Gate Depth Research Articles

Benchmarking Digital Quantum Simulations Above Hundreds of Qubits Using Quantum Critical Dynamics

The real-time simulation of large many-body quantum systems is a formidable task, that may only be achievable with a genuine quantum computational platform. Currently, quantum hardware with a number of qubits sufficient to make classical emulation challenging is available. This condition is necessary for the pursuit of a so-called quantum advantage, but it also makes verifying the results very difficult. In this paper, we flip the perspective and utilize known theoretical results about many-body quantum critical dynamics to qualitatively benchmark digital quantum hardware and various error mitigation techniques. In particular, we benchmark against known universal scaling laws in the Hamiltonian simulation of a time-dependent transverse-field Ising Hamiltonian of up to 133 qubits. Incorporating only basic error mitigation and suppression methods, our study shows reliable control up to a two-qubit gate depth of 28, featuring a maximum of 1396 two-qubit gates, before noise becomes prevalent. These results are transferable to applications such as Hamiltonian simulation, variational algorithms, optimization, or quantum machine learning. We demonstrate this on the example of digitized quantum annealing for optimization and identify an optimal working point in terms of both circuit depth and time step on a 133-site optimization problem. Published by the American Physical Society 2024

Platform tailored codesign of gate-based quantum simulation

The utility of near-term quantum computers and simulators is likely to rely upon software-hardware codesign, with error-aware algorithms and protocols optimized for the platforms they are run on. Here, we show how knowledge of noise in a system can be exploited to improve the design of gate-based quantum simulation algorithms. We demonstrate this codesign in the context of a trapped ion quantum simulation of the dynamics of a Heisenberg spin model. Specifically, we derive a theoretical noise model describing unitary gate errors due to heating of the ions' collective motion, finding that the temporal correlations in the noise induce an optimal gate depth. We then illustrate how tailored feedforward control, best applied at this optimum, can be used to partially mitigate unitary gate errors and improve the simulation outcome. Our results provide a practical guide to the codesign of gate-based quantum simulation algorithms. Published by the American Physical Society 2024

Impact of the recessed gate depth on the GaN metal-oxide-semiconductor high electron mobility transistor performances: New insights on mobility extraction

This paper provides a comprehensive study of the impact of the gate recess depth (RD) on the GaN-on-Si MOS-HEMTs DC performances. IDS = f(VGS) and IDS = f(VDS) measurements are conducted at 25 and 150 °C, respectively, in forward and blocking modes. The gate recessed depth (50, 150, and 350 nm) is modulated by adjusting the plasma etching time, which is a critical step for improving the dielectric/GaN interface quality and the gate channel electron mobility. Three distinct regions can be defined separately: the bottom, the sidewall, and the corner region being the junction between the two previous regions. To assess the impact of gate recessed depth (RD) on the several mobilities around the gate cavity first, we applied our previous methodology allowing us to extract the bottom (μbot) and the entire sidewall region mobility (μT), without distinction from the corner. The mobility of the transverse region was found surprisingly to increase with deeper RD. To gain insight into the impact of the RD on this transverse section, a new extraction methodology is proposed to extract separately the gate corner (μcorner) and sidewall (μSW) mobility. These extractions show that the corner mobility is found to be reduced compared to the sidewall one (μcorner < μSW) evidencing the different weighting contributions over the transverse mobility. Moreover, these mobilities are found to be more degraded compared to the bottom one, highlighting the different contributions on the on-state resistance (RON). Indeed, the on-state resistance is lowered with the shallower RD due to the reduced sidewall resistance contribution (lower sidewall length) and despite the incremental contribution of the bottom resistance (larger effective gate length). However, the shallower RD shows an increase in the drain–source leakage current in reason of a lower gate electrostatic control. Technology Computer Aided Design (TCAD) simulations of the three RD morphologies are carried out to validate the experimental trends and the proposed methodology.

Parallel Quantum Algorithm for Hamiltonian Simulation

We study how parallelism can speed up quantum simulation. A parallel quantum algorithm is proposed for simulating the dynamics of a large class of Hamiltonians with good sparse structures, called uniform-structured Hamiltonians, including various Hamiltonians of practical interest like local Hamiltonians and Pauli sums. Given the oracle access to the target sparse Hamiltonian, in both query and gate complexity, the running time of our parallel quantum simulation algorithm measured by the quantum circuit depth has a doubly (poly-)logarithmic dependence polylog⁡log⁡(1/ϵ) on the simulation precision ϵ. This presents an exponential improvement over the dependence polylog⁡(1/ϵ) of previous optimal sparse Hamiltonian simulation algorithm without parallelism. To obtain this result, we introduce a novel notion of parallel quantum walk, based on Childs' quantum walk. The target evolution unitary is approximated by a truncated Taylor series, which is obtained by combining these quantum walks in a parallel way. A lower bound Ω(log⁡log⁡(1/ϵ)) is established, showing that the ϵ-dependence of the gate depth achieved in this work cannot be significantly improved.Our algorithm is applied to simulating three physical models: the Heisenberg model, the Sachdev-Ye-Kitaev model and a quantum chemistry model in second quantization. By explicitly calculating the gate complexity for implementing the oracles, we show that on all these models, the total gate depth of our algorithm has a polylog⁡log⁡(1/ϵ) dependence in the parallel setting.

Quantum Circuit Design for Integer Multiplication Based on Schönhage–Strassen Algorithm

Quantum arithmetic circuits has attracted extensive attention recently since it plays fundamental roles in many applications of quantum computing. Specifically, quantum circuits for integer multiplication are of great significance to various quantum algorithms including Shor’s integer factorization and discrete logarithm algorithm. In this paper, we design a family of quantum circuits for integer multiplication based on the famous classical integer multiplication algorithm, Schönhage-Strassen algorithm. We have made slight modifications to the algorithm to simplify its quantum circuit implementation. As a result, the quantum circuit we designed has gate depth O(log2n). To the best of our knowledge, this is the first poly-logarithmic depth quantum circuit for integer multiplication which keeps the circuit size and the number of ancillary qubits sub-quadratic. Our design has size O(nlognloglogn) counted by elementary quantum gates which is the same as the time complexity of Schönhage-Strassen algorithm, and it consumes O(nlognloglogn) clean ancillary qubits. In addition, we also utilize a weaker version of Schönhage-Strassen algorithm to give a family of circuits which has depth at the same order O(log2n) but with significantly smaller constants, while still keeping the size and number of ancillary qubits sub-quadratic.

Pairwise‐Parallel Entangling Gates on Orthogonal Modes in a Trapped‐Ion Chain

AbstractParallel operations are important for both near‐term quantum computers and larger‐scale fault‐tolerant machines because they reduce execution time and qubit idling. This study proposes and implements a pairwise‐parallel gate scheme on a trapped‐ion quantum computer. The gates are driven simultaneously on different sets of orthogonal motional modes of a trapped‐ion chain. This work demonstrates the utility of this scheme by creating a Greenberger‐Horne‐Zeilinger (GHZ) state in one step using parallel gates with one overlapping qubit. It also shows its advantage for circuits by implementing a digital quantum simulation of the dynamics of an interacting spin system, the transverse‐field Ising model. This method effectively extends the available gate depth by up to two times with no overhead when no overlapping qubit is involved, apart from additional initial cooling. This scheme can be easily applied to different trapped‐ion qubits and gate schemes, broadly enhancing the capabilities of trapped‐ion quantum computers.

β-Ga2O3 MOSFETs electrical characteristic study of various etching depths grown on sapphire substrate by MOCVD

β-Ga2O3 thin films with both a 45 nm Si-doped conductive epilayer and unintentionally doped epilayer were grown on c-plane sapphire substrate by metalorganic chemical vapor deposition. β-Ga2O3 based metal–oxide–semiconductor field-effect transistors (MOSFETs) were fabricated with gate recess depths of 20 nm and 40 nm (it indicated gate depth with 70 nm and 50 nm, respective), respectively, and without said recessing process. The conductivity of β-Ga2O3 epilayers was improved through low in situ doping using a tetraethoxysilane precursor to increase MOSFET forward current density. After recessing, MOSFET operation was transferred from depletion to enhanced mode. In this study, the maximum breakdown voltage of the recessed 40 nm transistor was 770 V. The etching depth of a recessed-gate device demonstrates its influence on device electrical performance.

Accelerating the variational quantum eigensolver using parallelism

Quantum computers are getting larger and larger, but device fidelities may not be able to keep up with the increase in qubit numbers. One way to make use of a large device that has a limited gate depth is to run many small circuits simultaneously. In this paper we detail our investigations into running circuits in parallel on the Rigetti Aspen-M-1 device. We run two-qubit circuits in parallel to solve a simple instance of the Hubbard model using the variational quantum eigensolver (VQE). We present results for running up to 33 circuits in parallel (66 qubits), showing that with the use of error mitigation techniques it is possible to make use of, and gain a real-time speedup from, parallelisation on current quantum hardware. We obtain a speedup by 18× for exploring the VQE energy landscape, and by more than 8× for running VQE optimisation.

Extensive characterization and implementation of a family of three-qubit gates at the coherence limit

While all quantum algorithms can be expressed in terms of single-qubit and two-qubit gates, more expressive gate sets can help reduce the algorithmic depth. This is important in the presence of gate errors, especially those due to decoherence. Using superconducting qubits, we have implemented a three-qubit gate by simultaneously applying two-qubit operations, thereby realizing a three-body interaction. This method straightforwardly extends to other quantum hardware architectures, requires only a firmware upgrade to implement, and is faster than its constituent two-qubit gates. The three-qubit gate represents an entire family of operations, creating flexibility in the quantum-circuit compilation. We demonstrate a process fidelity of 97.90%, which is near the coherence limit of our device. We then generate two classes of entangled states, the Greenberger–Horne–Zeilinger and Dicke states, by applying the new gate only once; in comparison, decompositions into the standard gate set would have a two-qubit gate depth of two and three, respectively. Finally, we combine characterization methods and analyze the experimental and statistical errors in the fidelity of the gates and of the target states.

Exploring the scaling limitations of the variational quantum eigensolver with the bond dissociation of hydride diatomic molecules

AbstractMaterials simulations involving strongly correlated electrons pose fundamental challenges to state‐of‐the‐art electronic structure methods but are hypothesized to be the ideal use case for quantum computing algorithms. To date, no quantum computer has simulated a molecule of a size and complexity relevant to real‐world applications, despite the fact that the variational quantum eigensolver (VQE) algorithm can predict chemically accurate total energies. Nevertheless, because of the many applications of moderately sized, strongly correlated systems, such as molecular catalysts, the successful use of the VQE stands as an important waypoint in the advancement toward useful chemical modeling on near‐term quantum processors. In this paper, we take a significant step in this direction. We lay out the steps, write, and run parallel code for an (emulated) quantum computer to compute the bond dissociation curves of the TiH, LiH, NaH, and KH diatomic hydride molecules using the VQE. TiH was chosen as a relatively simple chemical system that incorporates d orbitals and strong electron correlation. Because current VQE implementations on existing quantum hardware are limited by qubit error rates, the number of qubits available, and the allowable gate depth, recent studies using it have focused on chemical systems involving s and p block elements. Through VQE + UCCSD calculations of TiH, we evaluate the near‐term feasibility of modeling a molecule with d‐orbitals on real quantum hardware. We demonstrate that the inclusion of d‐orbitals and the use of the UCCSD ansatz, which are both necessary to capture the correct TiH physics, dramatically increase the cost of this problem. We estimate the approximate error rates necessary to model TiH on current quantum computing hardware using VQE + UCCSD and show them to likely be prohibitive until significant improvements in hardware and error correction algorithms are available.

Molecular Energy Landscapes of Hardware-Efficient Ansätze in Quantum Computing.

Rapid advances in quantum computing have opened up new opportunities for solving the central electronic structure problem in computational chemistry. In the noisy intermediate-scale quantum (NISQ) era, where qubit coherence times are limited, it is essential to exploit quantum algorithms with sufficiently short quantum circuits to maximize qubit efficiency. The procedural construction of hardware-efficient ansätze provides one approach to design such circuits. However, refining the accuracy of the global minimum by increasing circuit depth may lead to a proliferation of local minima that hinders global optimization. To investigate this phenomenon, we explore the energy landscapes of hardware-efficient circuits to identify ground-state energies of the hydrogen, lithium hydride, and beryllium hydride molecules. We also propose a simple dimensionality reduction procedure that reduces quantum gate depth while retaining high accuracy for the global minimum, simplifying the energy landscape, and hence speeding up optimization from both software and hardware perspectives.

Faster Born probability estimation via gate merging and frame optimisation

Outcome probability estimation via classical methods is an important task for validating quantum computing devices. Outcome probabilities of any quantum circuit can be estimated using Monte Carlo sampling, where the amount of negativity present in the circuit frame representation quantifies the overhead on the number of samples required to achieve a certain precision. In this paper, we propose two classical sub-routines: circuit gate merging and frame optimisation, which optimise the circuit representation to reduce the sampling overhead. We show that the runtimes of both sub-routines scale polynomially in circuit size and gate depth. Our methods are applicable to general circuits, regardless of generating gate sets, qudit dimensions and the chosen frame representations for the circuit components. We numerically demonstrate that our methods provide improved scaling in the negativity overhead for all tested cases of random circuits with Clifford+T and Haar-random gates, and that the performance of our methods compares favourably with prior quasi-probability simulators as the number of non-Clifford gates increases.

Constrained quantum optimization for extractive summarization on a trapped-ion quantum computer

Realizing the potential of near-term quantum computers to solve industry-relevant constrained-optimization problems is a promising path to quantum advantage. In this work, we consider the extractive summarization constrained-optimization problem and demonstrate the largest-to-date execution of a quantum optimization algorithm that natively preserves constraints on quantum hardware. We report results with the Quantum Alternating Operator Ansatz algorithm with a Hamming-weight-preserving XY mixer (XY-QAOA) on trapped-ion quantum computer. We successfully execute XY-QAOA circuits that restrict the quantum evolution to the in-constraint subspace, using up to 20 qubits and a two-qubit gate depth of up to 159. We demonstrate the necessity of directly encoding the constraints into the quantum circuit by showing the trade-off between the in-constraint probability and the quality of the solution that is implicit if unconstrained quantum optimization methods are used. We show that this trade-off makes choosing good parameters difficult in general. We compare XY-QAOA to the Layer Variational Quantum Eigensolver algorithm, which has a highly expressive constant-depth circuit, and the Quantum Approximate Optimization Algorithm. We discuss the respective trade-offs of the algorithms and implications for their execution on near-term quantum hardware.

A novel E-mode GaN p-MOSFET featuring charge storage layer with high current density

In this work, a trench gate enhancement-mode GaN p-type metal oxide semiconductor field effect transistor featuring charge storage (CS) layer is proposed, which exhibits an effectively improved current density. Based on device simulations, the current density can be increased by 154% (@V DS = −5 V, V GS = −7 V) compared with conventional devices without CS layer. Besides, the impact of the critical parameters including AlGaN barrier thickness t, Al mole-fraction x, trench gate depth T recess, and negative charge concentration N CSL on device performance are studied and optimized. In this case, the p-MOSFETs show an on-current |I ON, max| of 14 mA mm−1, V TH of −0.47 V, I ON /I OFF of >108, and on-resistance R ON of 0.27 kΩ mm. The proposed GaN p-MOSFETs exhibit a promising method to improve the current drive capability of GaN p-channel devices.

Low-Latency Boolean Functions and Bijective S-boxes

In this paper, we study the gate depth complexity of (vectorial) Boolean functions in the basis of {NAND, NOR, INV} as a new metric, called latency complexity, to mathematically measure the latency of Boolean functions. We present efficient algorithms to find all Boolean functions with low-latency complexity, or to determine the latency complexity of the (vectorial) Boolean functions, and to find all the circuits with the minimum latency complexity for a given Boolean function. Then, we present another algorithm to build bijective S-boxes with low-latency complexity which with respect to the computation cost, this algorithm overcomes the previous methods of building S-boxes.As a result, for latency complexity 3, we present n-bit S-boxes of 3 ≤ n ≤ 8 with linearity 2n−1 and uniformity 2n−2 (except for 5-bit S-boxes for whose the minimum achievable uniformity is 6). Besides, for latency complexity 4, we present several n-bit S-boxes of 5 ≤ n < 8 with linearity 2n−2 and uniformity 2n−4.

Variational approaches to constructing the many-body nuclear ground state for quantum computing

We explore the preparation of specific nuclear states on gate-based quantum hardware using variational algorithms. Large-scale classical diagonalizations of the nuclear shell model have reached sizes of ${10}^{9}--{10}^{10}$ basis states but are still severely limited by computational resources. Quantum computing can, in principle, solve such systems exactly with exponentially fewer resources than classical computing. Exact solutions for large systems require many qubits and large gate depth, but variational approaches can effectively limit the required gate depth. We use the unitary coupled cluster approach to construct approximations of the ground-state vectors, later to be used in dynamics calculations. The testing ground is the phenomenological shell model space, which allows us to mimic the complexity of the internucleon interactions. We find that often one needs to minimize over a large number of parameters, using a large number of entanglements that makes the application on existing hardware challenging. Prospects for rapid improvements with more capable hardware are, however, very encouraging.

Nuclear two point correlation functions on a quantum computer

The calculation of dynamic response functions is expected to be an early application benefiting from rapidly developing quantum hardware resources. The ability to calculate real-time quantities of strongly-correlated quantum systems is one of the most exciting applications that can easily reach beyond the capabilities of traditional classical hardware. Response functions of fermionic systems at moderate momenta and energies corresponding roughly to the Fermi energy of the system are a potential early application because the relevant operators are nearly local and the energies can be resolved in moderately short real time, reducing the spatial resolution and gate depth required. This is particularly the case in quasielastic electron and neutrino scattering from nuclei, a topic of great interest in the nuclear and particle physics communities and directly related to experiments designed to probe neutrino properties. In this work we use current quantum hardware and error mitigation protocols to calculate response functions for a highly simplified nuclear model through calculations of a 2-point real time correlation function for a modified Fermi-Hubbard model in two dimensions with three distinguishable nucleons on four lattice sites.

Quantum Krylov subspace algorithms for ground- and excited-state energy estimation

Quantum Krylov subspace diagonalization (QKSD) algorithms provide a low-cost alternative to the conventional quantum phase estimation algorithm for estimating the ground and excited-state energies of a quantum many-body system. While QKSD algorithms typically rely on using the Hadamard test for estimating Krylov subspace matrix elements of the form, $\langle \phi_i|e^{-i\hat{H}\tau}|\phi_j \rangle$, the associated quantum circuits require an ancilla qubit with controlled multi-qubit gates that can be quite costly for near-term quantum hardware. In this work, we show that a wide class of Hamiltonians relevant to condensed matter physics and quantum chemistry contain symmetries that can be exploited to avoid the use of the Hadamard test. We propose a multi-fidelity estimation protocol that can be used to compute such quantities showing that our approach, when combined with efficient single-fidelity estimation protocols, provides a substantial reduction in circuit depth. In addition, we develop a unified theory of quantum Krylov subspace algorithms and present three new quantum-classical algorithms for the ground and excited-state energy estimation problems, where each new algorithm provides various advantages and disadvantages in terms of total number of calls to the quantum computer, gate depth, classical complexity, and stability of the generalized eigenvalue problem within the Krylov subspace.

Adaptive variational preparation of the Fermi-Hubbard eigenstates

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 adaptive method outperforms the non-adaptive counterpart in terms of fewer variational parameters, short gate depth, and scaling with the system size. The fidelity and energy of the prepared state appear to improve asymptotically with ansatz depth. We also demonstrate the application of adaptive variational methods by preparing excited states and Green functions using a proposed ADAPT-SSVQE algorithm. Lower depth, asymptotic convergence, noise tolerance of a variational approach, and a highly controllable, system-specific ansatz make the adaptive variational methods particularly well-suited for NISQ devices.

Decomposition of high-rank factorized unitary coupled-cluster operators using ancilla and multiqubit controlled low-rank counterparts

The factorized form of the unitary coupled-cluster approximation is one of the most promising methodologies to prepare trial states for strongly correlated systems within the variational quantum eigensolver framework. The factorized form of the UCC ansatz can be systematically applied to a reference state to generate the desired entanglement. The difficulty associated with such an approach is the requirement of simultaneously entangling a growing number of qubits, which quickly exceeds the hardware limitations of today's quantum machines. In particular, while circuits for singles and double excitations can be performed on current hardware, higher-rank excitations require too many gate operations. In this work, we propose a set of new schemes that trade off using extra qubits for a reduced gate depth to decompose high-rank UCC excitation operators into significantly lower depth circuits. These results will remain useful even when fault-tolerant machines are available to reduce the overall state-preparation circuit depth.