arXiv subjects

Juha Leppäkangas

Publications and source records attributed to Juha Leppäkangas.

At least 19 recordsLinked to original sources

arXiv2025

The impact of noise on the simulation of NMR spectroscopy on NISQ devices

With the surge of quantum computing platforms that continue to push the boundaries of capabilities of noisy intermediate-scale quantum computers, there is a growing interest in finding relevant applications and quantifying the corresponding error budgets. We present a simulation of nuclear magnetic resonance (NMR) spectroscopy of small organic molecules on publicly available cloud quantum computers. We are using two quantum computing platforms, namely IBM's quantum processors based on superconducting qubits and IonQ's Aria trapped ion quantum computer addressed via Amazon Braket. We analyze the impact of noise on the obtained NMR spectra, and we formulate an effective decoherence rate that quantifies the threshold noise that our proposed algorithm can tolerate. We show that the effective decoherence rate can be calculated using simple fidelity metrics that are available by cloud quantum computing providers. Our investigation paves the way to better employ such application-driven quantum tasks on current noisy quantum devices.

quant-ph↗

arXiv2025

Describing Trotterized Time Evolutions on Noisy Quantum Computers via Static Effective Lindbladians

We consider the extent to which a Trotterized time evolution implemented on a quantum computer is altered by the presence of decoherence. Given a specific set of assumptions regarding the manner in which noise processes acting on such a device can be modeled at the circuit level, we show how the effects of noise can be reinterpreted as a shift to the dynamics of the original system being simulated. In particular, we find that this shift can be described through the use of static Lindblad noise terms, which act in addition to the original unitary dynamics. The form of these noise terms depends not only on the underlying noise processes occurring on the device, but also on the original unitary dynamics, as well as the manner in which these dynamics are simulated on the device, i.e., the choice of quantum algorithm. We call this effectively simulated open quantum system the noisy algorithm model. Our results are confirmed through numerical analysis.

quant-ph↗

arXiv2025

Quantum algorithms for simulating systems coupled to bosonic modes using a hybrid resonator-qubit quantum computer

Modeling composite systems of spins or electrons coupled to bosonic modes is of significant interest for many fields of applied quantum physics and chemistry. A quantum simulation can allow for the solution of quantum problems beyond classical numerical methods. However, implementing this on existing noisy quantum computers can be challenging due to the mapping between qubits and bosonic degrees of freedom, often requiring a large number of qubits or deep quantum circuits. In this work, we discuss quantum algorithms to solve composite systems by augmenting conventional superconducting qubits with microwave resonators used as computational elements. This enables direct representation of bosonic modes by resonators. We derive efficient algorithms for typical models and propose a device connectivity that allows for feasible scaling of simulations with linear overhead. We also show how the dissipation of resonators can be a useful parameter for modeling continuous bosonic baths. Experimental results demonstrating these methods were obtained on the IQM Resonance cloud platform, based on high-fidelity gates and tunable couplers. These results present the first digital quantum simulation including a computational resonator on a commercial quantum platform.

quant-ph↗

arXiv2025

Demonstration of system-bath physics on a gate-based quantum computer

Algorithmic cooling can be used to find correlated states of many-body quantum systems. It is based on quantum circuits that perform nonunitary operations, whose implementation can be challenging on near-term quantum computers. In this work we develop a method that uses inherent qubit noise to implement nonunitary operations and algorithmic cooling. In our approach, qubit decay during quantum computation is used to simulate dissipation of auxiliary-spin bath, which cools down a simulated system towards its ground state. We test the algorithm on IBM-Q devices and demonstrate the relaxation of system spins to ferromagnetic and antiferromagnetic ordering, controlled by the definition of the system Hamiltonian. The ordering is stable as long as the algorithm is run. We are able to perform cooling and state stabilization for global systems of up to three system spins and four auxiliary spins. Our work paves the way for useful quantum simulations of many-body quantum systems on near-term quantum computers.

quant-ph↗

arXiv2023

The Discrete Noise Approximation in Quantum Circuits

When modeling the effects of noise on quantum circuits, one often makes the assumption that these effects can be accounted for by individual decoherence events following an otherwise noise-free gate. In this work, we address the validity of this model. We find that under a fairly broad set of assumptions, this model of individual decoherence events provides a good approximation to the true noise processes occurring on a quantum device during the implementation of a quantum circuit. However, for gates which correspond to sufficiently large rotations of the qubit register, we find that the qualitative nature of these noise terms can vary significantly from the nature of the noise at the underlying hardware level. The bulk of our analysis is directed towards analyzing what we refer to as the separability ansatz, which is an ansatz concerning the manner in which individual quantum operations acting on a quantum system can be approximated. In addition to the primary motivation of this work, we identify several other areas of open research which may benefit from the results we derive here.

quant-ph↗

arXiv2023

A quantum algorithm for solving open system dynamics on quantum computers using noise

In this paper we present a quantum algorithm that uses noise as a resource. The goal of our quantum algorithm is the calculation of operator averages of an open quantum system evolving in time. Selected low-noise system qubits and noisy bath qubits represent the system and the bath of the open quantum system. All incoherent qubit noise can be mapped to bath spectral functions. The form of the spectral functions can be tuned digitally, allowing for the time evolution of a wide range of open-system models at finite temperature. We study the feasibility of this approach with a focus on the solution of the spin-boson model and assume intrinsic qubit noise that is dominated by damping and dephasing. We find that classes of open quantum systems exist where our algorithm performs very well, even with gate errors as high as 1%. In general the presented algorithm performs best if the system-bath interactions can be decomposed into native gates.

quant-ph↗

arXiv2020

Probing the Tavis-Cummings level splitting with intermediate-scale superconducting circuits

We demonstrate the local control of up to eight two-level systems interacting strongly with a microwave cavity. Following calibration, the frequency of each individual two-level system (qubit) is tunable without influencing the others. Bringing the qubits one by one on resonance with the cavity, we observe the collective coupling strength of the qubit ensemble. The splitting scales up with the square root of the number of the qubits, which is the hallmark of the Tavis-Cummings model. The local control circuitry causes a bypass shunting the resonator, and a Fano interference in the microwave readout, whose contribution can be calibrated away to recover the pure cavity spectrum. The simulator's attainable size of dressed states with up to five qubits is limited by reduced signal visibility, and -- if uncalibrated -- by off-resonance shifts of sub-components. Our work demonstrates control and readout of quantum coherent mesoscopic multi-qubit system of intermediate scale under conditions of noise.

quant-ph↗

arXiv2019

Resonance inversion in a superconducting cavity coupled to artificial atoms and a microwave background

We demonstrate how heating of an environment can invert the line shape of a driven cavity. We consider a superconducting coplanar cavity coupled to multiple artificial atoms. The measured cavity transmission is characterized by Fano-type resonances with a shape that is continuously tunable by bias current through nearby (magnetic flux) control lines. In particular, the same dispersive shift of the microwave cavity can be observed as a peak or a dip. We find that this Fano-peak inversion is possible due to a tunable interference between a microwave transmission through a background, with reactive and dissipative properties, and through the cavity, affected by bias-current induced heating. The background transmission occurs due to crosstalk between the control and transmission lines. We show how such background can be accounted for by Jaynes-Cummings type models via modified boundary conditions between the cavity and transmission lines. We find generally that whereas resonance positions determine system energy levels, resonance shapes give information on system fluctuations and dissipation.

cond-mat.mes-hall↗

arXiv2019

Inelastic scattering of microwave radiation in the dynamical Coulomb blockade

We study scattering of propagating microwave fields by a DC-voltage biased Josephson junction. At sub-gap voltages, a small Josephson junction works merely as a non-linear boundary that can absorb, amplify, and diversely convert propagating microwaves. In the leading-order perturbation theory of the Josephson coupling energy, the spectral density and quadrature fluctuations of scattered thermal and coherent radiation can be described in terms of the well-known $P(E)$ function. Applying this, we study how thermal and coherent radiation is absorbed and amplified in an Ohmic transmission line and in a circuit with a resonance frequency. We show when a coherent input can create a two-mode squeezed output. In addition, we evaluate scattering amplitudes between arbitrary photon-number (Fock) states, characterizing individual photon multiplication and absorption processes occuring at the junction.

cond-mat.supr-con↗

arXiv2018

A bright on-demand source of anti-bunched microwave photons based on inelastic Cooper pair tunneling

The ability to generate single photons is not only an ubiquitous tool for scientific exploration with applications ranging from spectroscopy and metrology to quantum computing, but also an important proof of the underlying quantum nature of a physical process. In the microwave regime, emission of anti-bunched radiation has so far relied on coherent control of Josephson qubits, where precisely calibrated microwave pulses are needed, and the achievable bandwidth is limited by the anharmonicity of the qubit. Here, we demonstrate the operation of a bright on-demand source of quantum microwave radiation capable of emitting anti-bunched photons based on inelastic Cooper pair tunneling and driven by a simple DC voltage bias. It is characterized by its normalized second order correlation function of $g^{(2)}(0)\approx0.43$ corresponding to anti-bunching in the single photon regime. Our source can be triggered and its emission rate is tunable in situ exceeding rates obtained with current microwave single photon sources by more than one order of magnitude.

quant-ph↗

arXiv2018

Quantum simulation of the spin-boson model with a microwave circuit

We consider superconducting circuits for the purpose of simulating the spin-boson model. The spin-boson model consists of a single two-level system coupled to bosonic modes. In most cases, the model is considered in a limit where the bosonic modes are sufficiently dense to form a continuous spectral bath. A very well known case is the ohmic bath, where the density of states grows linearly with the frequency. In the limit of weak coupling or large temperature, this problem can be solved numerically. If the coupling is strong, the bosonic modes can become sufficiently excited to make a classical simulation impossible. Here, we discuss how a quantum simulation of this problem can be performed by coupling a superconducting qubit to a set of microwave resonators. We demonstrate a possible implementation of a continuous spectral bath with individual bath resonators coupling strongly to the qubit. Applying a microwave drive scheme potentially allows us to access the strong-coupling regime of the spin-boson model. We discuss how the resulting spin relaxation dynamics with different initialization conditions can be probed by standard qubit-readout techniques from circuit quantum electrodynamics.

quant-ph↗

arXiv2018

Effects of gate errors in digital quantum simulations of fermionic systems

Digital quantum simulations offer exciting perspectives for the study of fermionic systems such as molecules or lattice models. However, with quantum error correction still being out of reach with present-day technology, a non-vanishing error rate is inevitable. We study the influence of gate errors on simulations of the Trotterized time evolution of the quantum system with focus on the fermionic Hubbard model. Specifically, we consider the effect of stochastic over-rotations in the applied gates. Depending on the particular algorithm implemented such gate errors may lead to a time evolution that corresponds to a disordered fermionic system, or they may correspond to unphysical errors, e.g., violate particle number conservation. We substantiate our analysis by numerical simulations of model systems. In addition we establish the relation between the gate fidelity and the strength of the over-rotations in a Trotterized quantum simulation. Based on this we provide estimates for the maximum number of Trotter steps which can be performed with sufficient accuracy for a given algorithm. This in turn implies, apart from obvious limitations on the maximum time of the simulation, also limits on the system size which can be handled.

quant-ph↗

arXiv2018

Reconstructing the ideal results of a perturbed analog quantum simulator

Well-controlled quantum systems can potentially be used as quantum simulators. However, a quantum simulator is inevitably perturbed by coupling to additional degrees of freedom. This constitutes a major roadblock to useful quantum simulations. So far there are only limited means to understand the effect of perturbation on the results of quantum simulation. Here, we present a method which, in certain circumstances, allows for the reconstruction of the ideal result from measurements on a perturbed quantum simulator. We consider extracting the value of the correlator $\langle\hat{O}^i(t) \hat{O}^j(0)\rangle$ from the simulated system, where $\hat{O}^i$ are the operators which couple the system to its environment. The ideal correlator can be straightforwardly reconstructed by using statistical knowledge of the environment, if any $n$-time correlator of operators $\hat{O}^i$ of the ideal system can be written as products of two-time correlators. We give an approach to verify the validity of this assumption experimentally by additional measurements on the perturbed quantum simulator. The proposed method can allow for reliable quantum simulations with systems subjected to environmental noise without adding an overhead to the quantum system.

quant-ph↗

arXiv2018

Multiplying and detecting propagating microwave photons using inelastic Cooper-pair tunneling

The interaction between propagating microwave fields and Cooper-pair tunneling across a DC voltage-biased Josephson junction can be highly nonlinear. We show theoretically that this nonlinearity can be used to convert an incoming single microwave photon into an outgoing $n$-photon Fock state in a different mode. In this process, the electrostatic energy released in a Cooper-pair tunneling event is transferred to the outgoing Fock state, providing energy gain. The created multi-photon Fock state is frequency entangled and highly bunched. The conversion can be made reflectionless (impedance-matched) so that all incoming photons are converted to $n$-photon states. With realistic parameters multiplication ratios $n > 2$ can be reached. By two consecutive multiplications, the outgoing Fock-state number can get sufficiently large to accurately discriminate it from vacuum with linear post-amplification and power measurement. Therefore, this amplification scheme can be used as single-photon detector without dead time.

cond-mat.mes-hall↗

arXiv2017

Estimating the error of an analog quantum simulator by additional measurements

We study an analog quantum simulator coupled to a reservoir with a known spectral density. The reservoir perturbs the quantum simulation by causing decoherence. The simulator is used to measure an operator average, which cannot be calculated using any classical means. Since we cannot predict the result, it is difficult to estimate the effect of the environment. Especially, it is difficult to resolve whether the perturbation is small or if the actual result of the simulation is in fact very different from the ideal system we intend to study. Here, we show that in specific systems a measurement of additional correlators can be used to verify the reliability of the quantum simulation. The procedure only requires additional measurements on the quantum simulator itself. We demonstrate the method theoretically in the case of a single spin connected to a bosonic environment.

quant-ph↗

arXiv2017

Analyzing the spectral density of a perturbed analog quantum simulator using Keldysh formalism

Simulation of interacting electron systems is one of the great challenges of modern quantum chemistry and solid state physics. Controllable quantum systems offer the opportunity to create artificial structures which mimic the system of interest. An interesting quantity to extract from these quantum simulations is the spectral function. We map a noisy quantum simulator onto a fermionic system and investigate the influence of decoherence on the simulation of the spectral density using a diagrammatic approach on Keldysh contour. We show that features stronger than the single-qubit decoherence rate can be resolved, while weaker features wash out. For small systems, we compare our Keldysh approach to master-equation calculations.

quant-ph↗

arXiv2017

Creating photon-number squeezed strong microwave fields by a Cooper-pair injection laser

The use of artificial atoms as an active lasing medium opens a way to construct novel sources of nonclassical radiation. An example is the creation of photon-number squeezed light. Here we present a design of a laser consisting of multiple Cooper-pair transistors coupled to a microwave resonator. Over a broad range of experimentally realizable parameters, this laser creates photon-number squeezed microwave radiation, characterized by a Fano factor $F \ll 1$, at a very high resonator photon number. We investigate the impact of gate-charge disorder in a Cooper-pair transistor and show that the system can create squeezed strong microwave fields even in the presence of maximum disorder.

cond-mat.mes-hall↗

arXiv2016

Diagrammatic description of a system coupled strongly to a bosonic bath

We study a system-bath description in the strong coupling regime where it is not possible to derive a master equation for the reduced density matrix by a direct expansion in the system-bath coupling. A particular example is a bath with significant spectral weight at low frequencies. Through a unitary transformation it can be possible to find a more suitable small expansion parameter. Within such approach we construct a formally exact expansion of the master equation on the Keldysh contour. We consider a system diagonally coupled to a bosonic bath and expansion in terms of a non-diagonal hopping term. The lowest-order expansion is equivalent to the so-called $P(E)$-theory or non-interacting blip approximation (NIBA). The analysis of the higher-order contributions shows that there are two different classes of higher-order diagrams. We study how the convergence of this expansion depends on the form of the spectral function with significant weight at zero frequency.

cond-mat.mes-hall↗