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Journal of Physics D Applied Physics

Thermal noise in a solid state quantum computer

Cameron J. Wellard, Lloyd C. L. Hollenberg

Published Oct 10, 2002• 10 citations
Publisher

Abstract

The Kane proposal for the construction of a solid state quantum computer calls for the placement of a metallic A-gate above each nuclear qubit. Voltage biases applied to these A-gates are to be used to control the evolution of the qubits. In this paper, we consider the decohering effect of thermal fluctuations, the so-called Johnson noise, in the A-gate biases, on the average evolution of qubits undergoing single qubit rotations, as well as those that are not undergoing any operation at all. We find that although the errors introduced are of a different nature for each case, phase errors for the static qubits and both phase and bit-flip errors for qubits undergoing operations, the net error probability is similar for both, and low enough when compared to the timescale of single qubit operations for them to be corrected efficiently.

DOI
10.1088/0022-3727/35/20/306

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The Kane proposal for the construction of a solid state quantum computer calls for the placement of a metallic A-gate above each nuclear qubit. Voltage biases applied to these A-gates are to be used to control the evolution of the qubits. In this paper, we consider the decohering effect of thermal fluctuations, the so-called Johnson noise, in the A-gate biases, on the average evolution of qubits undergoing single qubit rotations, as well as those that are not undergoing any operation at all. We find that although the errors introduced are of a different nature for each case, phase errors for the static qubits and both phase and bit-flip errors for qubits undergoing operations, the net error probability is similar for both, and low enough when compared to the timescale of single qubit operations for them to be corrected efficiently.
Abstract : A key step in the construction of quantum computing technologies is the identification and elimination of unwanted sources of noise and its resulting quantum decoherence. In solid state devices, one important source of noise is the fluctuating electric and magnetic fields that come from the device elements themselves. The ultimate source of these fluctuations is the random electric currents that are strongest in the metallic electrodes and leads. This random motion has both thermal and quantum components, though in most devices presently under investigation, the thermal part dominates. In the past, this important physical effect has generally been modeled by picturing the device using an equivalent RC circuit and applying the Nyquist theorem to this circuit. This approach has limitations, since it depends on global quantities, rather than on the detailed geometry and the local electromagnetic properties of the components. Our aim in this research project was to compute the effect from first principles. We considered the underlying physical law (quantum electrodynamics) governing the devices in question. Given the position- and frequency-dependent dielectric function, the electromagnetic noise spectrum can be calculated, and the decohering effect can be deduced. Semiconducting quantum dot and superconducting flux qubits were investigated.
Quantum computers offer a route to outperform classical methods in tasks such as molecular simulation, motivating hybrid algorithms like the Variational Quantum Eigensolver (VQE) for near-term devices. Silicon spin qubits are a promising platform for scalable quantum computation, but their performance is limited by hardware imperfections -- most notably charge-noise-induced potential fluctuations and static miscalibration of gate-electrode voltages -- which degrade quantum gate fidelities and, ultimately, algorithmic accuracy. Here we develop a hardware-algorithm co-simulation framework for silicon quantum-dot processors that links 3D electrostatics to effective ggg-factors and exchange couplings, and propagates voltage-level noise through realistic control pulses. Using VQE for H2\mathrm{H}_2H2​ ground-state energy estimation as a circuit-level testbed, we study both static scaling/offset errors on the gate-electrode voltages and stochastic fluctuations modeled as random-telegraph noise with tunable amplitudes and switching times. At the gate level, we show that exchange-based two-qubit gates are roughly an order of magnitude more sensitive to these types of noise than ESR-driven single-qubit rotations. Quantum process tomography and Kraus-operator analysis further distinguish coherent and incoherent contributions and quantify the fraction of error that is, in principle, correctable by a compensating unitary. Embedding these noise models into the VQE circuit, we identify regimes of miscalibration strength and noise switching time compatible with chemically accurate energy estimates, and discuss how statistical post-processing based on the full distribution of noisy energy estimates could further improve accuracy.
Abstract : This thesis addresses the origin and effect of noise and fluctuations in quantum devices that find applications in quantum information processing. In the first half of the thesis, we consider a phenomenological model of the noise and study its effect on the fidelity of quantum measurements and operations that are essential for quantum computing. We focus primarily on quantum gate operations in phase qubits, detection of microwave photons and the measurement of the Berry curvature. Specifically, we examine the effect of the Ohmic noise on optimally controlled flux-biased phase qubits for one- and two-quadrature microwave pulses and demonstrate that twoquadrature pulses with fixed driving frequency are as robust as variable driving frequency, in the presence of environment. Next, we present a model to analyze the quantum efficiency of a microwave photon detector based on a current-biased Josephson junction and study the effect of decoherence on the detection efficiency of the detector. We also present alternative set-ups for microwave photon detection and provide a systematic method to compute the power absorbed by the detector. We then consider the effect of decoherence on the Berry curvature measurement, which employs a novel non-adiabatic protocol, and show that the curvature is immune to decoherence. In the second half of the thesis, we go beyond the phenomenological models of the noises and perform a detailed study of the microscopic description of the Johnson noise. Here we focus primarily on quantum dot devices. We present a formalism to compute relaxation rates in charge and spin qubits due to evanescent wave Johnson noise (EWJN) from the metallic gates that are in proximity to quantum dots. The EWJN is analyzed for the metallic gates that are characterized by both local and nonlocal dielectric response functions.
Qubits with strongly biased noise, in which phase-flip errors are orders of magnitude more frequent than bit-flips, arise both naturally, as in electron and nuclear spins, and by engineering, as in stabilized cat qubits. This noise structure holds the promise of reducing the daunting hardware overhead of fault-tolerant quantum computing, but exploiting it requires physical operations that do not convert frequent phase-flips into rare bit-flips. In this review, we analyze the most prominent fault-tolerant protocols for biased-noise qubits, organized according to the available set of such bias-preserving operations. When this set is restricted to the CZ gate together with preparation and measurement in the X basis, we show that the complexity of the required syndrome extraction gadgets essentially cancels the benefit of the noise bias: at experimentally relevant error rates, one may as well ignore the bias and rely on standard error correction designed for depolarizing noise. The situation changes drastically when a bias-preserving CX gate is available: the hierarchy of errors can then be reflected in the structure of the code, with frequent phase-flips corrected by a dedicated high-threshold code and rare bit-flips by concatenation with a high-rate code. The same hierarchy also enables hardware-efficient preparation of magic states. Finally, as a bias-preserving CX is forbidden in naturally biased platforms and challenging in engineered ones, we present a measurement-based architecture in which a high-fidelity quantum non-demolition readout of multi-qubit Pauli Z operators takes its place, extending these overhead reductions to a much broader range of physical platforms.
Abstract Quantum computers offer a route to outperform classical methods in tasks such as molecular simulation, motivating hybrid algorithms like the variational quantum eigensolver (VQE) for near-term devices. Silicon spin qubits are a promising platform for scalable quantum computation, but their performance is limited by hardware imperfections—most notably charge-noise–induced potential fluctuations and static miscalibration of gate-electrode voltages—which degrade quantum gate fidelities and, ultimately, algorithmic accuracy. Here we develop a hardware–algorithm co-simulation framework for silicon quantum-dot processors that links 3D electrostatics to effective g -factors and exchange couplings, and propagates voltage-level noise through realistic control pulses. Using VQE for H 2 ground-state energy estimation as a circuit-level testbed, we study both static scaling/offset errors on the gate-electrode voltages and stochastic fluctuations modeled as random-telegraph noise with tunable amplitudes and switching times. At the gate level, we show that exchange-based two-qubit gates are roughly an order of magnitude more sensitive to these types of noise than ESR-driven single-qubit rotations. Quantum process tomography and Kraus-operator analysis further distinguish coherent and incoherent contributions and quantify the fraction of error that is, in principle, correctable by a compensating unitary. Embedding these noise models into the VQE circuit, we identify regimes of miscalibration strength and noise switching time compatible with chemically accurate energy estimates, and discuss how statistical post-processing based on the full distribution of noisy energy estimates could further improve accuracy.