Universal Set Of Quantum Gates Research Articles

Quantum Gates with Different Robust Merits

AbstractA protocol for implementing a universal set of quantum gates, which are safeguarded from noise through geometric, dephasing‐free, and dynamical‐decoupling approaches is proposed. With properly designed Hamiltonians, the desired interactions are realized directly within the Schrödinger picture rather than relying on the interaction picture. This design confers two advantages. One is that the system's evolution remains continuously protected by the noise‐mitigation strategies at every stage, eliminating the need to revert to the Schrödinger picture. The other one is that the dynamical decoupling technique effectively averages out small residual free terms in the system's Hamiltonian, thus reducing the stringent requirements for precise control of system parameters to avoid errors. Furthermore, numerical results are presented to support our protocol by finding gate fidelities in the absence (presence) of noises or errors, without or with dynamical decoupling technique.

Arbitrary quantum circuits on a fully integrated two-qubit computation register for a trapped-ion quantum processor

We report on the implementation of arbitrary circuits on a universal two-qubit register that can act as the computational module in a trapped-ion quantum computer based on the quantum charge-coupled device architecture. A universal set of quantum gates is implemented on a two-ion Coulomb crystal of Be+9 ions using only chip-integrated microwave addressing. Individual-ion addressing is implemented using microwave micromotion sideband transitions; we obtain upper limits on addressing crosstalk in the register. Arbitrary two-qubit operations are characterized using the cycle benchmarking protocol. Published by the American Physical Society 2024

From Entanglement to Universality: A Multiparticle Spacetime Algebra Approach to Quantum Computational Gates Revisited

Alternative mathematical explorations in quantum computing can be of great scientific interest, especially if they come with penetrating physical insights. In this paper, we present a critical revisitation of our application of geometric (Clifford) algebras (GAs) in quantum computing as originally presented in [C. Cafaro and S. Mancini, Adv. Appl. Clifford Algebras 21, 493 (2011)]. Our focus is on testing the usefulness of geometric algebras (GAs) techniques in two quantum computing applications. First, making use of the geometric algebra of a relativistic configuration space (namely multiparticle spacetime algebra or MSTA), we offer an explicit algebraic characterization of one- and two-qubit quantum states together with a MSTA description of one- and two-qubit quantum computational gates. In this first application, we devote special attention to the concept of entanglement, focusing on entangled quantum states and two-qubit entangling quantum gates. Second, exploiting the previously mentioned MSTA characterization together with the GA depiction of the Lie algebras SO3;R and SU2;C depending on the rotor group Spin+3,0 formalism, we focus our attention to the concept of universality in quantum computing by reevaluating Boykin’s proof on the identification of a suitable set of universal quantum gates. At the end of our mathematical exploration, we arrive at two main conclusions. Firstly, the MSTA perspective leads to a powerful conceptual unification between quantum states and quantum operators. More specifically, the complex qubit space and the complex space of unitary operators acting on them merge in a single multivectorial real space. Secondly, the GA viewpoint on rotations based on the rotor group Spin+3,0 carries both conceptual and computational advantages compared to conventional vectorial and matricial methods.

Device structure and fabrication process for silicon spin qubit realizing process-variation-robust SWAP gate operation

In this study, we propose technologies for the device structure, gate fabrication process, and back-bias-assisted operation of Si spin qubits to realize the high robustness of the two-qubit SWAP gate operation against process variations. We performed quantum device simulations for MOS-type two-qubit devices and verified the benefits of these technologies on the SWAP gate fidelity. We clarified that these technologies significantly improve the robustness of the SWAP gate operation against process variations and achieve a 6σ-yield SWAP gate operation with 99% fidelity, assuming device size fluctuation of the International Roadmap for Devices and Systems (IRDS) target for 2022. The proposed technologies provide a solution for completing a universal quantum gate set for realizing universal quantum computers with silicon.

State-Independent Nonadiabatic Geometric Quantum Gates

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. Numerical simulations demonstrate that our scheme has significantly stronger gate robustness than the previous geometric and dynamical ones. Meanwhile, we give a detailed physical implementation of our scheme with the Rydberg atom system based on the Rydberg blockade effect, specifically for multiqubit control-phase gates, which exceeds the fault-tolerance threshold of multiqubit quantum gates within the considered error range. Therefore, our scheme provides a promising way for fault-tolerant quantum computation in atomic systems.

Hybrid classical-quantum machine learning based on dissipative two-qubit channels

Although the environmental effects, i.e., dissipation and decoherence seem to be the strongest adversaries in the quantum information realm, here, we address how dissipation can be harnessed for quantum state preparation and universal quantum computation. In this line, we propose a realistic scheme for hybrid classical-quantum neural networks based on dissipative two-qubit channels. In particular, we design a variational quantum circuit consisting of a set of universal quantum gates. We encode classical information in the initial states of a two-qubit system interacting with a global environment. This composite system plays the role of a dissipative quantum channel (DQC). A pooling layer concatenates the output states of the DQCs resulting in the outcome of the circuit. Both the DCQs and the pooling layer provide superposition and entanglement which are the key ingredients of any universal quantum computation protocol. Finally, we investigate the capability and adaptability of this model by doing some machine learning tasks. It is reasonable to postulate that a quantum computer based on DQCs may outperform a classical computer because, in contrast to the latter, the former is capable of producing atypical patterns through non-classical phenomena.

A high-performance compilation strategy for multiplexing quantum control architecture

Quantum computers have already shown significant potential to solve specific problems more efficiently than conventional supercomputers. A major challenge towards noisy intermediate-scale quantum computing is characterizing and reducing the various control costs. Quantum programming describes the process of quantum computation as a sequence, whose elements are selected from a finite set of universal quantum gates. Quantum compilation translates quantum programs to ordered pulses to the quantum control devices subsequently and quantum compilation optimization provides a high-level solution to reduce the control cost efficiently. Here, we propose a high-performance compilation strategy for multiplexing quantum control architecture. For representative benchmarks, the utilization efficiency of control devices increased by 49.44% on average in our work, with an acceptable circuit depth expansion executing on several real superconducting quantum computers of IBM.

Universal quantum gates, artificial neurons, and pattern recognition simulated by LC resonators

We propose to simulate quantum gates by \textit{LC} resonators, where the amplitude and the phase of the voltage describe the quantum state. By controlling capacitance or inductance of resonators, it is possible to control the phase of the voltage arbitrarily. A set of resonators acts as the phase-shift, the Hadamard and the CNOT gates. They constitute a set of universal quantum gates. We also discuss an application to an artificial neuron. As an example, we study a pattern recognition of numbers and alphabets by evaluating the similarity between an input and the reference pattern. We also study a colored pattern recognition by using a complex neural network.

Realization of arbitrary two-qubit quantum gates based on chiral Majorana fermions* *Project supported by the National Key R&D Program of China (Grant No. 2017YFA0303301), the National Natural Science Foundation of China (Grant No. 11921005), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB28000000), and Beijing Municipal Science & Technology Commission, China (Grant No. Z191100007219013).

Quantum computers are in hot-spot with the potential to handle more complex problems than classical computers can. Realizing the quantum computation requires the universal quantum gate set {T, H, CNOT} so as to perform any unitary transformation with arbitrary accuracy. Here we first briefly review the Majorana fermions and then propose the realization of arbitrary two-qubit quantum gates based on chiral Majorana fermions. Elementary cells consist of a quantum anomalous Hall insulator surrounded by a topological superconductor with electric gates and quantum-dot structures, which enable the braiding operation and the partial exchange operation. After defining a qubit by four chiral Majorana fermions, the single-qubit T and H quantum gates are realized via one partial exchange operation and three braiding operations, respectively. The entangled CNOT quantum gate is performed by braiding six chiral Majorana fermions. Besides, we design a powerful device with which arbitrary two-qubit quantum gates can be realized and take the quantum Fourier transform as an example to show that several quantum operations can be performed with this space-limited device. Thus, our proposal could inspire further utilization of mobile chiral Majorana edge states for faster quantum computation.

Compiling single-qubit braiding gate for Fibonacci anyons topological quantum computation

Topological quantum computation is an implementation of a quantum computer in a way that radically reduces decoherence. Topological qubits are encoded in the topological evolution of two-dimensional quasi-particles called anyons and universal set of quantum gates can be constructed by braiding these anyons yielding to a topologically protected circuit model. In the present study we remind the basics of this emerging quantum computation scheme and illustrate how a topological qubit built with three Fibonacci anyons might be adopted to achieve leakage free braiding gate by exchanging the anyons composing it. A single-qubit braiding gate that approximates the Hadamard quantum gate to a certain accuracy is numerically implemented using a brute force search method. The algorithms utilized for that purpose are explained and the numerical programs are publicly shared for reproduction and further use.

The germanium quantum information route

In the worldwide endeavor for disruptive quantum technologies, germanium is emerging as a versatile material to realize devices capable of encoding, processing, or transmitting quantum information. These devices leverage special properties of the germanium valence-band states, commonly known as holes, such as their inherently strong spin-orbit coupling and the ability to host superconducting pairing correlations. In this Review, we initially introduce the physics of holes in low-dimensional germanium structures with key insights from a theoretical perspective. We then examine the material science progress underpinning germanium-based planar heterostructures and nanowires. We review the most significant experimental results demonstrating key building blocks for quantum technology, such as an electrically driven universal quantum gate set with spin qubits in quantum dots and superconductor-semiconductor devices for hybrid quantum systems. We conclude by identifying the most promising prospects toward scalable quantum information processing.

Dirac Formulation for Universal Quantum Gates and Shor’s Integer Factorization in High-frequency Electric Circuits

Quantum computation may well be performed with the use of electric circuits. Especially, the Schr\"{o}dinger equation can be simulated by the lumped-element model of transmission lines, which is applicable to low-frequency electric circuits. In this paper, we show that the Dirac equation is simulated by the distributed-element model, which is applicable to high-frequency electric circuits. Then, a set of universal quantum gates (the Hadamard, phase-shift and CNOT gates) are constructed by networks made of transmission lines. We demonstrate Shor's prime factorization based on electric circuits. It will be possible to simulate any quantum algorithms simply by designing networks of metallic wires.

Quantum Computers for Next Generation

Computers reduce human effort and also focus on increasing the performance to push the technology forward. Many approaches have been devised to increase the performance of the computers. One such way is to reduce the size of the transistors used in the systems. Another very significant tactic is to use quantum computers. It proved to be very effective when used to factor large numbers. It was found that it could decrypt codes in 20 minutes which took billions of years with classical computers. This was a great motivation for focusing on this topic. A quantum computer allows a `quantum bit' or qubit to have three states - 0, 1, and 0 or 1. The last state is the coherent state. This enables an operation to be performed on two diverse values at the same time. However, this brings out a problem of decoherence. It becomes difficult to perform the computation using quantum computers. A quantum computer is desired to have five capabilities - scalable system, initialized state, long decoherence time, universal set of quantum gates, high efficiency measurements. Architecture of the quantum computer is the new research area. It is affected by quantum arithmetic, error management, and cluster-state computing. Without it, the quantum algorithms would not prove to be as efficient. To fully utilize the power of a quantum computer, the algorithms used should be based on quantum parallelism.

Monodromy matrices as universal set of quantum gates and dynamics of cold trapped ions

In this paper we describe a feasible construction of universal set of quantum gates using monodromy matrices of Fuchsian system. Fuchsian systems are considered as Schrödinger type equations and it is shown that such quantum systems are exactly solvable. We also show that dynamics of trapped cold ions may be described by a Fuchsian system which also describes the critical points of logarithmic potential associated with equilibrium positions of trapped ions in line geometry. Two different approaches to the inverse problem are also discussed.

Isolated vertices in continuous-time quantum walks on dynamic graphs

It was recently shown that continuous-time quantum walks on dynamic graphs, i.e., sequences of static graphs whose edges change at specific times, can implement a universal set of quantum gates. This result treated all isolated vertices as having self-loops, so they all evolved by a phase under the quantum walk. In this paper, we permit isolated vertices to be loopless or looped, and loopless isolated vertices do not evolve at all under the quantum walk. Using this distinction, we construct simpler dynamic graphs that implement the Pauli gates and a set of universal quantum gates consisting of the Hadamard, $T$, and CNOT gates, and these gates are easily extended to multi-qubit systems. For example, the $T$ gate is simplified from a sequence of six graphs to a single graph, and the number of vertices is reduced by a factor of four. We also construct a generalized phase gate, of which $Z$, $S$, and $T$ are specific instances. Finally, we validate our implementations by numerically simulating a quantum circuit consisting of layers of one- and two-qubit gates, similar to those in recent quantum supremacy experiments, using a quantum walk.

Universal quantum computing with parafermions assisted by a half-fluxon

Braiding of anyons such as Majoranas or parafermions provides only Clifford gates which do not form a universal set of quantum gates. We propose a robust and resource-efficient scheme to perform a non-Clifford gate on a logical qudit encoded in parafermionic zero modes via the Aharonov-Casher effect. This gate can be implemented by moving a half flux quantum around the pair of parafermionic zero modes. The parafermion modes can be realized in a two-dimensional set-up using existing proposals and a half fluxon carrying half flux quantum can be created as a part of a half fluxon/anti-half fluxon pair in a spin-triplet Josephson junction with a dipole defect. With an appropriate bias current pulse, the half fluxon can be braided around the parafermions. Supplementing this gate with the braiding of parafermions provides the avenue for universal quantum computing with parafermions without magic state distillation.

Graphane with carbon dimer defects: Robust in-gap states and a scalable two-dimensional platform for quantum computation

We study the energy level structures of the defective graphane lattice, where a carbon dimer defect is created by removing the hydrogen atoms on two nearest-neighbor carbon sites. Robust defect states emerge inside the bulk insulating gap of graphane. While for the stoichiometric half-filled system there are two doubly degenerate defect levels, there are four nondegenerate and spin-polarized in-gap defect levels in the system with one electron less than half filling. A universal set of quantum gates can be realized in the defective graphane lattice, by triggering resonant transitions among the defect states via optical pulses and \emph{ac} magnetic fields. The sizable energy separation between the occupied and the empty in-gap states enables precise control at room temperature. The spatial locality of the in-gap states implies a qubit network of extremely high areal density. Based on these results, we propose that graphane as a unique platform could be used to construct the future all-purpose quantum computers.

Quantum error correction and universal gate set operation on a binomial bosonic logical qubit

Logical qubit encoding and quantum error correction (QEC) have been experimentally demonstrated in various physical systems with multiple physical qubits, however, logical operations are challenging due to the necessary nonlocal operations. Alternatively, logical qubits with bosonic-mode-encoding are of particular interest because their QEC protection is hardware efficient, but gate operations on QEC protected logical qubits remain elusive. Here, we experimentally demonstrate full control on a single logical qubit with a binomial bosonic code, including encoding, decoding, repetitive QEC, and high-fidelity (97.0% process fidelity on average) universal quantum gate set on the logical qubit. The protected logical qubit has shown 2.8 times longer lifetime than the uncorrected one. A Ramsey experiment on a protected logical qubit is demonstrated for the first time with two times longer coherence than the unprotected one. Our experiment represents an important step towards fault-tolerant quantum computation based on bosonic encoding.

A Quantum Computation Model for Molecular Nanomagnets

Molecular nanomagnets can be considered as serious candidates for the definition of a scalable and reliable quantum computing technology: information is encoded on their spins and they ensure relaxation and decoherence times sufficiently long for the execution of tens of quantum operations. Among these devices, $\text{Cr}_7 \text{Ni}$ supramolecular complexes are extremely of interest since they implement a universal set of quantum gates, made of single-qubit gates and the two-qubit Controlled-phase gate. A model for analyzing $\text{Cr}_7 \text{Ni}$ molecules and a potential quantum computer architecture are proposed: starting from the energy parameters required for spin manipulations, these systems have been proved to implement elementary quantum algorithms. Within this paper, two, three and four-qubit systems have been analyzed: the simulation of quantum operations and the analysis of dynamical non-idealities have been done in parallel. Our approach enables the definition of an operating point - in terms of magnetic driving fields and latency - in which the execution of elementary quantum algorithms is characterized by negligible errors. The proposed model has been entirely implemented in MATLAB, thus obtaining a software infrastructure for the analysis of $\text{Cr}_7 \text{Ni}$ molecules that can be extended to quantum systems with analogous Hamiltonian and behavior.

Neural network operations and Susuki–Trotter evolution of neural network states

It was recently proposed to leverage the representational power of artificial neural networks, in particular Restricted Boltzmann Machines, in order to model complex quantum states of many-body systems [G. Carleo and M. Troyer, Science 355(6325) (2017) 602.]. States represented in this way, called Neural Network States (NNSs), were shown to display interesting properties like the ability to efficiently capture long-range quantum correlations. However, identifying an optimal neural network representation of a given state might be challenging, and so far this problem has been addressed with stöchastic optimization techniques. In this work, we explore a different direction. We study how the action of elementary quantum operations modifies NNSs. We parametrize a family of many body quantum operations that can be directly applied to states represented by Unrestricted Boltzmann Machines, by just adding hidden nodes and updating the network parameters. We show that this parametrization contains a set of universal quantum gates, from which it follows that the state prepared by any quantum circuit can be expressed as a Neural Network State with a number of hidden nodes that grows linearly with the number of elementary operations in the circuit. This is a powerful representation theorem (which was recently obtained with different methods) but that is not directly useful, since there is no general and efficient way to extract information from this unrestricted description of quantum states. To circumvent this problem, we propose a step-wise procedure based on the projection of Unrestricted quantum states to Restricted quantum states. In turn, two approximate methods to perform this projection are discussed. In this way, we show that it is in principle possible to approximately optimize or evolve Neural Network States without relying on stochastic methods such as Variational Monte Carlo, which are computationally expensive.