective Hamiltonians in three spin networks. These effective Hamiltonians are useful for coherence transfer experiments and implementation of quantum logic gates in NMR quantum computing. It is demonstrated that computing these time optimal pulse sequences can be reduced to geometric problems that involve computing sub-Riemannian geodesics on Homogeneous spaces.
To implement reliable quantum information processing, quantum gates have to be protected together with the qubits from decoherence. Here we demonstrate experimentally on nitrogen-vacancy system that by using continuous wave dynamical decoupling method, not only the coherence time is prolonged by about 20 times, but also the quantum gates is protected for the duration of controlling time. This protocol shares the merits of retaining the superiority of prolonging the coherence time and at the same time easily combining with quantum logic tasks. It is expected to be useful in task where duration …
Because of using geometric phases, nonadiabatic geometric gates have the robustness against control errors. On the other hand, decoherence still affects nonadiabatic geometric gates, which is a key factor in reducing their fidelities. In this paper, we show that based on the system Hamiltonian that realizes a nonadiabatic geometric gate, one may construct a new system Hamiltonian, by using which not only the geometric feature of the nonadiabatic geometric gate is preserved, but also the system's coherence is protected. As a result, a coherence-protected nonadiabatic geometric gate is realized …
We analyze the optimal basis for generating the maximum relative entropy of quantum coherence by an arbitrary gate on a two-qubit system. The optimal basis is not unique, and the high quantum coherence generating gates are also typically high entanglement generating ones and vice versa. However, the profile of the relative frequencies of Haar random unitaries generating different amounts of entanglement for a fixed amount of quantum coherence is different from the one in which the roles of entanglement and quantum coherence are reversed, although both follow the beta distribution.
For neutral atom qubits, the two-qubit gate is typically realized via the Rydberg blockade effect, which hints about the special status of the Rydberg level besides the regular qubit register states. Here, we carry out experimental and theoretical studies to reveal how the ground-Rydberg coherence of the control qubit atom affects the process of two-qubit Controlled-Z ($C_Z$) gate, such as the commonly used ground-Rydberg $π$-gap-$π$ pulse sequence originally proposed in Phys. Rev. Lett. \textbf{85}, 2208 (2000). We measure the decoherence of the control qubit atom after the $π$-gap-$π$ pulses…
We introduce unitary quantum gates for photon pair creation in spontaneous parametric down-conversion nonlinear crystals (NLs) and for photon path alignment. These are the two key ingredients for the method of "induced coherence without induced emission" and many ensuing variations thereof. The difficulty in doing so stems from an apparent mixing of the mode picture (such as the polarization of photons) and the Fock picture (such as the existence of the photons). We illustrate utility of these gates by obtaining quantum circuits for the experimental setups of the frustrated generation of photo…
Within the unified framework of exploiting the relative entropy as a distance measure of quantum correlations, we make explicit the hierarchical structure of quantum coherence, quantum discord and quantum entanglement in multipartite systems. On this basis, we introduce a new measure of quantum coherence, the basis-free quantum coherence and prove that this quantity is exactly equivalent to quantum discord. Furthermore, since the original relative entropy of coherence is a basis-dependent quantity, we investigate the local and nonlocal unitary creation of quantum coherence, focusing on the two…
We propose to apply the notion of the Schmidt number in order to show that a quantum memory or gate process is capable of maintaining a genuine multi-level quantum coherence. We present a simple criterion in terms of an average gate fidelity with respect to the input states of two mutually unbiased bases and demonstrate the coherence of the gate operation in several existing experiments. The Schmidt-number benchmark naturally includes the quantum benchmark as a specific case.
The entropic coherence is a necessary resource for non-energy preserving gates
Scuola Normale Superiore（高等师范学院）；Dipartimento di Fisica dell’Università di Pisa（比萨大学物理系）；Department of Applied Physics, University of Geneva（日内瓦大学应用物理系）；Física Teòrica: Informació i Fenòmens Quàntics, Department de Física, Universitat Autònoma de Barcelona（巴塞罗那自治大学物理系理论物理、信息与量子现象部门）；NEST, and Istituto Nanoscienze-CNR（NEST与意大利国家研究委员会纳米科学研究所）
A key requirement to perform simulations of large quantum systems on near-term quantum hardware is the design of quantum algorithms with short circuit depth that finish within the available coherence time. A way to stay within the limits of coherence is to reduce the number of gates by implementing a gate set that matches the requirements of the specific algorithm of interest directly in hardware. Here, we show that exchange-type gates are a promising choice for simulating molecular eigenstates on near-term quantum devices since these gates preserve the number of excitations in the system. Com…
The fidelity of the gate operation and the coherence time of neutral atoms trapped in an optical dipole trap are figures of merit for the applications. The motion of the trapped atom is one of the key factors which influence the gate fidelity and coherence time. The motion has been considered as a classical oscillator in analyzing the influence. Here we treat the motion of the atom as a quantum oscillator. The population on the vibrational states of the atom are considered in analyzing the gate fidelity and decoherence. We show that the fidelity of a coherent rotation gate is dramatically limi…
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 …
Long coherence times, large anharmonicity and robust charge-noise insensitivity render fluxonium qubits an interesting alternative to transmons. Recent experiments have demonstrated record coherence times for low-frequency fluxonia. Here, we propose a galvanic-coupling scheme with flux-tunable $\textit{XX}$ coupling. To implement a high-fidelity entangling $\sqrt{i\mathrm{SWAP}}$ gate, we modulate the strength of this coupling and devise variable-time identity gates to synchronize required single-qubit operations. Both types of gates are implemented using strong ac flux drives, lasting for onl…
A scheme is proposed for protecting quantum states from both independent decoherence and cooperative decoherence. The scheme operates by pairing each qubit (two-state quantum system) with an ancilla qubit and by encoding the states of the qubits into the corresponding coherence-preserving states of the qubit-pairs. In this scheme, the amplitude damping (loss of energy) is prevented as well as the phase damping (dephasing) by a strategy called the free-Hamiltonian-elimination We further extend the scheme to include quantum gate operations and show that loss and decoherence during the gate opera…
We prove upper and lower bounds relating the quantum gate complexity of a unitary operation, U, to the optimal control cost associated to the synthesis of U. These bounds apply for any optimal control problem, and can be used to show that the quantum gate complexity is essentially equivalent to the optimal control cost for a wide range of problems, including time-optimal control and finding minimal distances on certain Riemannian, subriemannian, and Finslerian manifolds. These results generalize the results of Nielsen, Dowling, Gu, and Doherty, Science 311, 1133-1135 (2006), which showed that …
The unavoidable effect of the environmental noise due to nuclear spins and charge traps is included in the study of the hybrid qubit dynamics. Hybrid qubit dues its name to the advantageous combination of manipulation speed of a charge qubit with the longevity of a spin qubit. It consists of three electrons confined through external gate voltages in a double quantum dot and deserves special interest in quantum computation applications due to its advantages in terms of fabrication, control and only electrical manipulation. Hybrid qubit is protected against global magnetic fluctuations since it …
The sensitivity of quantum systems to external disturbances is a fundamental problem for the implementation of functional quantum devices, quantum information and computation. Based on remarkable experimental progress in optics and ultra-cold gases, we study the consequences of a short-time (instantaneous) noise while an intensity-dependent phase acquisition is associated with a qubit propagating on $N$-cycle. By employing quantum coherence measures, we report emerging unstable regimes in which hitherto unknown quantum walks arise, such as self-focusing and breathing dynamics. Our results unve…
Finite group extensions offer a natural language to quantum computing. In a nutshell, one roughly describes the action of a quantum computer as consisting of two finite groups of gates: error gates from the general Pauli group P and stabilizing gates within an extension group C. In this paper one explores the nice adequacy between group theoretical concepts such as commutators, normal subgroups, group of automorphisms, short exact sequences, wreath products... and the coherent quantum computational primitives. The structure of the single qubit and two-qubit Clifford groups is analyzed in detai…
Nuclear-spin qubits have long coherence time and are desirably applied into quantum information processing. However, the existing methods either fail to address single nucleus (such as nuclear magnetic resonance), or severely affect nuclear coherence time (such as electrical nuclear manipulation based on hyperfine stark effect, ENMHSE). Here we propose an electrical nuclear manipulation called nuclear electric resonance which can on the one hand address the single nuclear qubit, and on the other keep the long coherence time. Applying this, we construct universal quantum gates with external ele…
A challenge for constructing large circuits of superconducting qubits is to balance addressability, coherence and coupling strength. High coherence can be attained by building circuits from fixed-frequency qubits, however, leading techniques cannot couple qubits that are far detuned. Here we introduce a method based on a tunable bus which allows for the coupling of two fixed-frequency qubits even at large detunings. By parametrically oscillating the bus at the qubit-qubit detuning we enable a resonant exchange (XX+YY) interaction. We use this interaction to implement a 183ns two-qubit iSWAP ga…
The superconducting fluxonium qubit has a great potential for high-fidelity quantum gates with its long coherence times and strong anharmonicity at the half flux quantum sweet spot. However, current implementations of two-qubit gates compromise fluxonium's coherence properties by requiring either a temporary population of the non-computational states or tuning the magnetic flux off the sweet spot. Here we realize a fast all-microwave cross-resonance gate between two capacitively-coupled fluxoniums with the qubit dynamics well confined to the computational space. We demonstrate a direct CNOT ga…
We present experimental results which demonstrate that nuclear magnetic resonance spectroscopy is capable of efficiently emulating many of the capabilities of quantum computers, including unitary evolution and coherent superpositions, but without attendant wave-function collapse. Specifically, we have: (1) Implemented the quantum XOR gate in two different ways, one using Pound-Overhauser double resonance, and the other using a spin-coherence double resonance pulse sequence; (2) Demonstrated that the square root of the Pound-Overhauser XOR corresponds to a conditional rotation, thus obtaining a…
We investigate the influence of AC driving fields on the coherence properties of one- and two-qubit gate operations. In both cases, we find that for suitable driving parameters, the gate purity improves significantly. A mapping of the time-dependent system-bath model to an effective static model provides analytical results. The resulting purity loss compares favorably with numerical results.
Kitaev's 0-$π$ qubit encodes quantum information in two protected, near-degenerate states of a superconducting quantum circuit. In a recent work, we have shown that the coherence times of a realistic 0-$π$ device can surpass that of today's best superconducting qubits [Groszkowski et al., New Journal of Physics 20 043053 (2018)]. Here we address controllability of the 0-$π$ qubit. Specifically, we investigate the potential for dispersive control and readout, and introduce a new, fast and high-fidelity single-qubit gate that can interpolate smoothly between logical X and Z. We characterize the …
A symmetric four-level closed-loop $\diamondsuit$ type (the diamond structure) atomic system driven by four coherent optical fields is investigated. The system shows rich quantum interference and coherence features. When symmetry of the system is broken, interesting phenomena such as single and double dark resonances appear. As a result, the double electromagnetically induced transparency effect is generated, which will facilitate the implementation of quantum phase gate operation.
Trapped ions are one of the most promising platforms for quantum computing due to the longest qubit coherence times and the highest gate fidelities. However, scaling the number of ions (qubits) in a linear Coulomb crystal is the key difficulty on the way to multi-qubit systems. One of the promising pathways to scale the number of qubits is to implement the pulsed non-adiabatic gates based on the sequence of State Dependent Kicks (SDKs). We have analytically and numerically studied the influence of coherent effects in the SDK sequence and, correspondingly, have deduced the influence of the indi…
We study quantum coherence in a semiconductor charge qubit formed from a GaAs double quantum dot containing a single electron. Voltage pulses are applied to depletion gates to drive qubit rotations and non-invasive state readout is achieved using a quantum point contact charge detector. We measure a maximum coherence time of ~7 ns at the charge degeneracy point, where the qubit level splitting is first-order-insensitive to gate voltage fluctuations. We compare measurements of the coherence time as a function of detuning with predictions from a 1/f noise model.
Recent experimental work on superconducting transmon qubits in 3D cavities show that their coherence times are increased by an order of magnitude compared to their 2D cavity counterparts. However to take advantage of these coherence times while scaling up the number of qubits it is advantageous to address individual qubits which are all coupled to the same 3D cavity fields. The challenge in controlling this system comes from spectral crowding, where leakage transition of qubits are close to computational transitions in other. Here it is shown that fast pulses are possible which address single …
We propose a new protocol to implement ultra-fast two-qubit phase gates with trapped ions using spin-dependent kicks induced by resonant transitions. By only optimizing the allocation of the arrival times in a pulse train sequence the gate is implemented in times faster than the trapping oscillation period $T<2π/ω$. Such gates allow us to increase the number of gate operations that can be completed within the coherence time of the ion-qubits favoring the development of scalable quantum computers.
Many theoretical problems in quantum technology can be formulated and addressed as constrained optimization problems. The most common quantum mechanical constraints such as, e.g., orthogonality of isometric and unitary matrices, CPTP property of quantum channels, and conditions on density matrices, can be seen as quotient or embedded Riemannian manifolds. This allows to use Riemannian optimization techniques for solving quantum-mechanical constrained optimization problems. In the present work, we introduce QGOpt, the library for constrained optimization in quantum technology. QGOpt relies on t…
Trapped atomic ions have been successfully used for demonstrating basic elements of universal quantum information processing (QIP). Nevertheless, scaling up of these methods and techniques to achieve large scale universal QIP, or more specialized quantum simulations remains challenging. The use of easily controllable and stable microwave sources instead of complex laser systems on the other hand promises to remove obstacles to scalability. Important remaining drawbacks in this approach are the use of magnetic field sensitive states, which shorten coherence times considerably, and the requireme…
We showed that quantum mechanical superposition can sustain in the process of ion transfer in protein membrane for a substantial period, in spite of the presence of the interactions with environmental modes of molecular vibration. The spectral temperature, as defined in quantum thermodynamical framework plays a significant role in maintaining the coherence. The ratio of decoherence time and dwell time has been calculated, which can be directly related to the degree of coherence. The results shead new light to build quantum information system of entangled ionic states in the voltage gated biolo…
Superconducting qubits are a promising platform for building a larger-scale quantum processor capable of solving otherwise intractable problems. In order for the processor to reach practical viability, the gate errors need to be further suppressed and remain stable for extended periods of time. With recent advances in qubit control, both single- and two-qubit gate fidelities are now in many cases limited by the coherence times of the qubits. Here we experimentally employ closed-loop feedback to stabilize the frequency fluctuations of a superconducting transmon qubit, thereby increasing its coh…
Quantum memories are an important building block for quantum information processing. Ideally, these memories preserve the quantum properties of the input. We present general criteria for measures to evaluate the quality of quantum memories. Then, we introduce a quality measure based on coherence satisfying these criteria, which we characterize in detail for the qubit case. The measure can be estimated from sparse experimental data and may be generalized to characterize other building blocks, such as quantum gates and teleportation schemes.
Nonadiabatic holonomic quantum computation has robust feature in suppressing control errors because of its holonomic feature. However, this kind of robust feature is challenged since the usual way of realizing nonadiabatic holonomic gates introduces errors due to systematic errors in the control parameters. To resolve this problem, we here propose a composite scheme to realize nonadiabatic holonomic gates. Our scheme can suppress systematic errors while preserving holonomic robustness. It is particularly useful when the evolution period is shorter than the coherence time. We further show that …
We experimentally demonstrate the migration of coherence between composite quantum systems and their subsystems. The quantum systems are implemented using polarization states of photons in two experimental setups. The first setup is based on linear optical controlled-phase quantum gate and the second scheme is utilizing effects of nonlinear optics. Our experiment allows to verify the relation between correlations of the subsystems and the coherence of the composite system, which was given in terms of a conservation law for maximal accessible coherence by Svozilík \emph{et al.} [Phys. Rev. Lett…
The faster speed and operational convenience of two-qubit gate with flux bias control makes it an important candidate for future large-scale quantum computers based on high coherence flux qubits. Based on a properly designed two-spin gadget which has small gaps during the evolution of energy levels, we build a CNOT-equivalent gate which can reach a fidelity larger than 99.9% within 40ns. Moreover, we also use the Schrieffer-Wolff Transformation to translate the spin model Ising coefficients schedule to circuit model flux bias schedule for realistic flux qubit circuits coupled by a tunable rf-s…
