arXiv subjects

Stephen D. Bartlett

Publications and source records attributed to Stephen D. Bartlett.

At least 37 records · Page 2Linked to original sources

arXiv2024

Mitigating errors in logical qubits

Quantum error correcting codes protect quantum information, allowing for large quantum computations provided that physical error rates are sufficiently low. We combine post-selection with surface code error correction through the use of a parameterized family of exclusive decoders, which are able to abort on decoding instances that are deemed too difficult. We develop new numerical sampling methods to quantify logical failure rates with exclusive decoders as well as the trade-off in terms of the amount of post-selection required. For the most discriminating of exclusive decoders, we demonstrate a threshold of 50\% under depolarizing noise for the surface code (or $32(1)\%$ for the fault-tolerant case with phenomenological measurement errors), and up to a quadratic improvement in logical failure rates below threshold. Furthermore, surprisingly, with a modest exclusion criterion, we identify a regime at low error rates where the exclusion rate decays with code distance, providing a pathway for scalable and time-efficient quantum computing with post-selection. We apply our exclusive decoder to the 15-to-1 magic state distillation protocol, and report a $75\%$ reduction in the number of physical qubits required, and a $60\%$ reduction in the total spacetime volume required, including accounting for repetitions required for post-selection. We also consider other applications, as an error mitigation technique, and in concatenated schemes. Our work highlights the importance of post-selection as a powerful tool in quantum error correction.

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arXiv2024

Low-overhead quantum computing with the color code

Fault-tolerant quantum computation demands significant resources: large numbers of physical qubits must be checked for errors repeatedly to protect quantum data as logic gates are implemented in the presence of noise. We demonstrate that an approach based on the color code can lead to considerable reductions in the resource overheads compared with conventional methods, while remaining compatible with a two-dimensional layout. We propose a lattice surgery scheme that exploits the rich structure of the color-code phase to perform arbitrary pairs of commuting logical Pauli measurements in parallel while keeping the space cost low. Compared to lattice surgery schemes based on the surface code with the same code distance, our approach yields about a $3\times$ improvement in the space-time overhead, obtained from a combination of a $1.5\times$ improvement in spatial overhead together with a $2\times$ speedup due to the parallelisation of commuting logical measurements. Even when taking into account the color code's lower error threshold using current decoders, the overhead is reduced by 10\% at a physical error rate of $10^{-3}$ and by 50\% at $10^{-4}$.

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arXiv2024

Assessment of error variation in high-fidelity two-qubit gates in silicon

Achieving high-fidelity entangling operations between qubits consistently is essential for the performance of multi-qubit systems and is a crucial factor in achieving fault-tolerant quantum processors. Solid-state platforms are particularly exposed to errors due to materials-induced variability between qubits, which leads to performance inconsistencies. Here we study the errors in a spin qubit processor, tying them to their physical origins. We leverage this knowledge to demonstrate consistent and repeatable operation with above 99% fidelity of two-qubit gates in the technologically important silicon metal-oxide-semiconductor (SiMOS) quantum dot platform. We undertake a detailed study of these operations by analysing the physical errors and fidelities in multiple devices through numerous trials and extended periods to ensure that we capture the variation and the most common error types. Physical error sources include the slow nuclear and electrical noise on single qubits and contextual noise. The identification of the noise sources can be used to maintain performance within tolerance as well as inform future device fabrication. Furthermore, we investigate the impact of qubit design, feedback systems, and robust gates on implementing scalable, high-fidelity control strategies. These results are achieved by using three different characterization methods, we measure entangling gate fidelities ranging from 96.8% to 99.8%. Our analysis tools identify the causes of qubit degradation and offer ways understand their physical mechanisms. These results highlight both the capabilities and challenges for the scaling up of silicon spin-based qubits into full-scale quantum processors.

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arXiv2024

Anyon condensation and the color code

The manipulation of topologically-ordered phases of matter to encode and process quantum information forms the cornerstone of many approaches to fault-tolerant quantum computing. Here we demonstrate that fault-tolerant logical operations in these approaches can be interpreted as instances of anyon condensation. We present a constructive theory for anyon condensation and, in tandem, illustrate our theory explicitly using the color-code model. We show that different condensation processes are associated with a general class of domain walls, which can exist in both space- and time-like directions. This class includes semi-transparent domain walls that condense certain subsets of anyons. We use our theory to classify topological objects and design novel fault-tolerant logic gates for the color code. As a final example, we also argue that dynamical `Floquet codes' can be viewed as a series of condensation operations. We propose a general construction for realising planar dynamically driven codes based on condensation operations on the color code. We use our construction to introduce a new Calderbank-Shor Steane-type Floquet code that we call the Floquet color code.

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arXiv2023

High-fidelity operation and algorithmic initialisation of spin qubits above one kelvin

The encoding of qubits in semiconductor spin carriers has been recognised as a promising approach to a commercial quantum computer that can be lithographically produced and integrated at scale. However, the operation of the large number of qubits required for advantageous quantum applications will produce a thermal load exceeding the available cooling power of cryostats at millikelvin temperatures. As the scale-up accelerates, it becomes imperative to establish fault-tolerant operation above 1 kelvin, where the cooling power is orders of magnitude higher. Here, we tune up and operate spin qubits in silicon above 1 kelvin, with fidelities in the range required for fault-tolerant operation at such temperatures. We design an algorithmic initialisation protocol to prepare a pure two-qubit state even when the thermal energy is substantially above the qubit energies, and incorporate radio-frequency readout to achieve fidelities up to 99.34 per cent for both readout and initialisation. Importantly, we demonstrate a single-qubit Clifford gate fidelity of 99.85 per cent, and a two-qubit gate fidelity of 98.92 per cent. These advances overcome the fundamental limitation that the thermal energy must be well below the qubit energies for high-fidelity operation to be possible, surmounting a major obstacle in the pathway to scalable and fault-tolerant quantum computation.

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arXiv2023

Transversal Diagonal Logical Operators for Stabiliser Codes

Storing quantum information in a quantum error correction code can protect it from errors, but the ability to transform the stored quantum information in a fault tolerant way is equally important. Logical Pauli group operators can be implemented on Calderbank-Shor-Steane (CSS) codes, a commonly-studied category of codes, by applying a series of physical Pauli X and Z gates. Logical operators of this form are fault-tolerant because each qubit is acted upon by at most one gate, limiting the spread of errors, and are referred to as transversal logical operators. Identifying transversal logical operators outside the Pauli group is less well understood. Pauli operators are the first level of the Clifford hierarchy which is deeply connected to fault-tolerance and universality. In this work, we study transversal logical operators composed of single- and multi-qubit diagonal Clifford hierarchy gates. We demonstrate algorithms for identifying all transversal diagonal logical operators on a CSS code that are more general or have lower computational complexity than previous methods. We also show a method for constructing CSS codes that have a desired diagonal logical Clifford hierarchy operator implemented using single qubit phase gates. Our methods rely on representing operators composed of diagonal Clifford hierarchy gates as diagonal XP operators and this technique may have broader applications.

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arXiv2023

Improved quantum error correction with randomized compiling

Current hardware for quantum computing suffers from high levels of noise, and so to achieve practical fault-tolerant quantum computing will require powerful and efficient methods to correct for errors in quantum circuits. Here, we explore the role and effectiveness of using noise tailoring techniques to improve the performance of error correcting codes. Noise tailoring methods such as randomized compiling (RC) convert complex coherent noise processes to effective stochastic noise. While it is known that this can be leveraged to design efficient diagnostic tools, we explore its impact on the performance of error correcting codes. Of particular interest is the important class of coherent errors, arising from control errors, where RC has the maximum effect -- converting these into purely stochastic errors. For these errors, we show here that RC delivers an improvement in performance of the concatenated Steane code by several orders of magnitude. We also show that below a threshold rotation angle, the gains in logical fidelity can be arbitrarily magnified by increasing the size of the codes. These results suggest that using randomized compiling can lead to a significant reduction in the resource overhead required to achieve fault tolerance.

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arXiv2022

The XP Stabiliser Formalism: a Generalisation of the Pauli Stabiliser Formalism with Arbitrary Phases

We propose an extension to the Pauli stabiliser formalism that includes fractional $2π/N$ rotations around the $Z$ axis for some integer $N$. The resulting generalised stabiliser formalism - denoted the XP stabiliser formalism - allows for a wider range of states and codespaces to be represented. We describe the states which arise in the formalism, and demonstrate an equivalence between XP stabiliser states and 'weighted hypergraph states' - a generalisation of both hypergraph and weighted graph states. Given an arbitrary set of XP operators, we present algorithms for determining the codespace and logical operators for an XP code. Finally, we consider whether measurements of XP operators on XP codes can be classically simulated.

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arXiv2022

A local pre-decoder to reduce the bandwidth and latency of quantum error correction

A fault-tolerant quantum computer will be supported by a classical decoding system interfacing with quantum hardware to perform quantum error correction. It is important that the decoder can keep pace with the quantum clock speed, within the limitations on communication that are imposed by the physical architecture. To this end we propose a local `pre-decoder', which makes greedy corrections to reduce the amount of syndrome data sent to a standard matching decoder. We study these classical overheads for the surface code under a phenomenological phase-flip noise model with imperfect measurements. We find substantial improvements in the runtime of the global decoder and the communication bandwidth by using the pre-decoder. For instance, to achieve a logical failure probability of $f = 10^{-15}$ using qubits with physical error rate $p = 10^{-3}$ and a distance $d=22$ code, we find that the bandwidth cost is reduced by a factor of $1000$, and the time taken by a matching decoder is sped up by a factor of $200$. To achieve this target failure probability, the pre-decoding approach requires a $50\%$ increase in the qubit count compared with the optimal decoder.

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arXiv2022

Fast estimation of outcome probabilities for quantum circuits

We present two classical algorithms for the simulation of universal quantum circuits on $n$ qubits constructed from $c$ instances of Clifford gates and $t$ arbitrary-angle $Z$-rotation gates such as $T$ gates. Our algorithms complement each other by performing best in different parameter regimes. The $\tt{Estimate}$ algorithm produces an additive precision estimate of the Born rule probability of a chosen measurement outcome with the only source of run-time inefficiency being a linear dependence on the stabilizer extent (which scales like $\approx 1.17^t$ for $T$ gates). Our algorithm is state-of-the-art for this task: as an example, in approximately $13$ hours (on a standard desktop computer), we estimated the Born rule probability to within an additive error of $0.03$, for a $50$-qubit, $60$ non-Clifford gate quantum circuit with more than $2000$ Clifford gates. Our second algorithm, $\tt{Compute}$, calculates the probability of a chosen measurement outcome to machine precision with run-time $O(2^{t-r} t)$ where $r$ is an efficiently computable, circuit-specific quantity. With high probability, $r$ is very close to $\min \{t, n-w\}$ for random circuits with many Clifford gates, where $w$ is the number of measured qubits. $\tt{Compute}$ can be effective in surprisingly challenging parameter regimes, e.g., we can randomly sample Clifford+$T$ circuits with $n=55$, $w=5$, $c=10^5$ and $t=80$ $T$ gates, and then compute the Born rule probability with a run-time consistently less than $10$ minutes using a single core of a standard desktop computer. We provide a C+Python implementation of our algorithms and benchmark them using random circuits, the hidden shift algorithm and the quantum approximate optimization algorithm (QAOA).

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arXiv2022

Low-overhead fault-tolerant quantum computing using long-range connectivity

Vast numbers of qubits will be needed for large-scale quantum computing due to the overheads associated with error correction. We present a scheme for low-overhead fault-tolerant quantum computation based on quantum low-density parity-check (LDPC) codes, where long-range interactions enable many logical qubits to be encoded with a modest number of physical qubits. In our approach, logic gates operate via logical Pauli measurements that preserve both the protection of the LDPC codes as well as the low overheads in terms of the required number of additional qubits. Compared with surface codes with the same code distance, we estimate order-of-magnitude improvements in the overheads for processing around one hundred logical qubits using this approach. Given the high thresholds demonstrated by LDPC codes, our estimates suggest that fault-tolerant quantum computation at this scale may be achievable with a few thousand physical qubits at comparable error rates to what is needed for current approaches.

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arXiv2022

Hierarchies of resources for measurement-based quantum computation

For certain restricted computational tasks, quantum mechanics provides a provable advantage over any possible classical implementation. Several of these results have been proven using the framework of measurement-based quantum computation (MBQC), where non-locality and more generally contextuality have been identified as necessary resources for certain quantum computations. Here, we consider the computational power of MBQC in more detail by refining its resource requirements, both on the allowed operations and the number of accessible qubits. More precisely, we identify which Boolean functions can be computed in non-adaptive MBQC, with local operations contained within a finite level in the Clifford hierarchy. Moreover, for non-adaptive MBQC restricted to certain subtheories such as stabiliser MBQC, we compute the minimal number of qubits required to compute a given Boolean function. Our results point towards hierarchies of resources that more sharply characterise the power of MBQC beyond the binary of contextuality vs non-contextuality.

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arXiv2022

Biphoton entanglement of topologically-distinct modes

The robust generation and manipulation of entangled multiphoton states on-chip has an essential role in quantum computation and communication. Lattice topology has emerged as a means of protecting photonic states from disorder but entanglement across different topologies remained unexplored. We report biphoton entanglement between topologically distinct spatial modes in a bipartite array of silicon waveguides. The results highlight topology as an additional degree of freedom for entanglement and open avenues for investigating information teleportation between trivial and topological modes.

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arXiv2021

Efficient diagnostics for quantum error correction

Fault-tolerant quantum computing will require accurate estimates of the resource overhead, but standard metrics such as gate fidelity and diamond distance have been shown to be poor predictors of logical performance. We present a scalable experimental approach based on Pauli error reconstruction to predict the performance of concatenated codes. Numerical evidence demonstrates that our method significantly outperforms predictions based on standard error metrics for various error models, even with limited data. We illustrate how this method assists in the selection of error correction schemes.

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arXiv2021

Universal Fault-Tolerant Quantum Computing with Stabiliser Codes

The quantum logic gates used in the design of a quantum computer should be both universal, meaning arbitrary quantum computations can be performed, and fault-tolerant, meaning the gates keep errors from cascading out of control. A number of no-go theorems constrain the ways in which a set of fault-tolerant logic gates can be universal. These theorems are very restrictive, and conventional wisdom holds that a universal fault-tolerant logic gate set cannot be implemented natively, requiring us to use costly distillation procedures for quantum computation. Here, we present a general framework for universal fault-tolerant logic with stabiliser codes, together with a no-go theorem that reveals the very broad conditions constraining such gate sets. Our theorem applies to a wide range of stabiliser code families, including concatenated codes and conventional topological stabiliser codes such as the surface code. The broad applicability of our no-go theorem provides a new perspective on how the constraints on universal fault-tolerant gate sets can be overcome. In particular, we show how non-unitary implementations of logic gates provide a general approach to circumvent the no-go theorem, and we present a rich landscape of constructions for logic gate sets that are both universal and fault-tolerant. That is, rather than restricting what is possible, our no-go theorem provides a signpost to guide us to new, efficient architectures for fault-tolerant quantum computing.

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arXiv2021

The XZZX Surface Code

Performing large calculations with a quantum computer will likely require a fault-tolerant architecture based on quantum error-correcting codes. The challenge is to design practical quantum error-correcting codes that perform well against realistic noise using modest resources. Here we show that a variant of the surface code -- the XZZX code -- offers remarkable performance for fault-tolerant quantum computation. The error threshold of this code matches what can be achieved with random codes (hashing) for every single-qubit Pauli noise channel; it is the first explicit code shown to have this universal property. We present numerical evidence that the threshold even exceeds this hashing bound for an experimentally relevant range of noise parameters. Focusing on the common situation where qubit dephasing is the dominant noise, we show that this code has a practical, high-performance decoder and surpasses all previously known thresholds in the realistic setting where syndrome measurements are unreliable. We go on to demonstrate the favourable sub-threshold resource scaling that can be obtained by specialising a code to exploit structure in the noise. We show that it is possible to maintain all of these advantages when we perform fault-tolerant quantum computation.

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arXiv2020

Dispersive readout of Majorana qubits

We analyze a readout scheme for Majorana qubits based on dispersive coupling to a resonator. We consider two variants of Majorana qubits: the Majorana transmon and the Majorana box qubit. In both cases, the qubit-resonator interaction can produce sizeable dispersive shifts in the MHz range for reasonable system parameters, allowing for submicrosecond readout with high fidelity. For Majorana transmons, the light-matter interaction used for readout manifestly conserves Majorana parity, which leads to a notion of quantum nondemolition (QND) readout that is stronger than for conventional charge qubits. In contrast, Majorana box qubits only recover an approximately QND readout mechanism in the dispersive limit where the resonator detuning is large. We also compare dispersive readout to longitudinal readout for the Majorana box qubit. We show that the latter gives faster and higher fidelity readout for reasonable parameters, while having the additional advantage of being manifestly QND, and so may prove to be a better readout mechanism for these systems.

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arXiv2020

Symmetry-protected self-correcting quantum memories

A self-correcting quantum memory can store and protect quantum information for a time that increases without bound with the system size and without the need for active error correction. We demonstrate that symmetry can lead to self-correction in 3D spin-lattice models. In particular, we investigate codes given by 2D symmetry-enriched topological (SET) phases that appear naturally on the boundary of 3D symmetry-protected topological (SPT) phases. We find that while conventional on-site symmetries are not sufficient to allow for self-correction in commuting Hamiltonian models of this form, a generalized type of symmetry known as a 1-form symmetry is enough to guarantee self-correction. We illustrate this fact with the 3D "cluster-state" model from the theory of quantum computing. This model is a self-correcting memory, where information is encoded in a 2D SET-ordered phase on the boundary that is protected by the thermally stable SPT ordering of the bulk. We also investigate the gauge color code in this context. Finally, noting that a 1-form symmetry is a very strong constraint, we argue that topologically ordered systems can possess emergent 1-form symmetries, i.e., models where the symmetry appears naturally, without needing to be enforced externally.

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