arXiv subjects

David P. DiVincenzo

Publications and source records attributed to David P. DiVincenzo.

At least 19 recordsLinked to original sources

arXiv2024

Observation of Josephson Harmonics in Tunnel Junctions

Approaches to developing large-scale superconducting quantum processors must cope with the numerous microscopic degrees of freedom that are ubiquitous in solid-state devices. State-of-the-art superconducting qubits employ aluminum oxide (AlO$_x$) tunnel Josephson junctions as the sources of nonlinearity necessary to perform quantum operations. Analyses of these junctions typically assume an idealized, purely sinusoidal current-phase relation. However, this relation is only expected to hold in the limit of vanishingly low-transparency channels in the AlO$_x$ barrier. Here we show that the standard current-phase relation fails to accurately describe the energy spectra of transmon artificial atoms across various samples and laboratories. Instead, a mesoscopic model of tunneling through an inhomogeneous AlO$_x$ barrier predicts percent-level contributions from higher Josephson harmonics. By including these in the transmon Hamiltonian, we obtain orders of magnitude better agreement between the computed and measured energy spectra. The presence and impact of Josephson harmonics has important implications for developing AlO$_x$-based quantum technologies including quantum computers and parametric amplifiers. As an example, we show that engineered Josephson harmonics can reduce the charge dispersion and the associated errors in transmon qubits by an order of magnitude, while preserving their anharmonicity.

quant-ph↗

arXiv2024

Perturbative power series for block diagonalisation of Hermitian matrices

Block diagonalisation of matrices by canonical transformation is important in various fields of physics. Such diagonalization is currently of interest in condensed matter physics, for modelling of gates in superconducting circuits and for studying isolated quantum many-body systems. While the block diagonalisation of a particular Hermitian matrix is not unique, it can be made unique with certain auxiliary conditions. It has been assumed in some recent literature that two of these conditions, ``least action" vs. block-off-diagonality of the generator, lead to identical transformations. We show that this is not the case, and that these two approaches diverge at third order in the small parameter. We derive the perturbative power series of the ``least action", exhibiting explicitly the loss of block-off-diagnoality.

quant-ph↗

arXiv2024

g-factor symmetry and topology in semiconductor band states

The $\bf{g}$ tensor, which determines the reaction of Kramers-degenerate states to an applied magnetic field, is of increasing importance in the current design of spin qubits. It is affected by details of heterostructure composition, disorder, and electric fields, but it inherits much of its structure from the effect of the spin-orbit interaction working at the crystal-lattice level. Here we uncover new symmetry and topological features of $\bf{g}=\bf{g}_L+\bf{g}_S$ for important valence and conduction bands in silicon, germanium, and gallium arsenide. For all crystals with high (cubic) symmetry, we show that large departures from the nonrelativistic value $g=2$ are guaranteed by symmetry. In particular, considering the spin part $\bf{g}_S(\bf{k})$, we prove that the scalar function $det(\bf{g}_S(\bf{k}))$ must go to zero on closed surfaces in the Brillouin zone, no matter how weak the spin-orbit coupling is. We also prove that for wave vectors $\bf{k}$ on these surfaces, the Bloch states $|u_{n\bf{k}}\rangle$ have maximal spin-orbital entanglement. Using tight-binding calculations, we observe that the surfaces $det(\bf{g}(\bf{k}))=0$ exhibit many interesting topological features, exhibiting Lifshitz critical points as understood in Fermi-surface theory.

quant-ph↗

arXiv2024

Perturbative Analysis of Quasi-periodic Patterning of Transmon Quantum Computers: Enhancement of Many-Body Localization

Recently it has been shown that transmon qubit architectures experience a transition between a many-body localized and a quantum chaotic phase. While it is crucial for quantum computation that the system remains in the localized regime, the most common way to achieve this has relied on disorder in Josephson junction parameters. Here we propose a quasi-periodic patterning of parameters as a substitute for random disorder. We demonstrate, using the Walsh-Hadamard diagnostic, that quasiperiodicity is more effective than disorder for achieving localization. In order to study the localizing properties of our new Hamiltonian for large, experimentally relevant system sizes, we use two complementary perturbation-theory schemes, one with respect to the many-body interactions and one with respect to hopping parameter of the free Hamiltonian.

quant-ph↗

arXiv2024

Lecture Notes on Quantum Electrical Circuits

During the last 30 years, stimulated by the quest to build superconducting quantum processors, a theory of quantum electrical circuits has emerged and this theory goes under the name of circuit quantum electrodynamics or circuit-QED. The goal of the theory is to provide a quantum description of the most relevant degrees of freedom. The central objects to be derived and studied are the Lagrangian and the Hamiltonian governing these degrees of freedom. Central concepts in classical network theory such as impedance and scattering matrices can be used to obtain the Hamiltonian and Lagrangian description for the lossless (linear) part of the circuits. Methods of analysis, both classical and quantum, can also be developed for nonreciprocal circuits. These lecture notes aim at giving a pedagogical overview of this subject for theoretically-oriented Master or PhD students in physics and electrical engineering, as well as Master and PhD students who work on experimental superconducting quantum devices and wish to learn more theory.

quant-ph↗

arXiv2023

Classical Chaos in Quantum Computers

The development of quantum computing hardware is facing the challenge that current-day quantum processors, comprising 50-100 qubits, already operate outside the range of quantum simulation on classical computers. In this paper we demonstrate that the simulation of classical limits can be a potent diagnostic tool potentially mitigating this problem. As a testbed for our approach we consider the transmon qubit processor, a computing platform in which the coupling of large numbers of nonlinear quantum oscillators may trigger destabilizing chaotic resonances. We find that classical and quantum simulations lead to similar stability metrics (classical Lyapunov exponents vs. quantum wave function participation ratios) in systems with $\mathcal{O}(10)$ transmons. However, the big advantage of classical simulation is that it can be pushed to large systems comprising up to thousands of qubits. We exhibit the utility of this classical toolbox by simulating all current IBM transmon chips, including the recently announced 433-qubit processor of the Osprey generation, as well as future devices with 1,121 qubits (Condor generation). For realistic system parameters, we find a systematic increase of Lyapunov exponents with system size, suggesting that larger layouts require added efforts in information protection.

quant-ph↗

arXiv2023

Where are the photons in a transmission-line pulse?

We develop a photonic description of short, one-dimensional electromagnetic pulses, specifically in the language of electrical transmission lines. Current practice in quantum technology, using arbitrary waveform generators, can readily produce very short, few-cycle pulses in microwave TEM guided structures (coaxial cables or coplanar waveguides) in a very low noise, low temperature setting. We argue that these systems attain the limit of producing pure coherent quantum states, in which the vacuum has been displaced for a short time, and therefore short spatial extent. When the pulse is bipolar, that is, the integrated voltage of the pulse is zero, then the state can be described by the finite displacement of a single mode. Therefore there is a definite mean number of photons, but which have neither a well defined frequency nor position. Due to the Paley-Wiener theorem, the two-component photon 'wavefunction' of this mode is not strictly bounded in space even if the vacuum displacement that defines it is bounded. This wavefunction's components are, for the case of pulses moving in a specific direction, complex valued, with the real and imaginary parts related by a Hilbert transform. They are thus akin to the 'analytic signals' of communication theory. When the pulse is unipolar no photonic description is possible -- the photon number can be considered to be divergent. We consider properties that photon counters and quantum non-demolition detectors must have to optimally convert and detect the photons in several example pulses, and we discuss some consequence of this optimization for the application of very short pulses in quantum cryptography.

quant-ph↗

arXiv2022

Consistent Quantization of Nearly Singular Superconducting Circuits

The theory of circuit quantum electrodynamics has successfully analyzed superconducting circuits on the basis of the classical Lagrangian, and the corresponding quantized Hamiltonian, describing these circuits. In many simplified versions of these networks, the modeling involves a Lagrangian that is singular, describing an inherently constrained system. In this work, we demonstrate the failure of the Dirac-Bergmann theory for the quantization of realistic, nearly singular superconducting circuits, both reciprocal and nonreciprocal. The correct treatment of nearly singular systems involves a perturbative Born-Oppenheimer analysis. We rigorously prove the validity of the corresponding perturbation theory using Kato-Rellich theory. We find that the singular limit of this regularized analysis is, in many cases, completely unlike the singular theory. Dirac-Bergmann, which uses the Kirchhoff's (and Tellegen's) laws to deal with constraints, predicts dynamics that depend on the detailed parameters of nonlinear circuit elements, e.g., Josephson inductances. By contrast, the limiting behavior of the low-energy dynamics obtained from the regularized Born-Oppenheimer approach exhibits a fixed point structure, flowing to one of a few universal fixed points as parasitic capacitance values go to zero.

quant-ph↗

arXiv2022

Explicit diagrammatic solution of normalised, nondegenerate Rayleigh-Schrödinger perturbation theory

We solve the coupled recurrence relations for eigenenergies and -vectors in nondegenerate Rayleigh-Schrödinger perturbation theory under the constraint that the approximate eigenvector be normalised to $1$ in every order. The series can be expressed in terms of diagrams that were first introduced by C. Bloch [Nucl. Phys. 6, 329 (1958)] for the degenerate, unnormalised case. Normalisation increases the number of terms and introduces a nontrivial dependence on the diagrams' topology to the coefficients.

quant-ph↗

arXiv2021

Transmon platform for quantum computing challenged by chaotic fluctuations

From the perspective of many body physics, the transmon qubit architectures currently developed for quantum computing are systems of coupled nonlinear quantum resonators. A significant amount of intentional frequency detuning (disorder) is required to protect individual qubit states against the destabilizing effects of nonlinear resonator coupling. Here we investigate the stability of this variant of a many-body localized (MBL) phase for system parameters relevant to current quantum processors of two different types, those using untunable qubits (IBM type) and those using tunable qubits (Delft/Google type). Applying three independent diagnostics of localization theory -- a Kullback-Leibler analysis of spectral statistics, statistics of many-body wave functions (inverse participation ratios), and a Walsh transform of the many-body spectrum -- we find that these computing platforms are dangerously close to a phase of uncontrollable chaotic fluctuations.

quant-ph↗

arXiv2021

Active resonator depletion with short microwave pulses

We propose a physical model to explain the phenomenon of photon depletion in superconducting microwave resonators in the dispersive regime, coupled to Josephson junction qubits, via short microwave pulses. We discuss the conditions for matching the amplitude and phase of the pulse optimally within the framework of the model, allowing for significant reductions in reset times after measurement of the qubits. We consider how to deal with pulses and transient dynamics within the input-output formalism, along with a reassessment of the underlying assumptions for a wide-band pulse.

quant-ph↗

arXiv2021

Circuit quantization with time-dependent magnetic fields for realistic geometries

Quantum circuit theory has become a powerful and indispensable tool to predict the dynamics of superconducting circuits. Surprisingly however, the question of how to properly account for a time-dependent driving via external magnetic fields has hardly been addressed so far. Here, we derive a general recipe to construct a low-energy Hamiltonian, taking as input only the circuit geometry and the solution of the external magnetic fields. A gauge fixing procedure for the scalar and vector potentials is given which assures that time-varying magnetic fluxes make contributions only to the potential function in the Schrödinger equation. Our proposed procedure is valid for continuum geometries and thus significantly generalizes previous efforts, which were based on discrete circuits. We study some implications of our results for the concrete example of a parallel-plate SQUID circuit. We show that if we insist on representing the response of this SQUID with individual, discrete capacitances associated with each individual Josephson junction, this is only possible if we permit the individual capacitance values to be negative, time-dependent or even momentarily singular. Finally, we provide some experimentally testable predictions, such as a strong enhancement of the qubit relaxation rates arising from the effective negative capacitances, and the emergence of a Berry phase due to time dependence of these capacitances.

cond-mat.mes-hall↗

arXiv2021

High-Fidelity Single-Qubit Gates for Two-Electron Spin Qubits in GaAs

Single-qubit operations on singlet-triplet qubits in GaAs double quantum dots have not yet reached the fidelities required for fault-tolerant quantum information processing. Considering experimentally important constraints and using measured noise spectra, we numerically minimize the effect of decoherence (including high-frequency 1/f-like noise) and show theoretically that quantum gates with fidelities higher than 99.9% are achievable. We also present a self-consistent tuning protocol which should allow the elimination of individual systematic gate errors directly in an experiment.

quant-ph↗

arXiv2020

Exact Rotating Wave Approximation

The Hamiltonian of a linearly driven two-level system, or qubit, in the standard rotating frame contains non-commuting terms that oscillate at twice the drive frequency, $ω$, rendering the task of analytically finding the qubit's time evolution nontrivial. The application of the rotating wave approximation (RWA), which is suitable only for drives whose amplitude, or envelope, $H_1(t)$, is small compared to $ω$ and varies slowly on the time scale of $1/ω$, yields a simple Hamiltonian that can be integrated relatively easily. We present a series of corrections to the RWA Hamiltonian in $1/ω$, resulting in an effective Hamiltonian whose time evolution is accurate also for time-dependent drive envelopes in the regime of strong driving, i.e., for $|H_1(t)| \lesssim ω$. By extending the Magnus expansion with the use of a Taylor series we introduce a method that we call the Magnus-Taylor expansion, which we use to derive a recurrence relation for computing the effective Hamiltonian. We then employ the same method to derive kick operators, which complete our theory for non-smooth drives. The time evolution generated by our kick operators and effective Hamiltonian, both of which depend explicitly on the envelope and its time derivatives, agrees with the exact time evolution at periodic points in time. For the leading Hamiltonian correction we obtain a term proportional to the first derivative of the envelope, which competes with the Bloch-Siegert shift.

quant-ph↗

arXiv2020

A reset-if-leaked procedure for encoded spin qubits

We report a substantially simplified procedure, based on group-theoretic reasoning, for the reduction of qubit leakage in exchange-only spin qubits. We to find exchange sequences which accomplish leakage reduction with only two additional spins and with as few as 14 nearest neighbor exchange interactions, less than half than previously reported. We show that the identified sequences are robust in the presence of realistic noise levels in the semiconductor environment. Our procedure also produces flag information that can be helpful in the implementation of quantum algorithms.

quant-ph↗

arXiv2020

Blind Oracular Quantum Computation

In the standard oracle model, an oracle efficiently evaluates an unknown classical function independent of the quantum algorithm itself. Quantum algorithms have a complex interrelationship to their oracles; for example the possibility of quantum speedup is affected by the manner by which oracles are implemented. Therefore, it is physically meaningful to separate oracles from their quantum algorithms, and we introduce one such separation here. We define the Blind Oracular Quantum Computation (BOQC) scheme, in which the oracle is a distinct node in a quantum network. Our work augments the client-server setting of quantum computing, in which a powerful quantum computer server is available on the network for discreet use by clients on the network with low quantum power. In BOQC, an oracle is another client that cooperates with the main client so that an oracular quantum algorithm is run on the server. The cooperation between the main client and the oracle takes place (almost) without communication. We prove BOQC to be blind: the server cannot learn anything about the clients' computation. This proof is performed within the composable security definitions provided by the formalism of Abstract Cryptography. We enhance the BOQC scheme to be runnable with minimal physical qubits when run on a solid-state quantum network; we prove that this scheme, which we refer to as BOQCo (BOQC-optimized), possesses the same security as BOQC.

quant-ph↗

arXiv2020

Refuting a Proposed Axiom for Defining the Exact Rotating Wave Approximation

For a linearly driven quantum two-level system, or qubit, sets of stroboscropic points along the cycloidal-like trajectory in the rotating frame can be approximated using the exact rotating wave approximation introduced in arXiv:1807.02858. That work introduces an effective Hamiltonian series $\mathcal H_{\text{eff}}$ generating smoothed qubit trajectories; this series has been obtained using a combination of a Magnus expansion and a Taylor series, a Magnus-Taylor expansion. Since, however, this Hamiltonian series is not guaranteed to converge for arbitrary pulse shapes, the same work hypothesizes an axiomatic definition of the effective Hamiltonian. The first two of the proposed axioms define $\mathcal H_{\text{eff}}$ to (i) be analytic and (ii) generate a stroboscopic time evolution. In this work we probe a third axiom---motivated by the smoothed trajectories mentioned above---namely, (iii) a variational principle stating that the integral of the Hamiltonian's positive eigenvalue taken over the full pulse duration is minimized by this $\mathcal H_{\text{eff}}$. We numerically refute the validity of this third axiom via a variational minimization of the said integral.

quant-ph↗

arXiv2020

What is measured when a qubit measurement is performed on a multi-qubit chip?

We study how single-qubit dispersive readout works alongside two qubit coupling. To make calculations analytically tractable, we use a simplified model which retains core characteristics of but is discretised compared to dispersive homodyne detection. We show how measurement speed and power determine what information about the qubit(s) is accessed. Specifically we find the basis the measurement is closest to projecting onto. Compared to the basis gates are applied in, this measurement basis is modified by the presence of photons in the readout resonator.

quant-ph↗