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One of the greatest challenges involved with constructing quantum computers is controlling or removing quantum decoherence. This usually means isolating the system from its environment as interactions with the external world cause the system to decohere. However, other sources of decoherence also exist. Examples include the quantum gates, and the lattice vibrations and background thermonuclear spin of the physical system used to implement the qubits. Decoherence is irreversible, as it is effectively non-unitary, and is usually something that should be highly controlled, if not avoided. Decoherence times for candidate systems in particular, the transverse relaxation time T₂ (for NMR and MRI technology, also called the dephasing time), typically range between nanoseconds and seconds at low temperature. Currently, some quantum computers require their qubits to be cooled to 20 millikelvins in order to prevent significant decoherence. A 2020 study argues that ionizing radiation such as cosmic rays can nevertheless cause certain systems to decohere within millisections.

One of the greatest challenges involved with constructing quantum computers is controlling or removing quantum decoherence. This usually means isolating the system from its environment as interactions with the external world cause the system to decohere. However, other sources of decoherence also exist. Examples include the quantum gates, and the lattice vibrations and background thermonuclear spin of the physical system used to implement the qubits. Decoherence is irreversible, as it is effectively non-unitary, and is usually something that should be highly controlled, if not avoided. Decoherence times for candidate systems in particular, the transverse relaxation time T₂ (for NMR and MRI technology, also called the dephasing time), typically range between nanoseconds and seconds at low temperature. Currently, some quantum computers require their qubits to be cooled to 20 millikelvins in order to prevent significant decoherence. A 2020 study argues that ionizing radiation such as cosmic rays can nevertheless cause certain systems to decohere within millisections.

构建量子计算机的最大挑战之一是控制或移除'''<font color="#ff8000"> 量子退相干Quantum decoherence</font>'''。这通常意味着将系统与其环境隔离，因为与外部世界的交互会导致系统去中心化。然而，也存在其他的消相干源。例如量子门，晶格振动和用于实现量子比特的物理系统的背景热核自旋。退相干是不可逆的，因为它实际上是非幺正的，如果不能避免的话，通常是应该高度控制的。对于候选系统，尤其是横向弛豫时间T₂（对于核磁共振和核磁共振技术，也称为去相时间），在低温下通常在纳秒和秒之间。目前，一些量子计算机要求将量子比特冷却到20毫开尔文，以防止严重的退相干。2020年的一项研究认为，宇宙射线等电离辐射仍然可以导致某些系统在毫秒范围内发生衰变。

构建量子计算机的最大挑战之一是控制或移除'''<font color="#ff8000"> 量子退相干Quantum decoherence</font>'''。这通常意味着将系统与其环境隔离，因为与外部世界的交互会导致系统去中心化。然而，也存在其他的消相干源。例如'''<font color="#ff8000"> 量子门，晶格振动</font>'''和用于实现量子比特的物理系统的背景热核自旋。退相干是不可逆的，因为它实际上是'''<font color="#ff8000"> 非酉Non-unitary</font>'''的，如果不能避免的话，通常应该高度控制。对于候选系统，尤其是横向弛豫时间T₂（对于核磁共振和核磁共振技术，也称为去相时间），在低温下通常在纳秒和秒之间。目前，一些量子计算机要求将量子比特冷却到20毫开尔文，以防止严重的退相干。2020年的一项研究认为，宇宙射线等电离辐射仍然可以导致某些系统在毫秒范围内发生衰变。

{{Main|Quantum decoherence}}

{{Main|Quantum decoherence}}

One of the greatest challenges involved with constructing quantum computers is controlling or removing [[quantum decoherence]]. This usually means isolating the system from its environment as interactions with the external world cause the system to decohere. However, other sources of decoherence also exist. Examples include the quantum gates, and the lattice vibrations and background thermonuclear spin of the physical system used to implement the qubits. Decoherence is irreversible, as it is effectively non-unitary, and is usually something that should be highly controlled, if not avoided. Decoherence times for candidate systems in particular, the transverse relaxation time ''T''₂ (for [[Nuclear magnetic resonance|NMR]] and [[MRI]] technology, also called the ''dephasing time''), typically range between nanoseconds and seconds at low temperature.<ref name="DiVincenzo 1995">{{cite journal |last=DiVincenzo |first=David P. |title=Quantum Computation |journal=Science |year=1995 |volume=270 |issue=5234 |pages=255–261 |doi= 10.1126/science.270.5234.255 |bibcode = 1995Sci...270..255D |citeseerx=10.1.1.242.2165 |s2cid=220110562 }} {{subscription required}}</ref> Currently, some quantum computers require their qubits to be cooled to 20 millikelvins in order to prevent significant decoherence.<ref>{{cite journal|last1=Jones|first1=Nicola|title=Computing: The quantum company|journal=Nature|date=19 June 2013|volume=498|issue=7454|pages=286–288|doi=10.1038/498286a|pmid=23783610|bibcode=2013Natur.498..286J|doi-access=free}}</ref> A 2020 study argues that [[ionizing radiation]] such as [[cosmic rays]] can nevertheless cause certain systems to decohere within millisections.<ref>{{cite journal |last1=Vepsäläinen |first1=Antti P. |last2=Karamlou |first2=Amir H. |last3=Orrell |first3=John L. |last4=Dogra |first4=Akshunna S. |last5=Loer |first5=Ben |last6=Vasconcelos |first6=Francisca |last7=Kim |first7=David K. |last8=Melville |first8=Alexander J. |last9=Niedzielski |first9=Bethany M. |last10=Yoder |first10=Jonilyn L. |last11=Gustavsson |first11=Simon |last12=Formaggio |first12=Joseph A. |last13=VanDevender |first13=Brent A. |last14=Oliver |first14=William D. |display-authors=5 |title=Impact of ionizing radiation on superconducting qubit coherence |journal=Nature |date=August 2020 |volume=584 |issue=7822 |pages=551–556 |doi=10.1038/s41586-020-2619-8 |pmid=32848227 |url=https://www.nature.com/articles/s41586-020-2619-8 |language=en |issn=1476-4687|arxiv=2001.09190 |s2cid=210920566 }}</ref>

One of the greatest challenges involved with constructing quantum computers is controlling or removing [[quantum decoherence]]. This usually means isolating the system from its environment as interactions with the external world cause the system to decohere. However, other sources of decoherence also exist. Examples include the quantum gates, and the lattice vibrations and background thermonuclear spin of the physical system used to implement the qubits. Decoherence is irreversible, as it is effectively non-unitary, and is usually something that should be highly controlled, if not avoided. Decoherence times for candidate systems in particular, the transverse relaxation time ''T''₂ (for [[Nuclear magnetic resonance|NMR]] and [[MRI]] technology, also called the ''dephasing time''), typically range between nanoseconds and seconds at low temperature.<ref name="DiVincenzo 1995">{{cite journal |last=DiVincenzo |first=David P. |title=Quantum Computation |journal=Science |year=1995 |volume=270 |issue=5234 |pages=255–261 |doi= 10.1126/science.270.5234.255 |bibcode = 1995Sci...270..255D |citeseerx=10.1.1.242.2165 |s2cid=220110562 }} {{subscription required}}</ref> Currently, some quantum computers require their qubits to be cooled to 20 millikelvins in order to prevent significant decoherence.<ref>{{cite journal|last1=Jones|first1=Nicola|title=Computing: The quantum company|journal=Nature|date=19 June 2013|volume=498|issue=7454|pages=286–288|doi=10.1038/498286a|pmid=23783610|bibcode=2013Natur.498..286J|doi-access=free}}</ref> A 2020 study argues that [[ionizing radiation]] such as [[cosmic rays]] can nevertheless cause certain systems to decohere within millisections.<ref>{{cite journal |last1=Vepsäläinen |first1=Antti P. |last2=Karamlou |first2=Amir H. |last3=Orrell |first3=John L. |last4=Dogra |first4=Akshunna S. |last5=Loer |first5=Ben |last6=Vasconcelos |first6=Francisca |last7=Kim |first7=David K. |last8=Melville |first8=Alexander J. |last9=Niedzielski |first9=Bethany M. |last10=Yoder |first10=Jonilyn L. |last11=Gustavsson |first11=Simon |last12=Formaggio |first12=Joseph A. |last13=VanDevender |first13=Brent A. |last14=Oliver |first14=William D. |display-authors=5 |title=Impact of ionizing radiation on superconducting qubit coherence |journal=Nature |date=August 2020 |volume=584 |issue=7822 |pages=551–556 |doi=10.1038/s41586-020-2619-8 |pmid=32848227 |url=https://www.nature.com/articles/s41586-020-2619-8 |language=en |issn=1476-4687|arxiv=2001.09190 |s2cid=210920566 }}</ref>

建造量子计算机的最大挑战之一是控制或消除[[量子退相干]]。这通常意味着将系统与其环境隔离，因为与外部世界的交互会导致系统去中心化。然而，也存在其他的消相干源。例如量子门，晶格振动和用于实现量子比特的物理系统的背景热核自旋。退相干是不可逆的，因为它实际上是非幺正的，如果不能避免的话，通常是应该高度控制的。候选系统的退相干时间，特别是横向弛豫时间“T”₂（对于[[核磁共振| NMR]]和[[MRI]]技术，也称为“去相位时间”），在低温下通常在纳秒到秒之间。.<ref name="DiVincenzo 1995">{{cite journal |last=DiVincenzo |first=David P. |title=Quantum Computation |journal=Science |year=1995 |volume=270 |issue=5234 |pages=255–261 |doi= 10.1126/science.270.5234.255 |bibcode = 1995Sci...270..255D |citeseerx=10.1.1.242.2165 |s2cid=220110562 }} {{subscription required}}</ref>目前，一些量子计算机要求将量子比特冷却到20毫开尔文，以防止严重的退相干。<ref>{{cite journal|last1=Jones|first1=Nicola|title=Computing: The quantum company|journal=Nature|date=19 June 2013|volume=498|issue=7454|pages=286–288|doi=10.1038/498286a|pmid=23783610|bibcode=2013Natur.498..286J|doi-access=free}}</ref>2020年的一项研究认为，尽管如此，诸如[宇宙射线]这样的[[电离辐射]]仍能导致某些系统在毫秒范围内退凝。<ref>{{cite journal |last1=Vepsäläinen |first1=Antti P. |last2=Karamlou |first2=Amir H. |last3=Orrell |first3=John L. |last4=Dogra |first4=Akshunna S. |last5=Loer |first5=Ben |last6=Vasconcelos |first6=Francisca |last7=Kim |first7=David K. |last8=Melville |first8=Alexander J. |last9=Niedzielski |first9=Bethany M. |last10=Yoder |first10=Jonilyn L. |last11=Gustavsson |first11=Simon |last12=Formaggio |first12=Joseph A. |last13=VanDevender |first13=Brent A. |last14=Oliver |first14=William D. |display-authors=5 |title=Impact of ionizing radiation on superconducting qubit coherence |journal=Nature |date=August 2020 |volume=584 |issue=7822 |pages=551–556 |doi=10.1038/s41586-020-2619-8 |pmid=32848227 |url=https://www.nature.com/articles/s41586-020-2619-8 |language=en |issn=1476-4687|arxiv=2001.09190 |s2cid=210920566 }}</ref>

建造量子计算机的最大挑战之一是控制或消除[[量子退相干]]。这通常意味着将系统与其环境隔离，因为与外部世界的交互会导致系统去中心化。然而，也存在其他的消相干源。例如量子门，晶格振动和用于实现量子比特的物理系统的背景热核自旋。退相干是不可逆的，因为它实际上是非幺正的，如果不能避免的话，通常是应该高度控制的。候选系统的退相干时间，特别是横向弛豫时间“T”₂（对于[[核磁共振| NMR]]和[[MRI]]技术，也称为“去相位时间”），在低温下通常在纳秒到秒之间。.<ref name="DiVincenzo 1995">{{cite journal |last=DiVincenzo |first=David P. |title=Quantum Computation |journal=Science |year=1995 |volume=270 |issue=5234 |pages=255–261 |doi= 10.1126/science.270.5234.255 |bibcode = 1995Sci...270..255D |citeseerx=10.1.1.242.2165 |s2cid=220110562 }} {{subscription required}}</ref>目前，一些量子计算机要求将量子比特冷却到20毫开尔文，以防止严重的退相干。<ref>{{cite journal|last1=Jones|first1=Nicola|title=Computing: The quantum company|journal=Nature|date=19 June 2013|volume=498|issue=7454|pages=286–288|doi=10.1038/498286a|pmid=23783610|bibcode=2013Natur.498..286J|doi-access=free}}</ref>2020年的一项研究认为，尽管如此，诸如[宇宙射线]]这样的[[电离辐射]]仍能导致某些系统在毫秒范围内退凝。<ref>{{cite journal |last1=Vepsäläinen |first1=Antti P. |last2=Karamlou |first2=Amir H. |last3=Orrell |first3=John L. |last4=Dogra |first4=Akshunna S. |last5=Loer |first5=Ben |last6=Vasconcelos |first6=Francisca |last7=Kim |first7=David K. |last8=Melville |first8=Alexander J. |last9=Niedzielski |first9=Bethany M. |last10=Yoder |first10=Jonilyn L. |last11=Gustavsson |first11=Simon |last12=Formaggio |first12=Joseph A. |last13=VanDevender |first13=Brent A. |last14=Oliver |first14=William D. |display-authors=5 |title=Impact of ionizing radiation on superconducting qubit coherence |journal=Nature |date=August 2020 |volume=584 |issue=7822 |pages=551–556 |doi=10.1038/s41586-020-2619-8 |pmid=32848227 |url=https://www.nature.com/articles/s41586-020-2619-8 |language=en |issn=1476-4687|arxiv=2001.09190 |s2cid=210920566 }}</ref>

These issues are more difficult for optical approaches as the timescales are orders of magnitude shorter and an often-cited approach to overcoming them is optical pulse shaping. Error rates are typically proportional to the ratio of operating time to decoherence time, hence any operation must be completed much more quickly than the decoherence time.

These issues are more difficult for optical approaches as the timescales are orders of magnitude shorter and an often-cited approach to overcoming them is optical pulse shaping. Error rates are typically proportional to the ratio of operating time to decoherence time, hence any operation must be completed much more quickly than the decoherence time.

A very different approach to the stability-decoherence problem is to create a topological quantum computer with anyons, quasi-particles used as threads and relying on braid theory to form stable logic gates.

A very different approach to the stability-decoherence problem is to create a topological quantum computer with anyons, quasi-particles used as threads and relying on braid theory to form stable logic gates.

Meeting this scalability condition is possible for a wide range of systems. However, the use of error correction brings with it the cost of a greatly increased number of required qubits. The number required to factor integers using Shor's algorithm is still polynomial, and thought to be between ''L'' and ''L''², where ''L'' is the number of qubits in the number to be factored; error correction algorithms would inflate this figure by an additional factor of ''L''. For a 1000-bit number, this implies a need for about 10⁴ bits without error correction.<ref>{{cite journal |title=Is Fault-Tolerant Quantum Computation Really Possible? |last=Dyakonov |first=M. I. |date=2006-10-14 |pages=4–18 |journal=Future Trends in Microelectronics. Up the Nano Creek |editor1=S. Luryi |editor2=J. Xu |editor3=A. Zaslavsky | arxiv=quant-ph/0610117|bibcode=2006quant.ph.10117D }}</ref> With error correction, the figure would rise to about 10⁷ bits. Computation time is about ''L''² or about 10⁷ steps and at 1&nbsp;MHz, about 10 seconds.

Meeting this scalability condition is possible for a wide range of systems. However, the use of error correction brings with it the cost of a greatly increased number of required qubits. The number required to factor integers using Shor's algorithm is still polynomial, and thought to be between ''L'' and ''L''², where ''L'' is the number of qubits in the number to be factored; error correction algorithms would inflate this figure by an additional factor of ''L''. For a 1000-bit number, this implies a need for about 10⁴ bits without error correction.<ref>{{cite journal |title=Is Fault-Tolerant Quantum Computation Really Possible? |last=Dyakonov |first=M. I. |date=2006-10-14 |pages=4–18 |journal=Future Trends in Microelectronics. Up the Nano Creek |editor1=S. Luryi |editor2=J. Xu |editor3=A. Zaslavsky | arxiv=quant-ph/0610117|bibcode=2006quant.ph.10117D }}</ref> With error correction, the figure would rise to about 10⁷ bits. Computation time is about ''L''² or about 10⁷ steps and at 1&nbsp;MHz, about 10 seconds.