Decoherence-free Subspaces Research Articles

Dynamically generated decoherence-free subspaces and subsystems on superconducting qubits

Decoherence-free subspaces and subsystems (DFS) preserve quantum information by encoding it into symmetry-protected states unaffected by decoherence. An inherent DFS of a given experimental system may not exist; however, through the use of dynamical decoupling (DD), one can induce symmetries that support DFSs. Here, we provide the first experimental demonstration of DD-generated decoherence-free subsystem logical qubits. Utilizing IBM Quantum superconducting processors, we investigate two and three-qubit DFS codes comprising up to six and seven noninteracting logical qubits, respectively. Through a combination of DD and error detection, we show that DFS logical qubits can achieve up to a 23% improvement in state preservation fidelity over physical qubits subject to DD alone. This constitutes a beyond-breakeven fidelity improvement for DFS-encoded qubits. Our results showcase the potential utility of DFS codes as a pathway toward enhanced computational accuracy via logical encoding on quantum processors.

Multi-ion Frequency Reference Using Dynamical Decoupling.

We present the experimental realization of a continuous dynamical decoupling scheme which suppresses leading frequency shifts in a multi-ion frequency reference based on ^{40}Ca^{+}. By near-resonant magnetic coupling of the ^{2}S_{1/2} and ^{2}D_{5/2} Zeeman sublevels using radio-frequency dressing fields, engineered transitions with reduced sensitivity to magnetic-field fluctuations are obtained. A second stage detuned dressing field reduces the influence of amplitude noise in the first stage driving fields and decreases 2nd-rank tensor shifts, such as the electric quadrupole shift. Suppression of the quadratic dependence of the quadrupole shift to 3(2) mHz/μm^{2} and coherence times of 290(20)ms on the optical transition are demonstrated even within a laboratory environment with significant magnetic field noise. Besides removing inhomogeneous line shifts in multi-ion clocks, the demonstrated dynamical decoupling technique may find applications in quantum computing and simulation with trapped ions by a tailored design of decoherence-free subspaces.

The effects of common reservoirs on the performance of a quantum refrigerator

In this work, we study and find that the performance of an autonomous refrigerator can be improved by means of collective dissipations of common reservoirs. The refrigerator is based on a four-level system with two degenerate levels, coupled to three thermal reservoirs with different temperatures. Our study reveals that utilizing only one common reservoir can not significantly enhance the refrigerator’s performance. However, when two reservoirs are shared simultaneously, the performance improvement becomes more evident. Furthermore, we find that the refrigerator’s performance can be further enhanced by operating in a regime where the decoherence-free subspace is present. Our results indicate that careful engineering is essential to maximize the benefits of common reservoirs in enhancing the performance of quantum thermal machines.

Kerr-effect-based quantum logical gates in decoherence-free subspace

The decoherence effect caused by the coupling between the system and the environment undoubtedly leads to the errors in efficient implementations of two (or three) qubit logical gates in quantum information processing. Fortunately, decoherence-free subspace (DFS) introduced can effectively decrease the influence of decoherence effect. In this paper, we propose some schemes for setting up a family of quantum control gates, including controlled-NOT (CNOT), Toffoli, and Fredkin gates for two or three logical qubits by means of cross-Kerr nonlinearities in DFS. These three logical gates require neither complicated quantum computational circuits nor auxiliary photons (or entangled states). The success probabilities of three logical gates are approximate 1 by performing the corresponding classical feed-forward operations based on the different measuring results of the X-homodyne detectors, and their fidelities are robust against the photon loss with the current technology. The proposed logical gates rely on only simple linear-optics elements, available single-qubit operations, and mature measurement methods, making our proposed gates be feasible and efficient in practical applications.

Entanglement Assisted Probe of the Non-Markovian to Markovian Transition in Open Quantum System Dynamics.

We utilize a superconducting qubit processor to experimentally probe non-Markovian dynamics of an entangled qubit pair. We prepare an entangled state between two qubits and monitor the evolution of entanglement over time as one of the qubits interacts with a small quantum environment consisting of an auxiliary transmon qubit coupled to its readout cavity. We observe the collapse and revival of the entanglement as a signature of quantum memory effects in the environment. We then engineer the non-Markovianity of the environment by populating its readout cavity with thermal photons to show a transition from non-Markovian to Markovian dynamics, ultimately reaching a regime where the quantum Zeno effect creates a decoherence-free subspace that effectively stabilizes the entanglement between the qubits.

Embedding Quantum Many-Body Scars into Decoherence-Free Subspaces.

Quantum many-body scars are nonthermal excited eigenstates of nonintegrable Hamiltonians, which could support coherent revival dynamics from special initial states when scars form an equally spaced tower in the energy spectrum. For open quantum systems, engineering many-body scarred dynamics by a controlled coupling to the environment remains largely unexplored. Here, we provide a general framework to exactly embed quantum many-body scars into the decoherence-free subspaces of Lindblad master equations. The dissipative scarred dynamics manifest persistent periodic oscillations for generic initial states, and can be practically utilized to prepare scar states with potential quantum metrology applications. We construct the Liouvillian dissipators with the local projectors that annihilate the whole scar towers, and utilize the Hamiltonian part to rotate the undesired states out of the null space of dissipators. We demonstrate our protocol through several typical models hosting many-body scar towers and propose an experimental scheme to observe the dissipative scarred dynamics based on digital quantum simulations and resetting ancilla qubits.

Optimal distributed multi-parameter estimation in noisy environments

We consider the task of multiple parameter estimation in the presence of strong correlated noise with a network of distributed sensors. The signals and the noises have different spatial dependence but are encoded with the same local generators. We study how to find and improve noise-insensitive strategies. We show that sequentially probing with GHZ states from the decoherence-free subspace that we identify is asymptotically optimal up to a factor of at most 4 in the limit of many repetitions. The implementation of such strategies only requires local read-out and ‘passive’ resources—an initially entangled state of the sensors and tunable local interaction strength.

Unraveling metastable Markovian open quantum systems

We analyze the dynamics of metastable Markovian open quantum systems by unraveling their average dynamics into stochastic trajectories. We use quantum reset processes as examples to illustrate metastable phenomenology, including a simple three-state model whose metastability is of classical type, and a two-qubit model that features a metastable decoherence-free subspace. In the three-state model, the trajectories exhibit classical metastable phenomenology: fast relaxation into distinct phases and slow transitions between them. This extends the existing correspondence between classical and quantum metastability. It enables the computation of committors for the quantum phases, and the mechanisms of rare transitions between them. For the two-qubit model, the decoherence-free subspace appears in the unraveled trajectories as a slow manifold on which the quantum state has a continuous slow evolution. This provides a classical (nonmetastable) analog of this quantum effect. We discuss the general implications of these results, and we highlight the useful role of quantum reset processes for analysis of quantum trajectories in metastable systems. Published by the American Physical Society 2024

Engineering Four-Qubit Fuel States for Protecting Quantum Thermalization Machine from Decoherence

Decoherence is a major issue in quantum information processing, degrading the performance of tasks or even precluding them. Quantum error-correcting codes, creating decoherence-free subspaces, and the quantum Zeno effect are among the major means for protecting quantum systems from decoherence. Increasing the number of qubits of a quantum system to be utilized in a quantum information task as a resource expands the quantum state space. This creates the opportunity to engineer the quantum state of the system in a way that improves the performance of the task and even to protect the system against decoherence. Here, we consider a quantum thermalization machine and four-qubit atomic states as its resource. Taking into account the realistic conditions such as cavity loss and atomic decoherence due to ambient temperature, we design a quantum state for the atomic resource as a classical mixture of Dicke and W states. We show that using the mixture probability as the control parameter, the negative effects of the inevitable decoherence on the machine performance almost vanish. Our work paves the way for optimizing resource systems consisting of a higher number of atoms.

Decoherence-free-subspace-based deterministic conversions for entangled states with heralded robust-fidelity quantum gates.

The decoherence-free subspace (DFS) serves as a protective shield against certain types of environmental noise, allowing the system to remain coherent for extended periods of time. In this paper, we propose two protocols, i.e., one converts two-logic-qubit Knill-Laflamme-Milburn (KLM) state to two-logic-qubit Bell states, and the other converts three-logic-qubit KLM state to three-logic-qubit Greenberger-Horne-Zeilinger states, through cavity-assisted interaction in DFS. Especially, our innovative protocols achieve their objectives in a heralded way, thus enhancing experimental accessibility. Moreover, single photon detectors are incorporated into the setup, which can predict potential failures and ensure seamless interaction between the nitrogen-vacancy center and photons. Rigorous analyses and evaluations of two schemes demonstrate their abilities to achieve near-unit fidelities in principle and exceptional efficiencies. Further, our protocols offer progressive solutions to the challenges posed by decoherence, providing a pathway towards practical quantum technologies.

Entanglement-enabled decoherence-free transmission of two-color photons through a single mode fiber.

We demonstrate decoherence-tolerant transmission of a Bell state through a single-mode fiber (SMF) using the photon frequency degree of freedom. To this end, a slightly non-degenerate polarization-entangled singlet, |Ψ -⟩=(|HV⟩-|VH⟩)/2, is localized at the SMF as the depolarization channel subject to random noise due to incessant fiber bending. Two-photon beats and quantum state tomography jointly verify the absence of collective decoherence, showing that |Ψ -⟩ is the sought-after one-dimensional decoherence-free subspace (DFS) pertaining to SMF. Efficient splitting and combining of photon streams in our DFS help outperform the DFS in time domain. This motivates us to attempt DFS-enabled fault-tolerant fiber transmission of biphoton qubits. Two-photon BB84 protocol is implemented in a polarization-maintaining fiber to which dephasing noise is relevant so that a two-dimensional DFS is appropriate. A low bit error rate 5.4% is achieved by encoding one-qubit information onto the biphoton state in spite of significant polarization fluctuation. Our scalable frequency-based DFS has a natural affinity for wavelength division multiplexing in fiber communication by design and as such is extensible to multi-particle entanglement.

Characterization of Quantum and Classical Critical Points for an Integrable Two-Qubit Spin–Boson Model

The class of two-interacting-qubit spin–boson models with vanishing transverse fields on the spin-pair is studied. The model can be mapped exactly into two independent standard single-impurity spin–boson models where the role of the tunneling parameter is played by the spin–spin coupling. The dynamics of the magnetization are analyzed for different levels of (an)isotropy. The existence of a decoherence-free subspace, as well as of different classical regimes separated by a critical temperature, and symptoms of quantum (first-order and Kosterlitz–Thouless type) phase transitions in the Ohmic regime are brought to light.

Stabilizer codes for open quantum systems

The Lindblad master equation describes the evolution of a large variety of open quantum systems. An important property of some open quantum systems is the existence of decoherence-free subspaces. A quantum state from a decoherence-free subspace will evolve unitarily. However, there is no procedural and optimal method for constructing a decoherence-free subspace. In this paper, we develop tools for constructing decoherence-free stabilizer codes for open quantum systems governed by the Lindblad master equation. This is done by pursuing an extension of the stabilizer formalism beyond the celebrated group structure of Pauli error operators. We then show how to utilize decoherence-free stabilizer codes in quantum metrology in order to attain the Heisenberg limit scaling with low computational complexity.

Measurement-Device-Independent Quantum Key Distribution Based on Decoherence-Free Subspaces with Logical Bell State Analyzer.

Measurement-device-independent quantum key distribution (MDI-QKD) enables two legitimate users to generate shared information-theoretic secure keys with immunity to all detector side attacks. However, the original proposal using polarization encoding is sensitive to polarization rotations stemming from birefringence in fibers or misalignment. To overcome this problem, here we propose a robust QKD protocol without detector vulnerabilities based on decoherence-free subspaces using polarization-entangled photon pairs. A logical Bell state analyzer is designed specifically for such encoding. The protocol exploits common parametric down-conversion sources, for which we develop a MDI-decoy-state method, and requires neither complex measurements nor a shared reference frame. We have analyzed the practical security in detail and presented a numerical simulation under various parameter regimes, showing the feasibility of the logical Bell state analyzer along with the potential that double communication distance can be achieved without a shared reference frame.

Effects of reservoir squeezing on trace-distance correlations and emergence of the pointer basis

We investigate theoretically the dynamics of 1-norm geometric quantum correlations and their classical counterparts in a two-qubit system. Both qubits are initially prepared in Bell-diagonal states and locally coupled to separated thermal squeezed baths or a common squeezed thermal bath via energy-preserving interactions. We then unveil the effects of reservoir squeezing on the abrupt changes in the evolution of geometric correlations. It is found that adequately tuning the squeezing phase can efficiently suppress the dephasing rate and delay the appearance of sudden transitions in geometric correlations. Further, we show that the squeezing phase of the bath renders a different avenue to enhance the finite time interval for frozen quantum correlation. On the other hand, in this context, we show that the squeezing strength of the reservoir exhibits a negative role. In addition, in the common bath case, we observe the steady-state correlations and decoherence-free subspace, which can be governed via squeezing parameters. Moreover, the abrupt change from a decaying regime to a constant nonzero value in classical correlation signals the emergence of a pointer-state basis. We show that the emergence of a pointer-state basis can be delayed by suitably adjusting the bath squeezing parameters. Remarkably, we find the optimal value of the squeezing phase, which introduces maximum retardation in the appearance of a pointer-state basis.

Scrambling of algebras in open quantum systems

Many quantitative approaches to the dynamical scrambling of information in quantum systems involve the study of out-of-time-ordered correlators (OTOCs). In this paper, we introduce an algebraic OTOC ($\mathcal{A}$-OTOC) that allows us to study information scrambling of generalized quantum subsystems under quantum channels. For closed quantum systems, this algebraic framework was recently employed to unify quantum information-theoretic notions of operator entanglement, coherence-generating power, and Loschmidt echo. The main focus of this work is to provide a natural generalization of these techniques to open quantum systems. We first show that, for unitary dynamics, the $\mathcal{A}$-OTOC quantifies a generalized notion of information scrambling, namely between a subalgebra of observables and its commutant. For open quantum systems, on the other hand, we find a competition between the global environmental decoherence and the local scrambling of information. We illustrate this interplay by analytically studying various illustrative examples of algebras and quantum channels. To complement our analytical results, we perform numerical simulations of two paradigmatic systems: the PXP model and the Heisenberg XXX model, under dephasing. Our numerical results reveal connections with many-body scars and the stability of decoherence-free subspaces.

Decoherence-free subspace and entanglement sudden death of multi-photon polarization states in fiber channels

The construction of quantum networks requires long-distance teleportation of multi-qubit entangled states. Here, we investigate the entanglement dynamics of GHZ and W states in fiber channels. In a fiber channel, the two most important phenomena that affect polarization entanglement are polarization mode dispersion (PMD) and polarization-dependent loss (PDL). We theoretically characterize how PMD and PDL vectors affect three-qubit states. In particular, upon quantifying the entanglement at the output states using concurrence and entanglement witnesses, we reveal the occurrence of entanglement sudden death and the appearance of decoherence-free subspaces in tripartite systems. Finally, we explore the evolution of GHZ and W state with an arbitrary number of photons in a fiber network and discuss the decoherence mechanism of the 4-party cluster state.

Scalable quantum computation based on nitrogen-vacancy centers in decoherence-free subspace

Due to its unique optical properties, nitrogen-vacancy centers in diamond show remarkable advantages in realizing quantum information processing and computation. This paper proposes a scalable quantum computing architecture based on solid-state NV centers. In our scheme, logical qubits are encoded in a decoherence-free subspace (DFS) with Larmor pairs (a pair of the nucleus). And the connection between multiple qubits is assisted by a cantilever probe. Then the high fidelity of the universal quantum gate is achieved by using a series of pulses. Our scheme provides physical feasibility for scalable quantum computing and may pave the way for large-scale quantum computing based on NV centers.

Symmetry-induced decoherence-free subspaces

Preservation of coherence is a fundamental yet subtle phenomenon in open systems. We uncover its relation to symmetries respected by the system Hamiltonian and its coupling to the environment. We discriminate between local and global classes of decoherence-free subspaces for many-body systems through the introduction of "ghost variables". The latter are orthogonal to the symmetry and the coupling to the environment does not depend on them. Constructing them is facilitated in classical phase space and can be transferred to quantum mechanics through the equivalent role that Poisson and Lie algebras play for symmetries in classical and quantum mechanics, respectively. Examples are given for an interacting spin system.

Quantum private information retrieval over a collective noisy channel

Quantum Private Information Retrieval (QPIR) allows a user (Alice) to retrieve a database item from the database owned by the database holder (Bob) in such a way that Alice can query only the database item she wants, but cannot get other items, and Bob does not know which item Alice queries. However, the real quantum channel between Alice and Bob is noisy, and the noise may result in not only the chance that Alice obtains a false item, but also that both parties may cheat by camouflaging themselves with noise. In this paper, we use the decoherence-free subspace (DFS) for QPIR, which we call DFS-QPIR. The DFS-QPIR protocol removes the effect of the channel noise on the errors in the retrieved item so that two parties cannot cheat by replacing the noisy channel with a noiseless one. It can work over a collective noisy channel while retaining high reliability, database security and user privacy simultaneously. While only the collective unitary noise is taken into account, the proposed DFS-QPIR protocol can be straightforwardly extended to more general collective noise channel.