Testing the context-independence of quantum gates

The actual gate performed on, say, a qubit in a quantum computer may depend, not just on the actual laser pulses and voltages we programmed to implement the gate, but on its context as well. For example, it may depend on what gate has just been applied to the same qubit, or on how much a long series of previous laser pulses has been heating up the qubit's environment. This paper analyzes several tests to detect such context-dependent errors (which include various types of non-Markovian errors). A key feature of these tests is that they are robust against both state preparation and measurement (SPAM) errors and gate-dependent errors. Since context-dependent errors are expected to be small in practice, it becomes important to carefully analyze the effects of statistical fluctuations and so we investigate the power and precision of our tests as functions of the number of repetitions and the length of the sequences of gates. From our tests an important quantity emerges: the logarithm of the determinant (log-det) of a probability (relative frequency) matrix $\mP.$ For this reason, we derive the probability distribution of the log-det estimates which we then use to examine the performance of our tests for various single- and two-qubit sets of measurements and initial states. Finally, we emphasize the connection between the log-det and the degree of reversibility (the unitarity) of a context-independent operation.

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Simulating of X-states and the two-qubit XYZ Heisenberg system on IBM quantum computer

Physica Scripta ◽

10.1088/1402-4896/ac49b0 ◽

2022 ◽

Author(s):

Fereshte Shahbeigi ◽

Mahsa Karimi ◽

Vahid Karimipour

Keyword(s):

Parameter Space ◽

Wide Class ◽

Quantum Computer ◽

Quantum Circuit ◽

Natural Generalization ◽

Quantum Gates ◽

Density Matrices ◽

Quantum Device ◽

Initial States ◽

X State

Abstract Two qubit density matrices which are of X-shape, are a natural generalization of Bell Diagonal States (BDSs) recently simulated on the IBM quantum device. We generalize the previous results and propose a quantum circuit for simulation of a general two qubit X-state, implement it on the same quantum device, and study its entanglement for several values of the extended parameter space. We also show that their X-shape is approximately robust against noisy quantum gates. To further physically motivate this study, we invoke the two-spin Heisenberg XYZ system and show that for a wide class of initial states, it leads to dynamical density matrices which are X-states. Due to the symmetries of this Hamiltonian, we show that by only two qubits, one can simulate the dynamics of this system on the IBM quantum computer.

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Quantum universality by state distillationIndirect quantum control for finite-dimensional coupled systems

Quantum Information and Computation ◽

10.26421/qic10.1-2-7 ◽

2010 ◽

Vol 10 (1&2) ◽

pp. 87-96

Author(s):

J. Nie ◽

H.C. Fu ◽

X.X. Yi

Keyword(s):

Quantum System ◽

Quantum Control ◽

Coherent Control ◽

Coupled Systems ◽

Preparation Technology ◽

State Preparation ◽

Finite Dimensional ◽

State Dependent ◽

Control Scheme ◽

Initial States

We present a new analysis on the quantum control for a quantum system coupled to a quantum probe. This analysis is based on the coherent control for the quantum system and a hypothesis that the probe can be prepared in specified initial states. The results show that a quantum system can be manipulated by probe state-dependent coherent control. In this sense, the present analysis provides a new control scheme which combines the coherent control and state preparation technology.

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Testing Quantum Coherence in Stochastic Electrodynamics with Squeezed Schrödinger Cat States

Atoms ◽

10.3390/atoms7020042 ◽

2019 ◽

Vol 7 (2) ◽

pp. 42 ◽

Cited By ~ 7

Author(s):

Wayne Huang ◽

Herman Batelaan

Keyword(s):

Quantum Mechanics ◽

Probability Distribution ◽

Interference Pattern ◽

Quantum Coherence ◽

Laser Pulses ◽

Quantum Probability ◽

Harmonic Oscillators ◽

Stochastic Electrodynamics ◽

Schrödinger Cat ◽

Cat States

The interference pattern in electron double-slit diffraction is a hallmark of quantum mechanics. A long-standing question for stochastic electrodynamics (SED) is whether or not it is capable of reproducing such effects, as interference is a manifestation of quantum coherence. In this study, we used excited harmonic oscillators to directly test this quantum feature in SED. We used two counter-propagating dichromatic laser pulses to promote a ground-state harmonic oscillator to a squeezed Schrödinger cat state. Upon recombination of the two well-separated wavepackets, an interference pattern emerges in the quantum probability distribution but is absent in the SED probability distribution. We thus give a counterexample that rejects SED as a valid alternative to quantum mechanics.

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Single-molecule imaging with longer X-ray laser pulses

IUCrJ ◽

10.1107/s2052252515016887 ◽

2015 ◽

Vol 2 (6) ◽

pp. 661-674 ◽

Cited By ~ 13

Author(s):

Andrew V. Martin ◽

Justine K. Corso ◽

Carl Caleman ◽

Nicusor Timneanu ◽

Harry M. Quiney

Keyword(s):

Single Molecule ◽

Laser Pulses ◽

Bragg Diffraction ◽

Single Molecule Imaging ◽

X Ray ◽

Damage Models ◽

Statistical Fluctuations ◽

Damage Processes ◽

The Impact ◽

Serial Femtosecond Crystallography

During the last five years, serial femtosecond crystallography using X-ray laser pulses has been developed into a powerful technique for determining the atomic structures of protein molecules from micrometre- and sub-micrometre-sized crystals. One of the key reasons for this success is the `self-gating' pulse effect, whereby the X-ray laser pulses do not need to outrun all radiation damage processes. Instead, X-ray-induced damage terminates the Bragg diffraction prior to the pulse completing its passage through the sample, as if the Bragg diffraction were generated by a shorter pulse of equal intensity. As a result, serial femtosecond crystallography does not need to be performed with pulses as short as 5–10 fs, but can succeed for pulses 50–100 fs in duration. It is shown here that a similar gating effect applies to single-molecule diffraction with respect to spatially uncorrelated damage processes like ionization and ion diffusion. The effect is clearly seen in calculations of the diffraction contrast, by calculating the diffraction of the average structure separately to the diffraction from statistical fluctuations of the structure due to damage (`damage noise'). The results suggest that sub-nanometre single-molecule imaging with 30–50 fs pulses, like those produced at currently operating facilities, should not yet be ruled out. The theory presented opens up new experimental avenues to measure the impact of damage on single-particle diffraction, which is needed to test damage models and to identify optimal imaging conditions.

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An Algorithm of Quantum Restricted Boltzmann Machine Network Based on Quantum Gates and Its Application

Shock and Vibration ◽

10.1155/2015/756969 ◽

2015 ◽

Vol 2015 ◽

pp. 1-7

Author(s):

Peilin Zhang ◽

Sheng Li ◽

Yu Zhou

Keyword(s):

Quantum Computer ◽

Quantum Circuit ◽

Classification Performance ◽

Generative Model ◽

Restricted Boltzmann Machine ◽

Quantum Gates ◽

Boltzmann Machine ◽

Discriminative Models

We present an algorithm of quantum restricted Boltzmann machine network based on quantum gates. The algorithm is used to initialize the procedure that adjusts the qubit and weights. After adjusting, the network forms an unsupervised generative model that gives better classification performance than other discriminative models. In addition, we show how the algorithm can be constructed with quantum circuit for quantum computer.

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Times of Execution of the CCNOT and CCCNOT Quantum Gates in a Quantum Computer based on a Quantum Dots Technology

Computación y Sistemas ◽

10.13053/cys-23-4-3033 ◽

2019 ◽

Vol 23 (4) ◽

Author(s):

Manuel Aoki Avila

Keyword(s):

Quantum Dots ◽

Quantum Computer ◽

Quantum Gates ◽

Computer Based

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Statistical constraints on state preparation for a quantum computer

Pramana ◽

10.1007/s12043-001-0019-7 ◽

2001 ◽

Vol 57 (4) ◽

pp. 683-687 ◽

Cited By ~ 5

Author(s):

Subhash Kak

Keyword(s):

Quantum Computer ◽

State Preparation

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GAS doesn't “turn the engine” when states are sequential or context-dependent

Behavioral and Brain Sciences ◽

10.1017/s0140525x04280207 ◽

2004 ◽

Vol 27 (6) ◽

pp. 901-902

Author(s):

Liane Gabora

Keyword(s):

Probability Distribution ◽

Selection Pressure ◽

Cognitive Change ◽

Selection Theory ◽

Classical Formalism ◽

Context Dependent

Selection theory requires multiple, simultaneously-actualized states. In cognition, each thought changes the “selection pressure” against which the next is evaluated; they are not simultaneously selected amongst. Cognitive change occurs not through selection among discrete “neural configurations,” but through interaction between conceptual web and context. This introduces a non-Kolmogorovian probability distribution, hence a classical formalism (e.g., selection theory) cannot be used.

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