Entangled Qubits Held Stable with 90.8 Per Cent Accuracy Using Novel Technique

Qihao Guo and colleagues at Purdue University have developed a new method for controlling and stabilising quantum states in superconducting qubits using engineered dissipation. They created programmable local reservoirs by parametrically driving coupling to readout resonators, achieving fidelity up to 90.8% in autonomously stabilised entangled single-excitation states. The method offers a scalable and hardware-efficient framework for preparing and controlling correlated many-body states, potentially advancing the development of more key and complex quantum systems.

Harnessing dissipation for strong many-body state preparation and control

A re-efficient framework is being developed for dissipative preparation and control of correlated many-body states in superconducting circuits. Generating and controlling entanglement in engineered quantum platforms is central to quantum information science. Advances in coherent control have enabled increasingly precise manipulation of quantum states. Advances in coherent control have enabled increasingly precise manipulation of quantum states, ranging from high-fidelity gate operations in digital quantum processors to analogue control of interacting many-body systems through tailored Hamiltonian dynamics

Superconducting circuits offer strong nonlinearities, flexible circuit design, and high tunability, enabling programmable interactions and coherent control of increasingly large qubit arrays. This has led to major advances in quantum computing and quantum simulation. Rather than viewing coupling to the environment solely as a limitation, the strong and tunable environment coupling available in engineered platforms has enabled engineered dissipation to become a resource for quantum control.

This approach is particularly natural in photonic and superconducting platforms, where finite excitation lifetimes necessitate continuous replenishment and stabilisation. By designing suitable couplings between the system and tailored environments, driven-dissipative dynamics autonomously steer the system toward target quantum states. In superconducting circuits, engineered dissipation has enabled autonomous cooling and qubit reset by transferring excitations into cold dissipative modes.

When combined with coherent driving, dissipative protocols can also stabilise metastable excited states and prepare multilevel states with tunable effective temperatures. In the many-body regime, incoherent pumping has been used to stabilise photonic Mott insulating states through the interplay of interactions and dissipation. Furthermore, engineered dissipation can also generate coherent correlations. Single-qubit superposition states are prepared using cavity-assisted bath engineering, and universal stabilisation has been demonstrated for a parametrically coupled qubit.

Dissipative protocols have enabled entanglement stabilisation of two-qubit Bell states, as well as few-qubit states using energy-resolved pumping or Raman processes. Superconducting circuits are well suited to this approach due to their tunable coupling to dissipative environments, with programmable local reservoirs created through parametrically driven coupling to readout resonators. Engineered dissipation has also enabled remote entanglement mediated by dissipative waveguide interactions and stabilisation of protected bosonic states for autonomous quantum error correction.

A complementary perspective is to use local dissipative processes that do not directly impose spatial or phase coherence, allowing the stabilised states to emerge from the interacting many-body spectrum through energy-selective injection and removal of excitations. Motivated by how particle and thermal reservoirs stabilise strongly correlated phases in condensed matter systems, such approaches aim to realise nonequilibrium steady states analogous to equilibrium phases at finite chemical potential. Therefore, developing programmable local reservoirs with controlled spectral selectivity offers a promising route toward dissipative preparation and stabilisation of correlated many-body states for quantum simulation and the generation of entangled resource states.

This work implements a hardware-efficient energy-selective local dissipation in superconducting circuits using only flux-tunable transmon qubits and local readout resonators, as illustrated in Fig0.1, which depicts a one-dimensional qubit lattice coupled to local incoherent pump and loss processes with controlled spectral selectivity. Section II discusses the implementation of parametrically engineered local reservoirs, while Section III shows stabilisation of entangled states in a coupled two-qubit system using local pumping and loss. Section IV investigates a scenario where local pump and loss interact through a shared dissipative mode, leading to modified steady-state correlations.

A one-dimensional array of coupled transmon qubits with programmable local dissipation is considered, realising a Bose-Hubbard model for microwave photons, HBH/ħ= X Ja† iaj + U 2X i ni(ni −1) + X i εini. Here, AI is the bosonic annihilation operator on site i, J is the nearest-neighbour tunneling rate, ni = a† iai is the on-site occupation, U is the on-site interaction, and εi is the site energy. Experiments perform on a device comprising four frequency-tunable transmons, each with individual frequency control and readout.

The qubits are tuned to a typical frequency of ωq ≈2π × 4.5GHz to form a degenerate lattice, with J ≈2π ×6MHz and U ≈ 2π×−250MHz. The system is described by an XY spin model in the hard-core limit with J ≪|U| and ni ≤1, with transmons exhibiting a typical relaxation rate Γ1 = 1/T1 ≈2π × 5kHz and local dephasing rate Γφ = 1/T ∗ 2 ≈2π × 60kHz. Programmable local reservoirs incoherently add or remove excitations from the qubit array. These energy-selective reservoirs are realised through parametric sideband interactions between the transmons and their readout resonators, induced by frequency modulation of the tunable transmons. The modulation amplitude and frequency set the effective coupling strength gD/S and the detuning δD/S between the reservoir and the qubit array, retaining the source-drain terminology used when treating microwave excitations as particles in the interacting transmon lattice.

The Hamiltonian of a single transmon lattice site coupled to its readout resonator is H/ħ= ωq(t)a†a + ωrb†b + g(a† + a)(b† + b) + U 2 n(n −1), where b is the resonator annihilation operator. The qubit and resonator are capacitively coupled with strength g and detuning ∆= ωr −ωq ≫g. Applying qubit frequency modulation, ωq(t) = ω0 q +Amod cos(ωmodt), using the local flux-bias line, induces resonant exchange between the qubit and the lossy readout resonator for ωmod ≈ωr −ω0 q (red sideband). Consequently, the qubit excitation tunnels to the resonator and subsequently decays at a rate equal to the resonator linewidth κr. Thus, red-sideband modulation implements a local, narrowband loss. In the rotating frame of the qubit and within the rotating-wave approximation, the effective Hamiltonian is HD/ħ≈δDb†b + gD(a†b + ab†) + U 2 n(n −1), with effective coupling gD = g J1( Amod ωmod ), where J1 is the first-order Bessel function of the first kind, and detuning δD = (ωr −ωmod) −ω0 q. The work is performed in the weak-coupling limit gD ≪κr, where the reservoir bandwidth is set by the resonator linewidth, κr ≈2π × 1.5MHz, through its coupling to the readout transmission line.

In this limit, the qubit population decays at a detuning-dependent rate ΓD(δD) = g2 D κr δ2 D+(κr/2)2, which reduces on resonance to ΓD = 4g2 D/κr. For ωmod ≈ωr + ω0 q (blue sideband), the modulation generates a coherent two-photon process that creates or annihilates one excitation in the qubit and one in the resonator. Because the resonator photon is rapidly lost at rate κr, the blue sideband implements a narrowband incoherent pump for the qubit array. The effective Hamiltonian is HS/ħ≈−δSb†b + gS(a†b† + ab) + U 2 n(n −1), with effective coupling gS = g J1 Amod ωmod, and detuning δS = (ωmod −ωr) −ω0 q. Energy-selective local reservoirs are applied to stabilise entangled two-qubit states, focusing on single-excitation Bell states |±⟩= (|ge⟩± |eg⟩)/ √ 2. A typical experiment starts with two neighboring qubits far detuned (detuning ∆≫J) and prepared in a well-controlled initial state.

The qubits are then tuned to resonance via fast flux control, and the flux modulations are turned on to enable the driven-dissipative reservoirs. After a variable interaction time, the flux modulations are turned off, and the two qubits are rapidly detuned to freeze population exchange. Subsequently, the two-qubit state is measured either directly in the population basis via multiplexed readout or, after applying single-qubit rotations, in arbitrary measurement bases.

Additional details of the experimental sequences and the calibration of single-qubit gates and readout are discussed in Appendices A and B. While quantum state tomography (QST) can fully characterise the two-qubit driven-dissipative dynamics through reconstruction of the density matrix, the exponential cost of QST measurements makes it impractical to scale to larger systems. Classical shadow estimation offers an approach where many properties can be predicted efficiently using relatively few measurements. Superconducting circuit experiments are well suited to this technique due to their tunable coupling to dissipative environments.

However, standard shadow estimation is susceptible to systematic errors from noisy or imperfect quantum operations and measurements. Engineered dissipation offers a method for controlling and stabilising quantum states in open systems. Superconducting circuits are well suited to this approach due to their tunable coupling to dissipative environments. Programmable local reservoirs are realised for superconducting qubits through parametrically driven coupling to readout resonators, creating energy-selective incoherent pump and loss. Using coupled superconducting qubits, entangled single-excitation states are autonomously stabilised with fidelity up to 90.8%.

High-fidelity entanglement sustained via programmable local reservoirs in superconducting qubits

Entanglement measures now reach 90.8%, a substantial improvement over previous attempts which struggled to surpass 70% fidelity for autonomously stabilised states. This breakthrough, achieved with superconducting qubits, demonstrates a new capacity for maintaining quantum coherence without constant external correction. Programmable local reservoirs, controlled energy sinks and sources, are implemented to achieve this level of stabilisation, paving the way for more complex and robust quantum systems.

This detailed analysis confirmed the robustness of the technique across a range of settings. In particular, a strong classical shadow estimation method is employed, enabling accurate and scalable characterisation of the quantum state, a vital step for verifying complex entanglement. Numerical studies then explored a configuration where the engineered pumping and loss processes shared a common dissipative mode, revealing reservoir-mediated interference and classically correlated steady states. This demonstrates potential for manipulating interactions beyond simple stabilisation.

Stabilising single quantum states paves the way for more complex multi-level control

Techniques for building stable quantum systems are being refined, key for advancements in computing and materials science. While this work demonstrates impressive fidelity in stabilising entangled qubits, it currently addresses only single-excitation states. Extending this method to multi-excitation states presents a considerable challenge, demanding precise control over the engineered dissipation and potentially requiring entirely new reservoir designs.

This demonstrates a viable pathway for building more complex quantum systems, even if current applications remain constrained to specific computational tasks. Further refinement targeting multi-excitation states will unlock broader potential in quantum simulation and computation. This technique utilises engineered dissipation, carefully controlling energy loss within superconducting circuits, to maintain qubit stability with nearly ninety percent fidelity. Engineered dissipation offers a new model for quantum control, moving beyond simply shielding qubits from environmental noise.

Engineered dissipation successfully stabilised entangled single-excitation states in superconducting qubits with a fidelity of up to 90.8 percent. This represents a new method for maintaining quantum coherence without continuous external correction, offering a hardware-efficient approach to controlling quantum states. Researchers implemented programmable local reservoirs to achieve this stabilisation and employed a robust classical shadow estimation technique for accurate state characterisation. The study also explored configurations revealing reservoir-mediated interference, demonstrating potential for manipulating interactions within the system.