arXiv subjects

Daniel A. Lidar

Publications and source records attributed to Daniel A. Lidar.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Error Correction and Dynamical Decoupling: Better Together or Apart?

Quantum error correction/detection (QEC/QED) and dynamical decoupling (DD) are tools for protecting quantum information. A natural goal is to combine them to outperform either approach alone. Such a benefit is not automatic: physical DD can conflict with encoded subspace, and QEC performance is governed by the errors that survive decoding, not just those DD suppresses. We analyze a hybrid memory cycle where DD is implemented logically (LDD) using normalizer elements of an $[[n,k,d]]$ stabilizer code, followed by a round of syndrome measurement and recovery (or, in the detection setting, postselection on a trivial syndrome). In an effective Pauli model with physical error probability $p$, LDD suppression factor $p_{DD}$, and recovery imperfection rate $p_{QEC}$ (or $p_{QED}$), we derive closed-form entanglement-fidelity expressions for QEC-only, QED-only, LDD-only, physical DD, and the hybrid LDD+QEC protocol. The formulas are expressed via a small set of code-dependent weight enumerator polynomials, making the role of the decoder and the LDD group explicit. For ideal recovery LDD+QEC outperforms QEC-only iff the conditional fraction of uncorrectable Pauli errors is larger in the LDD-suppressed sector than in the unsuppressed sector. In the low-noise regime, a sufficient design rule guaranteeing hybrid advantage is that LDD suppresses at least one minimum-weight uncorrectable Pauli error for the chosen recovery map. We show how stabilizer-equivalent choices of LDD generators can enforce this condition. We supplement our analysis with numerical results for the $[[7,1,3]]$ Steane code and a $[[13,1,3]]$ code, mapping regions of hybrid-protocol advantage in parameter space beyond the small-$p$ regime. Our work illustrates the need for co-design of the code, decoder, and logical decoupling group, and clarifies the conditions under which the hybrid LDD+QEC protocol is advantageous.

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arXiv2026

Probing Qubit Noise with a Channel-Resolved Post-Markovian Master Equation

Accurate noise characterization is essential for scaling quantum processors toward fault-tolerant operation. Although reduced qubit dynamics are often modeled with Markovian master equations, present-day devices can exhibit memory effects generated by residual qubit-qubit couplings, structured environments, and finite bath correlation times. Here we develop a channel-resolved, Post-Markovian Master Equation model for non-Markovian noise and test it in superconducting qubits. Using idle-evolution tomography on IBM Quantum processors, we identify complementary operational signatures of non-Markovianity, including violations of CP-divisibility and revivals of distinguishability-based information-backflow measures. We further derive a closed-form spectator-$ZZ$ model with local dissipation and show that it captures the observed transverse Bloch-vector revivals while leaving the longitudinal relaxation mode Markovian within the model. The fitted closed-form dynamics enable an analytical reconstruction of the transverse memory kernel, whose damped oscillatory structure captures the non-Markovian correction beyond the fitted Markovian baseline. Two-qubit tomography shows buildup and revivals of quantum mutual information on comparable timescales, supporting spectator-induced crosstalk as an important contributor to the observed memory effects. Our results connect operational non-Markovianity diagnostics, microscopic crosstalk modeling, and reduced memory-kernel reconstruction in a single experimental framework for superconducting quantum hardware.

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arXiv2026

QMCtwin: Master-Equation Simulation of Syndrome Statistics Beyond Pauli Noise

As quantum error correction moves toward large-scale experimental implementations, decoder performance increasingly depends on how faithfully hardware noise is translated into syndrome statistics. Standard stabilizer workflows achieve scalability by replacing device dynamics with stochastic Pauli or detector-error models, but this compression can discard coherent phase information, nonunital drift, continuous-time effects of always-on couplings, and correlations generated by simultaneous Hamiltonian and dissipative evolution. Here we present QMCtwin, a sign-problem-suppressed quantum Monte Carlo framework for master-equation simulation of QEC circuits, and apply it to a full syndrome-extraction round of a distance-$7$ rotated surface code with $97$ physical qubits. The open-system model includes realistic superconducting-device noise mechanisms such as relaxation, pure dephasing, coherent gate miscalibration, residual $ZZ$ crosstalk, and drive-qubit detuning. By directly estimating syndrome observables from the QMC-generated stochastic density matrix estimator, we compare the master-equation dynamics with their Pauli-twirled Clifford simulation counterparts. QMCtwin predicts syndrome-extraction biases and correlations between syndromes and proxies of logical-string-parity that are absent or strongly suppressed in the stochastic Pauli description. We introduce information-theoretic diagnostics that further quantify how information concerning syndromes versus string-parity proxies differs between the realistic master-equation simulation and the corresponding Pauli-twirled model. These results show that QMC-based master-equation digital twins can expose noise features hidden by conventional Pauli/Clifford noise models and provide a practical path toward more accurate decoder-facing syndrome models.

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arXiv2026

Demonstration of Exponential Quantum Speedup with Constant-Depth Compiled Circuits for Simon's Problem

We demonstrate exponential algorithmic quantum speedup for a restricted-Hamming-weight version of Simon's problem, in which the hidden string $b$ is promised to satisfy $\text{HW}(b)\le w$ for a Hamming-weight cutoff $w$, on present-day superconducting quantum processors. We introduce a hardware-aware compilation strategy that reduces the quantum part of each Simon query circuit to constant depth. The resulting compiled circuits have $O(1)$ depth, require only linear nearest-neighbor connectivity, map directly onto common device layouts, and avoid additional routing and SWAP overhead. Implemented on IBM's $156$-qubit Boston and $120$-qubit Miami processors, these circuits achieve sufficient fidelity to exhibit algorithmic quantum speedup without error suppression. Using the number-of-queries-to-solution (NTS) metric, we observe exponential speedup over the classical lower-bound benchmark for all restricted-Hamming-weight cutoffs $w\ge 4$ on Boston and across low-to-intermediate Hamming-weight cutoffs on Miami; at higher Hamming-weight cutoffs on Miami, we still observe polynomial speedup. The same construction also enables unrestricted instances of Simon's problem, corresponding to $w=n$ for problem size $n$, over the finite problem-size ranges for which our NTS computation is feasible; in this regime, the observed scaling advantage is not limited to the restricted-Hamming-weight setting. These results show that careful hardware-aware compilation can make quantum speedup experimentally accessible for a canonical hidden-subgroup problem in the NISQ regime.

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arXiv2026

Logical error estimation from syndrome data of surface-code experiments

Decoders for quantum error correction (QEC) experiments rely on detector error models (DEMs), which encode, for each error, its probability and the detectors and logical observables it flips. Here we show that estimating DEM event probabilities from experimental syndromes is feasible, avoids independent device benchmarking, and produces useful decoder priors for estimating and reducing decoded logical error probabilities. We evaluate our methods using open-source data from surface-code memory experiments performed on Google's Willow chip, and we carry out analogous surface-code experiments on IBM's \texttt{ibm\_miami} processor. Despite the different physical error scales of the Google and IBM devices, in both cases our estimated DEMs improve logical error probabilities relative to baseline device-informed DEMs, typically at the $5\%-10\%$ level and with larger gains in some IBM cases, without additional calibration circuits, decoder fine-tuning, or supervised fitting to logical outcomes.

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arXiv2026

Universal Hamiltonian control in a planar trimon circuit

Multimode circuits provide an avenue for flexible control of single and multi-qubit gates. In this work we implement a multimode circuit known as a trimon integrated in a planar geometry. The trimon features three transmon-like modes with strong all-to-all $ZZ$ coupling. We demonstrate high fidelity operations on the trimon, achieving flexible control of its rich state space. This includes qubit rotations conditioned on one or both other qubits, unconditional single-qubit rotations, and both excitation-conserving and double-excitation two-qubit entangling gates. Through multi-tone driving we are able to implement all 16 two-qubit Pauli operators in the two-qubit space. We further demonstrate using the trimon as a qudit with up to 8 states and higher coherence than typical transmon-based implementations. Our results show a compact, highly controllable device that can potentially replace transmons in standard superconducting processor architectures.

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arXiv2026

Analog-Digital Quantum Computing with Quantum Annealing Processors

Quantum annealing processors typically control qubits in unison, attenuating quantum fluctuations uniformly until the applied system Hamiltonian is diagonal in the computational basis. This simplifies control requirements, allowing annealing QPUs to scale to much larger sizes than gate-based systems, but constraining the class of available operations. Here we expand the class by performing analog-digital quantum computing in a highly-multiplexed, superconducting quantum annealing processor. This involves evolution under a fixed many-body Hamiltonian that, in the weak-coupling regime, is well-described by an effective XY model, together with arbitrary-basis initialization and measurement via auxiliary qubits. Operationally, this is equivalent to implementing single-qubit gates at the beginning and end of an analog quantum evolution. We demonstrate this capability with several foundational applications: single-qubit and two-qubit coherent oscillations with varying initialization and measurement bases, a multi-qubit quantum walk with fermionic dispersion in line with theory, and Anderson localization in a disordered chain. These experiments open the door to a wide range of new possibilities in quantum computation and simulation, greatly expanding the applications of commercially available quantum annealing processors.

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arXiv2026

Universal Weakly Fault-Tolerant Quantum Computation via Code Switching in the [[8,3,2]] Code

Code-switching offers a route to universal, fault-tolerant quantum computation by circumventing the limitation implied by the Eastin-Knill theorem against a universal transversal gate set within a single quantum code. Here, we present a fault-tolerant code-switching protocol between two versions of the $[[8, 3, 2]]$ code. One version supports weakly fault-tolerant single-qubit Clifford gates, while the other supports a logical $\overline{\mathrm{CCZ}}$ gate via transversal $T/T^\dagger$ together with logical $\overline{\mathrm{CZ}}$, $\overline{\mathrm{CNOT}}$, and $\overline{\mathrm{SWAP}}$ gates. Because both codes have distance 2, the protocol operates in a postselected, error-detecting regime: single faults lead to detectable outcomes, and accepted runs exhibit quadratic suppression of logical error rates. This yields a universal scheme for postselected fault-tolerant computation. We validate the protocol numerically through simulations of state preparation, code switching, and a three-logical-qubit implementation of Grover's search.

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arXiv2025

Surface code scaling on heavy-hex superconducting quantum processors

Demonstrating subthreshold scaling of a surface-code quantum memory on hardware whose native connectivity does not match the code remains a central challenge. We address this on IBM heavy-hex superconducting processors by co-designing the code embedding and control: a depth-minimizing SWAP-based "fold-unfold" embedding that uses bridge ancillas, together with robust, gap-aware dynamical decoupling (DD). On Heron-generation devices we perform anisotropic scaling from a uniform distance 3 code to anisotropic distance (dx,dz) = (3,5) and (5,3) codes. We find that increasing dz (dx) improves the protection of Z-basis (X-basis) logical states across multiple quantum error correction cycles. Even if global subthreshold code scaling for arbitrary logical initial states is not yet achieved, we argue that it is within reach with minor hardware improvements. We show that DD plays a major role: it suppresses coherent ZZ crosstalk and non-Markovian dephasing that accumulate during idle gaps on heavy-hex layouts, and it eliminates spurious subthreshold claims that arise when scaled codes without DD are compared against smaller codes with DD. To quantify performance, we derive an entanglement fidelity metric that is computed directly from X- and Z-basis logical-error data and provides per-cycle, SPAM-aware bounds. The entanglement fidelity metric reveals that widely used single-parameter fits used to compute suppression factors can mischaracterize or obscure code performance when their assumptions are violated; we identify the strong assumptions of stationarity, unitality, and negligible logical SPAM required for those fits to be valid and show that they do not hold for our data. Our results establish a concrete path to robust tests of subthreshold surface-code scaling under biased, non-Markovian noise by integrating QEC with optimized DD on non-native architectures.

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arXiv2025

Real-time Sign-Problem-Suppressed Quantum Monte Carlo Algorithm For Noisy Quantum Circuit Simulations

We present a real-time quantum Monte Carlo algorithm that simulates the dynamics of open quantum systems by stochastically compressing and evolving the density matrix under both Markovian and non-Markovian master equations. Our algorithm uses population dynamics to continuously suppress the sign problem, preventing its accumulation throughout the evolution. We apply it to a variety of quantum circuits and demonstrate significant speedups over state-of-art quantum trajectory methods and convergence to exact solutions even in non-Markovian regimes where trajectory methods fail. Our approach improves the efficiency of classical simulation of gate-based quantum computing, quantum annealing, and general open system dynamics.

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arXiv2025

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

In the absence of fault tolerant quantum error correction for analog, Hamiltonian quantum computation, error suppression via energy penalties is an effective alternative. We construct families of distance-$2$ stabilizer subsystem codes we call ``trapezoid codes'', that are tailored for energy-penalty schemes. We identify a family of codes achieving the maximum code rate, and by slightly relaxing this constraint, uncover a broader range of codes with enhanced physical locality, thus increasing their practical applicability. Additionally, we provide an algorithm to map the required qubit connectivity graph into graphs compatible with the locality constraints of quantum hardware. Finally, we provide a systematic framework to evaluate the performance of these codes in terms of code rate, physical locality, graph properties, and penalty gap, enabling an informed selection of error-suppression codes for specific quantum computing applications. We identify the $[[4k+2,2k,g,2]]$ family of subsystem codes as optimal in terms of code rate and penalty gap scaling.

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arXiv2025

A Fundamental Bound for Robust Quantum Gate Control

We derive a universal performance limit for coherent quantum control in the presence of modeled and unmodeled uncertainties. For any target unitary $W$ that is implementable in the absence of error, we prove that the worst-case (and hence the average) gate fidelity obeys the lower bound $F \ge \Flb\bigl(\tf \Omeff\bigr)$, where $\tf$ is the gate duration and $\Omeff$ is a single frequency-like measure that aggregates \emph{all} bounded uncertainty sources, e.g., coherent control imperfections, unknown couplings, and residual environment interactions, without assuming an initially factorizable system-bath state or a completely positive map. The bound is obtained by combining an interaction-picture averaging method with a Bellman-Gronwall inequality and holds for any finite-norm Hamiltonian decomposition. Hence it applies equally to qubits, multi-level qudits, and ancilla-assisted operations. Because $\Flb$ depends only on the dimensionless product $\tf\Omeff$, it yields a device-independent metric that certifies whether a given hardware platform can, in principle, reach a specified fault-tolerance threshold, and also sets a quantitative target for robust-control synthesis and system identification.

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arXiv2025

Demonstration of High-Fidelity Entangled Logical Qubits using Transmons

Quantum error correction (QEC) codes are necessary to fault-tolerantly operate quantum computers. However, every such code is inherently limited by its inability to detect logical errors. Here, we propose and implement a method that leverages dynamical decoupling (DD) to drastically suppress logical errors. The key to achieving this is to use the logical operators of the QEC code as DD pulses, which we refer to as logical dynamical decoupling (LDD). The resulting hybrid QEC-LDD strategy is in principle capable of handling arbitrary weight errors. We test QEC-LDD using IBM transmon devices and the [[4,2,2]] code, demonstrating performance that significantly exceeds the capabilities of using either this code or DD in isolation. We present a method that allows for the detection of logical errors affecting logically encoded Bell states, which, in this case, arise primarily from crosstalk among physical qubits. Building on this, we experimentally demonstrate high-fidelity entangled logical qubits.

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arXiv2025

Bias-tailored single-shot quantum LDPC codes

Quantum hardware rarely suffers equal amounts of bit-flip ($X$) and phase-flip ($Z$) errors; one type is often much more common than the other. A code that is ``bias-tailored'' can exploit this imbalance, lowering the fault-tolerance overhead. A complementary idea, called "single-shot" error correction, aims to recover from data errors and noisy measurements in a single round of stabilizer readout, avoiding slow repetition cycles. In this work, we combine these two ideas and build a hierarchy of new quantum codes. The full construction starts from the syndrome-encoded hypergraph product code and then tailors it to the dominant error type. The resulting code keeps the single-shot guarantee for every noise model while boosting the threshold whenever $X$ and $Z$ errors are asymmetric. By removing carefully chosen blocks of stabilizers we obtain two trimmed variants. The first, called the simplified code, cuts the physical-qubit count by $1/6$ and halves the number of stabilizer measurements, yet its minimum distance grows quadratically compared to the standard design and its biased noise threshold is unchanged. The second, called the reduced code, achieves the same hardware savings but trades away single-shot protection for purely $X$ or purely $Z$ noise; instead it remains single-shot under balanced, or depolarizing, noise. In settings where strongly biased noise is likely, either trimmed code offers a less resource-intensive alternative to the full construction. As a concrete illustration, we lift the two-dimensional XZZX surface code to a three-dimensional cubic lattice and show that this ``3D XZZX'' code is an explicit member of the simplified family. Taken together, these bias-tailored single-shot codes provide an adjustable set of code design alternatives, allowing tradeoffs between hardware overhead and noise types.

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arXiv2025

Virtual Z gates and symmetric gate compilation

The virtual Z gate has been established as an important tool for performing quantum gates on various platforms, including but not limited to superconducting systems. Many such platforms offer a limited set of calibrated gates and compile all other gates using combinations of X-type and virtual Z gates. Here, we show that the method of compilation has important consequences in an open quantum system setting. Specifically, we experimentally demonstrate that it is crucial to choose a compilation that is symmetric with respect to virtual Z rotations. An important example is dynamical decoupling (DD) sequences, where improper gate decomposition can result in unintended effects such as the implementation of the wrong sequence. Our findings indicate that in many cases the performance of DD is adversely affected by the incorrect use of virtual Z gates, compounding other coherent pulse errors. This holds even for DD sequences designed to be robust against systematic control errors. In addition, we identify another source of coherent errors: interference between consecutive pulses that follow each other too closely. This work provides insights into improving general quantum gate performance and optimizing DD sequences in particular.

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arXiv2025

Benchmarking quantum gates and circuits

Accurate noise characterization in quantum gates and circuits is vital for the development of reliable quantum simulations for chemically relevant systems and fault-tolerant quantum computing. This paper reviews a variety of key benchmarking techniques, including Randomized Benchmarking, Quantum Process Tomography, Gate Set Tomography, Process Fidelity Estimation, Direct Fidelity Estimation, and Cross-Entropy Benchmarking. We evaluate each method's complexities, the resources they require, and their effectiveness in addressing coherent, incoherent, and state preparation and measurement (SPAM) errors. Furthermore, we introduce deterministic benchmarking (DB), a novel protocol that minimizes the number of experimental runs, exhibits resilience to SPAM errors, and effectively characterizes both coherent and incoherent errors. The implementation of DB is experimentally validated using a superconducting transmon qubit, and the results are substantiated with a simple analytical model and master equation simulations. With the addition of DB to the toolkit of available benchmarking methods, this article serves as a practical guide for choosing and applying benchmarking protocols to advance quantum computing technologies.

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arXiv2025

Efficient Chromatic-Number-Based Multi-Qubit Decoherence and Crosstalk Suppression

The performance of quantum computers is hindered by decoherence and crosstalk, which cause errors and limit the ability to perform long computations. Dynamical decoupling is a technique that alleviates these issues by applying carefully timed pulses to individual qubits, effectively suppressing unwanted interactions. However, as quantum devices grow in size, it becomes increasingly important to minimize the time required to implement dynamical decoupling across the entire system. Here, we present "Chromatic-Hadamard Dynamical Decoupling" (CHaDD), an approach that efficiently schedules dynamical decoupling pulses for quantum devices with arbitrary qubit connectivity. By leveraging Hadamard matrices, CHaDD achieves a circuit depth that scales linearly with the chromatic number of the connectivity graph for general two-qubit interactions, assuming instantaneous pulses. This includes ZZ crosstalk, which is prevalent in superconducting QPUs. CHaDD's scaling represents an exponential improvement over all previous multi-qubit decoupling schemes for devices with connectivity graphs whose chromatic number grows at most polylogarithmically with the number of qubits. For graphs with a constant chromatic number, CHaDD's scaling is independent of the number of qubits. We report on experiments we have conducted using IBM QPUs that confirm the advantage conferred by CHaDD. Our results suggest that CHaDD can become a useful tool for enhancing the performance and scalability of quantum computers by efficiently suppressing decoherence and crosstalk across large qubit arrays.

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arXiv2024

Beating the Ramsey limit on sensing with deterministic qubit control

Quantum sensors promise revolutionary advances in medical imaging, energy production, mass detection, geodesy, foundational physics research, and a host of other fields. In many sensors, the signal takes the form of a changing qubit frequency, which is detected with an interference measurement. Unfortunately, environmental noise decoheres the qubit state, reducing signal-to-noise ratio (SNR). Here we introduce a protocol for enhancing the sensitivity of a measurement of a qubit's frequency in the presence of decoherence. We use a continuous drive to stabilize one component of the qubit's Bloch vector, enhancing the effect of a small static frequency shift. We demonstrate our protocol on a superconducting qubit, enhancing SNR per measurement shot by 1.65$\times$ and SNR per qubit evolution time by 1.09$\times$ compared to standard Ramsey interferometry. We explore the protocol theoretically and numerically, finding maximum enhancements of 1.96$\times$ and 1.18$\times$, respectively. We also show that the protocol is robust to parameter miscalibrations. Our protocol provides an unconditional enhancement in signal-to-noise ratio compared to standard Ramsey interferometry. It requires no feedback and no extra control or measurement resources, and can be immediately applied in a wide variety of quantum computing and quantum sensor technologies to enhance their sensitivities.

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