Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

CRC Press eBooks

Quantum Instruction Simulation

Nadia Nedjah, Luiza de Macedo Mourelle

Published Jan 5, 2023• 0 citations
Publisher

Abstract

This chapter discusses the execution of a quantum operation that manipulates a single quantum bit, showing the time diagram during its simulation. It illustrates the execution of an operation on non-entangled quantum bits, showing the time diagram during its simulation. When performing a quantum operation on two or more q-bits where at least one of them is entangled with another and/or when the quantum operation causes entanglement, the construction of the quantum operator by means of a tensor product is required. The coefficients of the basic quantum operators are read from memory MOP and stored in memory MSC when the operator is constructed for two q-bits. The construction of an operator for three or more q-bits requires the reading and writing of the coefficients in MSC, eventually occurring simultaneously, but always at different addresses.

DOI
10.1201/9781003344094-10

Related papers

Quantum Operators

Nadia Nedjah, Luiza de Macedo Mourelle

This chapter discusses the main operation of tensor product, which is behind almost all quantum information manipulation. Tensor products are exploited in a similar manner to yield quantum operators to be used with quantum states of two or more quantum bits. The magnitude of the inversion depends on the state of the control q-bit. It can be said that the CNOT operator is a NOT operator dependent on a second q-bit. It can be constructed out of two chained H operators. The Toffoli operator can be seen as an extension of the CNOT port. It is considered universal and it is possible to build based on any other quantum operator. The chapter shows that if not handled efficiently, it would require a lot of memory space, which makes the design emulate a quantum processor quite expensive to produce.

CRC Press eBooks•Jan 5, 2023•0 citations

Calculation Unit Micro-architecture

Nadia Nedjah, Luiza de Macedo Mourelle

This chapter provides an overall view regarding the function that must be executed by the calculation unit. The Calculation Unit UCA of the macro-architecture is responsible for multiplication of complex numbers, necessary for the execution of the tensor product of quantum operators, tensor product of q-bits, matrix product of operators and quantum register of q-bits as well as the sum of complex numbers. The construction of a quantum register starts by the tensor product of the q-bits specified in the first two instructions of the quantum operation. The q-bit that is specified in the third instruction would be tensorally multiplied with the register of two q-bits that was prepared in the previous iteration. The ability to simultaneously process more coefficients is possible, with the replication of the aforementioned sets, which must be accompanied by some minimal changes in the number of inputs corresponding to the multiplexers.

CRC Press eBooks•Jan 5, 2023•0 citations

Quantum Processor Macro-architecture

Nadia Nedjah, Luiza de Macedo Mourelle

This chapter discusses the overall hardware architecture of a quantum processor. Emulation of quantum processing requires primarily an efficient way to store and retrieve quantum information. The quantum processor employs different purpose memories. The proposed co-processor implements a quantum machine capable of performing certain quantum operations on a set of q-bits that form the machine quantum state. It is an isolated system that interacts with a host processor through communication channels. The main processor sends properly formatted commands that invoke quantum operations on q-bits, to manipulate the quantum state. The channel configuration is used because it considers the sequential characteristic of a quantum algorithm due to the potential dependence of the result of the previous operation on one or more q-bits. The full-duplex configuration would also be possible, given the required control related to data dependency. The interaction between the units and memories that compose the co-processor is done via data buses, address buses and/or control buses.

CRC Press eBooks•Jan 5, 2023•0 citations

Simulating Quantum Computation on a Macroscopic Model

Bart D’Hooghe, Guillaume Adenier, Andrei Yu. Khrennikov +3 more

We present examples of macroscopic systems entailing a quantum mechanical structure. One of our examples has a structure which is isomorphic to the spin structure for a spin 1/2 and another system entails a structure isomorphic to the structure of two spin 1/2 in the entangled singlet state. We elaborate this system by showing that an arbitrary tensor product state representing two entangled qubits can be described in a complete way by a specific internal constraint between the ray or density states of the two qubits, which describes the behavior of the state of one of the spins if measurements are executed on the other spin. Since any n‐qubit unitary operation can be decomposed into 2‐qubit gates and unary operations, we argue that our representation of 2‐qubit entanglement contributes to a better understanding of the role of n‐qubit entanglement in quantum computation. We illustrate our approach on two 2‐qubit algorithms proposed by Deutsch, respectively Arvind et al.

AIP conference proceedings•Jan 1, 2007•1 citation

Chapter 23: Quantum Computing

Peter M. Kogge

Quantum computing involves performing computations using devices that are governed by the rules of quantum mechanics170 rather than classical Newtonian physics. The effect of such a difference runs deep. First, and definitely unconventional, a quantum device’s state need not be a single value at a time, but can simultaneously hold an infinite number of possible state values. Next, much like the magnets of the Ising computing model (Chapter E11), if initialized properly, two or more quantum devices may exhibit quantum entanglement where a quantum state of any one device cannot be described independently of the others in the group. Manipulating one device results in changes to the state of the others. Together this means that a “quantum memory” can simultaneously contain an enormous number of different possible values and that applying a single operation to the group is like applying the operation to the ensemble of all states maintained in the system, simultaneously. If this becomes practical then the crystal ball analogy for NP problems (Section 7.5.4) becomes practical in polynomial time, and thus we would have achieved what is called today quantum supremacy.

Society for Industrial and Applied Mathematics eBooks•Jan 1, 2022•0 citations

APPLICATION OF LINEAR OPERATORS AND TENSOR PRODUCTS IN QUANTUM ENTANGLEMENT AND QUANTUM COMPUTING

Sevinchova Charosxon Maxmudjonovna, Worldly Knowledge Publishing Centre

Quantum computing is fundamentally based on the mathematical structure of complex Hilbert spaces, linear operators, tensor products, and unitary transformations. Among these concepts, tensor products provide the formal mechanism for constructing the state space of composite quantum systems, whereas linear and unitary operators describe quantum transformations, measurements, and computational gates. This article examines the mathematical relationship between linear operators and tensor products and analyzes their role in the formation, manipulation, and characterization of quantum entanglement. Particular attention is given to two-qubit systems, separable and entangled states, Schmidt decomposition, controlled operations, and the role of non-factorizable operators in quantum circuits. The analysis demonstrates that tensor products perform a dual function: they provide the mathematical representation of composite systems and enable the construction of local operations acting on individual subsystems. At the same time, genuinely entangling transformations, such as the controlled-NOT operation, cannot in general be represented as a single tensor product of independent local operators. Recent research further demonstrates that tensor-product and operator-Schmidt decompositions can be used to characterize operator entanglement, reduce circuit complexity, and construct efficient representations of quantum processes. The results establish that linear algebra and tensor-product structures are not merely formal tools but constitute the mathematical foundation connecting quantum entanglement with quantum computation.

HSR (London)•Oct 8, 2026•0 citations
This chapter discusses the execution of a quantum operation that manipulates a single quantum bit, showing the time diagram during its simulation. It illustrates the execution of an operation on non-entangled quantum bits, showing the time diagram during its simulation. When performing a quantum operation on two or more q-bits where at least one of them is entangled with another and/or when the quantum operation causes entanglement, the construction of the quantum operator by means of a tensor product is required. The coefficients of the basic quantum operators are read from memory MOP and stored in memory MSC when the operator is constructed for two q-bits. The construction of an operator for three or more q-bits requires the reading and writing of the coefficients in MSC, eventually occurring simultaneously, but always at different addresses.
This chapter discusses the main operation of tensor product, which is behind almost all quantum information manipulation. Tensor products are exploited in a similar manner to yield quantum operators to be used with quantum states of two or more quantum bits. The magnitude of the inversion depends on the state of the control q-bit. It can be said that the CNOT operator is a NOT operator dependent on a second q-bit. It can be constructed out of two chained H operators. The Toffoli operator can be seen as an extension of the CNOT port. It is considered universal and it is possible to build based on any other quantum operator. The chapter shows that if not handled efficiently, it would require a lot of memory space, which makes the design emulate a quantum processor quite expensive to produce.
This chapter provides an overall view regarding the function that must be executed by the calculation unit. The Calculation Unit UCA of the macro-architecture is responsible for multiplication of complex numbers, necessary for the execution of the tensor product of quantum operators, tensor product of q-bits, matrix product of operators and quantum register of q-bits as well as the sum of complex numbers. The construction of a quantum register starts by the tensor product of the q-bits specified in the first two instructions of the quantum operation. The q-bit that is specified in the third instruction would be tensorally multiplied with the register of two q-bits that was prepared in the previous iteration. The ability to simultaneously process more coefficients is possible, with the replication of the aforementioned sets, which must be accompanied by some minimal changes in the number of inputs corresponding to the multiplexers.
This chapter discusses the overall hardware architecture of a quantum processor. Emulation of quantum processing requires primarily an efficient way to store and retrieve quantum information. The quantum processor employs different purpose memories. The proposed co-processor implements a quantum machine capable of performing certain quantum operations on a set of q-bits that form the machine quantum state. It is an isolated system that interacts with a host processor through communication channels. The main processor sends properly formatted commands that invoke quantum operations on q-bits, to manipulate the quantum state. The channel configuration is used because it considers the sequential characteristic of a quantum algorithm due to the potential dependence of the result of the previous operation on one or more q-bits. The full-duplex configuration would also be possible, given the required control related to data dependency. The interaction between the units and memories that compose the co-processor is done via data buses, address buses and/or control buses.
We present examples of macroscopic systems entailing a quantum mechanical structure. One of our examples has a structure which is isomorphic to the spin structure for a spin 1/2 and another system entails a structure isomorphic to the structure of two spin 1/2 in the entangled singlet state. We elaborate this system by showing that an arbitrary tensor product state representing two entangled qubits can be described in a complete way by a specific internal constraint between the ray or density states of the two qubits, which describes the behavior of the state of one of the spins if measurements are executed on the other spin. Since any n‐qubit unitary operation can be decomposed into 2‐qubit gates and unary operations, we argue that our representation of 2‐qubit entanglement contributes to a better understanding of the role of n‐qubit entanglement in quantum computation. We illustrate our approach on two 2‐qubit algorithms proposed by Deutsch, respectively Arvind et al.
Quantum computing involves performing computations using devices that are governed by the rules of quantum mechanics170 rather than classical Newtonian physics. The effect of such a difference runs deep. First, and definitely unconventional, a quantum device’s state need not be a single value at a time, but can simultaneously hold an infinite number of possible state values. Next, much like the magnets of the Ising computing model (Chapter E11), if initialized properly, two or more quantum devices may exhibit quantum entanglement where a quantum state of any one device cannot be described independently of the others in the group. Manipulating one device results in changes to the state of the others. Together this means that a “quantum memory” can simultaneously contain an enormous number of different possible values and that applying a single operation to the group is like applying the operation to the ensemble of all states maintained in the system, simultaneously. If this becomes practical then the crystal ball analogy for NP problems (Section 7.5.4) becomes practical in polynomial time, and thus we would have achieved what is called today quantum supremacy.
Quantum computing is fundamentally based on the mathematical structure of complex Hilbert spaces, linear operators, tensor products, and unitary transformations. Among these concepts, tensor products provide the formal mechanism for constructing the state space of composite quantum systems, whereas linear and unitary operators describe quantum transformations, measurements, and computational gates. This article examines the mathematical relationship between linear operators and tensor products and analyzes their role in the formation, manipulation, and characterization of quantum entanglement. Particular attention is given to two-qubit systems, separable and entangled states, Schmidt decomposition, controlled operations, and the role of non-factorizable operators in quantum circuits. The analysis demonstrates that tensor products perform a dual function: they provide the mathematical representation of composite systems and enable the construction of local operations acting on individual subsystems. At the same time, genuinely entangling transformations, such as the controlled-NOT operation, cannot in general be represented as a single tensor product of independent local operators. Recent research further demonstrates that tensor-product and operator-Schmidt decompositions can be used to characterize operator entanglement, reduce circuit complexity, and construct efficient representations of quantum processes. The results establish that linear algebra and tensor-product structures are not merely formal tools but constitute the mathematical foundation connecting quantum entanglement with quantum computation.