We propose a new strategy to physically implement a universal set of quantum gates based on geometric phases accumulated in the nondegenerate eigenstates of a designated invariant operator in a periodic physical system. The system is driven to evolve in such a way that the dynamical phase shifts of the invariant operator eigenstates are the same (or {\it mod} $2π$) while the corresponding geometric phases are nontrivial.
We illustrate how this strategy to work in a simple but typical NMR-type qubit system.
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…
Comment on "Nongeometric Conditional Phase Shift via Adiabatic Evolution of Dark Eigenstates: A New Approach to Quantum Computation"
在[Phys. Rev. Lett. 95，080502（2005）]，Zheng提出了一种通过绝热通道实现条件相移的方案。作者声称，门是“既不是动力学的，也不是几何起源”的理由是，汉密尔顿不遵循循环变化。他进一步指出：“与绝热几何门相比，不需要非平凡的循环回路，从而避免了在获得所需立体角时的误差，这使得这种新的相位门优于几何门。本文指出几何运算，包括绝热完整性，都可以由非循环哈密顿算子导出，并证明了郑门是几何的。我们还认为，负责相移的非平凡环路是存在的，它需要与任何绝热几何门相同的精度。
One-step implementation of a multi-target-qubit controlled-phase gate with photonic qubits encoded via eigenstates of the photon-number parity operator
Much of the anticipation accompanying the development of a quantum computer relates to its application to simulating dynamics of another quantum system of interest. Here we study the building blocks for simulating quantum spin systems with linear optics. We experimentally generate the eigenstates of the XY Hamiltonian under an external magnetic field. The implemented quantum circuit consists of two CNOT gates, which are realized experimentally by harnessing entanglement from a photon source and by applying a CPhase gate. We tune the ratio of coupling constants and magnetic field by changing lo…
We propose a strategy for engineering multi-qubit quantum gates. As a first step, it employs an eigengate to map states in the computational basis to eigenstates of a suitable many-body Hamiltonian. The second step employs resonant driving to enforce a transition between a single pair of eigenstates, leaving all others unchanged. The procedure is completed by mapping back to the computational basis. We demonstrate the strategy for the case of a linear array with an even number N of qubits, with specific XX+YY couplings between nearest neighbors. For this so-called Krawtchouk chain, a 2-body dr…
Accurate, nontrivial quantum operations on many qubits are experimentally challenging. As opposed to the standard approach of compiling larger unitaries into sequences of 2-qubit gates, we propose a protocol on Hamiltonian control fields which implements highly selective multi-qubit gates in a strongly-coupled many-body quantum system. We exploit the selectiveness of resonant driving to exchange only 2 out of $2^N$ eigenstates of some background Hamiltonian, and discuss a basis transformation, the eigengate, that makes this operation relevant to the computational basis. The latter has a second…
We introduce and describe a class of simple facilitated quantum spin models in which the dynamics is due to the repeated application of unitary gates. The gates are applied periodically in time, so their combined action constitutes a Floquet unitary. The dynamics of the models we discuss can be classically simulated, and their eigenstates classically constructed (although they are highly entangled). We consider a variety of models in both one and two dimensions, involving Clifford gates and Toffoli gates. For some of these models, we explicitly construct conserved densities; thus these models …
Comment on Nongeometric Conditional Phase Shift via Adiabatic Evolution of Dark Eigenstate
在最近的一封信[Phy。Rev. Lett. 95，080502（2005）]，声称基于既不是动力学的也不是几何的波函数的新型量子力学相位，发现了用于量子计算的新型相位门。这个阶段的起源是一个黑暗的状态的绝热演化。我想指出，这些说法是有问题的。所谓的新相位门是基于一个相位，这并不是什么新鲜事，但已经知道了几十年。它是没有物理意义的东西，也是不可观察的。也有人指出，[quant-ph/0509150 v1][Phy. Rev. Lett. 95，080502（2005）]是不正确的，并且相位是已知的几何相位。在这里，我们提出了一个完全不同的论点。
We experimentally constructed an all-microwave scheme for the controlled-NOT (cNOT) gate between two superconducting transmon qubits in a three dimensional cavity. Our cNOT gate is based on the microwave-activated phase (MAP) gate, which requires an additional procedure to compensate the accumulated phases during the operation of the MAP gate. We applied Z-axis phase gates using microwave hyperbolic secant pulse on both qubits with adequate rotation angles systematically calibrated by separate measurements.We evaluated the gate performance of the constructed cNOT gate by performing two-qubit q…
Approximating the ground states of strongly interacting electron systems in quantum chemistry and condensed matter physics is expected to be one of the earliest applications of quantum computers. In this paper, we prepare highly accurate ground states of the Fermi-Hubbard model for small grids up to 6 sites (12 qubits) by using an interpretable, adaptive variational quantum eigensolver(VQE) called ADAPT-VQE. In contrast with non-adaptive VQE, this algorithm builds a system-specific ansatz by adding an optimal gate built from one-body or two-body fermionic operators at each step. We show this a…
We propose a novel proposal for geometric quantum gates using three- or two-level systems, in which a controllable variable, the detuning between the driving frequency and the atomic energy spacing, is introduced to realize geometric transformations. In particular, we can have two instantaneous eigenstates with opposite eigenvalues constituting a closed loop in the parameter space. The accumulated dynamical phase is then exactly cancelled when the loop is completed, which is beyond the traditional parallel-transport restriction. We apply the transitionless quantum driving, which renders revisi…
Experimental implementation of high-fidelity unconventional geometric quantum gates using NMR interferometer
遵循早期开发的非常规几何量子计算的关键思想[Phys. Rev. Lett. 91，197902（2003）]，在这里，我们提出了一个更一般的方案，在这样一个有趣的方式：$γ_{d}=α_{g}+ηγ_{g}$，其中$γ_{d}$和$γ_{g}$分别是动态和几何相位累积在量子门操作，与$η$作为一个常数和$α_{g}$是只依赖于操作的几何特征。更引人注目的是，我们展示了第一个实验，实现了一个通用的一套这样的广义非常规几何量子门高保真度的NMR系统。
Quantum computation has demonstrated advantages over classical computation for special hard problems, where a set of universal quantum gates is essential. Geometric phases, which have built-in resilience to local noise, have been used to construct quantum gates with excellent performance. However, this advantage has been smeared in previous schemes. Here, we propose a state-independent nonadiabatic geometric quantum-gate scheme that is able to realize a more fully geometric gate than previous approaches, allowing for the cancelation of dynamical phases accumulated by an arbitrary state. Numeri…
Several quantum many-body models in one dimension possess exact solutions via the Bethe ansatz method, which has been highly successful for understanding their behavior. Nevertheless, there remain physical properties of such models for which analytic results are unavailable, and which are also not well-described by approximate numerical methods. Preparing Bethe ansatz eigenstates directly on a quantum computer would allow straightforward extraction of these quantities via measurement. We present a quantum algorithm for preparing Bethe ansatz eigenstates of the spin-1/2 XXZ spin chain that corr…
We use quantum optimal control to identify fast collision-based two-qubit $\sqrt{\text{SWAP}}$ gates in ultracold atoms. We show that a significant speed up can be achieved by optimizing the full gate instead of separately optimizing the merge-wait-separate sequence of the trapping potentials. Our optimal strategy does not rely on the atoms populating the lowest eigenstates of the merged potential, and it crucially includes accumulation of quantum phases before the potentials are fully merged. Our analyses transcend the particular trapping geometry, but to compare with previous works, we prese…
Quantum computing and quantum simulation can be implemented by concatenation of one- and two-qubit gates and interactions. For most physical implementations, however, it may be advantageous to explore state components and interactions that depart from this universal paradigm and offer faster or more robust access to more advanced operations on the system. In this article, we show that adiabatic passage along the dark eigenstate of excitation exchange interactions can be used to implement fast multi-qubit Toffoli (C$_k$-NOT) and fan-out (C-NOT$^k$) gates. This mechanism can be realized by simul…
Realistic Gottesman-Kitaev-Preskill stabilizer states enable universal quantum computation
Institute for Quantum Science and Technology, and Department of Physics and Astronomy, University of Calgary（卡尔加里大学量子科学与技术研究所及物理与天文学系）；Xanadu Quantum Technologies Inc.（Xanadu量子技术有限公司）
Efficient verification of the functioning of quantum devices is a key to the development of quantum technologies, but is a daunting task as the system size increases. Here we propose a simple and general framework for verifying unitary transformations that can be applied to both individual quantum gates and gate sets, including quantum circuits. This framework enables efficient verification of many important unitary transformations, including but not limited to all bipartite unitaries, Clifford unitaries, generalized controlled-$Z$ gates, generalized controlled-NOT gates, the controlled-SWAP g…
We present a scheme that allows integration of the Berry curvature and thus determination of the Chern number of a qubit eigenstate manifold. Our proposal continuously couples the qubit with a meter system while it explores a quasi-adiabatic path in the manifold. The accumulated change of one of the meter observables then provides an estimate of the Chern number. By varying the initial state of the meter, we explore the delicate interplay between the measurement precision and the disturbance of the qubit. A simple argument yields a correction factor that allows estimation of the Chern number, …
The Variational Quantum Eigensolver (VQE) is a promising algorithm for Noisy Intermediate Scale Quantum (NISQ) computation. Verification and validation of NISQ algorithms' performance on NISQ devices is an important task. We consider the exactly-diagonalizable Lipkin-Meshkov-Glick (LMG) model as a candidate for benchmarking NISQ computers. We use the Bethe ansatz to construct eigenstates of the trigonometric LMG model using quantum circuits inspired by the LMG's underlying algebraic structure. We construct circuits with depth $\mathcal{O}(N)$ and $\mathcal{O}(\log_2N)$ that can prepare any tri…
Motivated by recent experiments of Zajac et al. [arXiv:1708.03530], we theoretically describe high-fidelity two-qubit gates using the exchange interaction between the spins in neighboring quantum dots subject to a magnetic field gradient. We use a combination of analytical calculations and numerical simulations to provide the optimal pulse sequences and parameter settings for the gate operation. We present a novel synchronization method which avoids detrimental spin flips during the gate operation and provide details about phase mismatches accumulated during the two-qubit gates which occur due…
We propose an adiabatic protocol for implementing a controlled-phase gate CZ$_θ$ with continuous $θ$ of neutral atoms through a symmetrical two-photon excitation process via the second resonance line, $6P$ in $^{87}$Rb, with a single-temporal-modulation-coupling of the ground state and intermediate state. Relying on different adiabatic paths, the phase factor $θ$ of CZ$_θ$ gate can be accumulated on the logic qubit state $|11\rangle$ alone by calibrating the shape of the temporal pulse where strict zero amplitudes at the start and end of the pulse are not needed. For a wide range of $θ$, we ca…
We present a study of the electromagnetic control of nonclassicality of the outgoing light field in a single atom cavity QED system. By exploring the energy eigenvalues and eigenstates, we show that the eigenstates are similar to the Jaynes-Cummings ladder of eigenstates and can be optically controlled by an external control field. Tuning the control field frequency to the one photon resonance, we show the superbunching behavior in the outgoing light field can be observed at the frequency of one photon resonance. We also show that there exists a magic control field intensity at which two photo…
This paper presents an alternative approach to geometric phases from the observable point of view. Precisely, we introduce the notion of observable-geometric phases, which is defined as a sequence of phases associated with a complete set of eigenstates of the observable. The observable-geometric phases are shown to be connected with the quantum geometry of the observable space evolving according to the Heisenberg equation. They are indeed distinct from Berry's phase \cite{Berry1984, Simon1983} as the system evolves adiabatically. It is shown that the observable-geometric phases can be used to …
A Recursive Module-Coupling Algorithm for Computing Low-Energy Eigenstates
National University of Singapore（新加坡国立大学）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；Institute of Advanced Intelligence and Computing (IAIC), Agency for Science, Technology and Research (A*STAR)（新加坡科技研究局高级智能与计算研究所）；Bioinformatics Institute, Agency for Science, Technology and Research (A*STAR)（新加坡科技研究局生物信息学研究所）
Geometric phases accompanying adiabatic quantum evolutions can be used to construct robust quantum control for quantum information processing due to their noise-resilient feature. A significant development along this line is to construct geometric gates using nonadiabatic quantum evolutions to reduce errors due to decoherence. However, it has been shown that nonadiabatic geometric gates are not necessarily more robust than dynamical ones, in contrast to an intuitive expectation. Here we experimentally investigate this issue for the case of nonadiabatic holonomic quantum computation~(NHQC) and …
