Conditional geometric phase shift gate, which is fault tolerate to certain errors due to its geometric property, is made by NMR technique recently under adiabatic condition. By the adiabatic requirement, the result is inexact unless the Hamiltonian changes extremely slowly in the process. However, in quantum computation, everything has to be completed within the decoherence time. High running speed of every gate in quantum computation is demanded because the power of quantum computer can be exponentially proportional to the maximum number of logic gate operation that can be taken sequentially within the decoherence time. Adiabatic condition makes any fast conditional Berry phase(cyclic adiabatic geometric phase) shift gate impossible. Here we show that by using a new designed sequence of simple operations with an additional vertical magnetic field, the conditional geometric phase shift can be done non-adiabatically. Therefore geometric quantum computation can be done in the same speed level of usual quantum computation.
We show that some composite pulses widely employed in NMR experiments are regarded as non-adiabatic geometric quantum gates with Aharanov-Anandan phases. Thus, we reveal the presence of a fundamental issue on quantum mechanics behind the traditional technique of the composite pulses. To examine the robustness of such composite pulses against fluctuations, we present a practical noise model in a two-level system. Then, we find that the composite pulses possesses purely geometrical nature even under a specific type of fluctuations.
We study a 2-qubit nuclear spin system for realizing an arbitrary geometric quantum phase gate by means of non-adiabatic operation. A single magnetic pulse with multi harmonic frequencies is applied to manipulate the quantum states of 2-qubit instantly. Using resonant transition approximation, the time dependent Hamiltonian of two nuclear spins can be solved analytically. The time evolution of the wave function is obtained without adiabatic approximation. The parameters of magnetic pulse, such as the frequency, amplitude, phase of each harmonic part as well as the time duration of the pulse, a…
Quantum processors are potentially superior to their classical counterparts for many computational tasks including factorization. Circuit methods as well as adiabatic methods have already been proposed and implemented for finding the factors of a given composite number. The main challenge in scaling it to larger numbers is the unavailability of large number of qubits. Here we propose a hybrid scheme that involves both classical and quantum computation, which reduces the number of qubits required for factorization. The classical part involves setting up and partially simplifying a set of bit-wi…
This article deals with non-adiabatic processes (i.e. processes excluded by the adiabatic theorem) from the geometrical (group-theoretical) point of view. An approximated formula for the probabilities of the non-adiabatic transitions is derived in the adiabatic regime for the case when the parameter-dependent Hamiltonian represents a smooth curve in the Lie algebra and the quantal dynamics is determined by the corresponding Lie group evolution operator. We treat the spin precession in a time-dependent magnetic field and the over-barrier reflection problem in a uniform way using the first-order…
Quantum algorithms could be much faster than classical ones in solving the factoring problem. Adiabatic quantum computation for this is an alternative approach other than Shor's algorithm. Here we report an improved adiabatic factoring algorithm and its experimental realization to factor the number 143 on a liquid crystal NMR quantum processor with dipole-dipole couplings. We believe this to be the largest number factored in quantum-computation realizations, which shows the practical importance of adiabatic quantum algorithms.
We clarify that the nonadiabatic scheme based on a parallel extension of the adiabatic scenario cannot realize the desired goal of quantum computation.
Quantum adiabatic algorithm is a method of solving computational problems by evolving the ground state of a slowly varying Hamiltonian. The technique uses evolution of the ground state of a slowly varying Hamiltonian to reach the required output state. In some cases, such as the adiabatic versions of Grover's search algorithm and Deutsch-Jozsa algorithm, applying the global adiabatic evolution yields a complexity similar to their classical algorithms. However, using the local adiabatic evolution, the algorithms given by J. Roland and N. J. Cerf for Grover's search [ Phys. Rev. A. {\bf 65} 0423…
Experimental realization of quantum information processing in the field of nuclear magnetic resonance (NMR) has been well established. Implementation of conditional phase shift gate has been a significant step, which has lead to realization of important algorithms such as Grover's search algorithm and quantum Fourier transform. This gate has so far been implemented in NMR by using coupling evolution method. We demonstrate here the implementation of the conditional phase shift gate using transition selective pulses. As an application of the gate, we demonstrate Grover's search algorithm and qua…
Recently, geometric phases, which is fault tolerate to certain errors intrinsically due to its geometric property, are getting considerable attention in quantum computing theoretically. So far, only one experiment about adiabatic geometric gate with NMR through Berry phase has been reported. However, there are two drawbacks in it. First, the adiabatic condition of Berry phase makes such gate very slowly. Second, the extra operation to eliminate the dynamic phase. As we know, geometric phase can exist both adiabatic(Berry phase) and nonadiabatic(Aharonov-Anandan phase). In this letter, we repor…
Recently, it is proposed to do quantum computation through the Berry's phase(adiabatic cyclic geometric phase) shift with NMR (Jones et al, Nature, 403, 869(2000)). This geometric quantum gate is hopefully to be fault tolerant to certain types of errors because of the geometric property of the Berry phase. Here we give a scheme to realize the NMR C-NOT gate through Aharonov-Anandan's phase(non-adiabatic cyclic phase) shift on the dynamic phase free evolution loop. In our scheme, the gate is run non-adiabatically, thus it is less affected by the decoherence. And, in the scheme we have chosen th…
High performance quantum information processing requires efficient control of undesired decohering effects, which are present in realistic quantum dynamics. To deal with this issue, a powerful strategy is to employ transitionless quantum driving (TQD), where additional fields are added to speed up the evolution of the quantum system, achieving a desired state in a short time in comparison with the natural decoherence time scales. In this paper, we provide an experimental investigation of the performance of a generalized approach for TQD to implement shortcuts to adiabaticity in nuclear magneti…
The experimental realisation of the basic constituents of quantum information processing devices, namely fault-tolerant quantum logic gates, requires conditional quantum dynamics, in which one subsystem undergoes a coherent evolution that depends on the quantum state of another subsystem. In particular, the subsystem may acquire a conditional phase shift. Here we consider a novel scenario in which this phase is of geometric rather than dynamical origin. As the conditional geometric (Berry) phase depends only on the geometry of the path executed it is resilient to certain types of errors, and o…
A proposal for applying non-adiabatic geometric phases to quantum computing, called the double-loop method [S.-L. Zhu and Z. D. Wang, Phys. Rev. A {\bf 67}, 022319 (2003)], is demonstrated in a liquid state NMR quantum computer. Using a spin echo technique, the original method is modified so that quantum gates are implemented in a standard high-precision NMR system for chemical analysis. We show that the dynamical phase is successfully eliminated and a one-qubit quantum gate is realized, although the fidelity is not so high.
Internal states of different ions in an electrodynamic trap are coupled when a static magnetic field is applied -- analogous to spin-spin coupling in molecules used for NMR. This spin-spin interaction can be used, for example, to implement quantum logic operations in ion traps using NMR methods. The collection of trapped ions can be viewed as a $N$-qubit molecule with adjustable coupling constants.
We propose an adiabatic quantum algorithm capable of factorizing numbers, using fewer qubits than Shor's algorithm. We implement the algorithm in an NMR quantum information processor and experimentally factorize the number 21. Numerical simulations indicate that the running time grows only quadratically with the number of qubits.
Much long before the appearing time of the Comment by Cen, Li, and Yan,, the main issue addresed there by Cen et al had been resolved already. The information offered by the Comment is selective and misleading.
In [Phys. Rev. Lett. 95, 080502 (2005)], Zheng proposed a scheme for implementing a conditional phase shift via adiabatic passages. The author claims that the gate is "neither of dynamical nor geometric origin" on the grounds that the Hamiltonian does not follow a cyclic change. He further argues that "in comparison with the adiabatic geometric gates, the nontrivial cyclic loop is unnecessary, and thus the errors in obtaining the required solid angle are avoided, which makes this new kind of phase gates superior to the geometric gates." In this Comment, we point out that geometric operations, …
We check a recent proposal [H. Goto and K. Ichimura Phys. Rev. A 70, 012305 (2004)] for controlled phase gate through adiabatic passage under the influence of spontaneous emission and the cavity decay. We show a modification of above proposal could be used to generate the necessary conditional phase gates in the two-qubit Grover search. Conditioned on no photon leakage either from the atomic excited state or from the cavity mode during the gating period, we numerically analyze the success probability and the fidelity of the two-qubit conditional phase gate by adiabatic passage. The comparison …
It is discussed the decoherence problems in ensemble large-scale solid state NMR quantum computer based on the array of P donor atoms having nuclear spin I = 1/2. It is considered here, as main mechanisms of decoherence for low temperature (< 0.1 K), the adiabatic processes of random modulation of qubit resonance frequency determined by secular part of nuclear spin interaction with electron spin of the basic atoms, with impurity paramagnetic atoms and also with nuclear spins of impurity diamagnetic atoms. It was made estimations of allowed concentrations of magnetic impurities and of spin temp…
The three-qubit conditional swap gate(Fredkin gate) is a universal gate that can be used to create any logic circuit and has many direct usages. In this paper, we experimentally realized Fredkin gate with only three transition pulses in solution of alanine. It appears that no experimental realization of Fredkin gate with fewer pulses has yet been reported up to now. In addition, the simple structure of our scheme makes it easy to be implemented in experiments.
We present robust radio frequency (rf) pulses that tolerate a factor of six inhomogeneity in the B1 field, significantly enhancing the potential of toroid cavity resonators for NMR spectroscopic applications. Both point-to-point (PP) and unitary rotation (UR) pulses were optimized for excitation, inversion, and refocusing using the gradient ascent pulse engineering (GRAPE) algorithm based on optimal control theory. In addition, the optimized parameterization (OP) algorithm applied to the adiabatic BIR-4 UR pulse scheme enabled ultra-short (50 microsec) pulses with acceptable performance compar…
As an ensemble scheme of solid-state NMR quantum computers the extension of Kane's many-qubits silicon scheme based on the array of 31 P donor atoms are spaced lengthwise of the strip gates is considered. The possible planar topology of such ensemble quantum computer is suggested. The estimation of the output NMR signal was performed and it was shown that for the number N>=10^5 of ensemble elements involving L~10^3 qubits each, the standard NMR methods are usable. As main mechanisms of decoherence for low temperature (<0.1K), the adiabatic processes of random modulation of qubit resonance freq…
In a recent letter [Phy. Rev. Lett. 95, 080502 (2005)], it is claimed that based on a new kind of quantum mechanical phase of wave function which is neither dynamical nor geometrical a new kind of phase gate for quantum computation is discovered. The origin of this phase is the adiabatic evolution of a dark state. I would like to point out that these claims are questionable. The so called new phase gate was based on a phase which was nothing new but has been known for decades. It is something which has no physical meaning and is not observable. It was also pointed out by [quant-ph/0509150v1] t…
Adiabatic pulses are used extensively to enable robust control of quantum operations. We introduce a new approach to adiabatic control that uses the superadiabatic quality or $Q$-factor as a performance metric to design robust, high fidelity pulses. This approach permits the systematic design of quantum control schemes to maximize the adiabaticity of a unitary operation in a particular time interval given the available control resources. The interplay between adiabaticity, fidelity and robustness of the resulting pulses is examined for the case of single-qubit inversion, and superadiabatic pul…
Geometric phases have been used in NMR, to implement controlled phase shift gates for quantum information processing, only in weakly coupled systems in which the individual spins can be identified as qubits. In this work, we implement controlled phase shift gates in strongly coupled systems, by using non-adiabatic geometric phases, obtained by evolving the magnetization of fictitious spin-1/2 subspaces, over a closed loop on the Bloch sphere. The dynamical phase accumulated during the evolution of the subspaces, is refocused by a spin echo pulse sequence and by setting the delay of transition …
In this paperwe propose two theoretical schemes for implementation of quantum phase gates by engineering the phase-sensitive dark state of two atoms subjected to Rydberg-Rydberg interaction. Combining the conventional adiabatic techniques and currently developed approaches of phase control, a feasible proposal for implementation of a geometric phase gate is presented, where the conditional phase shift (Berry phase) is achieved by adiabatically and cyclically changing the parameters of the driving fields. Here we find that the geometric phase acquired is related to the way how the relative phas…
In a recent Letter [Phys. Rev. Lett. {\bf 95}, 080502 (2005)], an interesting scheme was proposed to implement a type of conditional quantum phase gates with built-in fault-tolerant feature via adiabatic evolution of dark eigenstates. In this comment we elaborate the geometric nature of the gate scheme and clarify that it still belongs to a class of conventional geometric quantum computation.
We give a simple way to detect the geometric phase shift and the conditional geometric phase shift with Josephson junction system. Comparing with the previous work(Falcl G, Fazio R, Palma G.M., Siewert J and Verdal V, {\it Nature} {\bf 407}, 355(2000)), our scheme has two advantages. We use the non-adiabatic operation, thus the detection is less affected by the decoherence. Also, we take the time evolution on zero dynamic phase loop, we need not take any extra operation to cancel the dynamic phase.
We discuss how to prepare an Ising chain in a GHZ state using a single global control field only. This model does not require the spins to be individually addressable and is applicable to quantum systems such as cold atoms in optical lattices, some liquid- or solid-state NMR experiments, and many nano-scale quantum structures. We show that GHZ states can always be reached asymptotically from certain easy-to-prepare initial states using adiabatic passage, and under certain conditions finite-time reachability can be ensured. To provide a reference useful for future experimental implementations t…
This work addresses quantum adiabatic decoherence of many-body spin systems coupled with a boson field in the framework of open quantum systems theory. We generalize the traditional spin-boson model by considering a system-environment interaction Hamiltonian that represents a partition of non-interacting subsystems and highlights the collective correlation that appears exclusively due to the coupling with a common environment. Remarkably, this simple, exactly solvable model encompasses relevant aspects of a many-body open quantum system and features the subtle quantum effects that arise when t…
Geometric phase that manifests itself in number of optic and nuclear experiments is shown to be a useful tool for realization of quantum computations in so called holonomic quantum computer model (HQCM). This model is considered as an externally driven quantum system with adiabatic evolution law and finite number of the energy levels. The corresponding evolution operators represent quantum gates of HQCM. The explicit expression for the gates is derived both for one-qubit and for multi-qubit quantum gates as Abelian and non-Abelian geometric phases provided the energy levels to be time-independ…
We introduce an adiabatic transfer protocol for spin states in large quantum dot arrays that is based on time-dependent modulation of the Heisenberg exchange interaction in the presence of a magnetic field gradient. We refer to this protocol as spin-CTAP (coherent transport by adiabatic passage) in analogy to a related protocol developed for charge state transfer in quantum dot arrays. The insensitivity of this adiabatic protocol to pulse imperfections has potential advantages for reading out extended spin qubit arrays. When the static exchange interaction varies across the array, a quantum-co…
Backaction-evading measurements of mechanical motion can achieve precision below the zero-point uncertainty and quantum squeezing, which makes them a resource for quantum metrology and quantum information processing. We provide an exact expression for the conditional state of an optomechanical system in a two-tone backaction-evading measurement beyond the standard adiabatic approximation and perform extensive numerical simulations to go beyond the usual rotating-wave approximation. We predict the simultaneous presence of conditional mechanical squeezing, intra-cavity squeezing, and optomechani…
Grover's algorithm has achieved great success. But quantum search algorithms still are not complete algorithms because of Grover's Oracle. We concerned on this problem and present a new quantum search algorithm in adiabatic model without Oracle. We analyze the general difficulties in quantum search algorithms and show how to solve them in the present algorithm. As well this algorithm could deal with both single-solution and multi-solution searches without modification. We also implement this algorithm on NMR quantum computer. It is the first experiment which perform a real quantum database sea…
We investigate the tunable quantum entanglement and the probabilities of excitations in a system of three qubits in a non-stationary cavity due to the dynamical Lamb effect, caused by non-adiabatic fast change of the boundary conditions of the cavity. The transition amplitudes and the probabilities of excitation of qubits due to the dynamical Lamb effect have been evaluated. The conditional concurrence and the conditional residual tangle for each fixed amount of created photons are introduced and calculated as measures of the pairwise or three-way dynamical quantum entanglement of the qubits. …
Liquid phase NMR is a general purpose test-bed for developing methods of coherent control relevant to quantum information processing. Here we extend these studies to the coherent control of logical qubits and in particular to the unitary gates necessary to create entanglement between logical qubits. We report an experimental implementation of a conditional logical gate between two logical qubits that are each in decoherence free subspaces that protect the quantum information from fully correlated dephasing.
Geometric phases play a central role in a variety of quantum phenomena, especially in condensed matter physics. Recently, it was shown that this fundamental concept exhibits a connection to quantum phase transitions where the system undergoes a qualitative change in the ground state when a control parameter in its Hamiltonian is varied. Here we report the first experimental study using the geometric phase as a topological test of quantum transitions of the ground state in a Heisenberg XY spin model. Using NMR interferometry, we measure the geometric phase for different adiabatic circuits that …
Numerical simulation results are presented which suggest that a class of non-adiabatic rapid passage sweeps first realized experimentally in 1991 should be capable of implementing a universal set of quantum gates G_{u} that operate with high fidelity. The gates constituting G_{u} are the Hadamard and NOT gates, together with variants of the phase, π/8, and controlled-phase gates. The universality of G_{u} is established by showing that it can construct the universal set consisting of Hadamard, phase, π/8, and controlled-NOT gates. Sweep parameter values are provided which simulations indicate …
We propose an experimentally feasible scheme to achieve quantum computation based on nonadiabatic geometric phase shifts, in which a cyclic geometric phase is used to realize a set of universal quantum gates. Physical implementation of this set of gates is designed for Josephson junctions and for NMR systems. Interestingly, we find that the nonadiabatic phase shift may be independent of the operation time under appropriate controllable conditions. A remarkable feature of the present nonadiabatic geometric gates is that there is no intrinsic limitation on the operation time, unlike adiabatic ge…
We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size $n$. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxilary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum excitation gap, $g_{\rm min}={\cal O}(n 2^{-n/2})$, corresponding to the exponential complexity of the algorithm for Number P…
Risk-aware neural pulse compilation of continuously parameterized single-qubit gates with optimal-control benchmarking and NMR hardware validation
Koç University（科奇大学）；TÜBİTAK Research Institute for Fundamental Sciences (TBAE)（土耳其科学技术研究委员会基础科学研究院（TBAE））；Middle East Technical University（中东理工大学）；Shenzhen SpinQ Technology Co., Ltd.（深圳本源量子技术有限公司）
We study the dynamics of a nanomechanical resonator (NMR) subject to a measurement by a low transparency quantum point contact (QPC) or tunnel junction in the non-Markovian domain. We derive the non-Markovian number-resolved (conditional) and unconditional master equations valid to second order in the tunneling Hamiltonian without making the rotating-wave approximation and the Markovian approximation, generally made for systems in quantum optics. Our non-Markovian master equation reduces, in appropriate limits, to various Markovian versions of master equations in the literature. We find consid…
We study an architecture for implementing adiabatic quantum computation with trapped neutral atoms. Ground state atoms are dressed by laser fields in a manner conditional on the Rydberg blockade mechanism, thereby providing the requisite entangling interactions. As a benchmark we study the performance of a Quadratic Unconstrained Binary Optimization (QUBO) problem whose solution is found in the ground state spin configuration of an Ising-like model. We model a realistic architecture, including details of the atomic implementation, with qubits encoded into the clock states of 133Cs, effective B…
We present a fast scheme for arbitrary unitary control of interacting bosonic atoms in a double-well. Assuming fixed inter-well tunnelling rate and intra-well interaction strength, we control the many-atom state by a discrete sequence of shifts of the single-well energies. For strong interactions, resonant tunnelling transitions implement beam-splitter U(2) rotations among atom number eigenstates, which can be combined and, thus, permit full controllability. By numerically optimizing such sequences of couplings at avoided level crossings (CALC), we extend the realm of full controllability to a…
We present a novel method of performing quantum logic gates in trapped ion quantum computers which does not require the ions to be cooled down to their vibrational center of mass (CM) mode ground state. Our scheme employs adiabatic passages and the conditional phase shift first investigated by D'Helon and Milburn (C.~D'Helon and G.J.~Milburn, Phys. Rev. A {\bf 54}, 5141 (1996)).
Motivated for the fault tolerant quantum computation, quantum gate by adiabatic geometric phase shift is extensively investigated. In this paper, we demonstrate the nonadiabatic scheme for the geometric phase shift and conditional geometric phase shift. Essentially, the new scheme is simply to add an appropriate additional field. With this additional field, the state evolution can be controlled exactly on a dynamical phase free path. Geometric quantum gates for single qubit and the controlled NOT gate for two qubits are given.
We introduce two methods for speeding up adiabatic quantum computations by increasing the energy between the ground and first excited states. Our methods are even more general. They can be used to shift a Hamiltonian's density of states away from the ground state, so that fewer states occupy the low-lying energies near the minimum, hence allowing for faster adiabatic passages to find the ground state with less risk of getting caught in an undesired low-lying excited state during the passage. Even more generally, our methods can be used to transform a discrete optimization problem into a new on…
Two-qubit logical gates are proposed on the basis of two atoms trapped in a cavity setup. Losses in the interaction by spontaneous transitions are efficiently suppressed by employing adiabatic transitions and the Zeno effect. Dynamical and geometrical conditional phase gates are suggested. This method provides fidelity and a success rate of its gates very close to unity. Hence, it is suitable for performing quantum computation.
It has been established that the inclusive work for classical, Hamiltonian dynamics is equivalent to the two-time energy measurement paradigm in isolated quantum systems. However, a plethora of other notions of quantum work has emerged, and thus the natural question arises whether any other quantum notion can provide motivation for purely classical considerations. In the present analysis, we propose the conditional stochastic work for classical, Hamiltonian dynamics, which is inspired by the one-time measurement approach. This novel notion is built upon the change of expectation value of the e…
Small quantum systems non-weakly coupled to a bath become in the quantum regime surrounded by a cloud of photons or phonons, which modifies their thermodynamic behavior. Exactly solvable examples are the Brownian motion of a quantum particle in a harmonic confining potential and coupled to a harmonic quantum thermal bath, e.g. an ion in a Penning trap, and a spin immersed in a bosonic bath, as occurs in NMR physics. It appears that the Clausius inequality $\dbarrm Q\le T\d S$ can be violated. For non-adiabatic changes of system parameters the rate of energy dissipation can be negative, and, ou…
We present an all-optical implementation of quantum computation using semiconductor quantum dots. Quantum memory is represented by the spin of an excess electron stored in each dot. Two-qubit gates are realized by switching on trion-trion interactions between different dots. State selectivity is achieved via conditional laser excitation exploiting Pauli exclusion principle. Read-out is performed via a quantum-jump technique. We analyze the effect on our scheme's performance of the main imperfections present in real quantum dots: exciton decay, hole mixing and phonon decoherence. We introduce a…
A common approach to realize conditional-phase (CZ) gates in transmon qubits relies on flux control of the qubit frequency to make computational states interact with non-computational ones using a fast-adiabatic trajectory to minimize leakage. We develop a bipolar flux-pulsing method with two key advantages over the traditional unipolar variant. First, the action of the bipolar pulse is robust to long-timescale linear-dynamical distortions in the flux-control line, facilitating tuneup and ensuring atomic repeatability. Second, the flux symmetry of the transmon Hamiltonian makes the conditional…
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…
