arXiv subjects

B. M. Terhal

Publications and source records attributed to B. M. Terhal.

16 recordsLinked to original sources

arXiv2026

Coherent versus stochastic error injection on a repetition-code logical qubit in superconducting hardware

The performance of quantum error correction (QEC) codes is limited by the underlying physical noise. Theoretical studies show that coherent and stochastic noise have different effects when performing QEC with either surface or repetition codes. We use the bitflip repetition code, realized in a transmon quantum processor, as a testbed to experimentally study the impact of injecting coherent versus stochastic errors on the logical performance. We adapt a scalable free-fermion simulator to simulate the experiments and we modify a subset sampling technique to efficiently sample stochastic noise in the quantum circuit. In the experiment, we do not observe the difference in logical fidelity predicted by simulation for either the distance-3 or distance-5 repetition codes. We hypothesize that this discrepancy could be explained by small drifts in qubit frequencies, which introduce phase-coherent noise that `stochastifies' the injected coherent errors. Our work contributes to advancing an understanding of how coherent errors affect experimental QEC.

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arXiv2023

All-microwave leakage reduction units for quantum error correction with superconducting transmon qubits

Minimizing leakage from computational states is a challenge when using many-level systems like superconducting quantum circuits as qubits. We realize and extend the quantum-hardware-efficient, all-microwave leakage reduction unit (LRU) for transmons in a circuit QED architecture proposed by Battistel et al. This LRU effectively reduces leakage in the second- and third-excited transmon states with up to $99\% $ efficacy in $220~\mathrm{ns}$, with minimum impact on the qubit subspace. As a first application in the context of quantum error correction, we demonstrate the ability of multiple simultaneous LRUs to reduce the error detection rate and to suppress leakage buildup within $1\%$ in data and ancilla qubits over 50 cycles of a weight-2 parity measurement.

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arXiv2022

Phase flip code with semiconductor spin qubits

The fault-tolerant operation of logical qubits is an important requirement for realizing a universal quantum computer. Spin qubits based on quantum dots have great potential to be scaled to large numbers because of their compatibility with standard semiconductor manufacturing. Here, we show that a quantum error correction code can be implemented using a four-qubit array in germanium. We demonstrate a resonant SWAP gate and by combining controlled-Z and controlled-$\text{S}^{-1}$ gates we construct a Toffoli-like three-qubit gate. We execute a two-qubit phase flip code and find that we can preserve the state of the data qubit by applying a refocusing pulse to the ancilla qubit. In addition, we implement a phase flip code on three qubits, making use of a Toffoli-like gate for the final correction step. Both the quality and quantity of the qubits will require significant improvement to achieve fault-tolerance. However, the capability to implement quantum error correction codes enables co-design development of quantum hardware and software, where codes tailored to the properties of spin qubits and advances in fabrication and operation can now come together to scale semiconductor quantum technology toward universal quantum computers.

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arXiv2021

Fault-tolerant operation of a logical qubit in a diamond quantum processor

Solid-state spin qubits are a promising platform for quantum computation and quantum networks. Recent experiments have demonstrated high-quality control over multi-qubit systems, elementary quantum algorithms and non-fault-tolerant error correction. Large-scale systems will require using error-corrected logical qubits that are operated fault-tolerantly, so that reliable computation is possible despite noisy operations. Overcoming imperfections in this way remains a major outstanding challenge for quantum science. Here, we demonstrate fault-tolerant operations on a logical qubit using spin qubits in diamond. Our approach is based on the 5-qubit code with a recently discovered flag protocol that enables fault-tolerance using a total of seven qubits. We encode the logical qubit using a novel protocol based on repeated multi-qubit measurements and show that it outperforms non-fault-tolerant encoding schemes. We then fault-tolerantly manipulate the logical qubit through a complete set of single-qubit Clifford gates. Finally, we demonstrate flagged stabilizer measurements with real-time processing of the outcomes. Such measurements are a primitive for fault-tolerant quantum error correction. While future improvements in fidelity and the number of qubits will be required, our realization of fault-tolerant protocols on the logical-qubit level is a key step towards large-scale quantum information processing based on solid-state spins.

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arXiv2021

Logical-qubit operations in an error-detecting surface code

We realize a suite of logical operations on a distance-two logical qubit stabilized using repeated error detection cycles. Logical operations include initialization into arbitrary states, measurement in the cardinal bases of the Bloch sphere, and a universal set of single-qubit gates. For each type of operation, we observe higher performance for fault-tolerant variants over non-fault-tolerant variants, and quantify the difference through detailed characterization. In particular, we demonstrate process tomography of logical gates, using the notion of a logical Pauli transfer matrix. This integration of high-fidelity logical operations with a scalable scheme for repeated stabilization is a milestone on the road to quantum error correction with higher-distance superconducting surface codes.

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arXiv2020

Leakage detection for a transmon-based surface code

Leakage outside of the qubit computational subspace, present in many leading experimental platforms, constitutes a threatening error for quantum error correction (QEC) for qubits. We develop a leakage-detection scheme via Hidden Markov models (HMMs) for transmon-based implementations of the surface code. By performing realistic density-matrix simulations of the distance-3 surface code (Surface-17), we observe that leakage is sharply projected and leads to an increase in the surface-code defect probability of neighboring stabilizers. Together with the analog readout of the ancilla qubits, this increase enables the accurate detection of the time and location of leakage. We restore the logical error rate below the memory break-even point by post-selecting out leakage, discarding about 47% of the data. Leakage detection via HMMs opens the prospect for near-term QEC demonstrations, targeted leakage reduction and leakage-aware decoding and is applicable to other experimental platforms.

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arXiv2019

A fast, low-leakage, high-fidelity two-qubit gate for a programmable superconducting quantum computer

A common approach to realize conditional-phase (CZ) gates in transmon qubits relies on flux control of the qubit frequency to make computational states interact with non-computational ones using a fast-adiabatic trajectory to minimize leakage. We develop a bipolar flux-pulsing method with two key advantages over the traditional unipolar variant. First, the action of the bipolar pulse is robust to long-timescale linear-dynamical distortions in the flux-control line, facilitating tuneup and ensuring atomic repeatability. Second, the flux symmetry of the transmon Hamiltonian makes the conditional phase and the single-qubit phase of the pulsed qubit first-order insensitive to low-frequency flux noise, increasing fidelity. By harnessing destructive interference to minimize leakage, the bipolar pulse can approach the speed limit set by the exchange coupling. We demonstrate a repeatable, high-fidelity ($99.1\%$), low-leakage ($0.1\%$), and fast ($40~\mathrm{ns}$) CZ gate in a circuit QED quantum processor. Detailed numerical simulations with excellent match to experiment show that leakage is dominated by remaining short-timescale distortions and fidelity is limited by high-frequency flux noise.

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arXiv2018

Quantum phase estimation of multiple eigenvalues for small-scale (noisy) experiments

Quantum phase estimation is the workhorse behind any quantum algorithm and a promising method for determining ground state energies of strongly correlated quantum systems. Low-cost quantum phase estimation techniques make use of circuits which only use a single ancilla qubit, requiring classical post-processing to extract eigenvalue details of the system. We investigate choices for phase estimation for a unitary matrix with low-depth noise-free or noisy circuits, varying both the phase estimation circuits themselves as well as the classical post-processing to determine the eigenvalue phases. We work in the scenario when the input state is not an eigenstate of the unitary matrix. We develop a new post-processing technique to extract eigenvalues from phase estimation data based on a classical time-series (or frequency) analysis and contrast this to an analysis via Bayesian methods. We calculate the variance in estimating single eigenvalues via the time-series analysis analytically, finding that it scales to first order in the number of experiments performed, and to first or second order (depending on the experiment design) in the circuit depth. Numerical simulations confirm this scaling for both estimators. We attempt to compensate for the noise with both classical post-processing techniques, finding good results in the presence of depolarizing noise, but smaller improvements in $9$-qubit circuit-level simulations of superconducting qubits aimed at resolving the electronic ground-state of a $H_4$-molecule.

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arXiv2015

Encoding a Qubit into a Cavity Mode in Circuit-QED using Phase Estimation

Gottesman, Kitaev and Preskill have formulated a way of encoding a qubit into an oscillator such that the qubit is protected against small shifts (translations) in phase space. The idea underlying this encoding is that error processes of low rate can be expanded into small shift errors. The qubit space is defined as an eigenspace of two mutually commuting displacement operators $S_p$ and $S_q$ which act as large shifts/translations in phase space. We propose and analyze the approximate creation of these qubit states by coupling the oscillator to a sequence of ancilla qubits. This preparation of the states uses the idea of phase estimation where the phase of the displacement operator, say $S_p$, is approximately determined. We consider several possible forms of phase estimation. We analyze the performance of repeated and adapative phase estimation as the simplest and experimentally most viable schemes given a realistic upper-limit on the number of photons in the oscillator. We propose a detailed physical implementation of this protocol using the dispersive coupling between a transmon ancilla qubit and a cavity mode in circuit-QED. We provide an estimate that in a current experimental set-up one can prepare a good code state from a squeezed vacuum state using $8$ rounds of adapative phase estimation, lasting in total about $4 μ$ sec., with $94\%$ (heralded) chance of success.

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arXiv2014

Dispersive Qubit Measurement by Interferometry with Parametric Amplifiers

We perform a detailed analysis of how an amplified interferometer can be used to enhance the quality of a dispersive qubit measurement, such as one performed on a superconducting transmon qubit, using homodyne detection on an amplified microwave signal. Our modeling makes a realistic assessment of what is possible in current circuit-QED experiments; in particular, we take into account the frequency-dependence of the qubit-induced phase shift for short microwaves pulses. We compare the possible signal-to-noise ratios obtainable with (single-mode) SU(1,1) interferometers with the current coherent measurement and find a considerable reduction in measurement error probability in an experimentally-accessible range of parameters.

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arXiv2010

Qubit State Discrimination

We show how one can solve the problem of discriminating between qubit states. We use the quantum state discrimination duality theorem and the Bloch sphere representation of qubits which allows for an easy geometric and analytical representation of the optimal guessing strategies.

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arXiv2004

Security Trade-offs in Ancilla-Free Quantum Bit Commitment in the Presence of Superselection Rules

Security trade-offs have been established for one-way bit commitment in quant-ph/0106019. We study this trade-off in two superselection settings. We show that for an `abelian' superselection rule (exemplified by particle conservation) the standard trade-off between sealing and binding properties still holds. For the non-abelian case (exemplified by angular momentum conservation) the security trade-off can be more subtle, which we illustrate by showing that if the bit-commitment is forced to be ancilla-free an asymptotically secure quantum bit commitment is possible.

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arXiv1999

Unextendible Product Bases and Bound Entanglement

An unextendible product basis (UPB) for a multipartite quantum system is an incomplete orthogonal product basis whose complementary subspace contains no product state. We give examples of UPBs, and show that the uniform mixed state over the subspace complementary to any UPB is a bound entangled state. We exhibit a tripartite 2x2x2 UPB whose complementary mixed state has tripartite entanglement but no bipartite entanglement, i.e. all three corresponding 2x4 bipartite mixed states are unentangled. We show that members of a UPB are not perfectly distinguishable by local POVMs and classical communication.

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arXiv1998

Simulating quantum operations with mixed environments

We study the physical resources required to implement general quantum operations, and provide new bounds on the minimum possible size which an environment must be in order to perform certain quantum operations. We prove that contrary to a previous conjecture, not all quantum operations on a single-qubit can be implemented with a single-qubit environment, even if that environment is initially prepared in a mixed state. We show that a mixed single-qutrit environment is sufficient to implement a special class of operations, the generalized depolarizing channels.

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arXiv1998

The quantum capacity is properly defined without encodings

We show that no source encoding is needed in the definition of the capacity of a quantum channel for carrying quantum information. This allows us to use the coherent information maximized over all sources and and block sizes, but not encodings, to bound the quantum capacity. We perform an explicit calculation of this maximum coherent information for the quantum erasure channel and apply the bound in order find the erasure channel's capacity without relying on an unproven assumption as in an earlier paper.

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arXiv1997

Single quantum querying of a database

We present a class of fast quantum algorithms, based on Bernstein and Vazirani's parity problem, that retrieve the entire contents of a quantum database $Y$ in a single query. The class includes binary search problems and coin-weighing problems. Our methods far exceed the efficiency of classical algorithms which are bounded by the classical information-theoretic bound. We show the connection between classical algorithms based on several compression codes and our quantum-mechanical method.

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