Arbitrary Gate Research Articles

A new method for reversible circuit synthesis using a Simulated Annealing algorithm and don’t-cares

The synthesis of reversible circuits is a challenge on which many studies have been conducted. Different algorithms attempt to propose a more optimal implementation for each description of a reversible circuit, using reversible gates. In this paper, an algorithm is proposed which, by a heuristic method using a Simulated Annealing algorithm, tries to find a near-optimal circuit to the given truth table. Unlike previous methods, this method does not necessarily require a correct initial circuit to improve it. It can start from a correct circuit or a near-correct circuit or even from an empty circuit, and tries to get a circuit that is better than the initial circuit. It can also achieve different circuits in different runs that are better than the initial circuit. Finally, from the various circuits that this algorithm has produced in different runs, the best is selected as the final circuit. The proposed algorithm also tries to produce a circuit as simple as possible with respect to don’t-care combinations. Also, the current algorithm does not depend on the type of gates. Any library, including arbitrary reversible gates, can be used in this method.

Quantum computation with machine-learning-controlled quantum stuff

We formulate the control over quantum matter, so as to perform arbitrary quantum computation, as an optimization problem. We then provide a schematic machine learning algorithm for its solution. Imagine a long strip of ‘quantum stuff’, endowed with certain assumed physical properties, and equipped with regularly spaced wires to provide input settings and to read off outcomes. After showing how the corresponding map from settings to outcomes can be construed as a quantum circuit, we provide a machine learning framework to tomographically ‘learn’ which settings implement the members of a universal gate set. To that end, we devise a loss function measuring how badly a proposed encoding has failed to implement a given circuit, and prove the existence of ‘tomographically complete’ circuit sets: should a given encoding minimize the loss function for each member of such a set, it also will for an arbitrary circuit. At optimum, arbitrary quantum gates, and thus arbitrary quantum programs, can be implemented using the stuff.

Low-Cost Fredkin Gate with Auxiliary Space

Effective quantum information processing is tantamount in part to the minimization the quantum resources needed by quantum logic gates. Here, we propose an optimization of an n-controlled-qubit Fredkin gate with a maximum of 2n+1 two-qubit gates and 2n single-qudit gates by exploiting auxiliary Hilbert spaces. The number of logic gates required improves on earlier results on simulating arbitrary n-qubit Fredkin gates. In particular, the optimal result for one-controlled-qubit Fredkin gate (which requires three qutrit-qubit partial-swap gates) breaks the theoretical nonconstructive lower bound of five two-qubit gates. Furthermore, using an additional spatial-mode degree of freedom, we design a possible architecture to implement a polarization-encoded Fredkin gate with linear optical elements.

Optimal Universal Programming of Unitary Gates.

A universal quantum processor is a device that takes as input a (quantum) program, containing an encoding of an arbitrary unitary gate, and a (quantum) data register, on which the encoded gate is applied. While no perfect universal quantum processor can exist, approximate processors have been proposed in the past two decades. A fundamental open question is how the size of the smallest quantum program scales with the approximation error. Here we answer the question, by proving a bound on the size of the program and designing a concrete protocol that attains the bound in the asymptotic limit. Our result is based on a connection between optimal programming and the Heisenberg limit of quantum metrology, and establishes an asymptotic equivalence between the tasks of programming, learning, and estimating unitary gates.

Multi‐mode fault‐tolerant control strategy for cascaded H‐bridge multilevel inverters

This study proposes a multi-mode fault-tolerant control (FTC) strategy, for cascaded H-bridge multilevel inverters, to provide the most suitable fault tolerance scheme for different single or double arbitrary insulated gate bipolar transistor (IGBT) faults. Firstly, all faulty modes are classified into three fault clusters according to the number and location of faulty IGBTs. Then, the matching mechanism of the multi-mode FTC strategy corresponding to the three clusters is described, and the appropriate FTC algorithm is selected for each cluster. In particular, a new FTC method has been proposed for Cluster I that includes double IGBT fault in different H-bridges and different groups. This method improves the utilisation efficiency of healthy IGBTs in the faulty H-bridges, and minimises the voltage level drop after the fault. Finally, the multi-mode FTC strategy has been applied to a seven-level inverter through simulation. Results have shown significant improvement of the output voltage waveform symmetry and harmonic distortion reduction for the three clusters. The new FTC method has been applied to an experimental five-level inverter. The obtained results confirm the validity of the methodology. With the proposed strategy, the output voltage has a lower harmonic distortion and a better symmetry thanks to the attenuation of the undesirable DC component.

Blind quantum computation with hybrid model

Blind quantum computation (BQC) allows a client who has a few quantum abilities to interact and delegate her quantum computation to a server that has strong quantum computabilities, while the server learns nothing about client’s quantum inputs, algorithms, and outputs. In this article, a new BQC protocol with hybrid model is proposed, using the combination of rotation operators to construct arbitrary quantum gate. Our BQC protocol is divided into two phases. In the first phase, a new kind of function operation is designed and defined, that is, the client sends the classical message [Formula: see text] to the server and then the sever performs a corresponding function operation [Formula: see text], which has been defined. In the second phase, a rotation operator or identity operator is implemented by quantum gate teleportation where the server can’t know which quantum gate has been teleported. Combining these two phases, the server has no idea about client’s quantum algorithms. When the server performs the corresponding operation honestly, the client only needs to perform [Formula: see text] and [Formula: see text] operators.

Topological Quantum Compiling with Reinforcement Learning.

Quantum compiling, a process that decomposes the quantum algorithm into a series of hardware-compatible commands or elementary gates, is of fundamental importance for quantum computing. We introduce an efficient algorithm based on deep reinforcement learning that compiles an arbitrary single-qubit gate into a sequence of elementary gates from a finite universal set. It generates near-optimal gate sequences with given accuracy and is generally applicable to various scenarios, independent of the hardware-feasible universal set and free from using ancillary qubits. For concreteness, we apply this algorithm to the case of topological compiling of Fibonacci anyons and obtain near-optimal braiding sequences for arbitrary single-qubit unitaries. Our algorithm may carry over to other challenging quantum discrete problems, thus opening up a new avenue for intriguing applications of deep learning in quantum physics.

Chip-scale nonlinear photonics for quantum light generation

Nonclassical states of light are an essential resource for many emerging quantum technologies and applications ranging from information processing, encrypted communications, and networking to sensing, metrology, and imaging. Nonlinear optical processes in solid-state materials are widely used for generating quantum light, including single photons, entangled-photon pairs, and quadrature-squeezed states. Recent advances in nonlinear photonics have enabled the functionality of benchtop nonlinear instruments to be scaled down to a single chip without sacrificing efficiency or degrading the key performance metrics. The dramatic improvement in the size, weight, power, cost, and stability enabled by photonic integrated circuits has been essential for enabling the chip-scale generation, manipulation, and detection of quantum light at a steadily increasing degree of complexity and scale. Within the last decade, the authors have seen the progression from few-component photonic circuits operating on two photons to arrays of 18 identical heralded single-photon sources and reconfigurable devices operating with more than 650 components for multidimensional entanglement and arbitrary two-photon quantum gates. In this review, the authors summarize the history and recent key technological developments of chip-scale nonlinear quantum light generation based on integrated nonlinear photonics, recent advances in heterogeneous integrated methods, and approaches for system-level integration and demonstrated applications.

Quantum software engineering. Pt. I: Quantum Circuit (Gate) Model based Computing – education Lectures and pedagogical workshop

All the quantum algorithms are based on a certain quantum computing model, varying from the quantum circuit, one-way quantum computation, adiabatic quantum computation and topological quantum computation. These four models are equivalent in computational power; among them, the quantum circuit model is most frequently used. In the circuit model, it has been proved that arbitrary single-qubit rotations plus twoqubit controlled-NOT gates are universal, i.e. they can provide a set of gates to implement any quantum algorithm. This article discusses the goal for this research: it is to given a lightning-fast (as-barebones-as-possible) definition of the quantum circuit model computing and leisurely development of quantum computation before actually getting around to sophisticated algorithms. In this article the main ideas of quantum software engineering is described.

Quantum hyper-CPHASE gates with polarisation and orbital angular momentum degrees of freedom and generalisation to arbitrary hyper-conditional gates

In this paper, a controlled-phase (CPHASE) gate using the polarisation and orbital angular momentum degrees of freedom for single-photon two-qubit quantum logic is proposed. This is critical to the realisation of quantum cluster states and graph networks using transverse degrees of freedom. A generalisation of the proposed scheme to arbitrary number and kinds of degrees of freedom, for optical systems, as well as arbitrary operations to be conditionally performed is proposed.

AZTEK: Adaptive zero TE k-space trajectories.

Because of short signal lifetimes and respiratory motion, 3D lung MRI is still challenging today. Zero-TE (ZTE) pulse sequences offer promising solutions as they overcome the issue of short . Nevertheless, as they rely on continuous readout gradients, the trajectories they follow in k-space are not adapted to retrospective gating and inferred motion correction. We propose AZTEK (adaptive ZTE k-space trajectories), a set of 3D radial trajectories featuring three tuning parameters, to adapt the acquisition to any moving organ while keeping seamless transitions between consecutive spokes. Standard ZTE and AZTEK trajectories were compared for static and moving phantom acquisitions as well as for human thoracic imaging performed on 3 volunteers (1 healthy and 2 patients with lung cancer). For the static phantom, we observe comparable image qualities with standard and AZTEK trajectories. For the moving phantom, spatially coherent undersampling artifacts observed on gated images with the standard trajectory are alleviated with AZTEK. The same improvement in image quality is obtained in human, so details are more delineated in the lung with the use of the adaptive trajectory. The AZTEK technique opens the possibility for 3D dynamic ZTE lung imaging with retrospective gating. It enables us to uniformly sample the k-space for any arbitrary respiratory motion gate, while preserving static image quality, improving dynamic image quality and guaranteeing continuous readout gradient transitions between spokes, which makes it appropriate to ZTE.

Demonstrating a Continuous Set of Two-Qubit Gates for Near-Term Quantum Algorithms.

Quantum algorithms offer a dramatic speedup for computational problems in material science and chemistry. However, any near-term realizations of these algorithms will need to be optimized to fit within the finite resources offered by existing noisy hardware. Here, taking advantage of the adjustable coupling of gmon qubits, we demonstrate a continuous two-qubit gate set that can provide a threefold reduction in circuit depth as compared to a standard decomposition. We implement two gate families: an imaginary swap-like (iSWAP-like) gate to attain an arbitrary swap angle, θ, and a controlled-phase gate that generates an arbitrary conditional phase, ϕ. Using one of each of these gates, we can perform an arbitrary two-qubit gate within the excitation-preserving subspace allowing for a complete implementation of the so-called Fermionic simulation (fSim) gate set. We benchmark the fidelity of the iSWAP-like and controlled-phase gate families as well as 525 other fSim gates spread evenly across the entire fSim(θ,ϕ) parameter space, achieving a purity-limited average two-qubit Pauli error of 3.8×10^{-3} per fSim gate.

Noise-resistant phase gates with amplitude modulation

We propose a simple scheme for implementing fast arbitrary phase gates and employ pulse modulation to improve the gate robustness against different sources of noise. Parametric driving of a cavity is introduced to induce Rabi interactions between the cavity and qutrits, and then a two-qubit arbitrary phase gate is constructed by designing proper logical states. On this basis, we implement amplitude-shaped gates to obtain enhanced resilience to control errors in gate time and frequency detuning. By virtue of specifically designed logical states, the scheme displays intrinsic resistance to the energy relaxations of qutrits. Furthermore, we show that the gate robustness against cavity decay can be enhanced significantly with amplitude modulation.

Single-electron pumping in common-gate triple-dot devices with arbitrary asymmetric gate capacitance distributions

Single-electron pumping in common-gate triple-dot devices is examined for arbitrary asymmetric gate capacitance distributions. Here, the ratio of the three gate capacitances is assumed to be a + d/2:1:a − d/2, where a and d are arbitrary positive real numbers. To ensure that pumping occurs, the gate voltage should be swung such that the set of excess electron numbers in the three dots is (ns, nc, ns) at low gate voltage and (ns, nc + 1, ns) or (ns + 1, nc − 1, ns + 1) at high gate voltage, where ns and nc are arbitrary integers. Moreover, (a, d) should be within a region that depends on the set of excess electron numbers at high and low gate voltages. Thus, the regions for pumping in the a–d plane are revealed. The absolute value of the bias voltage for pumping is limited to a maximum value, called the critical voltage. The critical voltage is also demonstrated as a function of a and d. The largest critical voltage obtained in this study is 2.5 times that reported in previous work for common-gate triple-dot devices.

Nonadiabatic geometric quantum computation with optimal control on superconducting circuits

Quantum gates, which are the essential building blocks of quantum computers, are very fragile. Thus, to realize robust quantum gates with high fidelity is the ultimate goal of quantum manipulation. Here, we propose a nonadiabatic geometric quantum computation scheme on superconducting circuits to engineer arbitrary quantum gates, which share both the robust merit of geometric phases and the capacity to combine with optimal control technique to further enhance the gate robustness. Specifically, in our proposal, arbitrary geometric single-qubit gates can be realized on a transmon qubit, by a resonant microwave field driving, with both the amplitude and phase of the driving being time-dependent. Meanwhile, nontrivial two-qubit geometric gates can be implemented by two capacitively coupled transmon qubits, with one of the transmon qubits' frequency being modulated to obtain effective resonant coupling between them. Therefore, our scheme provides a promising step towards fault-tolerant solid-state quantum computation.

Solovay–Kitaev Approximations of Special Orthogonal Matrices

The circuit-gate framework of quantum computing relies on the fact that an arbitrary quantum gate in the form of a unitary matrix of unit determinant can be approximated to a desired accuracy by a fairly short sequence of basic gates, of which the exact bounds are provided by the Solovay–Kitaev theorem. In this work, we show that a version of this theorem is applicable to orthogonal matrices with unit determinant as well, indicating the possibility of using orthogonal matrices for efficient computation. We further develop a version of the Solovay–Kitaev algorithm and discuss the computational experience.

Bounds on Instantaneous Nonlocal Quantum Computation

Instantaneous nonlocal quantum computation refers to a process in which spacelike separated parties simulate a nonlocal quantum operation on their joint systems through the consumption of pre-shared entanglement. To prevent a violation of causality, this simulation succeeds up to local errors that can only be corrected after the parties communicate classically with one another. However, this communication is non-interactive, and it involves just the broadcasting of local measurement outcomes. We refer to this operational paradigm as local operations and broadcast communication (LOBC) to distinguish it from the standard local operations and (interactive) classical communication (LOCC). In this paper, we show that an arbitrary two-qubit gate can be implemented by LOBC with $\epsilon$-error using $O(\log(1/\epsilon))$ entangled bits (ebits). This offers an exponential improvement over the best known two-qubit protocols, whose ebit costs behave as $O(1/\epsilon)$. We also consider the family of binary controlled gates on dimensions $d_A\otimes d_B$. We find that any hermitian gate of this form can be implemented by LOBC using a single shared ebit. In sharp contrast, a lower bound of $\log d_B$ ebits is shown in the case of generic (i.e. non-hermitian) gates from this family, even when $d_A=2$. This demonstrates an unbounded gap between the entanglement costs of LOCC and LOBC gate implementation. Whereas previous lower bounds on the entanglement cost for instantaneous nonlocal computation restrict the minimum dimension of the needed entanglement, we bound its entanglement entropy. To our knowledge this is the first such lower bound of its kind.

Single-ion addressing via trap potential modulation in global optical fields

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 40Ca+ 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 different random sequences to each co-trapped ion. We identify the primary error sources and compare the results with single-ion experiments to better understand our experimental limitations. These experiments form a foundation for the universal control of two ions, confined in the same potential well, with a single gate laser beam.

Robust implementation of quantum gates despite always-on exchange coupling in silicon double quantum dots

Addressability of spin qubits in a silicon double quantum dot setup in the (1,1) charge configuration relies on having a large difference between the Zeeman splittings of the electrons. When the difference is not sufficiently large, the rotating wave approximation becomes inaccurate. We consider a device working in this regime, with always-on exchange coupling, and describe how a CZ gate and arbitrary one-qubit gates which are robust against charge noise can be implemented by smoothly pulsing the microwave source, while eliminating the crosstalk. We find that the most significant deviations from the rotating wave approximation, which are analogous to the Bloch-Siegert shift in a two-level system, can be compensated using local virtual gates.

Microwave-based arbitrary cphase gates for transmon qubits

Superconducting transmon qubits are of great interest for quantum computing and quantum simulation. A key component of quantum chemistry simulation algorithms is breaking up the evolution into small steps, which naturally leads to the need for non-maximally entangling, arbitrary CPHASE gates. Here we design such microwave-based gates using an analytically solvable approach leading to smooth, simple pulses. We use the local invariants of the evolution operator in $SU(4)$ to develop a method of constructing pulse protocols, which allows for the continuous tuning of the phase. We find CPHASE fidelities of more than $0.999$ and gate times as low as $100\text{ ns}$.