Session B48: Quantum Error Correction with Novel Qubits and Codes I

Quantum error correction with two bosonic modes

Encoding quantum information in bosonic modes is a promising way to realize error-corrected logical qubits for fault tolerant quantum computing.

In recent years there has been a lot of progress with qubits encoded in states of single bosonic modes. 

However, logical qubits encoded in the joint Hilbert space of two bosonic modes offer simpler error syndromes in comparison.

Advantageously, the error syndromes for these codes can be engineered in such a way that they are transparent to ancilla errors. 

In our experiment, we explore these two-mode bosonic encodings for quantum error correction in 3D superconducting microwave architecture. 

We use a cross-Kerr tuning parametric process, which was recently demonstrated in a single mode system, to dynamically modify the interaction 

Hamiltonian between the bosonic modes and an ancilla transmon. We use this method to also perform joint-Wigner tomography on the two-mode 

states.   

The performance of random Bosonic rotation codes

Bosonic error correcting codes utilize the infinite dimensional Hilbert space of a harmonic oscillator to encode a qubit and have seen experimental demonstrations of break even performance. Bosonic rotation codes are characterized by a discrete rotation symmetry in their Wigner functions and include codes such as the cat and binomial codes. Rotation codes can naturally protect against small loss and dephasing errors, which are the dominant sources of noise in physical quantum harmonic oscillators. We define several different notions of random bosonic rotation codes and numerically explore their performance against loss and dephasing. We find that random rotation codes can, on average, outperform cat codes. Furthermore, we find the best random rotation codes can outperform binomial codes for simultaneous loss and dephasing errors.   

Fault-Tolerant Operation of Bosonic Qubits with Discrete-Variable Ancillae

In this work, we introduce building blocks of error-corrected gadgets for bosonic qubits by leveraging ancilla-assisted bosonic operations through a generalized variant of path-independent quantum control (GPI). With these building blocks, we construct a universal set of error-corrected gadgets that tolerate a single photon loss and an arbitrary ancilla fault for four-legged cat qubits. Notably, our construction only requires dispersive coupling between bosonic modes and ancillae, as well as beam-splitter coupling between bosonic modes, both of which have been experimentally demonstrated with strong strengths and high accuracy. Using our scheme, each error-corrected bosonic qubit is only comprised of a single bosonic mode and a three-level ancilla, featuring the hardware efficiency of bosonic error correction in the full fault-tolerant setting. These developed fault-tolerant schemes can also be adapted for other rotation-symmetrical codes, offering a promising avenue toward scalable and robust quantum computation with bosonic qubits.   

Dual-rail encoding with superconducting cavities

Erasure qubits are an attractive paradigm for quantum error correction whereby most physical errors are detected and thus known to occur at a particular qubit location. We propose using the dual-rail encoding with superconducting cavities to realize an erasure qubit and describe a complete set of necessary hardware operations [1]. We coin this qubit the “dual-rail cavity qubit”. Much like its equivalent in quantum optics, the physical qubit is encoded in the single photon subspace of two bosonic modes. However, the non-linearities afforded by circuit quantum electrodynamics now allow for direct entangling gates and non-destructive error-detection. With the addition of a dispersively coupled transmon, we can realize a universal gate-based set of operations on our dual-rail cavity qubits that maintain the desired properties of erasure qubits. The dominant hardware errors arising from both the transmon and cavities are detectable with high probability, allowing us to treat them as erasure errors. With today’s coherence times, we expect the dual-rail cavity qubit to operate far below the relevant QEC thresholds. 

[1] Teoh et al. PNAS 2023    

A Dual-rail Qubit with Parametrically Coupled Transmons

Quantum error correction (QEC) is crucial to developing fault-tolerant quantum computers. Different physical platforms are working towards error rates below the surface code threshold. A new promising approach seeks to convert certain environmentally-induced state transitions into so-called qubit "erasures". These erasure errors can be monitored directly without destroying the qubit's entangled state, and can be discarded, requiring no further correction. The concept behind our erasure qubit relies on using the single-photon subspace of two parametrically coupled transmons as the logical qubit. This allows the conversion of dominant thermal relaxation errors, leakage out of computational subspace, to erasure errors. This system forms a "dual-rail" encoding, using two transmons where arbitrary single qubit operations are completely controlled with microwave parametric pulses. In this talk, we will describe our system design and operation, and show how dual-rail encoding largely improves the coherence of the erasure qubit over the individual transmon qubits.   

Converting leakage errors to erasure errors and cooling atoms while preserving coherence in neutral atoms for fault-tolerant quantum computation

Neutral atoms quantum information processing is growing in prominence with the recent demonstration of high-fidelity entangling gates and architectures that can be scaled to large numbers of qubits. One particular error channel that must be addressed is the loss of atoms that are weakly bound in optical traps. This leads to leakage errors that are detrimental to fault-tolerant quantum computation as they are not Pauli errors and need separate error correction protocols. In this work, we develop schemes for converting these leakage errors to erasure errors, which can be efficiently corrected by standard error correction protocols. Another critical roadblock for quantum computation with neutral atoms is the lack of schemes for cooling atomic motion while preserving the qubit coherence, which prevents us from doing arbitrarily long quantum computation. In this work, we extend the scheme for detecting leakage to cool atoms based on the work originally studied and recently revisited recently based on alkaline earth atoms with quantum information stored in the nuclear spin. For these atoms, one can use metastable states with narrow linewidth to employ the techniques of resolved sideband cooling. To avoid mixing electronic and nuclear degrees of freedom in the excited state, which we need for cooling, we consider moderate AC Stark shifts. This decouples the electronic and nuclear degrees of freedom and avoids the ``which way information’’ about the nuclear spin state and one can cool while preserving coherence.   

Proposal for Quantum Error Correction Scheme for Biased Errors Using Sparsely Connected Quasi-One-Dimensional Qubit Array

In recent years, semiconductor qubits have gained attention as a promising platform for quantum computing. While these qubits offer advantages such as the ability to operate at high temperatures and semiconductor integration technology, they also present challenges, including the qubits arrangement and highly biased noise. The experimentally realized arrangement of semiconductor qubits is mainly one-dimensional, and hence the realization of a sparsely connected quasi-one-dimensional qubit array is experimentally feasible. In this study, we propose a quantum error correction scheme for such a qubit arrangement, utilizing the concatenated code of the repetition code and the rotated surface code, where strongly biased errors are harnessed by exploiting the one-dimensional structure using the repetition code. Numerical calculations demonstrate that this approach significantly extends the lifetime of the logical qubit compared to the approach simply using the surface code on the same lattice. These findings make an important contribution to the realization of fault-tolerant quantum computation in semiconductor quantum computer.   

Long-range-enhanced surface codes

The surface code is a quantum error-correcting code for one logical qubit, protected by spatially localized parity checks in two dimensions. Due to fundamental constraints from spatial locality, storing more logical qubits requires either sacrificing the robustness of the surface code against errors or increasing the number of physical qubits. We bound the minimal number of spatially non-local parity checks necessary to add logical qubits to a surface code while maintaining, or improving, robustness to errors. We asymptotically saturate this bound using a family of hypergraph product codes, interpolating between the surface code and constant-rate low-density parity-check codes. Fault-tolerant protocols for logical operations generalize naturally to these longer-range codes, based on those from ordinary surface codes. We provide near-term practical implementations of this code for hardware based on trapped ions or neutral atoms in mobile optical tweezers. Long-range-enhanced surface codes outperform conventional surface codes using hundreds of physical qubits, and represent a practical strategy to enhance the robustness of logical qubits to errors in near-term devices.   

Fault-tolerant quantum computation with simple non-LDPC high-rate codes

I study a family of non-LDPC high-rate codes toward low-overhead fault-tolerant quantum computation. The coding rates of the codes studied in this work are higher than or as high as 20%. I develop a high-performance decoder dedicated to these codes. Exploiting the simple structure of the code family, I also propose fault-tolerant methods for logical Clifford and non-Clifford gates allowing simultaneous execution.   

Weakly Fault-Tolerant Computation in a Quantum Error-Detecting Code

Many quantum error correcting codes that achieve full fault-tolerance suffer from low ratios of logical to physical qubits and add significant overhead to encoded computations. This makes them difficult to implement on current noisy intermediate-scale quantum (NISQ) computers and results in the inability to perform quantum algorithms at useful scales with near-term quantum processors. Due to this, current calculations are generally done without encoding. We propose a middle ground between these two approaches: constructions in the [[n,n-2,2]] quantum error detecting code that can detect any error from a single faulty gate by measuring the stabilizer generators of the code and additional ancillas at the end of the computation. This achieves what we call weak fault-tolerance. As we show, this demonstrates a significant improvement over no error correction for low enough physical error probabilities and requires much less overhead than codes that achieve full fault-tolerance. We give constructions for a set of gates that achieve universal quantum computation in this error detecting code, while satisfying weak fault-tolerance up to analog errors on the physical rotation gate.   

Families of d=2 2D subsystem stabilizer codes for universal adiabatic quantum computation with two-body interactions

Bravyi's A matrix offers an approach to devising quantum error correction codes (QECC) characterized by geometric constraints. Since two-body interactions are sufficient for universal adiabatic quantum computation (AQC), we focus on the quantum error detection code (QEDC) with d=2. We discovered a family of codes satisfying the maximum code rate, and by slightly relaxing the code rate, we uncovered an extended spectrum of codes within this framework. These codes present enhanced geometric locality, which amplifies their practical utility. Furthermore, we also map the requisite connectivity to alternative configurations so that the total Manhattan distance is minimized, providing valuable insights into hardware design. Lastly, we give a systematic framework for the assessment of codes within the context of AQC in terms of code rate, physical and geometrical locality, graph complexity, and Manhattan distances on the graph. This facilitates informed decision-making in code selection for specific quantum computing applications.