PaperlayerView exact revision on arXiv

Source-linked AI summary

IBM Q Experience as a versatile experimental testbed for simulating open quantum systems

Guillermo García-Pérez, Matteo A. C. Rossi, Sabrina Maniscalco

arXiv:1906.07099v2quant-ph

TL;DR

Open-system experiments need platforms that combine broad model coverage with practical accessibility, while the usefulness and characterization of memory effects remain unresolved. This paper programs publicly accessible IBM Q Experience processors to simulate diverse one- and two-qubit open-system dynamics. It reports reservoir engineering, collisional models, non-Markovianity detection, and memory-related revivals in quantum channel capacity and extractable work.

  • Problem

    Experimental platforms generally demonstrate specific open-system models, while practical digital simulation remains constrained by gates, errors, and connectivity and non-Markovianity remains incompletely understood.

  • Method

    The paper uses IBM Q Experience processors and careful circuit decomposition to experimentally simulate one- and two-qubit open-system models across Markovian, non-Markovian, unital, and non-unital regimes.

  • Results

    The processors implement a broad collection of open-system dynamics, including reservoir engineering, collisional models, non-Markovianity witnesses, and memory-related channel-capacity and extractable-work revivals.

  • Takeaways & Limitations

    Publicly accessible few-qubit NISQ processors provide versatile testbeds for verifying theoretical open quantum systems results and predictions.

  • Takeaways & Limitations

    Dedicated laboratory experiments generally achieve higher precision and fidelity, whereas the IBM Q Experience offers broader model accessibility and simulation scope.

Abstract

from arXiv · show

The advent of Noisy Intermediate-Scale Quantum (NISQ) technology is changing rapidly the landscape and modality of research in quantum physics. NISQ devices, such as the IBM Q Experience, have very recently proven their capability as experimental platforms accessible to everyone around the globe. Until now, IBM Q Experience processors have mostly been used for quantum computation and simulation of closed systems. Here we show that these devices are also able to implement a great variety of paradigmatic open quantum systems models, hence providing a robust and flexible testbed for open quantum systems theory. During the last decade an increasing number of experiments have successfully tackled the task of simulating open quantum systems in different platforms, from linear optics to trapped ions, from Nuclear Magnetic Resonance (NMR) to Cavity Quantum Electrodynamics. Generally, each individual experiment demonstrates a specific open quantum system model, or at most a specific class. Our main result is to prove the great versatility of the IBM Q Experience processors. Indeed, we experimentally implement one and two-qubit open quantum systems, both unital and non-unital dynamics, Markovian and non-Markovian evolutions. Moreover, we realise proof-of-principle reservoir engineering for entangled state generation, demonstrate collisional models, and verify revivals of quantum channel capacity and extractable work, caused by memory effects. All these results are obtained using IBM Q Experience processors publicly available and remotely accessible online.

INTRODUCTION

Open-system digital simulation is experimentally promising but practically constrained by platform-dependent gates, errors, and connectivity. This paper demonstrates that IBM Q Experience processors can implement diverse one- and two-qubit open-system dynamics and test theoretical predictions.

  • Open quantum systems theory addresses environmental interactions, non-equilibrium dynamics, measurement, and noise in quantum technologies.
  • Memory effects motivate questions about whether non-Markovianity can serve as a resource, while its characterization remains incomplete.
  • Digital open-system simulators face practical challenges from platform-dependent gates, circuit decomposition, measurement errors, and qubit connectivity.
  • The paper uses IBM Q Experience processors to implement unital, non-unital, phase-covariant, non-phase-covariant, Markovian, and non-Markovian models.
  • The experiments include a non-Markovianity witness and demonstrate non-monotonic quantum channel capacity and extractable work associated with memory effects.
  • Small quantum processors are presented as versatile and robust testbeds for verifying open quantum systems results and predictions.

Markovian reservoir engineering

The experiment realizes Markovian reservoir engineering for a two-qubit system by composing dissipative pumps that drive arbitrary initial states toward an entangled Bell state. Varying the pump parameter accesses different open-system dynamics.

  • The two-qubit simulator uses dissipative dynamics whose stationary state is the maximally entangled Bell state |ψ−⟩.
  • Two channels pump the system from stabilizer +1 eigenspaces toward the −1 eigenspaces needed to generate |ψ−⟩.
  • Changing 0 ≤p ≤1 simulates different types of open-system dynamics, while p ≪1 yields a Lindblad-form master equation under repeated map application.
  • The composed map Φxx ◦Φzz generates |ψ−⟩ for any initial state.
  • The measured pumping maps agree well with theoretical predictions, although composing them increases sensitivity to circuit-depth errors.

Collisional model and essential non-Markovianity

The paper implements collisional models in which a system qubit sequentially interacts with environmental ancillae, using ancilla correlations to realize essential non-Markovianity. Weak coupling produces Markovian behavior, whereas correlated dynamics alternate between divisible and non-divisible intervals.

  • Collisional models represent environmental interaction as consecutive pairwise collisions between a system qubit and environmental ancillae.
  • For sufficiently many thermal ancilla collisions, the system dynamics can acquire GKSL form without relying on the Born-Markov approximation.
  • Correlated ancillae implement an experimentally studied model of essential non-Markovianity, defined by failure of P-divisibility.
  • The experiment compares classically correlated ancillae with uncorrelated ancillae prepared in |+⟩^⊗n.
  • When gτ < π/4, the uncorrelated-ancilla map produces Markovian dynamics, whereas the correlated map alternates between P-divisible and non-P-divisible intervals.
  • Oscillations of the qubit coherence with correlated ancillae provide a signature of essential non-Markovianity, while smaller separable-case oscillations arise from imperfect CNOT operations.

Markovian and non-Markovian dissipative dynamics

The paper simulates dissipative open-system dynamics on IBM Q processors, covering amplitude damping, collisional models, and non-Markovianity witnesses. Experimental observations are compared with theoretical predictions, including oscillations and memory effects in non-Markovian regimes.

  • Amplitude damping: The generalized amplitude damping model describes dissipative dynamics through a time-dependent decay rate γ(t).The model is derived for a bosonic zero-temperature reservoir with Lorentzian spectral density.
  • Collisional model: Correlated ancillae produce visible coherence oscillations in the collisional model, whereas increasing circuit depth also causes decoherence.The experiment simulates up to 7 collisions in the weak-coupling regime g = 1 and τ = π/6.
  • Amplitude damping: The coupling-to-width ratio R determines the qubit dynamics through the coefficient c1(t).R = γ0/λ, where γ0 is the coupling strength and λ is the Lorentzian half-height width.
  • Amplitude damping: 2R ≥1 marks intervals with negative decay rate, making the dynamical map non-CP-divisible and therefore non-Markovian.The simulations use R = 0.2 for Markovian dynamics and R = 100 for non-Markovian dynamics.
  • Non-Markovianity witness: The entanglement-based witness becomes oscillatory for the non-Markovian amplitude damping channel, signaling memory effects.The witness uses an initially maximally entangled system–ancilla state and local-observable measurements.

Depolarizing and Pauli channels

The paper implements depolarizing and time-dependent Pauli channels as digital open-system models. These simulations compare measured density-matrix dynamics with theory and demonstrate an application to extractable work under eternal non-Markovianity.

  • Depolarizing channel: The depolarizing channel leaves the qubit intact with probability p and applies bit-, phase-, or combined-flip errors with probability 1−p.The corresponding errors are represented by σx, σz, and σy.
  • Depolarizing channel: Measured density-matrix elements agree with theoretical predictions across several values of p and different initial states.The experiment uses tomography of a single-qubit state initially prepared with non-zero coherences.
  • Pauli channel: The time-dependent Pauli channel generalizes the depolarizing model through three time-dependent decay rates γx(t), γy(t), and γz(t).Equal rates γi(t) = γ recover the Markovian depolarizing channel.
  • Pauli channel: Negative decay rates require complete-positivity conditions involving all three decay rates.The resulting dynamics are generally not phase-covariant unless γx(t) = γy(t).
  • Application: The paper simulates an eternally non-Markovian Pauli channel and demonstrates oscillations in extractable work.The channel is non-CP-divisible for all times, linking the simulation to quantum thermodynamics.

DISCUSSION

The IBM Q Experience provides a versatile, publicly accessible testbed for implementing diverse open quantum-system dynamics and studying memory effects in communication and thermodynamics. Experiments demonstrate revivals in quantum channel capacity and extractable-work oscillations associated with non-Markovian dynamics, while dedicated platforms generally achieve higher precision and fidelity.

  • Discussion: Few-qubit NISQ devices implement diverse open-system dynamics, including Markovian and non-Markovian, unital and non-unital models.The demonstrated models include dephasing collisional, amplitude-damping, depolarizing, and Pauli channels.
  • Discussion: The IBM Q Experience serves as a versatile testbed for quantum communication and thermodynamics applications involving memory effects.The paper focuses on non-Markovian quantum channel capacity and extractable-work dynamics.
  • Discussion: Quantum channel capacity can revive after disappearing at finite channel lengths under memory effects, as demonstrated for R = 100, R = 200, and R = 400.The experiment compares measured capacity with theoretical predictions for a time-local amplitude-damping model.
  • Discussion: Revival of extractable work reflects the interplay between memory effects, quantum mutual information, and entropy dynamics.The work expression includes the evolved system entropy and correlations between the system and memory.
  • Discussion: Extractable-work oscillations appear for the eternally non-Markovian case but are absent in the comparison case, despite experimental imperfections.The results connect these oscillations to memory effects and distinguish their subtle origin.
  • Discussion: Dedicated laboratory experiments generally achieve higher precision and fidelity, whereas IBM Q Experience experiments offer broader model accessibility and remote availability.Open-source processors enable researchers without specialized training or sufficient resources to conduct experiments remotely.

METHODS

The experiments used publicly accessible IBM Q Experience processors, Qiskit circuits, and repeated measurements, while circuit design accounted for hardware connectivity and systematic errors. Statistical fluctuations were small, but relaxation, gate, crosstalk, and readout errors limited agreement with theory.

  • Implementation: Experiments ran Qiskit circuits on two 5-qubit processors and one 14-qubit processor, using 8192 shots per circuit.One- and two-qubit full state tomography was used when needed.
  • Error sources: Statistical fluctuations were approximately O(1/N) ≈ 0.011, making error bars indistinguishable from markers in Figs. 1–5.The reported discrepancies instead arose primarily from systematic hardware errors.
  • Error sources: Systematic errors included relaxation and decoherence, crosstalk and unwanted gate interactions, and readout errors.CNOT gate errors were about 10 times larger than single-qubit-unitary errors, while deviations were difficult to model because noise sources were interdependent.
  • Circuit design: Circuit design and compilation were adapted to available basis gates, physical connectivity, and qubit readout quality.Non-connected multiqubit gates require swaps, each including at least three CNOT gates.

Reservoir engineering

The reservoir-engineering circuits adapt Bell-state pumping to IBM hardware by mapping stabilizer information onto ancillae, applying conditional rotations, and reversing the mapping. They implement ZZ, XX, and composite pumps with system and environment qubits assigned on ibmqx2.

  • Hardware adaptation: The Bell-state pumping circuits were redesigned for IBM hardware because direct use of trapped-ion gates would produce circuits that were too long.The measurement process also changes basis with CNOT and Hadamard gates because the platform measures only in the computational basis.
  • Reservoir engineering: The adapted pumping circuits map system eigenspace information to an ancilla, conditionally modify the system, reverse the mapping, and reset through a fresh ancilla.Because IBM Q Experience devices lack reset operations, each pump uses a different ancilla.
  • Reservoir engineering: A CNOT between system qubits separates Bell-state information so σx eigenspace information resides in s1 and σz information in s2.Bell states |φ±⟩ map to |±⟩|0⟩, whereas |ψ±⟩ map to |±⟩|1⟩.
  • Reservoir engineering: The ZZ pump maps s2 onto ancilla aZZ and uses a conditional rotation whose angle controls pump efficiency through θ = 2 arcsin √p.The XX pump follows the same structure after an additional Hadamard on s1; the composite pump concatenates both circuits with redundant CNOTs removed.
  • Reservoir engineering: Figure 6 implements ZZ, XX, and combined ZZ–XX pumps on ibmqx2, using s1 and s2 as system qubits and aXX and aZZ as environment ancillae.State preparation and measurement are omitted from the displayed circuits.

Collisional model

The collisional-model circuit prepares a system and ancillae, applies sequential system–ancilla collisions, and measures the system in the σx basis. Correlated ancillae can be represented with a reduced GHZ-based preparation, while connectivity limits the number of direct collisions.

  • Collisional model: The collisional-model circuit prepares the system and ancillae, applies each collision sequentially, and measures the system in the σx basis.The collision unitary is implemented with a Z rotation Rz(gτ) between two CNOT gates.
  • Correlated environment: For correlated ancillae in ρcorr, each ancilla is maximally mixed and only three ancillae need preparation in a GHZ state.Tracing out one GHZ qubit yields the two-qubit correlated state ρE^(2), after which either remaining ancilla can be used for collisions.
  • Hardware constraints: The separable-ancilla circuit ran on ibmq_16_melbourne, whose connectivity allowed direct collisions with no more than three ancillae.Additional collisions require swaps, increasing simulation errors and possibly introducing memory effects.

Amplitude damping channel

The amplitude-damping implementation couples a system qubit to a vacuum environment and tunes the interaction angle to reproduce the channel. Its non-Markovianity witness measures entanglement fidelity with a maximally entangled ancilla.

  • Amplitude damping: The amplitude-damping circuit transforms α|0⟩s + β|1⟩s with a vacuum environment into a joint state whose excitation-transfer amplitude is controlled by θ.Choosing θ = arccos c1(t) produces the reduced system state specified by Eq. (11).
  • Non-Markovianity witness: The non-Markovianity witness fΦ measures the overlap of the channel output with a maximally entangled state.It is implemented by preparing |φ+⟩, applying the map to the system, and measuring the corresponding Bell-state probability.
  • Non-Markovianity witness: The Bell-state overlap can be measured through local σx, σy, and σz observables instead of an additional CNOT-based Bell-basis projection.Figure 8 shows the circuit for measuring σx ⊗ σx.

Depolarizing channel

The paper implements depolarizing dynamics with controlled Pauli operations and also realizes collisional-model circuits using separable or correlated ancillae. These circuits use platform-specific decompositions and measurements to simulate and characterize open-system behavior.

  • Depolarizing channel: Three ancillary qubits control CNOT, controlled-Y, and controlled-Z operations, implementing the depolarizing channel for any p in [0, 1].Each controlled gate is applied with probability sin^2(θ/2), with θ chosen so that this probability equals p.
  • Collisional model: Collisional-model circuits prepare three ancillae either in the separable |+ + +⟩ state or in the correlated GHZ state.Each collision uses a Z rotation between two CNOTs, followed by an X-basis measurement of system coherence.
  • Amplitude damping: The amplitude-damping circuit assigns q1, q2, and q3 to the system, environment, and witness ancilla, respectively.Setting θ = arccos c1(t) implements the channel, while basis rotations enable measurements of σx ⊗ σx and σy ⊗ σy.
  • Depolarizing channel: The depolarizing circuit uses q2 as the system qubit because it is the only qubit targetable with three CNOTs.The implementation was run on ibmqx2.

Pauli channel

The Pauli channel is formulated through its time-specific channel representation and implemented with either entangled two-qubit ancillae or a general three-ancilla construction. The latter can be less accurate on IBM Q Experience devices, while some channels are not realizable by simply varying independent ancilla preparations.

  • Pauli channel: At a specific time t, the Pauli channel is represented through the channel form associated with its master equation.The supplied passage introduces this time-specific representation without providing the full displayed expression.
  • Pauli channel: The depolarizing channel is a special case of the Pauli channel with p1 = p2 = p3 = p/4.This identifies the parameter constraint relating the two channel families.
  • Scope limitation: Preparing three ancillae in different states cannot implement every channel, including the eternally non-Markovian channel discussed in the paper.This is a scope limitation of that generalized three-ancilla construction.
  • Circuit implementation: A general Pauli channel can be implemented with two entangled ancilla qubits controlling controlled-X and controlled-Y operations.Applying both controlled-X and controlled-Y is effectively equivalent to applying controlled-Z.
  • Circuit implementation: The two-ancilla circuit is parameterized by θ1, θ2, and θ3, whose values are obtained by solving a system of equations.The ancilla state coefficients use ci = cos θi and si = sin θi.
  • Experimental accuracy: The three-ancilla circuit can implement the depolarizing channel but is more accurate than the entangled two-qubit Pauli-channel circuit on IBM Q Experience devices.The paper attributes the lower accuracy of the two-qubit circuit presumably to the entanglement it requires.
Loading 1906.07099v2…