Qubit Measurement Research Articles

Coherent qubit measurement in cavity-transmon quantum systems

A measurement of the time between quantum jumps implies the capability to measure the next jump. During the time between jumps the quantum system is not evolving in a closed or unitary manner. While the wave function maintains phase coherence it evolves according to a non-Hermitian effective Hamiltonian. So under null measurement the timing of the next quantum jump can change by very many orders of magnitude when compared to rates obtained by multiplying lifetimes with occupation probabilities obtained via unitary transformation. The theory developed in 1987 for atomic fluorescence is here extended to transitions in transmon qubits. These systems differ from atoms in that they are read out with a harmonic cavity whose resonance is determined by the state of the qubit. We extend our analysis of atomic fluorescence to this infinite level system by treating the cavity as a quantum system. We find that next photon statistics is highly nonexponential and when implemented will enable faster readout, such as on timescales shorter than the decay time of the cavity. Commonly used heterodyne measurements are applied on timescales longer than the cavity lifetime. The overlap between the next photon theory and the theory of heterodyne measurement which are described according to the stochastic Schr\"odinger equation is elucidated. In the limit of large dispersion the intrinsic error for next jump detection, at short time, tends to zero. Whereas for short-time dyne detection the error remains finite for all values of dispersion.

Measurement incompatibility and quantum advantage in communication

Measurement incompatibility stipulates the existence of quantum measurements that cannot be carried out simultaneously on single systems. We show that the set of input-output probabilities obtained from d-dimensional classical systems assisted with shared randomness is the same as the set obtained from d-dimensional quantum strategies restricted to compatible measurements with shared randomness in any communication scenario. Thus, measurement incompatibility is necessary for quantum advantage in communication, and any quantum advantage (with or without shared randomness) in communication acts as a witness to the incompatibility of the measurements at the receiver's end in a semi-device-independent way. We introduce a class of communication tasks - a general version of random access codes - to witness incompatibility of an arbitrary number of quantum measurements with arbitrary outcomes acting on d-dimensional systems, and provide generic upper bounds on the success metric of these tasks for compatible measurements. We identify all sets of three incompatible rank-one projective qubit measurements that random access codes can witness. Finally, we present the generic relationship between different sets of probability distributions - classical, quantum with or without shared randomness, and quantum restricted to compatible measurements with or without shared randomness - produced in communication scenarios.

Coherence-limited digital control of a superconducting qubit using a Josephson pulse generator at 3 K

Compared to traditional semiconductor control electronics (TSCE) located at room temperature, cryogenic single flux quantum (SFQ) electronics can provide qubit measurement and control alternatives that address critical issues related to scalability of cryogenic quantum processors. Single-qubit control and readout have been demonstrated recently using SFQ circuits coupled to superconducting qubits. Experiments where the SFQ electronics are co-located with the qubit have suffered from excess decoherence and loss due to quasiparticle poisoning of the qubit. A previous experiment by our group showed that moving the control electronics to the 3 K stage of the dilution refrigerator avoided this source of decoherence in a high-coherence three-dimensional transmon geometry. In this paper, we also generate the pulses at the 3 K stage but have optimized the qubit design and control lines for scalable two-dimensional transmon devices. We directly compare the qubit lifetime T1, coherence time T2*, and gate fidelity when the qubit is controlled by the Josephson pulse generator (JPG) circuit vs the TSCE setup. We find agreement within the daily fluctuations for T1 and T2*, and agreement within 10% for randomized benchmarking. We also performed interleaved randomized benchmarking on individual JPG gates demonstrating an average error per gate of 0.46% showing good agreement with what is expected based on the qubit coherence and higher-state leakage. These results are an order of magnitude improvement in gate fidelity over our previous work and demonstrate that a Josephson microwave source operated at 3 K is a promising component for scalable qubit control.

The unitary dependence theory for characterizing quantum circuits and states

Most existing quantum algorithms are discovered accidentally or adapted from classical algorithms, and there is the need for a systematic theory to understand and design quantum circuits. Here we develop a unitary dependence theory to characterize the behaviors of quantum circuits and states in terms of how quantum gates manipulate qubits and determine their measurement probabilities. Compared to the conventional entanglement description of quantum circuits and states, the unitary dependence picture offers more practical information on the measurement and manipulation of qubits, easier generalization to many-qubit systems, and better robustness upon partitioning of the system. The unitary dependence theory can be applied to systematically understand existing quantum circuits and design new quantum algorithms.

Fast high-fidelity parity measurement of spin qubits in quantum dots using modulated pulses

Spin qubits in semiconductor quantum dots are a promising candidate for scalable quantum computation. A key step in quantum error correction with spin qubits is the capability to perform high-fidelity parity measurement much faster than the coherence time and to generate entanglement deterministically. Here we propose a parity measurement scheme for two spin qubits by modulated pulses, using a superconducting resonator as a detector. We show that the distinction between spin-parity states can be achieved with a high fidelity within a short measurement time. The combination of parity measurement and feedback control allows the deterministic preparation of various spin entangled states. In addition, the method can be directly applied to parity measurements and surface codes of multiple spin qubits. These results pave the way for fault-tolerant quantum computation with spin qubits.

Naimark dilations of qubit POVMs and joint measurements

Measurement incompatibility is one of the cornerstones of quantum theory. This phenomenon appears in many forms, of which the concept of non-joint measurability has received considerable attention in the recent years. In order to characterise this non-classical phenomenon, various analytical and numerical methods have been developed. The analytical approaches have mostly concentrated on the qubit case, as well as to scenarios involving sets of measurements with symmetries, such as position and momentum or sets of mutually unbiased bases. The numerical methods can, in principle, decide any finite-dimensional and discrete joint measurability problem, but they naturally have practical limitations in terms of computational power. These methods exclusively start from a given set of measurements and ask whether the set possesses incompatibility. Here, we take a complementary approach by asking which measurements are compatible with a given measurement. It turns out, that this question can be answered in full generality through a minimal Naimark dilation of the given measurement: the set of interest is exactly those measurements that have a block-diagonal representation in such dilation. We demonstrate the use of the technique through various qubit examples, leading to an alternative characterisation of all compatible pairs of binary qubit measurements, which retrieves the celebrated Busch criterion. We further apply the technique to special examples of trinary and continuous qubit measurements.

Saturable Purcell filter for circuit quantum electrodynamics

We consider a typical circuit QED setup where an artificial atom encodes a qubit and is dispersively coupled to a measurement resonator that in turn is coupled to a transmission line. We show theoretically that by placing another artificial atom in this transmission line to act as a filter, the Purcell decay of the qubit into the transmission line is suppressed. When strong control fields are applied in the transmission line, the filter is saturated and effectively switched off. Such a Purcell filtering capability permits both the control and measurement of the qubit using the single transmission line, while maintaining the long coherence time of the qubit in the absence of the control pulses. We show that high fidelity Pauli ${\ensuremath{\sigma}}_{x}$ gates on the qubit can be realized using simple pulse shapes. For devices that already use one transmission line both for control and measurement of the qubit, our paper provides a way to completely filter out the qubit frequency without removing the possibility of controlling the system. Further, combining the proposed filter with frequency multiplexing potentially enables both control and measurement of several qubits using a single Purcell-filtered transmission line. This will enhance the scalability of superconducting quantum processors by decreasing the number of the required transmission lines.

Probing quantum devices with radio-frequency reflectometry

Many important phenomena in quantum devices are dynamic, meaning that they cannot be studied using time-averaged measurements alone. Experiments that measure such transient effects are collectively known as fast readout. One of the most useful techniques in fast electrical readout is radio-frequency reflectometry, which can measure changes in impedance (both resistive and reactive) even when their duration is extremely short, down to a microsecond or less. Examples of reflectometry experiments, some of which have been realized and others so far only proposed, include projective measurements of qubits and Majorana devices for quantum computing, real-time measurements of mechanical motion, and detection of non-equilibrium temperature fluctuations. However, all of these experiments must overcome the central challenge of fast readout: the large mismatch between the typical impedance of quantum devices (set by the resistance quantum) and of transmission lines (set by the impedance of free space). Here, we review the physical principles of radio-frequency reflectometry and its close cousins, measurements of radio-frequency transmission and emission. We explain how to optimize the speed and sensitivity of a radio-frequency measurement and how to incorporate new tools, such as superconducting circuit elements and quantum-limited amplifiers into advanced radio-frequency experiments. Our aim is threefold: to introduce the readers to the technique, to review the advances to date, and to motivate new experiments in fast quantum device dynamics. Our intended audience includes experimentalists in the field of quantum electronics who want to implement radio-frequency experiments or improve them, together with physicists in related fields who want to understand how the most important radio-frequency measurements work.

Anomalous energy exchanges and Wigner-function negativities in a single-qubit gate

Anomalous weak values and the Wigner function's negativity are well-known witnesses of quantum contextuality. We show that these effects occur when analyzing the energetics of a single-qubit gate generated by a resonant coherent field traveling in a waveguide. The buildup of correlations between the qubit and the field is responsible for bounds on the gate fidelity, but also for a nontrivial energy balance recently observed in a superconducting setup. In the experimental scheme, the field is continuously monitored through heterodyne detection and then postselected over the outcomes of a final qubit's measurement. The postselected data can be interpreted as the field's weak values and can show anomalous values in the variation of the field's energy. We model the joint system dynamics with a collision model, gaining access to the qubit-field entangled state at any time. We find an analytical expression of the quasiprobability distribution of the postselected heterodyne signal, i.e., the conditional Husimi-Q function. The latter grants access to all the field's weak values: we use it to obtain that of the field's energy change and display its anomalous behavior. Finally, we derive the field's conditional Wigner function and show that anomalous weak values and Wigner function negativities arise for the same values of the gate's angle.

Noise-resistant quantum state compression readout

Qubit measurement is generally the most error-prone operation that degrades the performance of near-term quantum devices, and the exponential decay of readout fidelity severely impedes the development of large-scale quantum information processing. Given these disadvantages, we present a quantum state readout method, named compression readout, that naturally avoids large multi-qubit measurement errors by compressing the quantum state into a single qubit for measurement. Our method generally outperforms direct measurements in terms of accuracy, and the advantage grows with the system size. Moreover, because only one-qubit measurements are performed, our method requires solely a fine readout calibration on one qubit and is free of correlated measurement error, which drastically diminishes the demand for device calibration. These advantages suggest that our method can immediately boost the readout performance of near-term quantum devices and will greatly benefit the development of large-scale quantum computing.

Measurement-Based Quantum Thermal Machines with Feedback Control

We investigated coupled-qubit-based thermal machines powered by quantum measurements and feedback. We considered two different versions of the machine: (1) a quantum Maxwell's demon, where the coupled-qubit system is connected to a detachable single shared bath, and (2) a measurement-assisted refrigerator, where the coupled-qubit system is in contact with a hot and cold bath. In the quantum Maxwell's demon case, we discuss both discrete and continuous measurements. We found that the power output from a single qubit-based device can be improved by coupling it to the second qubit. We further found that the simultaneous measurement of both qubits can produce higher net heat extraction compared to two setups operated in parallel where only single-qubit measurements are performed. In the refrigerator case, we used continuous measurement and unitary operations to power the coupled-qubit-based refrigerator. We found that the cooling power of a refrigerator operated with swap operations can be enhanced by performing suitable measurements.

Robust certification of unsharp instruments through sequential quantum advantages in a prepare-measure communication game

Communication games are one of the widely used tools that are designed to demonstrate quantum supremacy over classical resources in which two or more parties collaborate to perform an information processing task to achieve the highest success probability of winning the game. We propose a specific two-party communication game in the prepare-measure scenario that relies on an encoding-decoding task of specific information. We first demonstrate that quantum theory outperforms the classical preparation noncontextual theory and the optimal quantum success probability of such a communication game enables the semi-device-independent certification of qubit states and measurements. Further, we consider the sequential sharing of quantum preparation contextuality and show that, at most, two sequential observers can share the quantum advantage. The suboptimal quantum advantages for two sequential observers form an optimal pair which certifies a unique value of the unsharpness parameter of the first observer. Since the practical implementation inevitably introduces noise, we devised a scheme to demonstrate the robust certification of the states and unsharp measurement instruments of both the sequential observers.

Self-testing criteria for preparing-measuring qubit system

Self-testing is the high-level security verification of a claimed quantum device, confirming the quantum states prepared in the device and the measurements performed based solely on the observed statistics. The statistical correlations can realize the self-testing of the quantum system in the preparing-and-measuring scenario. However, most of previous studies focused on the self-testing of shared entangled states between devices, at present only a few researches are presented and the existing work can only simultaneously self-test the states and measurements when some witness inequalities reach a maximum violation. We focus on four-state preparation and the selected scenarios of two measurements. In this scenario, Armin Tavakoli et al. [Tavakoli A, Kaniewski J, Vértesi T, Rosset D, Brunner N 2018 <i>Phys. Rev. A</i> <b>98</b> 062307] have put forward a criterion based on the dimensional witness violation inequality which can achieve BB84 particles and corresponding Pauli measurements. However, in addition to the maximum violation of the inequality, any statistics with deviation from the maximum deviation cannot be self-tested. Besides, only the BB84 particle preparation and measurements system can be self-tested with that criterion, resulting in a large number of four-state preparation and two measurement systems that cannot be self-tested. Therefore, in this work, in addition to the maximum violation of that dimension inequality, we directly focus on the full observed statistics and further propose some new criteria for self-testing qubit quantum systems in the preparing-and-measiuring scenarios. And the self-testing criteria are proven in an ideal case. We construct a local isometry by using the constructions commonly used in device-independent cases, exchange the target system with the additional system, and realize the self-testing of more qubit state sets and measurement sets than BB84 particles. This meets the requirements for practical experiments to realize various tasks by different quantum state sets. In addition, we perform a robust analysis of the proposed criteria and use fidelity to describe the closeness of the state to the ideal state of the auxiliary system. Finally, an improved dimensional-dependent NPA method is used to optimize the lower bound of the robustness, making the new criteria practical under experimental noise. We use the YALIMP software package in MATLAB and the solver SEDUMI to solve this optimization problem. The present research increases the diversity of qubit state preparations and self-testing of measurement system, which is beneficial to the actual self-testing of different non-entangled single quantum systems.

Feedback-Based Quantum Optimization.

It is hoped that quantum computers will offer advantages over classical computers for combinatorial optimization. Here, we introduce a feedback-based strategy for quantum optimization, where the results of qubit measurements are used to constructively assign values to quantum circuit parameters. We show that this procedure results in an estimate of the combinatorial optimization problem solution that improves monotonically with the depth of the quantum circuit. Importantly, the measurement-based feedback enables approximate solutions to the combinatorial optimization problem without the need for any classical optimization effort, as would be required for the quantum approximate optimization algorithm. We demonstrate this feedback-based protocol on a superconducting quantum processor for the graph-partitioning problem MaxCut, and present a series of numerical analyses that further investigate the protocol's performance.

Qubit vitrification and entanglement criticality on a quantum simulator

Many elusive quantum phenomena emerge from a quantum system interacting with its classical environment. Quantum simulators enable us to program this interaction by using measurement operations. Measurements generally remove part of the entanglement built between the qubits in a simulator. While in simple cases entanglement may disappear at a constant rate as we measure qubits one by one, the evolution of entanglement under measurements for a given class of quantum states is generally unknown. We show that consecutive measurements of qubits in a simulator can lead to criticality, separating two phases of entanglement. Using up to 48 qubits, we prepare an entangled superposition of ground states to a classical spin model. Progressively measuring the qubits drives the simulator through an observable vitrification point and into a spin glass phase of entanglement. Our findings suggest coupling to a classical environment may drive critical phenomena in more general quantum states.

Projective Measurements Are Sufficient for Recycling Nonlocality.

Unsharp measurements are widely seen as the key resource for recycling the nonlocality of an entangled state shared between several sequential observers. Contrasting this, we here show that nonlocality can be recycled using only standard, projective, qubit measurements. Focusing on the Clauser-Horne-Shimony-Holt inequality and allowing parties to share classical randomness, we determine the optimal trade-off in the magnitude of Bell violations for a maximally entangled state. We then find that nonmaximally entangled states make possible larger sequential violations, which contrasts the standard Clauser-Horne-Shimony-Holt scenario. Furthermore, we show that nonlocality can be recycled using projective qubit measurements even when no shared classical randomness is available. We discuss the implications of our results for experimental implementations of sequential nonlocality.

Test of an Improved DNA and RNA Purification Protocol—Importance of Proteinase K and Co-Purified Small RNAs

Optimized and reliable DNA/RNA extraction protocols are a vital tool in clinical practice in the context of molecular testing. Here, we present our successful attempt to enhance the quantity of RNA isolated from clinical specimens, which we originally found challenging (breast and testis). We compared several purification methods with special focus on two AllPrep system-based protocols (QIAGEN). Our data suggest that addition of proteinase K may markedly increase RNA and, in some cases, also DNA yield. The extraction kit used, AllPrep DNA/RNA/miRNA universal kit, provides RNA amounts comparable with the phenol-chloroform extraction method; however, part of the final yield consisted of small RNAs, visible as a thick band in the bioanalyzer gel-like image (5S peak). The 5S peak, albeit in some cases dominating the bioanalyzer image, plays only a small role in RT-qPCR analysis, and Qubit or NanoDrop measurements can still be used as a reliable estimate of starting amounts of mRNA for downstream analyses. In conclusion, we showed that implementing a protocol containing a step of proteinase K digestion markedly increases RNA yield. The AllPrep DNA/RNA/miRNA Universal Kit can be successfully used for simultaneous extraction of DNA and total RNA, irrespective of the tissue of origin, and does not present inconveniences related to phenol-chloroform extraction.

High Fidelity State Preparation and Measurement of Ion Hyperfine Qubits with I>1/2.

We present a method for achieving high fidelity state preparation and measurement (SPAM) using trapped ion hyperfine qubits with nuclear spins higher than I=1/2. The ground states of these higher nuclear spin isotopes do not afford a simple frequency-selective state preparation scheme. We circumvent this limitation by stroboscopically driving strong and weak transitions, blending fast optical pumping using dipole transitions, and narrow microwave or optical quadrupole transitions. We demonstrate this method with the I=3/2 isotope ^{137}Ba^{+} to achieve a SPAM infidelity of (9.0±1.3)×10^{-5} (-40.5±0.6 dB), facilitating the use of a wider range of ion isotopes with favorable wavelengths and masses for quantum computation.

Maximum-confidence measurement for qubit states

In quantum state discrimination, one aims to identify unknown states from a given ensemble by performing measurements. Different strategies such as minimum-error discrimination or unambiguous state identification find different optimal measurements. Maximum-confidence measurements (MCMs) maximize the confidence with which inputs can be identified given the measurement outcomes. This unifies a range of discrimination strategies including minimum-error and unambiguous state identification, which can be understood as limiting cases of MCM. In this work we investigate MCMs for general ensembles of qubit states. We present a method for finding MCMs for qubit-state ensembles by exploiting their geometry and apply it to several interesting cases, including ensembles of two and four mixed states and ensembles of an arbitrary number of pure states. We also compare MCMs to minimum-error and unambiguous discrimination for qubits. Our results provide interpretations of various qubit measurements in terms of MCM and can be used to devise qubit protocols.

Fast Stabiliser Simulation with Quadratic Form Expansions

This paper builds on the idea of simulating stabiliser circuits through transformations of {quadratic form expansions}. This is a representation of a quantum state which specifies a formula for the expansion in the standard basis, describing real and imaginary relative phases using a degree-2 polynomial over the integers. We show how, with deft management of the quadratic form expansion representation, we may simulate individual stabiliser operations in O(n2) time matching the overall complexity of other simulation techniques \cite{Aaronson2004,Anders2006,Bravyi2016}. Our techniques provide economies of scale in the time to simulate simultaneous measurements of all (or nearly all) qubits in the standard basis. Our techniques also allow single-qubit measurements with deterministic outcomes to be simulated in constant time. We also describe throughout how these bounds may be tightened when the expansion of the state in the standard basis has relatively few terms (has low `rank'), or can be specified by sparse matrices. Specifically, this allows us to simulate a `local' stabiliser syndrome measurement in time O(n), for a stabiliser code subject to Pauli noise --- matching what is possible using techniques developed by Gidney \cite{gidney2021stim} without the need to store which operations have thus far been simulated.